86th Annual Conference of ‡e Indian Mathematical Society – An International Meet (Online Conference) December 17-20, 2020

Organized under the auspices of Department of Mathematics School of Advanced Sciences, VIT Vellore IMS 2020 - Committee

IMS - Executive President Prof. B. Sury Indian Statistical Institute, Bangaluru General Secretary Prof. Satya Deo Harish-Chandra Research Institute, Allahabad. Editor, ‡e Journal of the Prof. Sudhir R. Ghorpade Indian Mathematical Society Indian Institute of Technology - Bombay, Mumbai. Editor, ‡e Mathematics Student Prof. M. M. Shikare Center for Advanced Study in Mathematics, Pune. Academic Secretary Prof. Peeyush Chandra Formerly, IIT Kanpur Administrative Secretary Prof. B. N. Waphare Center for Advanced Study in Mathematics, Pune. Treasurer Prof. S. K. Nimbhorkar Dr Baba Saheb Ambedkar Marathawada University, Aurangabad. Librarian Prof. M. Pitchaimani Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai.

Organizing Committee Patron Dr. G. Viswanathan Chancellor, VIT Vellore Co-Patron Mr. G.V. Selvam Vice President, VIT Vellore Prof. Rambabu Kodali Vice Chancellor, VIT Vellore Prof. S. Narayanan Pro-Vice Chancellor, VIT Vellore Chair Person Prof. A. Mary Saral Dean, SAS, VIT Vellore Co-Chair Person Prof. K. Karthikeyan Head, Department of Mathematics, SAS, VIT Vellore Organising Secretary Prof. B. Rushi Kumar Associate Professor, Department of Mathematics, SAS, VIT Vellore Organising Committee Prof. Dinesh Kumar S Prof. Sri Rama Varaprasad Bhuvanagiri Prof. Sivaraj R Prof. Raja Das Prof. V Madhu Members (Faculty) Prof. Chandrasekaran V M Prof. Mubashir Unnissa M Prof. Murugusundaramoorthy G Prof. Easwaramoorthy D Prof. Selvakumar R Prof. Subramanyam Reddy A Prof. Natarajan G Prof. Yogalakshmi T Prof. Vijaya K Prof. Mokesh Rayalu G Prof. Gargi Chakraborty Prof. Nalliah M Prof. Anjaneyulu G S G N Prof. Roy S Prof. Phaneendra T Prof. Nandhini S Prof. Abdul Hameed Prof. Rajasekaran G Prof. ‘amizharasi Tamizhmani Prof. Balaji S Members (Faculty Contd…) Prof. Rajan Cha‹amvelli Prof. Kalaivani K Prof. Vallampati Ramachandra Prasad Prof. Praveen T Prof. Hemant Kumar Nashine Prof. Poornima T Prof. Indhira K Prof. Mythili G Y Prof. Gopalakrishna Gadiyar H Prof. Venkataramana B Prof. Padma R Prof. Gowrisankar A Prof. Rajendran P Prof. Udhaya Kumar R Prof. Yamuna M Prof. Gowsalya M Prof. Uma K Prof. Lakshmi Narayan Mishra Prof. Jagadeesh Kumar M S Prof. Ashish Kumar Prasad Prof. Akella V S N Murty Prof. Ramesh Kumar D Prof. Jitendra Kumar Prof. Sivanesan M Prof. Venkata Satyanarayana P Prof. Jagadesh Kumar K Prof. SK. Khadar Babu Prof. Karthika K Prof. Mellacheruvu Naga Srinivasu Prof. Rachna Bhatia Prof. Hemadri Reddy Reganti Prof. Manjari Sidharth Prof. Naga Satya Srinivas Akkiraju Prof. Amrit Das Prof. Ezhilmaran D Prof. Debroti Das Prof. Bala Anki Reddy Pol Prof. Amit Sharma Prof. Nageshwar Rao Ragi Prof. Murugan V Prof. Venkateswarlu B Prof. Prasad ‘eeda Prof. Peri Kameswara Kameswaran Prof. Parvez Alam Prof. Lakshminarayana P Prof. Pallavi Mishra Prof. Niranjan Hari Prof. Rajesh Bha‹ Prof. Saravanarajan M C Prof. Rajesh Maharana Prof. ‘ilagavathi K Prof. Renu Rani Prof. Anuradha D Prof. Sujasree M Prof. Kaspar S Prof. Sanjay Kumar Mohanty Prof. Vijayakumar A G Prof. Nandhini S Prof. Sharief Basha S Prof. Sumant Kumar Prof. Ravi Sankar J Prof. Umakanta Mishra Prof. Jagatheswari S Prof. Veeramani S Prof. Kavitha A Prof. Vijaykumar V Prof. Tamizharasi R Prof. Prabhujit Mohapatra Prof. Kalpana Priya D Prof. Abhishek Das Prof. Aruna K Prof. Ankush Chanda Prof. Jayalakshmi M Prof. Balasubramani N Prof. Kavitha K Prof. Chandru M Prof. Shobana Devi N Prof. Clement J Prof. Pallenivel K V Prof. Deepti Shakti Prof. D. V. Shibesh Kumar Prof. Kuvar Satya Singh Prof. Purusotham S Prof. Pradeep Kumar Saroj Prof. Deepa G Prof. Padigepati Naveen Prof. Manimaran A Prof. Prakash M Prof. Sujatha V Prof. Ramu Geddavalasa Prof. Raghavendar K Prof. Sunanda Saha Research Scholars Ms. M.S. Bhuvaneswari Mr. S. Gurunathan Volunteers Mr. G. Venkatesan Mr. T. ‘amizharasan (Abstract Book Preparation) Mr. M. Varadha Raj Indian Mathematical Society (Estd. 1907; Registration No. S-550, Delhi) h‹p://www.indianmathsociety.org.in

‘e Indian Mathematical Society (IMS) is the oldest Scienti€c Society in India. It was founded by Late Shri V. Ramaswami Aiyer in April 1907 with twenty founding members having its Headquarters at Pune. ‘e society was then known as ‘Analytic Club’ which was soon changed to ‘Indian Mathematical Club’. In 1910, however, the new revised Constitution of IMS was adopted and the club acquired its present name, the ’Indian mathematical Society’. ‘e objective of the Society is the promotion of Mathematics Education and Research. Its central activity is to inspire and encourage researchers, students and all the mathematics-loving persons. Professor B. Hanumantha Rao was the €rst President of the Society from 1907 to 1912.

Discovery of Srinivasa Ramanujan: When we pause to reƒect on the life of the greatest Indian mathemati- cal genius of modern times S.Ramanujan, we see that there were certain events that seemingly were necessary in order that Ramanujan and his mathematics be brought to posterity. One of these was V. Ramaswami Ai- yar’s founding of the Indian Mathematical Society. For had he not launched the Indian Mathematical Society, the next necessary episode, namely, Ramanujan’s meeting with Ramaswami Aiyar at his oce in 1910, would also have not taken place. Ramanujan had carried with him one of his notebooks, and Ramaswami Aiyar not only recognized the creative spirit that produced its contents, but he also had the wisdom to contact others in order to bring Ramanujan’s mathematics to others for appreciation and support. ‘e large mathematical community that has thrived on Ramanujan’s discoveries for nearly a century owes a huge debt to V. Ra- maswami Aiyar and the Indian Mathematical Society.

Annual Conferences of IMS : ‘e First, Second and ‘ird Conference of IMS were held respectively at Madras (1916), Bombay (1919) and Lahore (1921). One pleasantly notes that the IMS had jurisdiction beyond the boundaries of the present Indian State. ‘e Fourth Conference of IMS was organized at Pune in 1924. In those days the Conferences of the Society were organized intermi‹ently with a gap of more years than one. From 1951 onwards, the Conferences of the Society are being organized annually every year. ‘e Silver Ju- bilee Celebrations, on the occasion of completion of twenty €ve years of existence of IMS, were held at Pune on March 26, 1932 under the Presidentship of Wrangler Principal R.P. Paranjpye. It is at this conference that it was decided to start the publication of another periodical, as a part of this Silver Jubilee Celebrations, and accordingly the Society started a new Journal named ‘e Mathematics Student in 1933 - over and above the Journal of the Indian Mathematical Society which was being published from the beginning. ‘e 25th (Silver Jubilee) Conference of IMS was held at Allahabad in 1959 which was inaugurated by Late Pandit Jawahar Lal Nehru, the €rst Prime Minister of India. ‘e Platinum Jubilee 75th Annual Conference of the Society was held under the auspices of the Kalasalingam University, Krishnankoil, Tamil Nadu, in December 2009. On this occasion, a Commemorative Postage Stamp on the “Indian Mathematical Society” was issued by the Department of Posts (Philately Division), Government of India to mark the completion of the hundred years of the establishment of the Society.‘e Centenary Year Celebrations of the existence of the Society took place during 73rd Annual Conference of the Society held under the auspices of the University of Pune, Pune, in December 2007. Prof. S.T. Yau (Fields Medalist), Prof. Richard Hamilton (Clay Award winner) and Prof. S.R. S. Varadhan (Abel Prize Winner) delivered plenary lectures during the Conference.To mark the occasion of this Centenary Year, Special Volumes of the Journal (‘e Journal of the Indian Mathematical Society, ‘e Special Volume 1907-2007) as well as of the Mathematics Student (‘e Mathematics Student, Special Cen- tenary Volume (2007)) were published. All these years, the Society has motivated and inspired a very large number of budding mathematicians, and thus has served a great cause of promoting Mathematics Education and Research in the Country.

Main Academic Programs of the Annual Conferences: During every Annual Conference of the Soci- ety, the following Memorial Award Lectures are arranged as a part of the Academic Programme (each Award Lecture is of one hour duration with no parallel session). P.L. Bhatnagar Memorial Award Lecture (Instituted in 1987). SrinivasaRamanujan Memorial Award Lecture (Instituted in 1990). V. RamaswamyAiyer Memorial Award Lecture (Instituted in 1990). Hansaraj Gupta Memorial Award Lecture (Instituted in 1990). Ganesh Prasad Memorial Award Lecture (Instituted in 1993; and delivered every alternate year Further, as part of the Academic Programme, there are Plenary lectures by eminent Mathematicians, Symposia on current topics, Invited talks, and Research paper reading sessions. Periodicals published by the Society:‘e Society publishes two periodicals ‘e Journal of the Indian Math- ematical Society (JIMS; the journal; ISSN 019-5839) and ‘e Mathematical Student (MS; the Student; ISSN 0025-5742).

‡e Journal of the Indian Mathematical Society: From its very inception, the Society started publishing, ‘Progress Reports’. ‘e First Progress Report was published in September 1907. Till December 1908, in all, eight ‘Progress Reports’ were brought out. From 1909 the ‘Progress Reports’ were rechristened as Journal and it was published every two months till 1933. ‘e First Editor of ‘Progress Reports’ and later of the Journal of the Indian Mathematical Society (J. Ind. Math.Soc.) was M.T. Naraniengar who continued till 1927 and nurtured it for twenty years. Later the Editorship of JIMS was entrusted to R. Vaidyanathswamy who served as editor until 1950. During his tenure of editorship, in 1934, the present new series of JIMS was started and was turned into a quarterly Journal. It was due to the hard work put in by these two pioneering editors that the JIMS established itself as one of the leading international Journals, a position which it continues to hold even today. It must be mentioned that S. Ramanujan published 12 of his papers, including the €rst one; in the JIMS. Its online publication also started w.e.f. the year 2015. ‘e JIMS is currently indexed by the Math- ematical Reviews, Zentralbla‹ for Mathematics and the Scopus. It is also a UGC recognized journal.

‡e Mathematics Student: At the time of the Silver Jubilee Celebrations on the occasion of completion of twenty €ve years of existence of the Indian Mathematical Society in 1932, it was decided to start the pub- lication of another periodical, and accordingly the Society started a new Journal, named ‘e Mathematics Student, in 1933 with A NarasingaRao as its €rst editor. A Narasinga Rao worked as the founder editor al- most single handed with great devotion for eighteen years (1933-1950) and placed it on a €rm footing. It is a very popular periodical among the students as well as researchers in Mathematics. ‘e periodical is indexed by the Math Reviews, Zentralbla‹ for Mathematics and is a UGC recognized journal. It is also indexed by the Scopus.

IMS Library: ‘e Library of the Indian Mathematical Society was started in 1907 at the Fergusson College, Pune with Wrangler Principal R. P. Paranjpye as its €rst Librarian, who served in this capacity from 1907 to 1922. In 1950, the Library was shi‰ed to Madras (Chennai), and is now housed in the Campus of the Ra- manujan Institute for Advanced Study in Mathematics, University of Madras, Chennai ‘e Library receives many journals on Exchange basis and has a rich collection of back numbers of reputed mathematical journals received from all over the world. ‘e complete catalogue of the back volumes of all the periodicals published by the Society as well as those received in exchange by the Society and available in the IMS Library, Chennai, is now displayed on the IMS website. ‘ere is a spate of request for xerox copies of articles published in these journals and the Library a‹ends to these demands promptly. If a particular journal is not available in the IMS Library, the scholars/students are requested to contact other Libraries where it is likely to be available providing them with the addresses of those Libraries.

Awards and Prizes of the IMS: ‘e IMS gives every year the A.K. Agarwal Award for the best paper pub- lished in Number ‘eory, Combinatorics, Discrete Mathematics, Analysis and Algebra; it gives the A.M. Mathai Award for the best paper published in Applied Mathematics; it also gives the Satish Bhatanagar Award for the best paper published on the €eld of History of Mathematics in India. Other details on these prizes can be found on the website of the IMS.

Narasinga Rao Memorial Prize: ‘is Prize is awarded to the author of the best research paper published in the Journal of the Indian Mathematical Society or ‘e Mathematics Student. ‘e Prize carries a cash award of Rs. 2000/- along with a Certi€cate. ‘e Prize will be recommended by a commi‹ee consisting of ‘e Aca- demic Secretary, Indian Mathematical Society (Convener), Editor, Journal of the Indian Mathematical Society and the Editor, ‘e Mathematics Student. ‘e Prize will be awarded during the Inaugural Function of the Annual Conference of the Indian Mathematical Society.

P.L. Bhatnagar Memorial Prize: ‘is Prize is awarded annually to the top scorer(s) of the Indian team at the International Mathematical Olympiad. It consists of a cash Prize of Rs. 1000/- and a Certi€cate. ‘e Prize is presented during the Inaugural Session of the Annual Conference of the Indian Mathematical Society. Prizes for Best Research Paper Presentations: In order to encourage and inspire the young and budding research workers, the Society holds, during its Annual Conferences, a Special Session of Paper Presentation Competition for various Prizes to be awarded to the best research paper presented in each of the speci€ed areas as stipulated. ‘is Special Session is held as a part of the Academic Program.

Six IMS Prizes: Group-1: Discrete Mathematics (Combinatorics, Graph ‘eory, Posets), La‹ice ‘eory, Set ‘eory, Logic, Number ‘eory and related areas. Group-2: Algebraic Geometry, Geometry, Topology, Algebraic Topology, and related areas. Group-3: Measure ‘eory, Probability ‘eory, Stochastic Processes, and related areas. Group-4: Di‚erential/Integral/Functional equations and inequalities, Special Functions, Numerical Analysis and related areas. Group-5: Solid Mechanics, Fluid Mechanics, Electro-magnetic ‘eory, MagnetoHydrodynamics, Astronomy, Astrophysics, Relativity and related areas. Group-6: Operations Research, Optimization, Computational Mathematics, Information Technology, Biomath- ematics, History of Mathematics and related areas.

A M U Prize: ‘is prize is given to the best paper presented in the areas Algebra, Di‚erential Geometry and Functional Analysis.

V M Shah Prize: ‘is prize is given to the best paper presented in the areas of Real Analysis, Complex Analysis, Fourier Analysis, Harmonic Analysis, Approximation ‘eory and related areas.

Each of these eight prizes listed above carries a cash award of Rs.1000/- and a Certi€cate.

Guidelines for acceptance of Donations to the Society: If someone wants to support the Indian Math Society by making donations, the IMS has formulated some guidelines for these donations. ‘ese guidelines are uploaded with all details in the website of the IMS and the interested persons are requested to consult these guidelines and donate to strengthen the Society and its activities.

IMS Sponsored Lectures: To popularize Mathematics and to create awareness regarding the Society and its activities in the Country, the Society has a scheme of Sponsored Lectures by eminent mathematicians of India and abroad. It provides a token support to a number of Departments / Institutions for organizing popular, semi-technical and technical lectures.

IMS News Letters: Two News Le‹ers (one in March & the second in August every year) are published by the Society for the bene€t of its members. ‘e newsle‹ers carry important information and announcements of the Society and are uploaded on the website of the IMS. Detailed information on the newsle‹ers may be obtained by referring to the latest News Le‹er No 42 from the IMS Website.

Now the IMS has its own Head-†arters: ‘e ambitious project of having a head quarter of the IMS has now taken the €rm big step. Recently, the IMS has purchased a plot of land near Pune air port measuring about 44,000 sq ‰ on the side of a road. ‘e registration of the land was done in Feb 2020 in the presence of Prof. Satya Deo, General Secretary, Prof. B.N. Waphare, Administrative Secretary, Prof. S.K. Nimbhorkar, Treasurer and Prof. M.M. Shikare, the Editor, Math Student. Now we are in the process of drawing a Master Plan for developing the IMS campus with all facilities a‰er taking opinion of all Council Members.

Prof. Satya Deo General Secretary, Indian Mathematical Society (IMS) Indian Mathematical Society (Estd. 1907; Registration No. S-550, Delhi) h‹p://www.indianmathsociety.org.in PRESIDENT

Prof B. Sury did his B.Sc. (Hons.- Mathematics) from the University of Delhi in 1979 and M.Sc. (Mathematics) from IIT Delhi in 1981. He got his Ph.D. from the Tata Institute of Fundamental Research, Bom- bay in January 1991 under the supervision of Professor M S Raghu- nathan, F.R.S. ‘e topic was ‘Algebraic groups and discontinuous sub- groups’. During 1981-1999, he was at the TIFR and, then moved to the Bangalore centre of the Indian Statistical Institute in May 1999 where he is a Professor (HAG) at present and has also served as Associate Dean.

His research Interests are : Linear algebraic groups over global and local €elds, Diophantine equations, Division algebras, Central ex- tensions of p-adic groups, Density theorems in number theory, K- theory of Chevalley groups, Combinatorial number theory, Computa- tion of class groups, Character theory of €nite groups, Packing prob- lems.

He is Fellow of the National Academy of Sciences, India; National Coordinator in charge of the mathematics Olympiad programme in India since 2016; Mathematician member of the Mathematics newsle‹er commi‹ee at ICM 2010. He also gave Invited Talk in ICM satellite conference in 2018 (Brazil).

Prof Sury is in the Editorial Board of (i) Proceedings of the Mathematical Sciences, Indian Academy of Sci- ences, (ii) ‘e Mathematics Newsle‹er of the Ramanujan Mathematical Society, (iii) ‘e Indian Journal of Pure and Applied Mathematics, (iv) ‘e Mathematics Student, (v) Resonance, a journal of undergraduate of Science Education, (vi) Blackboard, a Bulletin of the Mathematics Teachers’ Association (India).

Prof Sury has held visiting positions Max Planck Institut Fur Mathematik at Bonn, University of Toronto, Uni- versity of Waterloo, Fields Institute for Mathematics, University of North Carolina at Greensboro, University of Glasgow, Hebrew University at Jerusalem, Universitat Kaiserslautern, International Centre for ‘eoreti- cal Phsycis at Trieste, Steklov Mathematical Institute at St.Petersburg, Universite de Paris VII, University of Manchester, University of Edinburgh, Imperial College London.

In particular he visited University of Glasgow in 2001 under the UK Royal Society - INSA exchange Pro- gramme; St. Petersburg department of Steklov Institute for Mathematics under Indo-Russian Project and VAJRA project with Maxim Vsemirnov, Deputy Director, St.Petersburg dept of Steklov Institute.

Publications include 90 plus research papers, 3 books, 1 book edited, more than 50 expository and educa- tional articles for students of di‚erent levels. He supervised PhD students and mentored several postdoctoral fellows.

Prof. B. Sury Stat-Math Unit Indian Statistical Institute 8th Mile Mysore Road Bangalore 560059 India h‹ps://www.isibang.ac.in/ sury/ Email: sury at isibang dot ac dot in INDIAN STATISTICAL INSTITUTE BANGALORE CENTRE STATISTICS AND MATHEMATICS UNIT

Telephone: 080-28483002/003/004/005/006 8th Mile, Mysore Road Telegram: STATISTICA R.V. College Post Fax: 080-28484265 BANGALORE 560 059, INDIA

Message

I am happy to be a part of the 86th Annual Conference of the Indian Mathematical Society to be held at VIT Vellore during December 17-20, 2020. I am extremely glad to welcome all the participants to the conference. The prevalent circumstances have forced upon us an online mode of activity. Nevertheless, this could ensure more participation than may have been possible if a physical meeting were to take place that would necessitate people from different parts of the country to travel. In fact, there are invited talks by distinguished speakers from outside India as well.

The IMS is the oldest mathematical society of our country with luminaries like V. Ramaswami Aiyer, V. Vijayaraghavan, P L Bhatnagar and Hansraj Gupta having served as Presidents in yester years. Its annual conference is an event the mathematics community looks forward to enthusiastically every year.

This year’s conference includes symposia on diverse themes ranging from subjects like Topology and Number Theory to Industrial Mathematics and History of Mathematics. As an icing on the cake, this occasion is used as an opportunity to felicitate the celebrated mathematician-cum-institution builder Professor K. Chandrasekharan. The Memorial Award lectures named after INDIAN STATISTICAL INSTITUTE BANGALORE CENTRE STATISTICS AND MATHEMATICS UNIT

Telephone: 080-28483002/003/004/005/006 8th Mile, Mysore Road Telegram: STATISTICA R.V. College Post Fax: 080-28484265 BANGALORE 560 059, INDIA personages such as Ramanujan, Bhatnagar and Hansraj Gupta are awaited with anticipation as they showcase the work of some of the brightest minds in our country. So are the IMS competition paper presentations. At the end of the conference, a special session is planned to discuss funding opportunities available for the development of mathematics.

The local organizer of the conference Professor Rushi Kumar as well as the Academic Secretary of the IMS Professor Peeyush Chandra have to be congratulated for planning a meeting of such a high caliber. Notwithstanding the online modality of conduct, I am confident this conference will play a big role in reaching out to the mathematics community in our country. Such meetings would also make our community visible to the society at large and promote awareness of the importance of our subject. I wish the conference success in its endeavor.

With best regards,

(B. SURY) Professor (HAG), Indian Statistical Institute, 8th Mile Mysore Road, Bangalore 560059, India. Message from the General Secretary ‘e 86th annual conference of the Indian Mathematical Society is taking place at VIT, Vellore during Dec 17-20, 2020. Because of the ongoing COVID-19 pandemic, this would be the €rst time in the History of IMS that we would be having a virtual confer- ence. ‘e host institute has to make all the necessary arrange- ments for the conference in a new format which needs special at- tention for all the events and a robust technology. I am sure the VIT, having already organized several virtual conferences, will be able to organize this conference also in a smooth manner. We have chalked out a nice academic programme. ‘e guests, speak- ers as well as the participants will have an entirely new experi- ence of listening to talks by the eminent mathematicians and re- search scholars. ‘e oce bearers of the IMS also will have an op- portunity to conduct the proceedings with meticulous care and plan- ning.

I wish the organizers of the conference a great success in managing this conference.

Professor Satya Deo General Secretary, Indian Mathematical Society (IMS) Harish-Chandra Research Institute, Allahabad December 12, 2020, Allahabad. Message from the Academic Secretary It is my pleasure to welcome all the participants to the 86th An- nual Conference of the Indian Mathematical Society – An Interna- tional Meet being organized under the auspices of the Department of Mathematics, VIT Vellore. Normally we have a physical meet- ings but the present pandemic conditions forced the organizers to go for the online mode. As VIT, Vellore is well equipped to orga- nize such events, we are very hopeful that it will be a successful event.

We received very encouraging responses from the speakers as well as from the Symposia convenors. ‘us we have eminent speakers from India as well as from outside. ‘ere has also been a tremendous re- sponse of participants. We received large number of papers for var- ious Prizes and so this year there will be two sessions for Competi- tion Paper presentations. Also the number of contributory papers re- ceived this year is 224, so we have many parallel sessions for it. ‘e online mode made it possible to have such sessions till late in the evening.

We have also planned a session on ‘Funding Opportunities for Mathematics’ with a hope that it will create awareness to young researchers.

‘e Local Organizing Secretary, Prof Rushi Kumar and his team has been working very hard for this new experience of having Online Conference. ‘is has given us an opportunity to reach out to large number on researchers in Mathematics. I wish the conference a great success.

Peeyush Chandra Prof. Peeyush Chandra, FNASc Academic Secretary Indian Mathematical Society (IMS) Professor (Retired) Department of Mathematics & Statistics, IIT Kanpur About VIT Vellore Institute of Technology (VIT), Vellore, one of the premier institutes in India loacted in Tamil Nadu, was established in 1984. It is a major, comprehensive, student-centred research institution dedicated to ex- cellence in teaching, research and service. VIT comprises of various schools and interdisciplinary research centres o‚ering undergraduate, post graduate and research programmes in various engineering disciplines. ‘e institute was established with the aim of providing quality higher education at par with international standards. VIT Vellore campus has a cosmopolitan atmosphere with students from all corners of the globe. Memoranda of Understanding with various international universities and industries are the major strength of VIT. Mission of VIT is to educate students from all over India, including those from the local and rural areas, and from other countries, so that they can become enlightened individuals, improving the living standards of their families, industries and society. VIT provides individual a‹ention, world-class quality education and takes care of character building. ‘ere are student and faculty exchange programs, to encourage joint re- search projects for the mutual bene€t. VIT Vellore obtainedgrade “A” for all the programs o‚ered by the University during the re-accreditation processes in February 2015. ‘e University was recently Ranked No.1 Private Engineering Institution by MHRD, Govt. of India. VIT – Recognized as Institution of Eminence (IoE) by Government of India. About SAS, VIT ‘e School of Advanced Sciences (SAS) includes Mathematics, Physics and Chemistry disciplines. ‘e School o‚ers M.Sc., M.Phil. and Ph.D. programmes in these domains. ‘e faculty of the entire School comprises quali€ed and goal-oriented members whose research expertise includes major frontier areas in Mathematics and Physics, Chemistry. ‘e School has been receiving research grants from various funding agencies such as DST, CSIR, DRDO, NBHM, BRNS, IGCAR, AERBA, NRB,ISRO and ARDB. ‘e School has also been recognised by DST for support under the FIST programme. ‘e School will be conducting various programmes such as InoVIT, National Science day, National Mathematics day and VIT Mathematical Meet, which are National and Regional level Math and Science contests for school children to create and encourage Mathematical and Scienti€c innovations among the students. For further details: https://vit.ac.in/schools/sas About Department of Mathematics ‘e department was established in 1984 as a part of the then existing Vellore Engineering College. ‘e de- partment o‚ers opportunities for the education and research in a wide spectrum of areas in Mathematics such as: Algebra and Analysis, Di‚erential Equations and their applications, Graph theory and applications, Cryp- tography, Numerical Analysis and Scienti€c Computing, Functional analysis,Mathematical Biology, Statistics and Operations Research, Fluid Dynamics, Solid mechanics, CFD, Cosmology,Topology,Mathematical Mod- elling etc. ‘e department runs several foundational courses in Mathematics for all students in Vellore campus pursuing various degree programs of the Institute. Besides, the Department also o‚ers specialized courses in Masters Programs in Data Science, Computational Statistics and Data Analytics, Business Statistics and Ph.D. degrees in Mathematics. ‘e department also contributes substantially towards organizing extension programmes such as conference, workshops, seminars and symposia on the latest topics. ‘e department has strongly motivated faculty with diverse specialization in Mathematical/ Statistical/ Computing sciences providing a potential for pursuing research in basic sciences as well as in interdisciplinary areas of science, engineering and technology. ‘e department is commi‹ed to train the students to make them motivated and dedicated engineers and scientists. ®

VIT UNIVERSITY (Estd. u/s. 3 of UGC !v:J. 1956) Dr. G. VISWANATHAN Founder& Chancellor FormerMember of Parliament Former Minister, Govtof Tamil Nadu President,Education Promotion Societyfor India, New Delhi

Message

I am glad that the Department of Mathematics, School of Advanced Sciences, VIT Vellore, is hosting the 86th Annual Conference of the Indian Mathematical Society (IMS-2020), from 17 to 20 December 2020. The Indian Mathematical Society (IMS) is the oldest and the largest Mathematical Society of the country. Every year, the society organizes its annual conference at different locations in India. The Conference aims at helping students, experts and scholars keep abreast of the latest developments in the fieldof Mathematics.

The conference serves as an effective platform for scientists, educators and scholars from various institutions and industries across the world to share their ideas and present their work. I believe the conference would contribute significantly to the knowledge repository of Mathematics.

I congratulate the organizing team on facilitating this mega event at VIT, Vellore. I wish this conference emerges as an outstanding contribution to the Mathematics research community.

I welcome the IMS officials, invitees, speakers, delegates and participants,and wish them a fruitful time.

I wish the IMS-2020 a grand success.

Dr.G.Viswana an Founder & Chancellor

Vellore - 632 014 10/12/2020

Vcllorc- 632 014. Ta.mil Nadu, India; Tel.: +91 416 2243100 Fax: +91 416 2243092; E-mail: [email protected] Chcnnai Campus: Vandalur - KelambakJcam Road, Chcnnai - 600 127, India; Tel.: +91 44 3993 1555; Fax: +914439932.555 www.vit.ac.in

VIT. � Vellore Institute of Technology �����i!',;,� (Deemed to be University under section 3 of UGC Act, I 956) 09.12.2020

Dr. S. Narayanan Pro-Vice Chancellor MESSAGE

I am delighted to note that the Department of Mathematics, School of Advanced Sciences is organizing the 86th Annual Conference of the Indian Mathematical Society (IMS-2020).

A maJor field of research which is the highlight of this international conference is Mathematics. I am sure this conference will promote top level research and offer global perspectives on quality research in general, thus making the discussions and presentations internationallycompetitive by focusingon the recent outstanding achievements in the field of Mathematics, and addressing futuretrends and needs.

I take this opportunity to congratulate.. the members of the organizing committee for their dedication and tireless efforts to organize the conferenceof this scale.

I wish the deliberations of the conference a grand success!

�l)'l-b S. Narayanan

Vellore - 632 014, Tamil Nadu, India; Phone: 91 - 416 - 2243091 (10 Lines) Fax: 91- 416 - 2243092 E-mail: [email protected] www.vit.ac.in Message from the Dean, SAS It is our pleasure and a great honor to host the “86th Annual Conference of the Indian Mathematical Society” (IMS 2020) from 17th to 20th Decem- ber 2020 at the Department of Mathematics, School of Advanced Sciences, VIT Vellore.

IMS being the oldest and the largest Mathematical Society of the country, creates a unique platform for Mathematicians all over In- dia and abroad to congregate and exchange mutual ideas. It hosts specialized lectures by eminent scientists who provide an update of the recent developments in various frontline topics on the sub- ject. ‘is conference will not only keep the participants abreast of the latest development in Mathematics, it will also pave a way for the young Mathematicians to interact fruitfully with stalwarts in the €eld.

Mathematics in today’s world structures a dream for future development and provides alternatives to complicated experimental setups. I believe that this conference will enrich us both on fundamental and advanced topics of the subject. I take this occasion to welcome all the delegates and thank the members of the IMS for giving us this opportunity to organize this conference.

I wish all the delegates to have fruitful discussions on these four days in the plethora of mathematicians and get fullest bene€ts of this conference.

I congratulate the organizing commi‹ee members and wishing all success for the conference.

Prof Mary Saral A Dean, School of Advanced Sciences Vellore Institute of Technology. Message from the Head Department of Mathematics It is my pleasure to welcome you to the 86th Annual Conference of the Indian Mathematical Society (IMS-2020) organized by the Department of Mathematics, School of Advanced Sciences, VIT, Vellore. Mathemat- ical sciences play an essential role in the physical, chemical and bio- logical sciences, engineering, medicine, economics, €nance and social sciences. Mathematical sciences have become integral to many emerg- ing industries, and the increasing technological sophistication of our armed forces has made the mathematical sciences central to national de- fence.

To say a few words about this department we must begin with the fact that our Mathematics department is one of the starting departments in VIT. Over the years this department has had copious inter- disciplinary collaborations and interactions in diverse areas with researchers and pio- neers in several advanced €elds of Mathematics. At present, we have 118 faculty members and 209 research scholars engaged in research covering all the frontline topics of Mathematics. We o‚er the courses, Integrated MSc in Computational Statistics and Data Analytics, MSc in Data Science and MSc in Business Statistics. Apart from that we also o‚er courses starting from basic under graduate Mathematics to specialized courses on advanced mathematics for our B,Sc/BCA/BBA/B.Com/B.Sc(Agree)/ B.Tech/ B.Arch/ B.DES/ M.Tech/ MBA /MCA/M.Sc/Int. M.Tech students. ‘is department not only focuses on training in the rudiments of Mathematics, it also emphasizes in o‚ering advanced courses on applications in modern day technology and research in multi-dimensional areas.

I take this occasion to welcome all the delegates and thank the members of the IMS for giving us this op- portunity to organize this conference. I wish you a fruitful discussions for these four days in the plethora of mathematicians and wish you good luck in your future endeavors.

I also congratulate the local organizing secretary, all faculty members, research scholars of Mathematics de- partment, sta‚ members for their e‚orts in organizing and participating in this conference.

I wish the conference, a grand success and wish all participants to have a feast of learning, knowledge devel- opment and sharing of experiences.

Prof K Karthikeyan, Professor & Head Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore Message from the Organizing Secretary It is our great honor to welcome all the delegates to the ”86th An- nual Conference of Indian Mathematical Society” (IMS 2020). ‘e or- ganizing team and other colleagues at VIT Vellore together with the oce bearers of IMS put in their best e‚orts to make all the neces- sary arrangements to host a virtual international meet IMS-2020 con- ference. We are sure that all of you are going to celebrate the days 17 - 20 December 2020 as an academic festive. We hope that all the participants would make use of this opportunity and interact thor- oughly.

IMS is a unique platform where the a‹ention is drawn from var- ious sectors. ‘e need of the day is to make signi€cant inter- disciplinary collaborations without diluting the core €elds. ‘is is a big challenge. We are con€dent that this conference helps many younger colleagues to make a big step in this direction. To encourage joint research projects, a special session on funding for Mathematics projects is arranged to all the IMS 2020 partici- pants.

It is a great privilege for the Department of Mathematics, School of Ad- vanced Sciences, VIT, Vellore is to organize this event for the €rst time in VIT, Vellore. We take this op- portunity to thank IMS Council. ‘e support by VIT management is greatly acknowledged. We also thank distinguished Mathematicians and colleagues across the country who made to this occasion. We also thank our Chancellor, Vice President, Vice Chancellor, Pro-Vice Chancellor, Registrar, Dean: School of Advanced Sciences, HoD: Department of Mathematics and all other faculty members, all research scholars of depart- ment of Mathematics, institute authorities and sta‚ members for their invaluable support.

My sincere thanks to all IMS executives and in particular to IMS General Secretary Prof. Satya Deo, Academic secretary Prof. Peeyush Chandra, IMS treasurer Prof. S K Nimbhorkar for their continued support to organize IMS-2020.

It is our privilege to host IMS conference 2020 at VIT, Vellore. Wish you all a very happy and fruitful confer- ence.

Prof Rushi Kumar B Local Organizing Secretary, IMS 2020 Plenary Speaker - Prof M S Raghunathan

Prof M S Raghunathan Head of the National Centre for Mathematics, Indian Institute of Technology, Mumbai.

Professor Madabusi Santanam (M. S.) Raghunathan is a world class mathematician from India with a high international repute. He is presently Distinguished Professor at Centre of Excellence in Basic Sciences (CEBS) and is also Head of the National Centre for Mathematics at Indian Institute of Technology, Mumbai. He wrote his PhD thesis under the guidance of Professor M.S.Narasimhan and was awarded the degree by the Univer- sity of Bombay in 1966. His central theme of research has been “Discrete Subgroups of Lie Groups.” His book on the same topic is a classic work in that area. He has made remarkable contributions on the problems of rigidity and arithmeticity.

A‰er completing his PhD from TIFR Bombay, he spent a year at the Institute for Advanced Study, Princeton, US. He then joined TIFR Bombay and worked there for a long period of time. He was appointed Professor of Eminence on Homi Bhabha Chair. He has held visiting positions in reputed academic institutions in the US, Europe and Japan, and has spoken at several international conferences. Prof Raghunathan has played an important role in the growth of School of Mathematics at TIFR which is now an international centre of excellence. He has also played an important role in the promotion of mathematics through various national scienti€c bodies, in both advisory and administrative capacities. One of his most important contributions is in chairing the National Board for Higher Mathematics (NBHM). Raghunathan was a member of the Board since its inception in 1983 and became its chairman in 1987. He organised the Srinivas Ramanujan Centenary Celebrations in Chennai in 1987, with an international conference a‹ended by the foremost number theorists. He was the main force in organizing the International Congress of Mathematicians (ICM 2010) at Hyderabad in India. ‘is was the €rst ever ICM held in India.

Prof Raghunathan has received several honours. He is a Fellow of the Royal Society, UK (FRS). He is also a Fellow of ‘e World Academy of Sciences (TWAS), Fellow of the American Mathematical Society, Fellow of all the three Science Academies of India. He is a recipient of Shanti Swarup Bhatnagar Prize and the Country’s Civilian Award Padma Bhushan. Plenary Speaker - Prof Harald Upmier

Prof Harald Upmeier University of Tuebingen, Germany

Professor Harald Upmeier obtained his PhD (1975) at the University of Tuebingen (Germany), with a thesis on in€nite-dimensional Lie groups. In the 1980’s he moved to the United States (University of Pennsylvania and University of Kansas) before returning to Germany (1994) for a Chair in Mathematics at the University of Marburg. More recently, he has been a frequent visitor to leading research centers in India, for example the TATA Institute (Mumbai), the Harish-Chandra Institute (Allahabad) and the Indian Institute of Science (Bengaluru), where he currently holds an Infosys Visiting Chair Position for three years.

Harald Upmeier is working in geometric analysis in several complex variables, studying Hilbert spaces of holomorphic functions (Bergman type spaces) and operators/operator algebras acting on these Hilbert spaces. ‘is theory is particularly rich for the so-called bounded symmetric domains, where the underlying Hilbert spaces carry representations of a semi-simple Lie group, leading to deep problems in representation theory and the combinatorics of partitions. On the geometric side, the main challenge is that the boundary of sym- metric domains is not smooth in general, but has an interesing strati€cation into lower-dimensional strata. ‘is strati€cation has deep consequences for the associated operator C∗-algebras and the structure of Hilbert submodules of Bergman spaces.

Professor Upmeier is the author of four books on complex analysis and operator theory, and is a Fellow of the American Mathematical Society. 31st Srinivasa Ramanujan Memorial Award Speaker

Prof Anish Ghosh Tata Institute of Fundamental Research, Bombay

Prof Anish Ghosh is a member of the faculty at the Tata Institute of Fundamental Research. He works on ergodic theory on homogeneous spaces, discrete groups and associated number theory and geometry. He is a fellow of the Indian Academy of Sciences and is a recipient of the NASI-SCOPUS young scientist award, the B. M. Birla Science Prize and the DST Swarnajayanti Fellowship. 34th P.L. Bhatnagar Memorial Award Speaker

Prof Neela Nataraj Department of Mathematics, Indian Institute of Technology, Mumbai.

Prof. Nataraj has been working at the Department of Mathematics, Indian Institute of Technology Bombay (IIT Bombay) since 2003. She has contributed to the state-of-the-art numerical analysis of partial di‚erential equations (PDEs) with emphasis on thin/very thin plate bending problems governed by fourth-order lin- ear/nonlinear elliptic systems. Her research activities involve investigation of both fundamental and applied problems by theory and computations; a priori and a posteriori error analysis and optimal control problems governed by PDE constitute highlights. As far as application problems are concerned, she has worked exten- sively in €nite element and €nite volume methods for nonlinear systems of PDEs that occur in laser surface hardening of steel, Kelvin-Voigt ƒuids, von Karm´ an´ plates, nematic liquid crystals, tumour growth, etc. She has published more than €‰y papers in international journals of high repute. She has so far supervised/co- supervised nine students for their Ph.Ds, and is guiding four students presently.

Prof. Nataraj served as the €rst woman Head of the Department of Mathematics at IIT Bombay (2016-2018). She is currently the Professor-in-Charge of IIT Bombay-Monash Research Academy, one of the major collab- orations engaged in research through joint Ph.D. programs between IIT Bombay and Monash University. She is presently the Chair of the Executive Commi‹ee of Indian Women and Mathematics and is also a Member of the International Mathematics Union Commi‹ee for Women in Mathematics. Prof. Nataraj is an elected Fellow of the National Academy of Sciences (FNASc) India. She is a recipient of Best Teacher award conferred by the Indian National Science Academy (INSA), New Delhi for the year 2019. 31st Hansraj Gupta Memorial Award Speaker

Prof Dinesh Khurana Panjab University

Prof Dinesh Khurana was born in Kashmir and did graduation and post-graduation from University of Kash- mir. A‰er doing PhD from Panjab University, he was appointed as a Lecturer in the same University in 2000. He is presently working as a Professor in Panjab University. He has also taught for a quarter in Ohio Univer- sity and for three years in IISER Mohali. He works in algebra and most of his research is in non-commutative ring theory. He is an elected fellow of NASI and on the editorial board of Indian Journal of Pure and Applied Mathematics. He is also convener of the commi‹ee for Instructional School for Teachers (ISTs) of National Center for Mathematics (NCM). 31st V Ramaswami Aiyer Memorial Award Speaker

Prof Sanoli Gun Institute of Mathematical Sciences, Chennai.

Sanoli Gun is a faculty member of Institute of Mathematical Sciences, Chennai. She did her Phd in Harish- Chandra research Institute, Allahabad followed by post-doctoral positions at University of Toronto, Canada and een’s University, Canada. She is interested in Number ‘eory. She was a regular associate at ICTP, Italy as well as an associate of Indian Academy of Sciences. She is a recipient of SERB women excellence award. She is in the editorial board of Proceedings of Indian Academy, Journal of Ramanujan Math Society, Indian Journal of Pure and Applied Mathematics and RMS newsle‹er 86th Annual Conference of Indian Mathematical Society An International Meet VIT Vellore, December 17-20, 2020 Schedule

December 17, 2020 10:00 – 11:30 Inauguration 11:30 – 11:40 Break Presidential Address (Technical): Prof B Sury, I.S.I. Bangalore, President IMS 11:40 – 12:40 ”Groups over Global and Local Fields - Some Œemes” Chair Person: Prof S Bhargava Satish Bhatnagar Award Lecture: Prof. M.D. Srinivas, Centre for Policy Studies, 12:45 – 13:15 Chennai ”Pandiagonal Magic Squares: From Nag¯ arjuna¯ To Nar¯ ayan¯ . a Pan. d. ita To Vija- yaraghavan” Chairperson: Prof S G Dani 13:15 – 14:00 Lunch Break Plenary Talk 1: Prof M S Raghunathan, CEBS Mumbai th 14:00 – 15:00 ”Some Major Indian Contributions to Mathematics in the 20 Century” Chairperson: Prof Satya Deo 31st Srinivasa Ramanujan Memorial Award Lecture: Prof Anish Ghosh, TIFR 15:15 – 16:15 Mumbai ”Œe Unreasonable E‚ectiveness of Ergodic Œeory in Number Œeory” Chairperson: Prof N D Baruah 16:30 – 19:30 Session of Competition Paper Presentation 1 (AMU Prize, V M Shah Prize and IMS Prize Group 1)

December 18, 2020 34th P L Bhatnagar Memorial Award Lecture: Prof Neela Nataraj, IIT Bombay, 9:00 – 10:00 Mumbai ”Lower-order Nonstandard Finite Element Methods for Biharmonic Plates” Chairperson: Prof G P Rajasekhar A M Mathai Awardee Lecture: Dr P Prakash, Amrita Viswa Vidyapeetham, 10:05 – 10:35 Coimbatore ”Invariant Subspaces and Exact Solutions of Nonlinear PDEs” Chairperson: Prof B N Waphare 10:35 – 10:45 Break Symposia (in Parallel Sessions) (i) Graph ‡eory and Combinatorics (in honour of Prof S. S. Shrikhande) (Convenor: Prof S Sane, Chennai Mathematical Institute) 10:45 – 13:15 Speakers: Prof R Balakrishnan, Prof Bhaskar Bagchi, Prof M K Srinivasan, Prof Rjendra Pawale, Prof S Sane (ii) Biomechanics (Convenor: Prof B V Ratish Kumar, IIT Kanpur) Speakers: Prof G R K Acharya, Prof P V S N Murthy, Prof P Muthu, Prof Meena Pargei, Prof B V Rathish Kumar 13:15 – 14:00 Lunch Break 31st Hansraj Gupta Memorial Award Lecture: Prof Dinesh Khurana, Panjab 14:00 – 15:00 University, Chandigarh ”Some Glimpses into Noncommutative Ring Œeory” Chairperson: Prof S Arumugam A. K. Agarwal Award Lecture: Dr Jagmohan Tanti, Central University of Jhark- 15:05 – 15:35 hand, Ranchi ”Euler’s Criterion for lth Power non residues with l a Prime” Chairperson: Prof Sudhir Ghorpade A Narasinga Rao Prize Lecture: Dr R B Yadav, Sikkim University, Sikkim 15:35 – 16:05 ”On Some Categories of Riemannian Manifolds” Chairperson: Prof M M Shikare Invited Talks (in Parallel Sessions) Talk 1: Prof S Saravanan, Bharathiar University, Coimbatore ”Sharp Nonlinear Stability Limits for Centrifugal Convection in Porous Media” 16:10 – 16:40 Chairperson: Prof G R K Acharya Talk 2: Dr Pradip Majhi, University of Calcu‹a, Kolkata ”Coˆon Solitons within the Framework of Almost Kenmotsu 3-h-Manifolds” Chairperson: Prof G P Youvaraj 16:45 – 19:45 Session for Competition Paper Presentations 2 (IMS Prize Groups 4, 5 and 6) 20:00 – 21:00 Cultural Programme

December 19, 2020 31st V Ramaswami Aiyer Memorial Award Lecture: Prof Sanoli Gun, IMSc 9:00 – 10:00 Chennai ”On bounds of Fourier-coecients of Half-integer Weight Cusp Forms” Chairperson: Prof Dipendra Prasad Invited Talks (in Parallel Sessions) Talk 1: Prof S P Tewari, IIT Dhanbad ”Automata Œeory Based on Residuated Laˆices” 10:05 – 10:35 Chairperson: Prof Asma Ali Talk 2: Prof K S Charak, University of Jammu, Jammu ”Normal Families of Holomorphic Functions of Several Complex Variables” Chairperson: Prof Sanjib K Da‹a 10:35 – 10:45 Break Symposia (in Parallel Sessions) (i) Chandrasekharan Centenary Symposium in Number ‡eory (Convenor: Prof K Srinivas, Institute of Mathematical Sciences) 10:45 – 13:15 Speakers: Prof Shanta Laishram, Prof Stephen Baier, Prof Jaban Meher, Prof R Padma, Prof K Srinivas (ii) Topology and Geometry (Convenor: Prof P Sankaran, Institute of Mathematical Sciences) Speakers: Prof Mahender Singh, Prof Vimala Ramani, Prof Ramesh Kasilingam, Prof Raisa Dsouza, Prof Harish Seshardi 13:15 – 14:00 Lunch Break Plenary Talk 2: Prof. Harald Upmeier, University of Marbug, Germany 14:00 – 15:00 ”Toeplitz Operators and Hilbert Modules on Bounded Symmetric Domains” Chairperson: Prof Amin So€ Symposia (in Parallel Sessions) (i) History of Indian Mathematics (Convenor: Prof M S Sriram, Prof. K.V. Sarma Research Foundation) 15:05 – 17:35 Speakers: Prof Avinash Sataye, Prof Amartya Du‹a, Prof Venkateswara Pai, Prof C S Aravinda, Prof M S Sriram (ii) Industrial Mathematics: Modelling, Optimization, Simulation (Convenor: Prof S Sundar, IIT Madras) Speakers: Prof Agnieszka Wylomanska, Prof ‘omas Goetz, Prof Sudarshan Ti- wari, Prof Sivaram Ambikasaran, Prof Panchatcharam Mariappan, Prof S Sundar Contributory Paper Presentations 1 (4 Parallel Sessions) Section B (1 – 15) - Chairperson: Prof V M Chandrasekaran 17:45 – 19:30 Section H (1 – 15) - Chairperson: Prof S Srinivas Section E (1 – 14) - Chairperson: Prof Shruti Dubey Section F (1 – 16) - Chairperson: Prof A K Das Contributory Paper Presentations 2 (4 Parallel Sessions) Section A (1 – 12) - ChairpersonL: Prof R Selvakumar 18:00 – 19:30 Section C (1 – 12) - Chairperson: Prof G Murugusundaramoorthy Section H (16 – 27) - Chairperson: Prof S Sreenadh Section I (1 – 12) - Chairperson: Prof Joydip Dhar

December 20, 2020 Invited Talk: Prof Ravi P Agarwal, Texas A&M University, USA 9:00 – 10:00 ”Are We Prepared To Accept Œe Reality?” Chairperson: Prof Manjul Gupta Invited Talks (in Parallel Sessions) Talk 1: Prof Samares Pal, University of Kalyani ”Catastrophic Changes in Coral Reef Dynamics under Macroalgal Toxicity, Over€sh- 10:00 – 10:30 ing and Invasion of Predators” Chairperson: Prof Nita Shah Talk 2: Prof Shakir Ali, Aligarh Muslim University ”Jordan ∗-derivations and Related Maps in Rings” Chairperson: Prof S K Nimbhorkar Contributory Paper Presentations 3 (5 Parallel Sessions) Section A (13 – 24) - Chairperson: Prof Deepa Sinha Section C (13 – 23) - Chairperson: Prof S P Tiwari 10:30 – 12:00 Section D (1 – 11) - Chairperson: Prof Ajay Shukla Section G (1 – 12) - Chairperson: Prof Jitendra Kumar Section I (13 – 23) - Chairperson: Prof P Muthu 12:00 onwards General Body Meeting Contributory Paper Presentations 4 (5 Parallel Sessions) Section C (25 – 36) - Chairperson: Prof S Ahmed Ali Section D (12 – 21) - Chairperson: Prof P K Jain 14:00 – 15:30 Section H (28 – 39) - Chairperson: Prof P V S N Murthy Section I (24 – 37) - Chairperson: Prof Meenakshi Wasadikar Section H (40 – 51) - Chairperson: Prof S K Tomar A Special Session on ‘Funding Opportunities for Mathematics’ 15:40 – 16:40 Speakers: Prof Satya Deo, Prof Chandam Dalawant, Prof Mythily Ramaswamy, Prof S Sundar, Prof V Vetrivel, Prof G P Rajasekhar, Prof Peeyush Chandra (Coorindator) 16:45 onwards Valedictory Function Contents

Presidential Address (Technical) PAT Groups Over Global And Local Fields - Some ‘emes...... 1

Plenary Talks P1 Some Major Indian Contributions To Mathematics In ‘e 20th Century....4

P2 Toeplitz Operators And Hilbert Modules On Bounded Symmetric Domains..4

Memorial Award Lectures ML1 ‘e Unreasonable E‚ectiveness Of Ergodic ‘eory In Number ‘eory....6

ML2 Lower-Order Nonstandard Finite Element Methods For Biharmonic Plates..6

ML3 Some Glimpses Into Noncommutative Ring ‘eory...... 6

ML4 On Bounds Of Fourier-Coecients Of Half-Integer Weight Cusp Forms....6

IMS Award Lectures

AL1 Pandiagonal Magic Squares: From Nag¯ arjuna¯ To Nar¯ ayan¯ . a Pan. d. ita To Vija- yaraghavan...... 8

AL2 Invariant Subspaces And Exact Solutions Of Nonlinear PDEs...... 8

AL3 Euler’s Criterion For lth Power Non Residues With l A Prime...... 9

AL4 On Some Categories Of Riemannian Manifolds...... 9

Invited Talks IT1 Are We Prepared To Accept ‘e Reality?...... 12

IT2 Sharp Nonlinear Stability Limits For Centrifugal Convection In Porous Media 12

IT3 Co‹on Solitons Within ‘e Framework Of Almost Kenmotsu 3-h-Manifolds. 12

IT4 Automata ‘eory Based On Residuated La‹ices...... 13

IT5 Normal Families Of Holomorphic Functions Of Several Complex Variables.. 13

IT6 Catastrophic Changes In Coral Reef Dynamics Under Macroalgal Toxicity, Over-

€shing And Invasion Of Predators...... 13

IT7 Jordan ∗-Derivations And Related Maps In Rings...... 14

xxix Symposium Talks

Graph ‡eory and Combinatorics GTC1 ‘e List Chromatic Number Of A Graph...... 16

GTC2 P-Adic Invariants For asi-Symmetric 2-Designs...... 16

GTC3 Subspaces, Subsets, And Motzkin Paths...... 16

GTC4 Contributions Of S. S. Shrikhande Towards λ-Design Conjecture...... 17

GTC5 An Introduction To ‘e Life And Work Of S.S. Shrikhande...... 17

Biomechanics BM1 Bio-Fluid Dynamics: Fluid Mechanical Aspects Of Microcirculation...... 18

BM2 Magnetic Drug Targeting In A Microvessel With Multifunctional Nanoparticle

Based Carrier Particle...... 18

BM3 Mathematical Models Of Physiological Fluid Flows...... 19

BM4 Cardiac Electrical Activity In A Human Cardiac Tissue: ‘eory, Computation

And Application...... 19

BM5 An Overview Of Cardiovascular Flow Studies: Mathematical ‘eory, Numeri-

cal Analysis And Computational Simulation...... 19

Chandrasekharan Centenary Symposium in Number ‡eory NT1 Lucas Sequences And Its Arithmetic...... 20

n NT2 Prime Powers Dividing Products Of Consecutive Integer Values Of x2 + 1 . 20

NT3 Mod p Modular Forms And Simple Congruences...... 20

NT4 ‘e Discrete Logarithm Problem Over Prime Fields: Non-Canonical Li‰s And

Logarithmic Derivatives...... 20

NT5 Hardy’s ‘eorem For General L-Functions...... 21

Topology and Geometry TG1 Doodles On Surfaces And Associated Groups...... 22

TG2 On ‘e Zero-Divisor Cup-Length Of Real Oriented Grassmann Manifolds.. 22

TG4 Smooth Structures On CP m For 5 ≤ m ≤ 8 ...... 22 TG3 ‘e Topology Of Real Bo‹ Manifolds...... 22

TG5 On ‘e Volume Of Fano Manifolds...... 23

History of Indian Mathematics HIM1 Generalized Brahmagupta-Jayadeva-Bhaskara¯ Problem...... 24

HIM2 On Zero-Divided Numbers In Ancient Indian Mathematics...... 24

HIM3 Brahmagupta’s Bhavan¯ a¯ And Reading Mathematics From Sanskrit Texts... 25 HIM4 Continued Fraction Technique In ‘e Kerala School Of Astronomy...... 25

HIM5 Second Order Taylor Series For ‘e Sine And Cosine Functions In ‘e Kerala

School Of Astronomy And Mathematics...... 26

Industrial Mathematics: Modelling, Optimization, Simulation

IM1 Selection Of ‘e Informative Frequency Band In A Bearing Fault Diagnosis In

‘e Presence Of Non-Gaussian Noise-‘e Stochastic-Based Approach.... 27

IM2 Covid-19-Simulations For Germany...... 27

IM3 A Meshfree Particle Method For Simulations Of Fluid Flows And Interacting

Particle Systems...... 27

IM4 Fast Direct Solver For High Frequency EM Sca‹ering...... 28

IM5 A Point Source Model To Represent Heat Distribution Without Calculating ‘e

Joule Heat During Radiofrequency Ablation...... 28

IM6 Pedestrian Crowd Dynamics Models...... 28

Papers for Competition Session

A M U Prize

AMU-1 Modules Invariant Under Clean Endomorphisms Of ‘eir Injective Hulls... 30

AMU-2 Duality Of Locally asi-Convex Convergence Groups...... 30

V M Shah Prize

VMS-1 A Note On ‘e Value Distribution Of A Di‚erential Monomial And Some Nor-

mality Criteria...... 31

VMS-2 A New Two-Dimensional aternion Fractional Fourier Transform...... 31

VMS-3 Inequalities And Applications Of aternion Windowed Linear Canonical Trans-

form...... 31

VMS-4 antitative Approximation On A New Class Of Szasz-Mirakjan´ Operators

Having Preserving Property...... 31

VMS-5 Binomial Distribution And Its Geometric Properties Associated With Univa-

lent Functions...... 32

IMS Prize Group 1

IPG1-1 Some Properties Of k-Tuple t-Core Partitions...... 33

IPG1-2 Direct Summands Of Goldie Extending Elements In Modular La‹ices..... 33 IMS Prize Group 4 IPG4-1 On Some Series Representation Between R-Function And Fractional Calculus

Operators...... 34

IPG4-2 Approximation Of Solutions For Nonlinear Functional Integral Equations Us-

ing Homotopy Perturbation...... 34

IPG4-3 Aposteriori Error Estimation Of Subgrid Multiscale Stabilized Finite Element

Method For Transient Stokes Model...... 34

IPG4-4 Latest Inversion Free Iterative Scheme For Solving A Pair Of Non-Linear Ma-

trix Equations...... 35

δ IPG4-5 ‘e Polynomial Ln, ξ(X) And Fractional Calculus...... 35 IPG4-6 Finite Di‚erence Heat Transfer Analysis In Square La‹ice When Pivotal Points

Exist Near Curved Boundaries...... 35

IMS Prize Group 5 IPG5-1 ‘e Inƒuence Of Magnetic And Gravitational Fields In A Non-Ideal Dusty Gas

With Heat Conduction And Radiation Heat Flux...... 36

IPG5-2 Mathematical Study Of Reƒection Of QP And QSV Waves From ‘e Stress-

Free/rigid Surface Of A Micro-Mechanically Modeled Piezoelectric Fiber-Reinforced

Composite Half-Space...... 36

IMS Prize Group 6 IPG6-1 Cross Di‚usion Induced Spatiotemporal Pa‹ern In Di‚usive Nutrient-Phytoplankton

Model With Nutrient Recycling...... 37

IPG6-2 An Answer To ‘e Challenges In A CT-Data Based Realistic Complex Artery

Network Flow Study...... 37

Contributory Paper Presentations

Section A: Combinatorics, Graph ‡eory, Logic, Discrete Mathematics A1 Generalized Fuzzy P And Q-Continuous Maps...... 40

A2 Some Properties Of Bipolar Doubt Intuitionistic Fuzzy K-Ideals In BCK/ BCI-

Algebras...... 40

A3 A Real Life Problem In Decision Making Using Hendecagonal Fuzzy Numbers 40

A4 A Note On ‘e Relationship Between Julia Set And Independence Polynomial

Of A Graph...... 40

A5 A Real Life Decision Making Problem As An Application Of Fuzzy Logic... 41

A6 Edge Chromatic Polynomials Of S-Valued Graphs...... 41 A7 Blocks In A S−valued Semigraph...... 41

A8 Characterization Of Semi Spli‹ing Block Graph...... 41

A9 Local Vertex Antimagic Labeling For Disconnected Graphs...... 42

A10 Local Distance Antimagic Vertex Coloring Of Graphs...... 42

A11 Topological Indices Of ‘e Clustered Graphs...... 42

A12 A Note On Reversibility Related To Idempotents...... 43

A13 Solving Transportation Problem Using Graph Algorithms...... 43

A14 Results On Generalized Divisor Sum Function ση Of Certain Standard Graphs 43

A15 Local Distance Antimagic Graphs...... 43

A16 Local Edge Antimagic Labeling Of Cycle Related Graphs...... 44

A17 Genetic Algorithm To ‘e Biobjective Multiple Travelling Salesman Problem 44

A18 Signed Roman Domination In An Interval Graph With Adjacent Cliques Of

Size 3...... 44

A19 Claw-Decomposition Of Kneser Graphs...... 45

A20 On ‘e Zero Forcing Number Of Complementary Prism Graphs...... 45

A21 Edge Chromatic Number Of Zero-Divisor Graphs Of Some Semi-Local Rings. 45

A22 S-Cordial And Total S-Cordial Labeling In Signed Graphs...... 45

A23 A Note On Edge-Fault Tolerance In Augmented Cubes...... 46

Section B: Algebra, Number ‡eory, Lattice ‡eory and History of Mathematics B1 On Cechˇ Fuzzy Interior Spaces And Fuzzy Pretopological Spaces Determined

By Implicators...... 47

B2 Demonstration And Proof Of A Unique Property Of Mersenne Primes.... 47

B3 Data Encryption To Decryption By Using Laplace Transform...... 47

B4 Principal Ideal In Regular Rings...... 47

B5 Notation On Rough Fuzzy Ideals In G−rings And Its Properties...... 48

B6 Cubic Magni€ed Translation On β−Subalgebras...... 48

B7 Structure Of MBJ - Neutrosophic Set Applied On β-Filter...... 48

B8 A Fast Prime-Factorization Of Large Integers And Its Applications To Ane

Ciphers...... 49

B9 ‘e G-Vetex Colour Partition Algebra As A Centralizer Algebra Of An × G . 49

B10 Commutativity Of Prime Rings With Symmetric Biderivations Satisfying Cer-

tain Relations...... 49

B11 Some Results On ‘e Density Of Integral Sets With Missing Di‚erences... 50

B12 Matrices Over Non-Commutative Rings As Sums Of Fourth Powers...... 50 B13 Connecting Monomiality estions With ‘e Structure Of Rational Group Al-

gebras...... 50

B14 asi Factorable Incidence Functions...... 51

B15 Commutarias And Commutator Subgroup Of Finite p-Groups...... 51

Section C: Real and Complex Analysis (including Special Functions, Summability and Trans-

forms etc) and Teaching of Mathematics C1 On Subclasses Of Univalent Functions De€ned By Opoola Di‚erential Operator 52

C2 On Multiplication And Division ‘eorems Of Entire Algebroidal Functions Of

‘eir Relative Growth Indicators Of Higher Index In ‘e Light Of P-Adic Analysis 52

C3 Bounds For Probability Of ‘e Genaralized Distribution For Certain Q-Starlike

And Q-Convex Error Functions Related To Shall-Shaped Region...... 52

C4 Boas Transform Of Wavelets And ‘eir Applications...... 53

C5 On Con€gurations Of Five Periodic Herman Rings...... 53

C6 Convolution Conditions For New Subclass Of Negative Analytic Functions As-

sociated With Polylogarithm Functions De€ned By Linear Di‚erential Operator 53

C7 Obtain Subclass Of Multivalant Function Connected With Convalution Of Poly-

logarithm Functions...... 53

C8 On Extension Of Mi‹ag-Le„er Function...... 54

C9 A Note On ‘e Convergence Of Wavelet Fourier Series...... 54

C10 A New Subclass Of Negative Multivalent Functions Involving Polylogarithm

Functions...... 54

C11 On ‘e Study Of De€ciencies Of Di‚erential Equation Under ‘e Flavour Of

p-Adic Co-Prime Polynomial...... 54

C12 Few Results On Relative (K, n) Valiron Defact From ‘e View Point Of Inta-

grated Modult Of Logarathamic Derivative Of Entire And Meromorpic Functions 55

C13 Common Fixed Point ‘eorems For A Pair Of Mappings In Bicomplex Valued

Metric Spaces...... 55

C14 On g-Mellin Transform: Construction, Convexity And Applications...... 55

C15 Common Fixed Point ‘eorems For ‘ree Self Mapping In Bicomplex Valued

Metrix Spaces...... 56

C16 Some Common Fixed Point ‘eorems In Bicomplex Valued Metric Spaces Un-

der Both Rational Type Contraction And Coupled Fixed Point Mappings... 56

C17 A Study Of Extended Beta Function With Its Applications...... 56

C18 On ‘e Location Of Zeros Of Transcendental Entire Functions...... 57

C19 On ‘e Generalization Of Enstrom-Kakeya¨ ‘eorem For Entire Functions.. 57 C20 Inclution Relation Between Subclass Of Pascu Type Harmonic Functions Based

On Mi‹ag-Le„ar Functions...... 57

C21 Certain Subclass Of Meromorphic Functions Associated With Bessel Function 58

C22 On Relative Defects Of Special Type Of Di‚erential Polynomial In Connection

With ‘eir Integrated Moduli Of Logarithmic Derivative...... 58

C23 Bicomplexial Approch Of Some Well Known Result In Complex Analysis.. 58

C24 Zalcman Conjecture And Hankel Determinant Of Order ‘ree For Recipro-

cal Of Bounded Turning Functions And α-Convex Functions Associated With

Exponential Function...... 59

C25 On A Common Fixed Point ‘eorem In Bicomplex Valued b-Metric Space.. 59

C26 Some Exceptional Value ‘eorems Of Entire Functions Under ‘e Treatment

Of Bicomplex Analysis...... 59

C27 Fractional Fourier Transforms With ‘e Flip Operator...... 60

C28 Starlike Functions Associated With ‘e Parabolic Region In ‘e Right Half Plane 60

C29 Certain Subclass Of Analytic Function With Negative Coecients De€ned By

Catas Operator...... 60

C30 Analytic Functions Of Complex Order Involving Hadamard Product..... 60

C31 Growth Properties Of Solutions Of Linear Di‚erence Equations With Coe-

cients Having Finite Logarithmic Order...... 61

C32 Implications Of Baker Omi‹ed Value...... 61

C33 Existance Of Entire Solutions Of Di‚erence Equations...... 61

C34 Fractional Wavelet Transform In Rn ...... 61 C35 A Note On ‘e Bicomplex Version Of Enstrom-Kakeya¨ ‘eorem...... 62

C36 Inequalities For ‘e Maclaurin’s Coecients Of Spiralike Functions Involving

q-Di‚erential Operator...... 62

Section D: Functional Analysis, Measure ‡eory, Probability ‡eory and Stochastic Processes,

and Information ‡eory D1 A Generalization Of ‘e Density Zero Ideal...... 63

D2 A Note On Toeplitz, Hankel And Composition Operators On ‘e Bergman Space 63

D3 Analysis Of Retrial eueing System With Two Way Communication, Work-

ing Breakdown And Collision...... 63

D4 Simulation Of Markov Chain Monte Carlo Method For Analysis Of Sunspot

Cycles...... 64

D5 Iterative Approximation Of Common Fixed Points With Simulation Results In

Banach Spaces...... 64 D6 ‘e Mean Deviation Generating Functions And A New Measure Of Dispersion 64

D7 Inequality For Maximum Modulus Of Rational Functions...... 65

D8 Associate Space Of Grand Bochner Lebesgue Spaces Without Radon-Nikodym´

Property...... 65

D9 Rubio De Francia Extrapolation ‘eorem In Variable Lebesgue Spaces.... 65

D10 Analysis Of MMAP/P H1,PH2/1 Pre-Emptive Priority Retrial eueing Sys- tem Under Constant Retrial Policy With Orbital Search, Standby Server, Vaca-

tion, Impatient Behavior Of Customers, Breakdown And Repair...... 66

D11 Fractals In Controlled Hausdor‚ Metric Space...... 66

D12 New Generalized ‘Useful’ Entropies Using Weighted asi-Linear Mean With

Utility...... 66

D13 An Application Of Intuitionistic Fuzzy Multisets In An Investment Decision

Making Problem...... 67

D14 ∆m-Statistical Convergence Of Order α Of Generalized Di‚erence Sequences

In Probabilistic Normed Spaces...... 67

D15 Distance Functions (π, β) And A Fixed Point Result In Ordered Metric Spaces 67

D16 Bulk Service eueing System With Multiple Vacation And Remaining Service

By Standby Server During ‘e Breakdown Period...... 67

I O I O D17 Analysis Of MAP1 , MAP2 /P H1 ,PH2 /1 Retrial eue With Single Vaca- tion, Closedown, Setup, Optional Service, Balking And Two Way Communication 68

D18 Best Approximations, Distance Formulas And Orthogonality In C∗-Algebras 68

D19 A Study On MAP/P H1,PH2/2 eue With Unreliable Servers And Vacation 68 D20 MAP/P H(1),PH(2)/2 With Interaction, Multiple Vacation And Repair.. 69

D21 On Existence Results Of Generalized Evolution Equation With Non-Instantaneous

Impulses Over ‘e Banach Space...... 69

Section E: Di‚erential, Integral and Functional Equations E1 First-Order Nonlinear Dynamic Initial Value Problems...... 70

E2 An Uncountable, Measure Zero, Dense Set Of Non-Monotone Points Of Con-

tinuous Functions...... 70

E3 Stability And Boundedness Criteria For Impulsive Fractional Di‚erential Equa-

tions In Caputo Sense With Initial Time Di‚erence...... 70

E4 Classi€cation Of Delay Di‚erential Equations With Constant Coecients To

Solvable Lie Algebras...... 71

E5 A Study Of ‘e Reproducing Kernel Hilbert Space Method For Poor Nutrition

In ‘e Life Cycle...... 71 E6 Existence Assertion Of Solution In ‘e Space `p, p > 1 For Fractional In€nite System Of Integral Equations Of Nonlinear Type...... 71

E7 Periodic Boundary Value Problem For System Of Caputo Sequential Di‚eren-

tial Equations Of Fractional Order...... 71

E8 Solutions Of Rossby Waves With Dissipation ‘rough Symmetries...... 72

E9 Optical Solitons With Generalized ‘ird-Order Nonlinear Schrodinger¨ Equa-

tion Via Lie Symmetry Analysis...... 72

E10 A Novel Technique For Solving ‘e Higher-Dimensional System Of Nonlinear

Coupled Partial Di‚erential Equation...... 72

E11 A Result On ‘e Approximate Controllability Of Fractional Di‚erential Equa-

tions Of Order 1 < R < 2 ...... 73

E12 Existence And Uniqueness Of Classical And Mild Solutions Of Impulsive Frac-

tional Evolution Equations...... 73

E13 On Approximate Controllability Of A Class Of Neutral Hilfer Fractional Stochas-

tic Di‚erential Systems By Using Wright Function...... 73

E14 An E‚ective Iterative Method And Existence Result For A Class Of Second-

Order Four-Point Nonlinear BVPs...... 74

Section F: Geometry and Topology F1 Some ξ-Pre-Continuous Maps...... 75

F2 p∗-Continuous Maps And Its Generalization Via Ideal...... 75

F3 Intuitionistic Fuzzy Almost Generalized E-Continuous Mappings...... 75

F4 Kaehlerian Spaces Admi‹ing In H-Projective Vector Field With Constant Scalar

Curvature...... 75

F5 Lower Bounds For Regular Genus And Gem-Complexity Of PL 4-Manifolds

With Boundary...... 76

F6 On Some Intuitionistic p−Sets And Intuitionistic q−Sets...... 76

F7 Comprehensive asi-Einstein Spacetime With Application To General Rela-

tivity...... 76

F8 On W2-Curvature Tensor Of ‘e Projective Semi-Symmetric Connection... 77

F9 On Selection Of Generalized Continuous Multifunctions...... 77

F10 On Somewhat Pairwise Fuzzy β Continuous Map...... 77

F11 On Nonempty Intersection Properties In Metric Spaces...... 78

F12 On Interval Type-2 Fuzzy Rough Sets And ‘eir Topological Structures.... 78

F13 Space-Time Admi‹ing Generalized Conharmonic Curvature Tensor...... 78 F14 Some Geometric Estimates On Warped Product Lightlike Submanifolds Of In-

de€nite Kaehler Manifolds...... 78

F15 Screen Generic Lightlike Submanifolds Of Inde€nite Nearly Kaehler Manifolds 79

Section G: Numerical Analysis, Approximation ‡eory and Computer Science

G1 A Fi‹ed Galerkin Finite Element Method For Singularly Perturbed Di‚erential

Equations With A Small Negative Shi‰...... 80

G2 Numerical Solution For Fractional Variable-Order Di‚erential Equation With

Delay...... 80

G3 A Fixed Point Approach To ‘e Existence-Uniqueness Of Coupled-Elliptic Non-

linear Partial Di‚erential For Convection In Porous Media...... 80

G4 On Fuzzy Contra g∗β-Continuous Functions...... 81

G5 Generalized Di‚erential adrature Method For Vibration Analysis Of Non-

Homogeneous Orthotropic ‘in Rectangular Plates...... 81

G6 Power Series Convergence Method For An Operator Based On Multivariate

q-Lagrange Polynomials...... 81

G7 A Novel Two Steps Numerical Method To Solve Non-Linear Equations.... 82

G8 A Numerical Scheme Based On Haar Wavelet Nonstandard Finite Di‚erence

Method For ‘e Solution Of A Class Of Generalized Burgers’ Equation.... 82

G9 An E‚ective Numerical Technique To Solve Lane-Emden Equations Based On

‘e Galerkin Finite Element Method...... 82

G10 Application Of Haar Wavelet On A Class Of System Of Coupled Lane-Emden

Equation...... 83

G11 Contour Based Analysis For Image Classi€cation...... 83

G12 Exact And Nonstandard Finite Di‚erence Schemes For ‘e Generalized Form

Of Burgers Fisher Equation...... 83

Section H: Solid Mechanics, Fluid Mechanics, Astrophysics and Relativity, and related areas

H1 A Study Of Unsteady Magnetohydrodynamic Flow Of An Incompressible, Vis-

cous, Electrically Conducting Fluid Bounded By Two Non-Conducting Vertical

Plates In Presence Of Inclined Magnetic Field...... 84

H2 Nonlinear Evolution Of Weak Discontinuity Waves In Darcy-Type Porous Media 84

H3 On Swirling Flows Near Rotating Disks...... 84

H4 Heat And Mass Transfer E‚ects On Linearly Accelerated Isothermal Inclined

Plate...... 85 H5 MHD ‘ree-Dimensional Flow Of Powell Eyring Fluid Over A Bidirectional

Non-Linear Stretching Surface With Temperature Dependent Conductivity,

Heat Absorption/generation...... 85

H6 Finite Di‚erence Computation Of Free Magneto-Convective Powell-Eyring Nanoƒuid

Flow Over A Permeable Cylinder With Variable ‘ermal Conductivity.... 85

H7 Coupled Radiative And Convective Heat Transfer In Enclosures...... 86

H8 Impact Of Inclined Magnetic Field On ‘e Peristaltic Flow Of A Couple Stress

Fluid With Heat Transfer...... 86

H9 On ‘e Azimuthal Shear Instability Of Inviscid Incompressible Swirling Flows 86

H10 Numerical Study Of An Electrically Conducting ‘ree-Dimensional Casson

Fluid Flow Over Porous Elastic Sheet With Non-Uniform Heat Source/Sink

And Soret E‚ect...... 87

H11 E‚ect Of Viscoelasticity And Internal Current On Wave A‹enuation..... 87

H12 Mathematical Model Of MHD Flow And Heat Transfer Between A Solid Ro-

tating And Stationary Permeable Disk...... 87

H13 Radiative Newtonian Carreau Nanoƒuid ‘rough Stretching Cylinder Consid-

ering First Order Chemical Reaction...... 88

H14 Bioconvective Flow Of Eyring-Powell Fluid Suspended With Microorganisms

In ‘e Presence Of Non-Linear ‘ermal Radiation, Activation Energy And

Variable ‘ermal Conductivity...... 88

H15 Numerical Simulation Of Blood Nanoƒuid Flow Over ‘ree Di‚erent Geome-

tries By Means Of Gyrotactic Microorganisms: Applications To ‘e Flow Of A

Circulatory System...... 88

H16 Cross Di‚usion And Heat Source E‚ects On A ‘ree Dimensional MHD Flow

Of Maxwell Nanoƒuid Over A Stretching Surface With Chemical Reaction.. 89

H17 Similarity Solutions Of One-Dimensional MHD Shock Wave In A Non-Ideal

Gas With ‘e E‚ect Of Viscosity...... 89

H18 Gravity E‚ects On ‘e Onset Of Transient Convection In A Porous Medium. 89

H19 A Study With Magnetic Field On Stenosed Artery Of Blood Flow...... 90

H20 Soret And Heat Generation E‚ects On An Unsteady Free Convective Flow Past

An Exponentially Accelerated Plate With Constant Mass Flux...... 90

H21 Dufour And Soret E‚ects On MHD Flow Of Cu−W ater And Al2O3 −W ater Nanoƒuid Flow Over A Permeable Rotating Cone...... 90

H22 Entropy Generation On EMHD Stagnation Point Flow Of Hybrid Nanoƒuid

Over A Stretching Sheet: Homotopy Perturbation Solution...... 91 H23 Natural Convection In A Nanoƒuid Saturated Porous Medium Under Time-

Periodic Gravity Modulation...... 91

H24 Soret And Dufore E‚ects On MHD Flow ‘rough ‘e Porous Medium About

A Rotating Vertical Cone In Presence Of ‘ermal Radiation...... 91

H25 E‚ective ‘ermal Conductivity And MHD Convection Flows Of Non Newto-

nian Nanoƒuid From Horizontal Circular Cylinder...... 92

H26 Ca‹aneo-Christov Heat Flux Model For MHD Sakiadis Flow Of A Carrearu

Fluid Subject To artic Autocatalysis Chemical Reaction...... 92

H27 Signi€cance Of Nanoparticle Aggregation Of Nanoƒuid Flow In An Irregular

Channel...... 92

H28 E‚ects Of MHD And Electro-Magnetic Fields In Nanoƒuid Over A Stretching

Sheet...... 93

H29 ‘e Study Of Rayleigh-Benard´ Convection In Vertically Oscillating Hybrid

Nanoliquids...... 93

H30 Analysis Of Fluid Flow In Triangular Cavity Using FEM...... 93

H31 ‘e E‚ect Of ‘e Viscosity Of Ohe Porous Solid On Ohe Parallal Plate Chan-

nal Flow Of Ree-Eyring Liquid When ‘e Dividers Are Provided With Non-

Erodible Porous Lining...... 94

H32 Wall Slip E‚ects On Nanoƒuid Flow In A Porous Channel...... 94

H33 E‚ect Of Heat Transfer In A Micropolar Fluid On ‘e Onset Of Rayleigh-

Benard-Chandrasekhar´ Convection With Porous Medium Under Time Periodic

Boundary Temperature And Internal Heat Source...... 94

H34 MHD Combined Convection Flow Over A Moving Non-Isothermal Vertical

Plate With Soret And Dufour E‚ects And Viscous Dissipation...... 95

H35 Triple Di‚usive Convection In Temperature And Electric Field Dependent Vari-

able Viscosity In A Newtonian Dielectric Liquid With Internal Heat Source. 95

H36 Linear And Non-Linear Analysis Of Internal Heat Modulation On Rayleigh-

Benard´ Convection In Ferromagnetic Liquids With Couple Stress...... 95

H37 Linear And Nonlinear Analysis Of Two-Frequency Time-Periodic Boundary

Temperature On Rayleigh-Benard´ Convection...... 96

H38 Nonlinear Rayleigh-Benard´ Convection In Variable Viscosity Ferromagnetic

Liquids...... 96

H39 Analytic Solution Of Bloch Equation For A Time Varying Magnetic Field In

‘e Transverse Direction...... 96 H40 Stability Of Microscopic Body Cosmological Model In Barber Self-Creation

‘eory Of Gravitation...... 97

H41 Bianchi Type-III Cosmological Model Barber Self-Creation ‘eory Of Gravitation 97

H42 Exact Solution For Cosmological Constant Problem, Variable Gravitational Con-

stant Problem And Other Cosmological Problems And ‘e Continuity Between

Anisotropic And Isotropic Cosmology With Single Type Of Scalar Field And

Scale Factor...... 97

H43 Bianchi Type VI0 String Cosmological Model In Lyra’s Manifold...... 98

H44 Wet Dark Fluid Cosmological Model In Barber Self-Creation ‘eory Of Grav-

itation...... 98

H45 Stability Of Bianchi Type-IX Cosmological Model In Brans -Dicke ‘eory Of

Gravitation...... 98

H46 Hamiltonian Formalism Of Bianchi Type 1 Model For Di‚erent Types Cosmic

Fluid And E‚ect Of Bulk Viscosity On intessence Model And Scalar Field

Potential...... 98

H47 Propagation Of Stoneley Waves In Non-Local Elastic Medium...... 99

H48 Remarks On ‘e Dynamic Responce Of Irregular Orthotropic Viscoelastic Half-

Sace Sunjected To A Moving Line Load...... 99

H49 Investigation Of ‘ermal Excitation Induced By Laser Pulses And ‘ermal

Shock In ‘e Half Space Medium With Variable ‘ermal Conductivity.... 99

H50 Investigation On SH-Wave Propagation In A Porous Piezoelectric Composite

With Mechanically And Electrically Perfect Interfacial Boundaries...... 100

H51 Study Of Torsional Problem In Micro-Isotropic, Micro-Elastic Solid...... 100

Section I: Mathematical Modelling, Bio-Mathematics, Operations Research I1 Bifurcation And Chaos In A Discrete Predator-Prey Model With Holling Type-

III Functional Response And Harvesting E‚ect...... 101

I2 Nonlinear Dynamical Behaviour Of An SEIR Mathematical Model: E‚ect Of

Information, Saturated Treatment And Time Delay...... 101

I3 Painleve Property Analysis Of Self Interacting Four Species Food Chain Math-

ematical Model And Its Generalization To N-Species...... 101

I4 ‘e Role Of Media On ‘e Dynamics Of Zika Outbreak: A Modeling Approach 102

I5 Mathematical Model Of Corona Virus (COVID-2019) With Limited Resources:

A Case Study Of India...... 102

I6 E‚ect Of Catheter On Unsteady Fluid Flow ‘rough An Inclined Stenosed Artery 102 I7 ICU Domain Adaptation On Survival Prediction Models Built With Neural Net-

works...... 103

I8 Analysis Of A Modi€ed Fractional Predator-Prey Model With Disease Infection 103

I9 Analysis Of E‚ect Of Social Status On Depression By Using Logistic Regression 104

I10 Mathematical Modeling Of COVID-19 Pandemic Dynamics With Non-Pharmaceutical

Interventions As Control Strategy...... 104

I11 Stabilty Analysis Of A Predator-Prey System With Square Root Functional Re-

sponse...... 104

I12 A Mathematical Study On Corona Virus Model With Two Infectious States.. 105

I13 Dynamical Behaviors Of Fuzzy Prey Predator In SIR Epidemic Model..... 105

I14 Dynamics Of Fractional Illicit Drug Consumption Model With Holling Type-III

Functional Response...... 105

I15 A Robust Technique For Brain Tumor Detection Using Type-II Fuzzy Logic. 106

I16 Dynamics In A Prey-Predator Model With Susceptible-Infected-Recovered (SIR)

Epidemic Disease In ‘e Prey...... 106

I17 ‘e Di‚erence Equation Based Mathematical Model For Life-Cycle Of Host-

Parasitoid Systems...... 106

I18 Dynamics Of IGP System With Provision Of Additional Food To Both Prey And

Predator...... 107

I19 Describing Tumour Growth ‘rough Mathematical Modelling...... 107

I20 Ring Construction For Error Correcting Codes Using Jacobson Radical: A Cod-

ing ‘eoretic Model For Genetic Sequence Analysis...... 107

I21 Compartment Modelling And Eigenvalue Expansion To Study ‘e Drug Con-

centration In Capillary And Tissue Regions Surrounding ‘e Malignant Tumour 108

I22 Forecasting Electric Energy Consumption In India Using Univariate Time-Series

Analysis...... 108

I23 Analysis Of Lap Times In Formula-1 Motorsport Due To Regulation Changes

Using Polynomial Regression...... 109

I24 An EPQ Model For Delayed Deteriorating Items With Time Dependent Cubic

Demand And Shortages...... 109

I25 Hexadecagonal Fuzzy Transportation Problem...... 109

I26 Tandem Fluid Model Driven By An MX/M/1 eue Subject To Balking And

Vacations...... 110

I27 An Economic Production antity Model For ‘ree Levels Of Production With

Weibull Distribution Deterioration And Shortage Under Inƒation...... 110 I28 Recent Trends Of Applications Of Business Analytics Using Operations Research 110

I29 Solving Open Travelling Salesman Subset-Tour Problem ‘rough A Hybrid

Genetic Algorithm...... 111

I30 Analysis Of Intuionistic Fuzzy Transportation Problem...... 111

I31 An Economic Order antity Model With Reverse Logistics Inventory Model

In Circular Economy...... 111

I32 Review Article On eueing Inventory Models...... 112

I33 Bargaining Of A Wholesale Price For An Optimal Manufacturer With A Re-

tailer In A One-Channel Supply Chain...... 112

I34 Modelling Of Deteriorating Systems Using Fuzzy Warranty Cost With Preven-

tive Repairs...... 112

I35 Rough Hesitant Bipolar Neutrosophic Linear Programming Problem..... 112

I36 Lexi-Search Approach For ‘e ‘ree Index Assignment Problem...... 113

I37 Bipolar Vague ELECTRE 1 Method For MCDM Problems...... 113

Author Index

IMS - 2020 1 VIT-Vellore Presidential Address (Technical)

Groups over Global and Local Fields - Some Themes (PAT) B. Sury Indian Statistical Institute, Bangalore

We discuss four types of questions to which we have been able to contribute a li‹le bit. ‘e four themes are roughly: (i) arithmetic groups with particular emphasis on the Congruence Subgroup Problem;

(ii) p-adic groups and their central extensions; (iii) division algebras over global and local €elds; (iv) abstract group theoretic questions on arithmetic groups.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 2 VIT-Vellore

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS Plenary Talks IMS - 2020 4 VIT-Vellore

(P1) Some Major Indian Contributions to Mathematics in the 20th Century M.S. Raghunathan Centre for Excellence in Basic Sciences, Mumbai

During the 20th century, Indian mathematicians working in India have made highly signi€cant contributions to diverse mathematical €elds. ‘e €rst notable contribution ante-dates Srinivasa Ramanujan. ‘ere were quite a few works of note in the pre-independence period, but the mid €‰ies ushered in a new era when Indian mathematicians’ contributions became a considerable inƒuence in the very evolution of certain €elds. In this talk I will describe some high points of Indian mathematics during the last century. ‘e choice of material I will speak on is necessarily mostly limited to areas of mathematics I am familiar with; so will be far from comprehensive in its coverage. Even in the areas I have some acquaintance with, my emphasis will naturally be dictated by my taste. Also I will not elaborate much on work by Indian mathematicians working outside India nor on work done in the present century. I do not have the same kind of familiarity with work done in the last two decades that I have with the earlier work .

(P2) Toeplitz Operators and Hilbert Modules on Bounded Symmetric Domains Harald Upmeier University of Marburg, Germany [email protected]

Bounded symmetric domains D are domains of holomorphy in Cn which can be realized as homogeneous spaces D = G/K, where G is a semi-simple Lie group and K is a maximal compact subgroup. ‘ey play a fundamental role in representation theory of G and the theory of automorphic functions for discrete sub- groups of G. ‘e (scalar) holomorphic series of representations discovered by Harish-Chandra can be real- ized as weighted Bergman spaces of holomorphic functions on D. ‘ese Bergman spaces Hν , depending on a scalar parameter ν, carry an important class of operators, the so-called Toeplitz operators, which are related to the geometric quantization program, viewing D as a non-compact Kahler¨ manifold.

In the talk we present two recent results concerning Toeplitz operators which are invariant under the maximal compact subgroup K. By the Peter-Weyl decomposition of the Bergman spaces, these operators are charac- terized by their eigenvalues, labeled by all integer partitions m1 ≥ m2 ≥ · · · ≥ mr of length r = rank(D). Using deep results in the combinatorics of partitions (Young diagrams) we determine these eigenvalues for a certain class of “fundamental” partitions, revealing an interesting interplay between the covariant and con- travariant quantization method.

In the second part of the talk we consider Hilbert submodules of the weighted Bergman spaces and construct the associated eigenbundle, which classically is spanned by the reproducing kernel functions, but in our gen- eral situation is not a line bundle any more but a complex linear €bre space in the sense of coherent analytic sheaves. ‘e €bres of the bundle are identi€ed with the space of sections on a certain Peirce manifold, gen- eralizing projective space and the Grassmannians.

‘is work originates from the author’s stay at the Indian Institute of Science, Bengaluru.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS Memorial Award Lectures IMS - 2020 6 VIT-Vellore

31st Srinivasa Ramanujan Memorial Award Lecture

(ML1) The Unreasonable Effectiveness of Ergodic Theory in Number Theory Anish Ghosh School of Mathematics, TIFR Bombay, Mumbai

Ergodic theory can be described as the mathematical study of the long term behaviour of dynamical sys- tems. Recent decades have seen several spectacular applications of ergodic theory to a seemingly completely di‚erent branch of mathematics, namely number theory. I will describe some instances of this fruitful math- ematical interaction.

34th P.L. Bhatnagar Memorial Award Lecture

(ML2) Lower-order Nonstandard Finite Element Methods for Biharmonic Plates Neela Nataraj Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai 400076

‘e few popular piecewise quadratic schemes for the biharmonic equation based on triangles are the non- conforming Morley €nite element method, the discontinuous Galerkin €nite element method, the C0 interior penalty scheme and the WOPSIP scheme. All the schemes are modi€ed in their right-hand side F replaced −2 by F ◦ (JIM ) and then are quasi-optimal in their respective discrete norms even for data F ∈ H (Ω). ‘e smoother JIM is de€ned for piecewise smooth input function by a (generalized) Morley interpolation IM followed by a companion operator J . Energy norm and piecewise lower-order error estimates without data oscillations for the modi€ed schemes are discussed.

31st Hansraj Gupta Memorial Award Lecture

(ML3) Some Glimpses into Noncommutative Ring Theory Dinesh Khurana Department of Mathematics, Panjab University, Chandigarh [email protected]

Besides listing some basic di‚erences between commutative and non-commutative ring theory, we will present our work on some of the typical problems which are trivial for commutative rings.

31st V Ramaswami Aiyer Memorial Award Lecture

(ML4) On bounds of Fourier-coefficients of Half-integer Weight Cusp Forms Sanoli Gun Institute of Mathematical Sciences, Chennai

In this talk, we will discuss about omega results of Fourier-coecients of half-integer weight cusp forms which are not necessarily eigenforms. (‘is is a joint work with Kohnen and Soudararajan)

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS Award Lectures IMS - 2020 8 VIT-Vellore

Satish Bhatnagar Award Lecture

(AL1) Pandiagonal Magic S€ares: From Nag¯ arjuna¯ To Nar¯ ayan¯ . a Pan. d. ita To Vijayaraghavan M.D. Srinivas Centre for Policy Studies, Chennai [email protected]

A pandiagonal magic square is a magic square where the entries along all the broken diagonals also add up to the magic sum. In India, the mathematics of magic squares was known as Bhadragan. ita and the Indian scholars paid special a‹ention to the study of pandiagonal magic squares from ancient times. ‘e ancient text Kacchaput.a ascribed to Nag¯ arjuna¯ (1st century CE) describes a method for constructing 4 × 4 pandi- agonal magic squares. Varahamihira¯ (c.550 CE) describes a 4 × 4 pandiagonal magic square in the chapter on perfumery in his Br.hatsam. hita,¯ and the properties of such a sarvatobhadra have been discussed by his commentator Bhat.t.otpala (c.10th century). Pandiagonal magic squares have been found in the inscriptions at the Jaina temples in Dudhai and Khajuraho (c.10-11 centuries).

‘e seminal text Gan. itakaumud¯i (c. 1350) of Nar¯ ayan¯ . a Pan. d. ita devotes an entire chapter to Bhadragan. ita, which contains many signi€cant results on the construction of magic squares in general, and pandiagonal squares in particular. Nar¯ ayan¯ . a formulates and solves a linear indeterminate equation in order to charac- terise all the arithmetic sequences which can be employed to construct magic squares of a given order and speci€ed sum. He describes a method for constructing 4×4 pandiagonal magic squares using a succession of turagagati or horse movements and explicitly demonstrates that there are 384 pandiagonal squares of order four. Nar¯ ayan¯ . a also describes a folding method of construction of doubly-even and odd order magic squares, which can be used to construct pandiagonal magic squares of all odd orders not divisible by 3, and all even orders divisible by 4.

Further properties of 4 × 4 pandiagonal magic squares have been discovered recently by B. Rosser and R. J. Walker (1938), and by the renowned Indian mathematician T. Vijayaraghavan (1941), who were all unaware of Nar¯ ayan¯ . a’s work and came up with new demonstrations of his result that there are 384 pandiagonal squares of order 4. Vijayaraghavan has also presented a much simpler algorithm for the construction of these magic squares.

AM Mathai Award Lecture

(AL2) Invariant Subspaces and Exact Solutions of Nonlinear PDEs P. Prakash Department of Mathematics, Amrita Vishwa Vidyapeetham, Coimbatore-641112, INDIA. [email protected], p [email protected]

In this talk, a systematic study for constructing the invariant subspaces of scalar and coupled nonlinear PDEs using the invariant subspace method. Also, we explicitly present that the generalized convection-reaction- di‚usion equation admits more than one invariant subspaces in di‚erent dimensions which in turn helps to derive more than one di‚erent type of exact solution. ‘e obtained exact solutions can be expressed in terms of polynomial, exponential, and trigonometric functions. In addition, we show how the invariant subspace method can be extended to fractional nonlinear PDEs. Finally, we also extend this method to time-fractional nonlinear PDEs with time-delay.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 9 VIT-Vellore

A.K. Agarwal Award Lecture

Euler’s Criterion for lth Power non residues with l a Prime (AL3) Jagmohan Tanti Central University of Jharkhand, Ranchi, Jharkhand, India [email protected]

Let l ≥ 2 be a prime, p a prime ≡ 1 (mod l) and γ a primitive root (mod p). If an integer D with (p, D) = 1, is an lth power nonresidue (mod p) then D(p−1)/l is an lth root of unity α(6≡ 1) (mod p). Euler’s criterion (p−1)/l (p−1)/l of order l (mod p) studies the explicit conditions when D ≡ γ (mod p), i.e., when Indγ D ≡ 1 (mod l). In this talk we discuss the Euler’s criterion of order l when the ring of integers in the cyclotomic extension of Q of order l is a PID. Conditions are obtained in terms of Jacobi sums of order l.

A Narasinga Rao Prize Lecture

On Some Categories of Riemannian Manifolds (AL4) R.B. Yadav Department of Mathematics, Sikkim University [email protected]

In mathematics we study mathematical structures and relations between them. For example, continuous functions between topological spaces in topology, homomorphisms between groups in group theory, linear transformations between linear spaces in linear algebra, smooth functions between manifolds in the theory of smooth manifolds and functors between categories in category theory are such relations. ‘ese rela- tions are de€ned in such way that they relate the structures of the objects between which they are de€ned. Such relations are called morphisms in category theory. Only well known morphisms between two Rieman- nian manifolds are isometries and conformal maps. ‘ese morphisms are isomorphisms in their respective categories of Riemannian manifolds. But these morphisms are too restrictive. In this talk we discuss two categories of Riemannian manifolds di‚erent from the previously known categories. We also discuss some properties of such categories and compare them with the previously known ones.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 10 VIT-Vellore

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS Invited Talks IMS - 2020 12 VIT-Vellore

(IT1) Are We Prepared To Accept The Reality? Ravi P. Agarwal Department of Mathematics, Texas A&M University-Kingsville, 700 University Blvd., Kingsville, TX, USA [email protected]

In this lecture an a‹empt is being made to convince the world, especially we Indians that in reality Bharat, the Greater India, is the origin of mathematics. ‘is will correct what most of the historians of Mathematics have claimed in their books, and we have accepted it religiously. We will also try to reassure that Mathematics as well as Proof cannot be de€ned. Further, we shall discuss features of Upapa‹is (word in Pali, Sanskrit, and Marathi languages) in Indian Mathematics.

(IT2) Sharp Nonlinear Stability Limits for Centrifugal Convection in Porous Media S. Saravanan UGC DRS Centre for Di‚erential Equations and Fluid Dynamics, Department of Mathematics, Bharathiar University, Coimbatore 641 046, Tamil Nadu [email protected]

‘is talk is about determining nonlinear stability limits for a thermal convective ƒow in a rotating porous medium subjected to an alternating direction of centrifugal force €eld. ‘e medium is homogeneous and exhibit rotationally invariant hydrodynamic and thermal properties. ‘e Darcy and the Brinkman models of ƒow through porous media are used to describe the momentum balance and the Boussinesq approximation is invoked to represent buoyancy. In order to understand possible instabilities a linear theory based on normal mode approach is applied €rst. By introducing a suitable energy functional a nonlinear analysis is then carried out. ‘e unconditional nonlinear stability limits are found exploiting the variational principles. ‘e compound matrix method is then employed to solve the eigenvalue problems arising from the nonlinear and linear theories. E‚ects of various control parameters on the stability characteristics are predicted. ‘e region of subcritical bifurcation is demarcated and failure of the linear theory is established.

(IT3) Cotton Solitons within the Framework of Almost Kenmotsu 3-h-Manifolds Pradip Majhi Department of Pure Mathematics, University of Calcu‹a, 35, Ballygunge Circular Road, Kolkata -700019, West bengal, India. [email protected]

In this paper, we consider the notion of Co‹on soliton within the framework of almost Kenmotsu 3-h- manifolds. First we consider that the potential vector €eld is pointwise collinear with the Reeb vector €eld and prove a non-existence of such Co‹on soliton. Next we assume that the potential vector €eld is orthog- onal to the Reeb vector €eld. It is proved that such a Co‹on soliton on a non-Kenmotsu almost Kenmotsu 3-h-manifold such that the Reeb vector €eld is an eigen vector of the Ricci operator is steady and the manifold is locally isometric to H2(−4) × R.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 13 VIT-Vellore

Automata Theory Based on Residuated Lattices (IT4) S.P. Tiwari Department of Mathematics & Computing, Indian Institute of Technology (ISM), Dhanbad-826004, India [email protected]

‘e concept of category theory introduced by Eilenberg and Mac Lane has shown to be useful in the de- velopment of many aspects of theoretical computer science. ‘e minimal realization problem (which states that given a language, one can design a machine that realizes it) was studied in a fairly general category theory se‹ing by Goguen, is well known. However, an analogous minimal realization could not be provided for stochastic automata. In the case of automata based on multi-valued logic, we recently studied minimal realization problem under certain conditions. In this talk, we brieƒy explain the use of mathematical concepts involved in residuated la‹ices to study automata based on such la‹ices; and the construction of a minimal automaton based on residuated la‹ices.

Normal Families of Holomorphic Functions of Several Complex (IT5) Variables K.S. Charak Department of Mathematics, University of Jammu, Jammu-180 006, India kscharak7@redi‚mail.com

‘eory of normal families of meromorphic functions initiated by Paul Montel in 1907 now forms an integral part of function theory. In fact, this theory is responsible for many exciting advances in the area of complex dynamics, but there has also been many far reaching internal developments in the theory during the last over hundred years. In my talk, I shall present some recent developments in normal families of holomorphic functions of several complex variables for which a parallel theory is under process.

Catastrophic Changes in Coral Reef Dynamics under Macroalgal (IT6) Toxicity, Overfishing and Invasion of Predators Samares Pal Department of Mathematics, University of Kalyani, Kalyani 741235, India [email protected]

Coral reefs can undergo relatively rapid changes in the dominant biota, a phenomenon referred to as phase shi‰. Degradation of coral reefs is o‰en associated with changes in community structure towards macroalgal dominated reef ecosystem due to the reduction in herbivory caused by over€shing. We investigate coral- macroalgal phase shi‰ due to the e‚ects of harvesting of herbivorous reef-€sh by means of a continuous time model in a food chain. It is shown that the system is capable of exhibiting the existence of two stable con€gurations of the community under the same environmental conditions by allowing saddle-node bifurca- tions that involves in creation and destruction of €xed points and associated hysteresis e‚ect. Moreover, it is observed that in presence of low coral recruitment rate on algal turf and reduction in herbivory, the system exhibits hysteresis through a saddle-node bifurcation and a transcritical bifurcation.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 14 VIT-Vellore

(IT7) Jordan ∗-derivations and Related Maps in Rings Shakir Ali Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India [email protected]

Let R be a ring with involution 0∗0. An additive map D : R −→ R is called a ∗-derivation (resp. Jordan ∗-derivation) if D(xy) = D(x)y∗ + xD(y)(resp. D(x2) = D(x)x∗ + xD(x)) holds for all x, y ∈ R. A Jordan ∗ ∗ -derivation D of R is called inner if there exists a ∈ R such that Da(x) = xa − ax for all x ∈ R. ‘e study of Jordan ∗-derivations was motivated by the problem of representability of quadratic forms by bilinear forms (see [Proc. Amer. Math. Soc. 100(1987), 133-136] for details). It turns out that the question of whether each quadratic forms can be represented by some bilinear form is intimated connected with the structure of Jordan ∗-derivations (viz., [Stud. Math. 97(1991), 157-165] and [Proc. Amer. Math. Soc. 119(1993), 1105-1113], where further reference can be found).

In this talk, we will discuss the recent progress made on the topic and its related areas. Moreover, some examples and counter examples will be scrutinize for questions raised naturally.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS Symposium Talks IMS - 2020 16 VIT-Vellore

s Graph ‡eory and Combinatorics

(GTC1) The List Chromatic Number of a Graph R. Balakrishnan Department of Mathematics, Bharathidasan University, Tiruchirappalli - 620 024. [email protected]

A list assignment of a graph G is a mapping L which assigns to each vertex v of G a se L(v) of permissible colours. An L− colouring of G is a coloring c of G such that c(v) ∈ L(v) for each vertex v of G. We say that G is L−colourable if there exists a proper L−colouring of G. A k−list assignment of G is a list assignment L of G with |L(v)| = k for each vertex v of G. A graph G is k−choosable if G is L− colourable for each k−list assignment L. ‘e choice number ch(G) of G (also called the list chromatic number χ`(G)) of G is the least k for which G is k−choosable. Clearly χ(G) ≤ ch(G), for each graph G. However, the di‚erence ch(G) − χ(G) can be arbitrarily large. In fact, for each positive integer k ≥ 3, there exists a bipartite graph G with χ`(G) = k.

We present the result χ`(Kn,n) ≤ blog2 nc + 2 : A celebrated result of Carsten ‘omssen states that every planar graph is 5-choosable. However, there are planar graphs which are not 4-choosable. We present one such planar graph due to Choi and Cowen. In addition, we also discuss chromatically choosable graphs, that is, graphs for which the chromatic number and the choice number are equal.

(GTC2) p-adic Invariants for asi-symmetric 2-designs. Bhaskar Bagchi Indian Statistical Institute, Bengaluru Centre, Bengaluru

We try to push to its logical limit the technique introduced by Professor Shrikhande in 1953 to prove analogues of the Shrikhande-Ryser-Chowla theorem for ane resolvable designs. ‘e result is the introduction of certain invariants for strongly regular graphs : one invariant called the discriminant and a p-adic invariant for each prime p. Given a strongly regular graph G, we prove analogues of Schutzenberger theorem and Shrikhande-Ryser-Chowla theorem : necessary conditions for existence of a quasi-symmetric 2-design with block graph G and a given ‘defect’ (absolute di‚erence of the two intersection numbers). ‘e conditions are solely in terms of the graph invariants introduced, and the defect, so the results are e‚ective when we can calculate the graph invariants explicitly. We do this in two cases : complete multi-partite graphs and co-triangular graphs, leading to parametric restrictions on strongly resolvable 2-designs and triangular 2- designs, respectively.

(GTC3) Subspaces, Subsets, and Motzkin paths Murali K. Srinivasan Department of Mathematics, IIT Bombay, Mumbai [email protected]

In a beautiful paper Vogt and Voigt solved the problem of constructing an explicit symmetric chain decom- position of the subspace la‹ice. We use their idea to code subspaces by Motzkin paths and give an explicit symmetric Boolean decomposition of the subspace la‹ice.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 17 VIT-Vellore

Contributions of S. S. Shrikhande towards λ-design Conjecture (GTC4) Rajendra M. Pawale Department of Mathematics, University of Mumbai, Kalina, Mumbai 400098, [email protected]

Let v, k and λ be integers with 0 < λ < k < v.A (v, k, λ) symmetric design is a pair (X, β), where X is a €nite set with v elements, called points and β is a €nite family of subsets of X, called blocks with |β| = |X|, such that each block contains k points and each pair of points occurs in λ blocks.

A λ-design is a pair (X, β), where X is a €nite set with v elements called points and β is a family of subsets of X called blocks, with |β| = |X| such that

1. for all Bi,Bj ∈ β, i 6= j, |Bi ∩ Bj| = λ;

2. for all Bj ∈ β, |Bj| = kj > λ, and not all kj are equal. ‘e only known examples of λ-designs are obtained by the following procedure: Let k 6= 2λ, and (X, ζ) be a symmetric (v, k, k − λ) design with block set ζ = {C1,C2,...,Cv}. ‘en

β = {B ⊂ X : B = C1 or B = (Ci \ C1) ∪ (C1 \ Ci) for some 2 ≤ i ≤ v}, is the block system of a λ-design. ‘is construction is called complementation with respect to the block C1 and λ-designs obtained by this procedure are called type-1 λ-designs.

‘e λ-design conjecture, also known as Ryser-Woodall conjecture due to Ryser and Woodall, states that all λ-designs are type-1.

Shrikhande and Singhi had made signi€cant contributions towards establishing truthfulness of this conjec- ture, which is still open. We discuss the present status of the λ-design conjecture.

An Introduction to the Life and Work of S.S. Shrikhande (GTC5) Sharad S. Sane Chennai Mathematical Institute, Chennai-603103 [email protected], [email protected]

Since the symposium is in the memory of Professor S.S. Shrikahnde, who passed away this year, the talk is an a‹empt to present some of the milestones of mathematical achievements of Shrikhande along with some personal reminiscences about his towering personality.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 18 VIT-Vellore

Biomechanics

(BM1) Bio-Fluid Dynamics: Fluid Mechanical Aspects of Microcirculation G. Radhakrishnamacharya Indian Institute of Information Technology Design and Manufacturing, Kurnool

‘e fundamental principles of bio-ƒuid dynamics and, in particular, cardiovascular system are explained. ‘e ƒuid mechanical aspects of pulse and blood pressure are illustrated. ‘e ƒuid mechanical and physiological reasons for studying the ƒows in larger blood vessels and microcirculation separately are presented.

With a view to be‹er understand the ƒow situation in microcirculation (ƒow in smaller vessels like arteri- oles, capillaries and venules), a two-ƒuid model has been proposed to describe ƒuid ƒow in small diameter tubes consisting of a non-Newtonian ƒuid (Je‚rey ƒuid model) in the core region and Newtonian ƒuid in the peripheral region. Analytical expressions for e‚ective viscosity, core hematocrit and mean hematocrit are obtained. ‘e e‚ects of various parameters, namely, Je‚rey parameter (λ1), tube hematocrit (H0) and tube radius (a) on e‚ective viscosity, core hematocrit and mean hematocrit have been studied. It is found that the e‚ective viscosity decreases as the Je‚rey parameter increases but increases with tube hematocrit and tube radius. ‘e mean hematocrit decreases as Je‚rey parameter increases but increases with tube hematocrit and tube radius. It is also noticed that the ƒow exhibits the anomalous Fahraeus-Lindquist e‚ect.

(BM2) Magnetic Drug Targeting in a Microvessel with Multifunctional Nanoparticle based Carrier Particle P.V.S.N. Murthya, Sachin Shawb, Abhijit Sutradharc aDepartment of Mathematics, Indian Institute of Technology Kharagpur, West Bengal 721302, India bDepartment of Mathematics and Statistical Sciences, Botswana International University of Science and Technology (BIUST), Private Mail Bag 16, Palapye cDepartment of Basic Sciences, Indian Institute of Technology Bhubaneswar, Odisha 752050, India.

A review of non-invasive magnetic drug targeting of a multifunctional carrier particle in blood stream ƒow- ing in impermeable and permeable microvessels is done. Mathematical modelling of magnetic drug targeting in these microvessels is discussed using most popular Casson and Herschel-Bulkley models to describe the non-Newtonian nature of blood ƒowing in the microvessels of diameter 100 micrometers. A dilute solution suspended with the carrier particle is injected into the microvessel upstream from the tumor located inside the body. A rare-earth cylindrical magnet is positioned in the vicinity of body surface to capture the carrier particle near the tumor zone.

A particular model considering the signi€cant buoyancy force, ƒuidic force, drag force and inertia e‚ect in the equation of motion of the carrier particle and the external magnetic force experienced by the carrier particle is analyzed. Along with the therapeutics, biocompatible F e3O4 nanoparticles of spherical shape are assumed to be present in the carrier particle. Consequently, an e‚ective density for the carrier particle is introduced. ‘e numerical solution of the resulting coupled nonlinear equations of motion is obtained. ‘e trajectories of the carrier particle is obtained under varying parametric conditions. It is evident that the non- Newtonian nature of blood signi€cantly changes the particle trajectories. ‘ese results also indicated that lesser magnetization is required to a‹ract the carrier particle more e‚ectively near the tumor location due to the consideration of buoyant force along with the acceleration of the carrier particle. An optimal placement of the external magnet from the axis of the microvessel makes an ecient capture of the carrier particle near the targeted site.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 19 VIT-Vellore

Mathematical models of physiological fluid flows (BM3) P. Muthu Department of Mathematics, National Institute of Technology (NIT), Warangal [email protected] In this talk, we will discuss about mathematical models of certain physiological ƒuid ƒows such as (i) ƒow in renal tubule (ii) solute transfer in glomerular capillaries and (iii) synovial joint lubrication. Relevant liter- ature from the past and the present is described along with an explanation of importance of studying these ƒow situations. An overview of various computational methods which are used to solve these problems is presented. ‘e simulated results are interpreted with available experimental data to emphasize the need of modelling of physiological systems for be‹er understanding of their functioning.

Cardiac Electrical Activity in a Human Cardiac Tissue: Theory, (BM4) Computation and Application Meena Pargaeia, B.V. Rathish Kumarb aG.P.G.C. Champawat, Aliated to Kumaun University, U.K. India ([email protected]) bIndian Institute of Technology, Kanpur, India ([email protected]) ‘e heart electrical conduction system propagates the electrical impulse originated from the sinoatrial node (SA) called cardiac pacemaker, situated in the le‰ atrium, due to which heart muscle starts to contract, and then this signal travels to the whole heart, and the contraction of entire heart muscle takes place. ‘e basis of the electrical activity is the action potential, which is facilitated by ionic channels and the ionic cell trans- porters that enable the movement of ions across the cardiac cell membrane. Myocardial ischemia takes place when the blood ƒow to the heart and oxygen supply to the heart is abnormal. It is one of the leading causes of sudden death. Due to this myocardial ischemia metabolism and electrophysiological changes appear which results in the alteration of cardiac electrical activity.

In this talk, a modi€ed human ventricular TT06 cell level model (ODEs) coupled with the tissue level Mon- odomain model (PDE) is considered to analyze the inƒuence of myocardial ischemia on the cardiac electrical activity of human cardiac tissue (HCT). ‘e apriori €nite element error estimate of this PDE-ODE system for the numerical scheme is found to be as o(h2 + k). A HCT (domain) is modeled in such a way that it consists multiple ischemic subregion (subdomain). ‘e coupled system of partial and ordinary di‚erential equations in this modeled domain is solved numerically using the Q1 €nite element in space and backward Euler €- nite di‚erence (BEFD) method in time. We evaluate the impact of the increasing size of the ischemic region and the presence of the multiple ischemic regions having equal or di‚erent intensities on the neighboring healthy part of the cardiac tissue. It is observed that with the increase in the ischemic region size by a factor €ve times, there is an additional almost 10 % drop in the action potential duration (APD) in the neighboring healthy regions. Increasing the number of ischemic regions from 1 to 4 leads to a 39 % drop in APD.

An Overview of Cardiovascular Flow Studies: Mathematical Theory, (BM5) Numerical Analysis and Computational Simulation B.V. Rathish Kumar IIT Kanpur [email protected] Virtual Cardiovascular ƒow analysis has now become a widely accepted viable approach to assist in clinical diagnosis and surgical decision making across the world. In this talk, to begin with we will touch upon the essential mathematical and numerical analytical aspects that play a crucial role prior to carrying out compu- tational simulations to unravel the physics behind the cardiovascular ƒow dynamics, which by far continues to remain a challenge especially in the clinically declared pathological conditions. ‘en we will move forward to get glimpses of diseased condition of arterial vessels and the ways to model the same including patient speci€c modelling based on CT/MRI data. Subsequently we will discuss in a nutshell the outcome of compu- tational simulations on HPC platforms of few pathological cases based on both academic, which are essential in developmental phase, and clinical data, including few of the essential parallel computing methods to realize such solution in real time.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 20 VIT-Vellore

Chandrasekharan Centenary Symposium in Number ‡eory

(NT1) Lucas Se€ences and its Arithmetic Shanta Laishram Indian Statistical Institute, New Delhi [email protected]

‘e Fibonacci sequence, which is one of the most well known integer sequences, is a special example of a general family of Lucas sequences. In this talk, I will some arithmetic of the Lucas sequences, and in particular, I will discuss about the following result proved recently. Let {Un}n≥0 be a Lucas sequence. We show that if Un is a product of factorials, then n ∈ {1, 2, 3, 4, 6, 8, 12} which is independent of the Lucas sequence. Further we show that if Un is a product of Catalan numbers or the middle binomial coecients, 2m
then n ∈ {1, 2, 3, 4, 6, 8, 12, 16}. Here the m−th middle binomial coecient is Bm = m and the m−th 1 2m
Catalan number is Cm = m+1 m .

n (NT2) Prime Powers Dividing Products of Consecutive Integer Values of x2 + 1 Stephan Baier RKMVERI, PO Belur Math, Dist Howrah 711202, West Bengal, India [email protected]

n ‘is is joint work with Pallab Kanti Dey (RKMVERI). Let n be a positive integer and f(x) := x2 + 1. We study orders of primes dividing products of the form Pm,n := f(1)f(2) ··· f(m). We prove that if 12 n+1 n−1 m > max{10 , 4 }, then there exists a prime divisor p of Pm,n such that ordp(Pm,n) ≤ n · 2 . For n = 2, we establish that for every positive integer m, there exists a prime divisor p of Pm,2 such that ordp(Pm,2) ≤ 4. Consequently, Pm,2 is never a €‰h or higher power. ‘is extends work of Cilleruelo who studied the case n = 1.

(NT3) Mod p Modular Forms and Simple Congruences Jaban Meher NISER, Bhubaneswar [email protected]

We €rst give a description of the algebra of modular forms on the congruence subgroup Γ0(2) modulo a prime p. ‘is result parallels results of Swinnerton-Dyer in the SL2(Z) case, Katz on the subgroup Γ(N) for N ≥ 3, Gross on the subgroup Γ1(N) for N ≥ 4. We next apply the theory of mod p modular forms on Γ0(2) to prove the non-existence of simple congruences for Fourier coecients of quotients of certain Eisenstein series on Γ0(2). ‘is is a joint work with Sujeet Kumar Singh.

(NT4) The Discrete Logarithm Problem Over Prime Fields: Non-canonical Lifts and Logarithmic Derivatives R. Padma Department of Mathematics School of Advanced Sciences, VIT Vellore [email protected]

Many public key cryptographic protocols currently in use are based on the computational hardness of the discrete logarithm problem. A polynomial time algorithm for the discrete logarithm problem in the case of anomalous curves was invented by N. P. Smart, I. A. Semaev, T. Satoh and K. Araki independently. In this talk we will modify their method using ideas from elementary number theory to a‹ack the discrete logarithm problem over prime €elds. ‘is is joint work with H. Gopalakrishna Gadiyar.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 21 VIT-Vellore

Hardy’s Theorem for General L-functions (NT5) K. Srinivas ‘e Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai-600113. [email protected]

‘e Riemann Hypothesis (RH) asserts that all the non-trivial zeros of the Riemann zeta-function ζ(s), s = 1 σ + it lie on the critical line σ = 2 . As a €rst step towards RH, G. H. Hardy, in 1914 showed that in€nitely many of them lie on the critical line. In this talk, we shall discuss the extension of Hardy’s approach to more general L-functions.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 22 VIT-Vellore

Topology and Geometry

(TG1) Doodles on Surfaces and Associated Groups Mahender Singh Indian Institute of Science Education and Research (IISER) Mohali [email protected]

Study of certain equivalence classes of a €nite collection of immersed circles without triple or higher inter- sections on closed oriented surfaces can be thought of as a planar analogue of virtual knot theory where the genus zero case corresponds to classical knot theory. It is intriguing to know which class of groups serves the purpose that braid and virtual braid groups serve in classical and virtual knot theory, respectively. Kho- vanov proved that twin groups, a class of right angled Coxeter groups with only far commutativity relations do the job for genus zero case. We showed in some recent works that an appropriate class of groups called virtual twin groups €ts into the theory for higher genus case. ‘e talk would give an overview of some recent developments on the subject.

(TG2) On the Zero-divisor Cup-length of Real Oriented Grassmann Manifolds

Vimala Ramani Anna University, Guindy, Chennai [email protected]

For a path-connected topological space X, the K-zero-divisor cup-length, where K is any €eld, is a co- homological lower bound for the topological complexity of X. For real oriented Grassmann manifolds G˜n,k, 3 ≤ k ≤ [n/2], we compute the rational zero-divisor cup-length in terms of n and k. We also prove ˜ that, for certain in€nite families of real oriented Grassmannians Gn,3, the Z2-zero-divisor cup-length is a be‹er lower bound for the topological complexity than the Q-zero-divisor cup-length.

(TG4) Smooth Structures on CP m for 5 ≤ m ≤ 8 Ramesh Kasilingam Department of Mathematics, IIT Madras, Chennai [email protected]

We classify up to di‚eomorphism all smooth manifolds homeomorphic to the complex projective m−space CP m for m = 5, 6, 7 and 8. As an application, for m = 7 and 8, we obtain a bound on the number of smooth homotopy complex projective m−spaces with given Pontryagin classes up to orientation-preserving di‚eomorphism. We also show that there exists a smooth manifold which is tangentially homotopy equivalent but not homeomorphic to CP 8.

(TG3) The Topology of Real Bott Manifolds Raisa Dsouza St Joseph’s College, Bengaluru

In this talk we introduce small covers and a particular class of examples of small covers known as Real Bo‹ Manifolds. We discuss a few topological properties of these objects and also see an interesting relation between these objects and acyclic directed graphs.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 23 VIT-Vellore

On the volume of Fano Manifolds (TG5) Harish Seshadri IISc Bengaluru

I will discuss a recent result of K. Zhang which gives an optimal volume bound for Kahler¨ manifolds with positive Ricci curvature.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 24 VIT-Vellore

History of Indian Mathematics

(HIM1) Generalized Brahmagupta-Jayadeva-Bhaskara¯ Problem Avinash Sathaye Department of Mathematics, University of Kentucky, Lexingon KY, USA [email protected]

One of the famous problems in the history Indian Mathematics is the one stated by Brahmagupta in the sev- enth century and completely solved by Bhaskara¯ in twel‰h century. ‘e problem is to solve the equation Dx2 + 1 = y2 where D is a given nonsquare positive integer and the desired solutions x, y are integers. In seventeenth century, the same equation was contemplated by Fermat without the knowledge of Indian his- tory and he posed it as a challenge to the mathematicians. Its solution led to many techniques in adratic forms in number theory and the high point was the work of Gauss in eighteenth century.

We discuss a generalized version of the original problem which asks for all possible integers c such that Dx2 + c = y2 for some integers x, y.

‘e generalized question naturally arises from the method of the Indian solution which consists of solving the generalized problem for some convenient c and then cleverly modify it to lead to the desired solution.

We present a solution to the generalized problem by the same method as Bhaskara¯ by using the ‘eory of Bhaskara¯ forms in Ayyangar’s paper “New light on Bhaskara’s¯ chakravala …” in JIMS(1929-1930) vol. 18.

We also compare and contrast the solution with the techniques of using the Gauss’ theory of adratic forms in Number ‘eory.

(HIM2) On Zero-Divided Numbers in Ancient Indian Mathematics Amartya Kumar Du‹a Indian Statical Institute, Kolkata [email protected]

It was in ancient India that zero received its €rst clear acceptance as an integer in its own right. In 628 CE, Brahmagupta describes in detail rules of operations with numbers — positive, negative and zero — and thus, in e‚ect, imparts a ring structure on integers with zero as the additive identity. ‘e various Sanskrit names for zero include kha, s´unya,¯ purn¯ .a. ‘ere was an awareness about the perils of zero and yet ancient Indian mathematicians not only embraced zero as a number but allowed it to participate in all four arithmetic operations, including as a divisor in a division. But division by zero is strictly forbidden in the present edi€ce of mathematics. Consequently, verses from ancient stalwarts like Brahmagupta and Bhaskar¯ ach¯ arya¯ refer- ring to numbers with “zero in the denominator” shock the modern reader. Certain examples in the B¯ijagan. ita (1150 CE) of Bhaskar¯ ach¯ arya¯ appear as absurd nonsense. But then there was a time when square roots of neg- ative numbers were considered non-existent and forbidden; even the validity of subtracting a bigger number from a smaller number (i.e., the existence of negative numbers) took a long time to gain universal acceptance. Is it not possible that we too have con€ned ourselves to a certain safe convention regarding the zero and that there could be other approaches where the ideas of Brahmagupta and Bhaskar¯ ach¯ arya,¯ and even the examples of Bhaskar¯ ach¯ arya,¯ will appear not only valid but even natural?

Enterprising modern mathematicians have created elaborate legal (or technical) machinery to overcome the limitations imposed by the prohibition against use of zero in the denominator. ‘e most familiar are the methods of calculus with its concept of limit, results like l’Hopital’sˆ rules, and a language which enables 1 one to express intuitive ideas like 0 = ∞ through legally permi‹ed euphemisms. Less well-known are the devices of commutative algebra, algebraic geometry and algebraic number theory like “localisation” which describes a legal structure for directly writing fractions with zero in the denominator without any subterfuge, and the more sophisticated ideas of “valuation theory” which admit multiple levels of in€nities and thereby provide higher-dimensional algebraic analogues of l’Hopital’sˆ rules.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 25 VIT-Vellore

In this talk we shall highlight an algebraic model proposed by Prof. Avinash Sathaye for understanding Bhaskar¯ ach¯ arya’s¯ treatment of khahara, (numbers with) zero in the denominator, including the appar- ently erroneous examples in the algebra treatise B¯ijagan. ita. A crucial ingredient of this model is the ubiq- uitous concept of “idempotent” in modern algebra (elements e satisfying e2 = e). ‘e commentary by Kr.s.n. adaivajna(c.1548)˜ indicates that idempotence was indeed envisaged as a natural property of numbers like zero and its reciprocal, the khahara. While historians of mathematics have tried to analyse Bhaskar¯ ach¯ arya’s¯ khahara in the framework of calculus, the diculties with his examples disappear in the algebraic inter- pretation based on idempotents.

Prof. Sathaye’s interpretation of Bhaskar¯ ach¯ arya’s¯ khahara also gives a new meaning to certain mysterious u‹erances of Ramanujan recorded by P.C. Mahalanobis.

Brahmagupta’s Bhavan¯ a¯ and Reading Mathematics from Sanskrit Texts (HIM3) C.S. Aravinda TIFR Centre for Applicable Mathematics, Bangalore [email protected]

As an example of deciphering mathematical results from old Sanskrit texts, we will show how to read Brah- magupta’s celebrated composition law, on solutions of the Brahmagupta-Pell equation, from his original Sanskrit verses.

Continued Fraction Techni€e in the Kerala School of Astronomy (HIM4) Venketeswara Pai R Department of Humanities and Social Sciences Indian Institute of Science Education and Research (IISER) Pune – 411008. [email protected]

A brilliant school of astronomers and mathematicians founded by Madhava¯ (c. 1340 - 1420) ƒourished in Ker- th th ala between 14 - 17 century CE. One among them was Putumana Somayaji,¯ the author of Karan. apaddhati (c. 1532 - 1560), which explains the mathematical basis of the vakya¯ system of computing the planetary po- sitions, in which the true positions of planets are found directly from mnemonics along with some simple arithmetical operations. Now, the calculation of the mean positions of the planets would be the €rst step in the computation of the true positions.‘ese would be proportional to the rates of motion of the planets which would involve ratios of large numbers. Some other variables needed for obtaining the true positions also involve ratios of large ‘mulitipliers’ and ‘divisor’. Karan. apaddhati describes a mathematical technique known as vallyupasam. hara¯ which is a variant of kut..taka method for solving linear indeterminate equations. In Karan. apaddhati, this method is used for obtaining smaller multipliers and divisors for the aforesaid ratios. vallyupasam. hara¯ method of transforming the vall¯i (a row of numbers) is essentially the recursive process of calculating the successive convergents of the continued fraction associated with the ratio. In Karan. apaddhati, it is the simple continued fraction expansions that is used. In a later text called Dr.kkaran. a (1606 CE), prob- ably authored by Jyes.t.hadeva, we have a variant of this method in which semi-regular continued fraction expansions are prescribed, with modi€ed recursion relations.

Consider the problem of computing the true position of the Moon on some speci€c date, using the Vakya¯ method. ‘is would involve €nding a date which is close to the speci€c date, on which the mean and true longitudes are equal at Sunrise. ‘is would imply that the ‘anomaly of the Moon’(an auxiliary variable which appears in the expression for the true longitude) is zero at that time. ‘is known as the khan. d. adina. Finding the khan. d. adina is indeed an interesting mathematical problem, involving the kut..taka method to solve a linear indeterminate equation.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 26 VIT-Vellore

(HIM5) Second Order Taylor Series for the Sine and Cosine Functions in the Kerala School of Astronomy and Mathematics M.S. Sriram Prof. K.V. Sarma Research Foundation, Adyar, Chennai. [email protected]

‘e sine function is a necessary ingredient for most calculations in the mathematical astronomy of the yore. ‘e Indian texts on siddhantic¯ astronomy beginning with Aryabhat¯ .¯iya (499 CE) give the table of sines, mostly corresponding to a 24-fold division of the quadrant: the values of sin(iα) are speci€ed, where i = 1, 2,..., 24, 90◦ 0 and α = 24 = 225 . ‘e value of sin θ for a general value of θ = iα + βα, (β < 1) is obtained from interpo- [sin((i+1)α)−sin(iα)] lation: sin(iα + βα) = sin(iα) + βα × α . In his Khan. d. akhadyaka¯ (665 CE), Brahmagupta gives a second-order interpolation formula for the sine function (actually valid for any function).

‘e sine of the ‘anomaly’ appears in the expression for the ‘true longitude’ of a planet. So, the rate of change of the true longitude, or the ‘true daily motion’ would involve the rate of change of the sine function. ‘e correct expression for this, employing the cosine as the ‘rate of change’ of the sine, was given by Munjala¯ (932 CE) in his Laghumanasa¯ and also by Aryabhat¯ .a–II (950 CE) in his Mahasiddh¯ anta¯ . In his Siddhanta¯ siroman´ . i (1150 CE), Bhaskara-II¯ recognises the ‘true daily motion’ as the instantaneous velocity, and explains how the cosine function appears in the expression for it. Actually, the true longitude involves the inverse-sine function, and in his Tantrasangraha˙ (1500 CE), N¯ilakan. t.ha Somayaj¯ ¯i gives the correct expression for the in- stantaneous velocity, involving the derivative of the inverse-sine.

In Yuktibhas¯.a¯ (1530 CE) of Jyes.t.hadeva (well known for the proofs of the in€nite series expansions of π and sine and cosine functions), the rate of change of the sine and cosine functions is discussed in more detail. It gives the second order Taylor series for the sine and cosine functions, explicitly. In later Kerala texts like Sphut.anirn. ayatantra (1593 CE) of Acyuta Pis.arat¯ .i and also Dr.kkaran. a (1606 CE), possibly a work of Jyes.t.hadeva, the second order Taylor series for the sine function is explicitly used. ‘is is in the context of the procedure for €nding the true longitudes of planets.

[Note : In Indian mathematics and astronomy, the sine is actually the ‘length of the opposite side’ in a right triangle with a given hypotenuse . Moreover, the argument of the sine is the relevant arc, not the ‘angle’.]

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 27 VIT-Vellore

Industrial Mathematics: Modelling, Optimization, Simulation

Selection of the Informative Fre€ency Band in a Bearing Fault (IM1) Diagnosis in the Presence of Non-Gaussian Noise-the stochastic-based approach Agnieszka Wylomanska´ Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wroc?aw University of Science and Technology, Poland. [email protected]

‘e vibration signals acquired on machines usually have complex spectral structure. As the signal of interest (SOI) is weak (especially at an early stage of damage) and covers some frequency range (around structural resonance), it requires its extraction from a raw observation. Until now, most of the techniques assumed the presence of Gaussian noise. Unfortunately, there are cases when the non-informative part of the signal (considered as the noise) is non-Gaussian due to the random disturbances or nature of the process executed by the machine. ‘us, the problem can be formulated as the extraction of the SOI from the non-Gaussian noise. Recently this problem has been recognized by several authors and some new ideas have been developed. In this presentation, we would like to compare these techniques for benchmark signals (Gaussian noise, cyclic impulsive signals, non-cyclic impulsive signals with random amplitudes and locations of impulses and a mixture of all of them). Our analysis will cover classical methods and recently introduced algorithms based on the stochastic analysis of the vibration signals represented in time-frequency maps. A discussion on the eciency of each method will be provided.

Covid-19-Simulations for Germany (IM2) ‘omas Goetz Mathematical Institute, University Koblenz, Germany. [email protected]

In the talk we will report about the di‚erent modeling and simulation approaches in Koblenz. As part of the MOCOS consortium we are conducting stochastic microstructure simulations together with the universities of Kaiserslautern, Trier and Wroclaw. In Koblenz we are also doing parameter estimations based on SIR-type models. ‘ese models allow to simulate e‚ects of schools openings, the inƒuence of household structures onto the disease dynamics and to estimate the number of undetected cases. Since all this is ongoing and very active current research work, the special focus of the talk is not yet €xed.

A Meshfree Particle Method for Simulations of Fluid Flows and (IM3) Interacting Particle Systems Sudarshan Tiwari Department of Mathematics University of Kaiserslautern, Germany [email protected]

‘e talk will be divided into two parts. ‘e €rst part consists of the introduction of a mesh free particle method, called the Finite Pointset Method (FPM) and its application to simulate complex ƒow problems. ‘is is a fully Lagrangian method, where particle move with their velocities. ‘e spatial di‚erential operators at an arbitrary particle position is approximated from its surrounding cloud of points based on the weighted least squares method. ‘is is a generalized €nite di‚erence approximation. We simulate ƒows by solving the incompressible Navier-Stokes equations. We use the Chorin’s projection scheme in the meshfree framework. We present di‚erent simulation results for single- and multiphase ƒow problems. .

In the second part, we present models for interaction particle system. We present the microscopic model €rst and then show its hydrodynamic equations. By modeling di‚erent forces we present the simulations of material ƒows, pedestrian ƒow and the swarming of birds. ‘e hydrodynamic limit equations are solved by the FPM.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 28 VIT-Vellore

(IM4) Fast Direct Solver for High Fre€ency EM Scattering Sivaram Ambikasaran IIT Madras [email protected]

‘e talk will focus on constructing a fast direct solver that scales as O(n log n) instead of O(n3), where ‘n’ is the number of unknowns in the discretized linear system, for high frequency electromagnetic sca‹ering problems.

(IM5) A Point Source Model to Represent Heat Distribution Without Calculating the Joule Heat during Radiofre€ency Ablation Panchatcharam Mariappan Department of Mathematics and Statistics, IIT Tirupati, India panch.m@ii‹p.ac.in

Numerous liver cancer oncologists suggest bridging therapies to limit cancer growth until donors are avail- able. Interventional radiology including radiofrequency ablation (RFA) is one such bridging therapy. ‘is locoregional therapy aims to produce an optimal amount of heat to kill cancer cells, where the heat is pro- duced by a radiofrequency (RF) needle. Less experienced Interventional Radiologists (IRs) require a so‰ware- assisted smart solution to predict the optimal heat distribution as both overkilling and untreated cancer cells are problematic treatment. ‘erefore, two of the big three partial di‚erential equations, (1) heat equation to predict the heat distribution and (2) Laplace equation for electric potential along with di‚erent cell death models are widely used in the last three decades. However, solving two di‚erential equations and a cell death model is computationally expensive when the number of €nite compact coverings of a liver topologi- cal structure increases in millions. Since the heat source from the Joule losses q = σ|∇V |2 is obtained from Laplace equation σ∆V = 0, it is named as Joule heat model. In this lecture, we represent the heat distribu- tion from the RF needle by a point source model instead of the traditional Joule heat model. ‘e idea behind this model is to solve σ∆V = δ0 where δ0 is a Dirac-delta distribution which can also be represented by 2 √1 −x /4 lim → 0 2 π e . ‘erefore, using the fundamental solution of Laplace equation we represent the so- lution of Joule heat model using an alternative model called Point Source model which is given by Gaussian distribution 2 X 1 X − |x−xi| q(x) = Cje 2σ2 Ki xi∈Ω j

where Ki and Cj are obtained by using needle parameters. ‘is model is employed in one of the so‰ware solution called RFA Guardian which predicted the treatment outcome very well for more than 100 patients.

(IM6) Pedestrian Crowd Dynamics Models S. Sundar DAAD Research Ambassador, Department of Mathematics Indian Institute of Technology Madras, Chennai 600 036

Pedestrian crowd dynamics is a complex and intriguing topic which is being researched widely. Social scien- tists opine that crowd behaviour is not completely irrational and individuals are mostly guided by reason and rules of behaviour. Mathematical modeling of the pedestrian crowd is a valuable tool for understanding the dynamics of the problem. Varied discrete and continuous modelling approaches ranging from macroscopic to microscopic length scales have been explored by scientists and mathematicians. ‘is talk presents a simple and elegant model “‘e Social Force Model” proposed by D. Helbing and P. Molnar in 1995. In this micro- scopic model, the motion of the pedestrians is assumed to be driven by non-physical social or behavioural forces and governed by kinematic equations. ‘e model reproduces many of the self-organization phenom- ena, observed in reality, through computer simulations. ‘is modeling approach is well-founded and the governing equations give a framework to understand and predict qualitatively and sometimes quantitatively certain aspects of pedestrian and crowd movement.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS Papers for Competition Session IMS - 2020 30 VIT-Vellore

A M U Prize

(AMU-1) Modules Invariant under Clean Endomorphisms of their Injective Hulls Manoj Kumar Patel Department of Mathematics National Institute of Technology Nagaland Dimapur -797103, Nagaland, India [email protected]

A module is quasi-injective if and only it is invariant under endomorphisms of its injective hull. In this paper we study the class of modules which are invariant under all clean endomorphisms of their injective hulls and show that this class of modules coincide with the class of quasi-injective modules. Some facts and results of this class of modules are obtained. We also establish some relations of clean-invariant modules with automorphism-invariant modules, idempotent-invariant modules, pseudo-continuous modules and Utumi modules. Apart from this we have given several sucient conditions under which automorphism-invariant modules to be clean-invariant.

(AMU-2) Duality of Locally asi-Convex Convergence Groups Pranav Sharma Department of Mathematics, Lovely Professional University, Punjab-144411. [email protected]

In the realm of the convergence spaces, the generalisation of topological groups is the convergence groups, and the corresponding extension of the Pontryagin duality is the continuous duality. We prove that local quasi-convexity is a necessary condition for a convergence group to be c-reƒexive. Further, we prove that every character group of a convergence group is locally quasi-convex.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 31 VIT-Vellore

V M Shah Prize

A Note on the Value Distribution of a Differential Monomial and some (VMS-1) Normality Criteria Bikash Chakraborty Department of Mathematics, Ramakrishna Mission Vivekananda Centenary College, Rahara, West Bengal 700 118, India [email protected], [email protected]

In this paper, we prove some value distribution results which lead to some normality criteria for a family of analytic functions. ‘ese results improve some recent results.

A New Two-dimensional aternion Fractional Fourier Transform (VMS-2) Khinal Parmar SVKM’s NMIMS MPSTME, V. L. Mehta Road, Vile-Parle (W), Mumbai-400056, Maharashtra, India. [email protected]

In this paper, a new two-dimensional quaternion fractional Fourier transform is developed. ‘e properties such as linearity, shi‰ing and derivatives of quaternion valued function are studied. ‘e convolution theorem, Plancherel type theorem and inversion formula are also established.

Ine€alities and Applications of aternion Windowed Linear (VMS-3) Canonical Transform Manab Kundu Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad 826004, Jharkhand, India. [email protected]

In this paper, we study the logarithmic uncertainty principle, Lieb uncertainty principle and local uncertainty principle for the quaternion windowed linear canonical transform (QWLCT). Further we brieƒy introduce some applications of QWLCT of a linear time varying system.

antitative Approximation on a New Class of Szasz-Mirakjan´ Operators (VMS-4) having Preserving Property Rishikesh Yadav Applied Mathematics and Humanities Department, Sardar Vallabhbhai National Institute of Technology, Surat, Gujarat 395 007, India [email protected]

‘is article deals with the approximation properties of generalized version of Szasz-Mirakjan´ operators which preserve ax, a > 1 (€xed) and x ≥ 0. We study uniform convergence of the operators by using some auxil- iary results and also error estimations are determined by considering the function from di‚erent spaces. ‘e convergence of said operators is shown and analyzed by graphics, also, in the same direction, we compare the proposed operators with Szasz-Mirakjan´ operators for the rate of convergence. A Voronovskaya-type theorem is studied and a comparison is shown under a sense of convexity with Szasz-Mirakjan´ operators. To describe the quantitative means of an asymptotic formula, we quantitatively approach to the Voronovskaya- type theorem, moreover, a Gruss¨ Voronovskaya type theorem is proved. In the last section, a modi€ed se- quence is constructed in the space of integrable function.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 32 VIT-Vellore

(VMS-5) Binomial Distribution and its Geometric Properties Associated with Univalent Functions S. Santhiya School of Advanced Sciences, Vellore Institute of Technology, Vellore-632014, India. [email protected]

‘e applications of hypergeometric function, conƒuent hypergeometric functions, Wrights function, gener- alized Bessel functions are interesting topics of research in Geometric Function ‘eory. In 2014, Porwal (J. Comput. Anal., ID 984135) introduced Poisson distribution series and give a nice application on analytic uni- valent functions and co-relates probability density function with univalent function. A‰er the appearance of this paper several researchers introduced hypergeometric distribution series, hypergeometric distribution type series, conuent hypergeometric distribution series, Binomial distribution series, and obtain sucient conditions and inclusion relations for various classes of univalent functions. Based on their work, in this pa- per we introduced new functions belonging to the class L (A, B, θ) of analytic functions involving a power series whose coecients are probabilities of Binomial distribution series and studied its geometric properties associated with univalent functions. Motivated by the work given by Sheeza et al. (Kyungpook Math. J., vol. 59, pp. 301-314) and Nazeer et al. (J. Comput. Anal. Appl., Vol. 26, pp. 11-17), we de€ne the following j−n j−n j−n j−n new functions Qp (z),Np,λ (z),Mp,λ,γ (z),Kp (z) and further €nd some analogous conditions for the functions de€ned by binomial distribution series belongs to the class L (A, B, θ).

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 33 VIT-Vellore

IMS Prize Group 1

Some Properties of k-tuple t-core Partitions (IPG1-1) Ranganatha Dasappa Department of Mathematics, Central University of Karnataka, Kalaburagi-585367, Karnataka, India [email protected]

In this paper, we generalize some results due to Saikia and Boruah on congruence properties for A3,9(n), A9,3(n) and A4,8(n), where At,k(n) denote the number of k-tuple partitions of n where each partition is t-core.

Direct Summands of Goldie Extending Elements in Modular Lattices (IPG1-2) Rupal C. Shro‚ School of Mathematics and Statistics, MIT World Peace University, Pune 411038, India. rupal.shro‚@mitwpu.edu.in

In this paper we study some results on direct summands of Goldie extending elements in modular la‹ice. An element a of a la‹ice L with 0 is said to be a Goldie extending element if and only if for every b ≤ a there exists a direct summand c of a such that b ∧ c is essential in both b and c. Some characterizations of a decomposition of a Goldie extending elements in a modular la‹ices are given.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 34 VIT-Vellore

IMS Prize Group 4

(IPG4-1) On Some Series Representation between R-function and Fractional Calculus Operators Ankit Pal Department of Applied Mathematics and Humanities, Sardar Vallabhbhai National Institute of Technology, Surat, Gujarat 395 007, India. [email protected]

In this paper, we propose some fractional integral identities between R-function and Riemann-Liouville frac- tional integral operators. Further we consider R integral operator to derive series expansions in terms of classical Riemann-Liouville fractional operators We also investigate an analytical solution of fractional free electron laser equation involving R-function.

(IPG4-2) Approximation of Solutions for Nonlinear Functional Integral E€ations using Homotopy Perturbation Lakshmi Narayan Mishra Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology (VIT) University, Vellore 632 014, Tamil Nadu, India [email protected], [email protected]

‘is manuscript deals with the solutions of some nonlinear functional integral equations using the concept of measure of noncompactness. Firstly, we verify the existence of solutions to the equation using the generalised Darbo €xed point theorem and then come up with an ecient iterative algorithm to €nd an approximate solu- tion by applying homotopy perturbation method and Adomian decompostion. Also, we justify the eciency of the algorithm with the help of an example. Finally an error analysis with the upper bound of errors is presented.

(IPG4-3) Aposteriori Error Estimation of Subgrid Multiscale Stabilized Finite Element Method for Transient Stokes Model Manisha Chowdhury Indian Institute of Technology, Kanpur, U‹ar Pradesh, India. [email protected]

In this study, we present a novel stabilized €nite element analysis for transient Stokes model. ‘e algebraic subgrid multiscale approach has been employed to arrive at the stabilized coupled variational formulation. Derivation of the stabilized form as well as stability analysis of it’s fully discrete formulation are presented elaborately. Discrete inf-sup condition for pressure stabilization has been proven. For the time discretization the fully implicit schemes have been used. A detailed derivation of the aposteriori error estimate for the stabilized subgrid multiscale €nite element scheme has been presented. Numerical experiment has been carried out to verify theoretically established order of convergence.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 35 VIT-Vellore

Latest Inversion Free Iterative Scheme for Solving a Pair of Non-linear (IPG4-4) Matrix E€ations Sourav Shil Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore-632014, TN, India [email protected]

∗ −1 ∗ −1 In this work, the following system of non-linear matrix equations are considered, X1 +A X1 A+B X2 B = ∗ −1 ∗ −1 I, X2 + C X2 C + D X1 D = I, where A, B, C, D are arbitrary n × n matrices, I is identity matrix of order n. Some conditions for existence of positive de€nite solution are discussed here and also convergence analysis of newly developed algorithm for €nding the maximal positive de€nite solution and its convergence rate as well. Two examples are also provided here in support of our results.

δ,ξ (IPG4-5) The Polynomial Ln (x) and Fractional Calculus Vinod Kumar Jatav Department of Applied Mathematics and Humanities, Sardar Vallabhbhai National Institute of Technology, Surat-395 007, Gujarat, India. [email protected]

In this paper, we give composition formulas of generalized fractional integral involving the polynomials δ,ξ Ln (x) and also obtain Riemann-Liouville fractional derivative and some integral transforms of polynomials δ,ξ Ln (x).

Finite Difference Heat Transfer Analysis in S€are Lattice when (IPG4-6) Pivotal Points Exist near Curved Boundaries P. Reddaiah Department of Mathematics, Kadapa, Andhra Pradesh, India. [email protected]

In this paper I did Finite Di‚erence Heat Transfer Analysis in Square La‹ice When Pivotal Points Exist Near Curved Boundaries. To determine Pivotal Points at other than curved boundaries we use Central Di‚erence Partial Operator Molecule. To determine Pivotal Points at curved boundaries we use ∇2 operator for unevenly spaced points. A‰er €nding pivotal point values I did heat transfer analysis a‰er plo‹ing in Graphical Repre- sentation. How temperature is distributed in Square La‹ice is plo‹ed as Contour Diagram. I did heat transfer analysis in x traverse direction. Using Mathematica 9 Version So‰ware I did Mathematical Computations.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 36 VIT-Vellore

IMS Prize Group 5

(IPG5-1) The Influence of Magnetic and Gravitational Fields in a Non-ideal Dusty Gas with Heat Conduction and Radiation Heat Flux P.K. Sahu Department of Mathematics, Government Shyama Prasad Mukharjee College, Sitapur-497111, Chha‹isgarh, India. [email protected]

Similarity solutions for a spherical shock wave in a mixture of small solid particles of micro size and a non- ideal gas are discussed under the inƒuence of the gravitational €eld and magnetic €eld with conductive as well as radiative heat ƒuxes. ‘e solid particles are uniformly distributed in the mixture, and the shock wave is assumed to be driven by a piston. It is assumed that the equilibrium ƒow-conditions are maintained and the moving piston continuously supplies the variable energy input. Due to the central mass at the origin (Roche model), the medium is considered to be under the inƒuence of the gravitational €eld. ‘e density of the undisturbed medium is assumed to be constant in order to obtain the self-similar solutions. Distribution of gas-dynamical quantities are discussed through €gures. It is obtained that the magnetic €eld has a decaying e‚ect on shock strength. It is shown that due to an increase in the gravitational parameter the compressibility of the medium at any point in the ƒow €eld behind the shock front decreases. ‘e non-idealness of the gas causes a decrease in the shock strength and widens the disturbed region between the piston and the shock. It is interesting to note that in the presence of azimuthal magnetic €eld the pressure and density vanish at the piston and hence a vacuum is formed at the center of symmetry, which is in excellent agreement with the laboratory condition to produce the shock wave.

(IPG5-2) Mathematical Study of Reflection of qP and qSV Waves from the Stress-free/rigid Surface of a Micro-mechanically Modeled Piezoelectric Fiber-Reinforced Composite Half-space Sayantan Guha Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines) Dhanbad, Dhanbad-826004, Jharkhand, India [email protected]

‘e present article has two primary objectives: Firstly, to present the micro-mechanics model of Piezoelectric Fiber-Reinforced Composite (PFRC) and demonstrate some of its advantages over monolithic piezoelectric materials. Secondly, to analytically study wave reƒection phenomenon at the stress-free/rigid surface of a PFRC. ‘e PFRC structure comprises of PZT-5A €ber-epoxy matrix combination and is modeled employing the Strength of Materials technique with Rule of Mixtures. Some advantages of the PFRC in contrast to mono- lithic piezoelectric materials are graphically demonstrated. Due to the incidence of a quasi-longitudinal or quasi-transverse wave, three reƒected waves viz. quasi-longitudinal (qP), quasi-transverse (qSV), and electro- acoustic (EA) waves are generated in the PFRC. ‘e closed-form expressions of amplitude ratios of all reƒected waves are derived utilizing appropriate electro-mechanical boundary conditions at both the stress-free and the rigid surface. However, the amplitude ratios of reƒected waves cannot be used exclusively to validate the numerical results. Hence, the expressions of energy ratios of all reƒected waves and interaction energy are derived using the amplitude ratios, which exhibit the inƒuence of existing parameters, and the Law of Con- servation of Energy is established. Despite the endless advantages of PFRC, no mathematical studies have been performed yet on wave reƒection phenomenon at the stress-free/rigid surface of a PFRC half-space. ‘e present work is framed to explore the same for contemplating the phenomenon in constructed smart structures. ‘erefore, this work presents a novel e‚ort to develop a connection between derivation of the composite’s micro-mechanics model and analyze wave reƒection phenomenon in it.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 37 VIT-Vellore

IMS Prize Group 6

Cross Diffusion Induced Spatiotemporal Pattern in Diffusive (IPG6-1) Nutrient-Phytoplankton Model with Nutrient Recycling Sarita Kumari Department of Mathematics & Computing, Indian Institute of Technology (ISM),Dhanbad, India [email protected]

In this paper we have proposed a mathematical model of spatiotemporal interaction between the nutrient and phytoplankton. ‘e interaction between nutrient and phytoplankton has been considered with Holling type-III functional response and nutrient recycling. We have also consider the e‚ect of cross di‚usion in the model system. ‘e stability analysis for non-spatial and spatial model system has been carried out. Special focus has been given to investigate the selection of spatiotemporal pa‹erns in the neighbourhood of a critical parameter using the amplitude equation. Choosing approperiate control parameter from the Turing space, existence conditions for stable pa‹erns are derived using the amplitude equations. We have performed the numerical simulation and observed the e‚ect of time evolution, cross di‚usion and rate of toxin release by phytoplankton on the density distribution of species by spatial pa‹erns. Cross di‚usion plays an important role for Turing instability and formation of spots to stripe like pa‹ern.

An Answer to the Challenges in a CT-Data based Realistic Complex (IPG6-2) Artery Network Flow Study Sumit Kumar School of Biomedical Engineering, Indian Institute of Technology (BHU), Varanasi, 221005, India. [email protected]

Study of realistic human arterial network ƒow dynamics is well known to be faced with the challenges like a) apt geometric modelling, b) bifurcation zone meshing and c) selection of right rheological model for the capturing the hemodynamics correctly in the entire network under study. In this study, we provide an answer to correctly trace the physics behind the hemodynamics in a complex and realistic 3D human arterial network consisting of abdominal artery (AA) branching into le‰ and right iliac arteries and their further branching. For this, we accurately reconstruct the 3D geometry using subject speci€c CT-Scan DICOM imaging data and devise a correct strategy for mesh generation with MIMICS-18 in complex bifurcation zones and also establish the right rheological model choice for unraveling the physics behind the blood ƒow dynamics in a complex network. Localized grid generation strategy is used for discretization of the domain. Detailed large scale numerical simulations are carried out by FLUENT solver under €nite volume paradigm and results are validated with the experimental studies from the literature. While the results based on Newtonian model and Power-law based Non-Newtonian model look nearly the same in large large arterial segments like AA the Non-Newtonian rheological model is found to give be‹er results in iliac bifurcation zone, where the size of arterial vessel gets reduced to less than one-fourth of that of AA. ‘is work present new tools for the three- dimensional model reconstruction, geometric analysis, mesh generation and the CFD investigation applied to blood ƒow in complex arterial network.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 38 VIT-Vellore

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS Contributory Paper Presentations IMS - 2020 40 VIT-Vellore

Section A: Combinatorics, Graph ‡eory, Logic, Discrete Mathematics

(A1) Generalized Fuzzy P and Q-Continuous Maps Sujeet Kumar Chaturvedi, J.K. Maitra Department of Mathematics and Computer Sciences, R.D. University Jabalpur M.P. INDIA [email protected], jkmrdvv@redi‚mail.com In this chapter we have introduced the concept of fuzzy P-sets and fuzzy Q-sets in the category of generalized fuzzy topological spaces. Further we establish several results regarding P-Continuity and Q-Continuity in generalized fuzzy topological spaces.

(A2) Some Properties of Bipolar Doubt Intuitionistic Fuzzy K-ideals in BCK/ BCI-algebras R. Angelin Subaa, K.R. Sobhab aAssistant Professor, Department of Mathematics, Women’s Christian College, Nagercoil-629001, Tamilnadu, India. bAssistant Professor, Sree Ayyappa College for Women, Chunkankadai, Nagercoil. (Aliated to Manonmaniam Sundaranar University, Abishekapa‹i, Tirunelveli-627012, Tamilnadu,India) [email protected], [email protected] In this research paper, we investigate bipolar doubt intuitionistic fuzzy K-ideals in BCK/ BCI-algebras. ‘e purpose of the study is to introduce the concept of bipolar doubt intuitionistic fuzzy K-ideals are connected with bipolar doubt intuitionistic fuzzy subalgebra and bipolar doubt intuitionistic fuzzy ideals. Here we im- plement the characterization of Bipolar doubt intuitionistic fuzzy K-ideals using doubt intuitionistic positive α-level cut and doubt intuitionistic β-level cut set and some of its properties are analyzed.

(A3) A Real Life Problem in Decision Making using Hendecagonal Fuzzy Numbers Javaid Ahmad Shah, Rakesh Kumar Tripathi Department of mathematics, Dr. APJ Abdul Kalam University Indore (M.P) India. [email protected] Most issues in life involve decision processes of one or another form, as trivial as we might consider them. To have ability to make consistent and correct choices is the essence of any decision process pervade with uncertainty. ‘ere are number of techniques to solve decision making problems, one such technique is to use Hendecagonal fuzzy numbers. Such fuzzy numbers are used to represent the uncertainty or vagueness of eleven linguistic variables. ‘is paper presents an evaluation regarding the selection of teaching sta‚ for an institute, among several candidates so that appropriate persons are selected which are suitable for the required job and also which will improve the performance of the institute and that of students as well.

(A4) A Note on the Relationship between Julia Set and Independence Polynomial of a Graph K.U. Sreejaa, P.B. Vinodkumarb, P.B. Ramkumarb aDepartment of Mathematics,K.K.T.M. Government College, Pullut, ‘rissur , India bDepartment of Mathematics, Rajagiri School of Engineering and Technology,Kochi, India [email protected] Graph polynomials are widely studied and have found many applications in di‚erent €elds of science. ‘ere are number of graph polynomials.We use independence polynomial to construct and study some Julia sets.‘e various relations between independence polynomial, energy, Julia set and Hausdor‚ dimension of graphs are closely examined.As a special graph Petersen graph’s connectivity is examined and it is found that its Julia set is disconnected.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 41 VIT-Vellore

A Real Life Decision Making Problem as an Application Of Fuzzy Logic (A5) Rakesh Kumar Tripathi, Showkat Ahmad Bhat Dr. A.P.J. Abdul Kalam University, Indore, India [email protected], [email protected]

Fuzzy sets are very useful tool to tackle with the concept of vagueness and uncertainty in decision making process. In this paper, we apply the theory of fuzzy sets to solve a real world decision making problem. ‘e aim of this paper is to present a fuzzy logic framework for employee selection process.

Edge Chromatic Polynomials of S-valued Graphs (A6) A. Arul Devia, V. ‘iruvenib aDepartment of Mathematics Sri Ramanas College of Arts and Science for Women Aruppuko‹ai bDepartment of Mathematics S.B.K. College Aruppuko‹ai. [email protected], [email protected]

In his monograph “Semirings and their applications” Jonathan Golan has introduced the notion of R valued graphs where R is a semiring. In the year 2015 Chandramouleeswaran and his scholars introduced the notion of semiring valued graphs (brieƒy called S-valued graphs). Many research has been carried out in S-valued graphs such as vertex domination, edge domination, vertex edge domination, colouring of S-valued graphs and so on. ‘is paper discusses the concept of edge S-chromatic polynomial associated with a given S-valued graph. Also we introduce the notion of vertex-edge colouring of a S-valued graph and the corresponding S-chromatic polynomial.

Blocks in a S−valued Semigraph (A7) S. Nivetha, M. Chandramouleeswaran Department of Mathematics Sri Ramanas College of Arts and Science for Women Aruppuko‹ai. [email protected], [email protected]

In his monograph on “Semigraphs and their applications”, Sampath Kumar introduced the notion of semi- graphs in the year 2000. Since then many researchers worked on the theory of semigraphs. Motivated by introduction of the term R− valued graphs, where R is a semiring, in the year 2015, Chandramouleeswaran and others studied the concept of semiring valued graphs (S−valued graphs). ‘e above two works moti- vated us to study semiring valued semigraphs. ‘is paper studies the connected sets in a S−valued semi- graph. Also we discuss the graphs associated with the given S−valued semigraph. We prove some simple characterisations of a block in a S−valued semigraph.

Characterization of Semi Splitting Block Graph (A8) Nivedha Baskar, Tabitha Agnes Mangam, Mukti Acharya Department of Mathematics, Christ (Deemed to be University), Bengaluru, India [email protected]

For any graph G, the semi spli‹ing block graph SB(G) of a graph is obtained by taking a copy of G, for each vertex in G a new vertex is added which is made adjacent to all the vertices of G adjacent to that vertex and for each block in G a new vertex is added which is made adjacent to all the vertices of that block. We study the distance parameters like diameter, radius of semi spli‹ing block graph of cyclic and acyclic connected graph. A graph G is said be self centered if all the vertices of G are of same eccentricity. We characterized graphs whose SB(G) are self centered. A graph G is said to be semi spli‹ing block graph if there exist a ∼ graph H such that SB(H) = G. We characterized graphs which are semi spi‹ing block graph.

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(A9) Local Vertex Antimagic Labeling for Disconnected Graphs R. Shankar, M. Nalliah Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, India - 632014. [email protected], [email protected]

Let G = (V,E) be a graph of order p and size q having no isolated vertices. A bijection f : E → {1, 2, 3, ..., q} P is called a local antimagic labeling if for all uv ∈ E we have w(u) 6= w(v), the weight w(u) = e∈E(u) f(e), where E(u) is the set of edges incident to u. A graph G is local antimagic if G has a local antimagic labeling. ‘e local antimagic chromatic number χla(G) is de€ned to be the minimum number of colors taken over all colorings of G induced by local antimagic labelings of G. In this paper, we determine the local antimagic chromatic number for disconnected graph of path graph, cycle and friendship graph.

(A10) Local Distance Antimagic Vertex Coloring of Graphs T. Divya, S. Devi Yamini Department of Mathematics, Vellore Institute of Technology, Chennai, India [email protected]

Let G = (V,E) be a graph of order n without isolated vertices. ‘e function f : V → {1, 2, 3, ..., n} be a P bijection. ‘e weight w(v) of a vertex v is w(v) = z∈N(v) f(z), where N(v) is the open neighbourhood of v. If w(u) 6= w(v) for any two adjacent vertices u and v, then f is said to be a local distance antimagic labeling. A graph G is local distance antimagic if G admits a local distance antimagic labeling. ‘is induces a proper coloring where the vertex v is assigned the color w(v). ‘e minimum number of colors required for proper coloring of G induced by local distance antimagic labeling of G is called the local distance antimagic chromatic number denoted by χld(G). In this paper, we introduced this new parameter and determined the local distance antimagic chromatic number of some graphs.

(A11) Topological Indices of the Clustered Graphs T. Yogalakshmi, S. Gurunathan Department of Mathematics, SAS, VIT, Vellore, India [email protected]

Clustering deals with di‚erent kinds of a‹ributes to identify communities within large group. For the past few decays telecommunication, radar detection, image processing plays a major role in networking. Networking strategy was €rst used in telecommunication to reduce the time required for a call to go through. Intercon- nection networks is more ecient in parallel system performance and helps to realize the transportation of data between processors and memory modules. In these recent days, Optoelectronic system architecture have the capability of multiprocessors which are e‚ectively emphasized by networking. Topological indices trans- form the molecular graphs into a numeric quantity which characterize the topology of that graph. Topological descriptors €nd applications in quantitative structural properties, quantum chemistry, crystalline materials and pharmaceutical €elds. Now-a-days researchers scrutinize the concepts on Topological indices such as, Randic index, Zagreb index, atom-bond connectivity index which are exploited to estimate the bioactivity of chemical compounds and the premises of topology in networking. In this paper, clustered graphs have been orginated from an algorithm. Degree based indices such as €rst and second Zagreb, €rst and second Multiplicative Zagreb, Hyper Zagreb, Atom-Bond Connectivity (ABC) and Geometric indices of the clustered graphs have been computed. Moreover, the regression analysis on randic, SCI, ABC, ISI and GA indices of the clustered graphs have been established which intreprets that those indices are highly correlated with R = 0.99. Besides the neighbourhood based indices such as ABC4 and GA5 have been found.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 43 VIT-Vellore

A Note on Reversibility Related to Idempotents (A12) P. Jaish Ramanujan School of Mathematical Sciences, Department of Mathematics, Pondicherry University, Puducherry - 605 014, India

Let R be a ring and I(R) denote the set of all idempotent elements in R . In this article, we show that the ring of 2 × 2 matrices over an arbitrary reversible ring R with I(R) = {0, 1} is quasi-reversible, which is an answer to the question in [Bull. Korean Math. Soc., 56(4) (2019) 993-1006] given by Da Woon Jung et al. Further, we show that the converse part is also true.

Solving Transportation Problem using Graph algorithms (A13) Kanchana M, Kavitha K Department of Mathematics, Vellore Institute of Technology, Vellore, India [email protected]

Graphs are the tool for modeling and description of real life network systems. Many graph algorithms plays huge role in €nding the optimal path for the transportation problems with many aspects on it. ‘e transporta- tion, social networks, pipelines are all considered as a graph or a network model and solved using the shortest path algorithms. In this we obtain the optimal path by Dijsktra, Kruskal, Generalized Dijsktra, Extension of Kruskal and Path labeling algorithm. ‘e complexity of the algorithms are listed.

Results on Generalized Divisor Sum Function ση of Certain Standard (A14) Graphs R. Vignesha, Kalyani Desikana, A. Elamparithib aDivision of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai, India bDepartment of Mathematics, Dr. G S Kalyanasundaram Memorial School, Kumbakonam, India [email protected]

In general, for any non-negative number n ∈ R, the generalized divisor sum function ση(n) is de€ned as the sum of the non-negative factors of n that are raised to ηth powers, where η ∈ N.It can be represented as P η ση(n) = f ‘is paper is concerned with calculating the general form of ση(n) which we denote as Sη f/n and we arrived at the exact expressions for the generalized divisor function for few standard graphs. Some standard graphs that we considered are Crown Graph, Gear Graph, Helm Graph, Flower Graph, Web Graph, Generalized Peterson Graph, CnCm, Cocktail Party Graph, Tadpole Graph, Windmill Graphs, Zero-Divisor Graphs, and certain classes of Divisor Function Graphs.

Local Distance Antimagic Graphs (A15) V. Priyadharshini, M. Nalliah Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore - 632014, Tamilnadu, India. [email protected], [email protected]

Let G be a graph with n vertices and m edges with no isolated vertices. A bijection f : V → {1, 2, 3, . . . , n} is called local distance antimagic labeling, if any two adjacent vertices u and v with its vertex-weights w(u) 6= P w(v), where vertex-weight w(u) is de€ned as w(u) = wN(u) f(w). ‘e local distace antimagic chromatic number χda(G) is de€ned to be the minimum number of colors taken over all colorings of G induced by local distace antimagic labelings of G. In this paper, we introduced a new parameter χda(G) and we obtained some basic results. We determied the local distance antimagic labeling for star graph, sub-divisional star graph and double star graph.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 44 VIT-Vellore

(A16) Local Edge Antimagic Labeling of Cycle Related Graphs S. Rajkumar, M. Nalliah Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore - 632014, Tamilnadu, India. [email protected], [email protected] Let G = (V,E) be a graph of order p and size q having no isolated vertices. A bijection f : V → {1, 2, 3, ..., p} 0 is called a local edge antimagic labeling if any two adjacent edges e = uv and e = vw of G, with w(e) 6= 0 0 w(e ), where the edge weight is w(e = uv) = f(u) + f(v) and w(e ) = f(v) + f(w). A graph G is local 0 edge antimagic if G has a local edge antimagic labeling. ‘e local edge antimagic chromatic number χlea(G) is de€ned to be the minimum number of colors taken over all colorings of G induced by local edge antimagic labelings of G. In this paper, we obtain the local edge antimagic chromatic number is maximum degree of G, where G is a Generalized friendship graph of cycle graph, Generalized friendship graph of fan graph and Disconnected graph of Cycles kCn.

(A17) Genetic Algorithm to the Biobjective Multiple Travelling Salesman Problem Shayathri Linganathan, Purusotham Singamse‹y Department of Mathematics, Vellore Institute Technology, Vellore, India [email protected], [email protected] ‘e travelling salesman problem (TSP) and its variants have been studied extensively due to its wide range of real world applications, yet there are challenges in providing the ecient algorithms to deal some of its variants. ‘e multiple travelling salesman problem (MTSP) is the generalization of TSP, aims to determine m-shortest routes for msalesmen all of which start and end at a depot city such that they cover all the n-cities without intervening. ‘is leads to disproportionate distribution of number of cities to be covered by each salesman. ‘is paper presents, a biobjectve MTSP (BMTSP), where the €rst objective is to minimize the total travel distance and the other minimizes the total cost along with the load balancing constraint. ‘e optimal solution of this problem may not be possible at one point as it involves tradeo‚ between two objectives. A metaheuristic algorithm called Genetic Algorithm (GA) is proposed to obtain the Pareto ecient routes of BMTSP. Firstly, the n-cities are proportionately distributed to msalesmen next the initial solution is gener- ated with the help of greedy search algorithm feed into GA. Further, GA is designed by inducting di‚erent operators such as crossover, mutation and reverse operators to provide the Pareto routes. ‘e experiments are carried out on di‚erent datasets from TSPLIB. ‘e simulation results show the eciency of the proposed algorithm.

(A18) Signed Roman Domination in an Interval Graph with Adjacent Cli€es of Size 3 M. Reddappaa, C. Jaya Subba Reddyb, B. Maheswaric aDepartment of Mathematics, S. V. University, Tirupati-517502. bDepartment of Mathematics, S. V. University, Tirupati-517502. cProfessor (Retd.), Department of Applied Mathematics, S. P. MahilaVisvavidyalayam, Tirupati-517502. [email protected], [email protected], [email protected] ‘e theory of Graphs is an important branch of Mathematics that was developed exponentially. ‘e theory of domination in graphs is rapidly growing area of research in graph theory today. It has been studied ex- tensively and €nds applications to various branches of Science & Technology.

Interval graphs have drawn the a‹ention of many researchers for over 40 years. ‘ey form a special class of graphs with many interesting properties and revealed their practical relevance for modeling problems arising in the real world. ‘e theory of domination in graphs introduced by Ore and Berge is a fast growing area of research in graph theory today. An introduction and an extensive overview on domination in graphs and related topics is surveyed and detailed in the two books by Haynes et.al.

In this paper a study of signed Roman domination in an interval graph with adjacent cliques of size 3 is carried out.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 45 VIT-Vellore

Claw-decomposition of Kneser Graphs (A19) C. Sankari Department of Mathematics, A.V.V.M. Sri Pushpam College (Aliated to Bharathidasan University), Poondi, ‘anjavur, Tamil Nadu, India. [email protected]

A claw is a star with three edges. ‘e Kneser graph KGn,2 is the graph whose vertices are the 2-element sub- sets of n-elements, in which two vertices are adjacent if and only if their intersection is empty. In this paper, we prove that KGn,2 is claw-decomposable, for all n ≥ 6. Further, we discuss about claw-decomposition of KGn,2(λ).

On the Zero Forcing Number of Complementary Prism graphs (A20) M.R. Raksha, C. Dominic Department of Mathematics, Christ(Deemed to be university), Karnataka, India [email protected]

Zero forcing number of a graph G denoted by Z(G) is the minimum cardinality among all the zero forcing sets of the graph G. In this paper, we €nd few bounds on zero forcing number of the complementary prism graph GG based on the maximum degree of the graph G. Also we determine the zero forcing number of few complementary prism graph of some basic graphs. Finally, we €nd Zero forcing number of some special type of complementary prism graph. We establish the result, if G or G is disconnected graph of order n, then Z(GG) = n − 1, as one of the main result.

Edge Chromatic number of Zero-divisor graphs of some Semi-local rings (A21) Subhash Mallinath Gadeda, Nithya Sai Narayanab aR.K. Talreja College of Arts, Science & Commerce, Ulhasanagar−03, District: ‘ane, Mumbai, Maharashtra, India bN.E.S Ratnam College of Arts, Science & Commerce, Bhandup(W), Mumbai [email protected], [email protected]

A simple graph G is said to be of Class-1 if the Edge Chromatic number χ1(G) = ∆(G). In this paper we prove that the zero-divisor graphs of the Semi-local ring R = F1 ×F2 ×F3, where F1,F2,F3 are €nite €elds, belongs to Class-1.

S-cordial and Total S-Cordial Labeling in Signed Graphs (A22) Divya Antoney, Tabitha Agnes Mangam, Mukti Acharya Department of Mathematics CHRIST (Deemed to be University), Bengaluru, India. [email protected]

Let S = (G, σ) be a signed graph, where G is the underlying graph. ‘e line signed graph L(S) of a signed graph S is de€ned by V (L(S)) = E(S) and the vertices are joined by an negative edge in L(S) if and only if the corresponding edges are negative and adjacent to each other in S and positive in all other cases. Let L(S) be a line signed graph of S whose vertices have signs of the corresponding edges in S. ‘e L(S) is said to be S-cordial if the di‚erence between the positive and negative signs of the vertices (edges) di‚er by atmost one in L(S). ‘e L(S) is said to be total S-cordial if the di‚erence between the positive and negative signs in L(S) di‚er by atmost one in L(S). In this paper, we characterized signed graphs such as signed paths, signed cycles, signed star and signed bistars whose line signed graph admit S-cordial and total S-cordial labeling. We also €nd the characterization of some classes of signed graphs whose line signed graph admit S-cordial and total S-cordial labeling with respect to negation and switching in them.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 46 VIT-Vellore

(A23) A Note on Edge-fault Tolerance in Augmented Cubes Amruta Shinde, Y.M. Borse Department of Mathematics, Savitribai Phule Pune University Pune, 411 007, India [email protected]

‘e augmented cube AQn is a variation of the hypercube network. In this paper, we obtain an upper bound on conditional h-edge connectivity of AQn, for odd integer h. Furthermore, we prove that in augmented cube AQn (n ≥ 3) if h = 3 then the upper bound is same as the lower bound on conditional 3-edge connectivity which is equal to 8n − 16.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 47 VIT-Vellore

Section B: Algebra, Number ‡eory, Lattice ‡eory and History of Mathematics

On Cechˇ Fuzzy Interior Spaces and Fuzzy Pretopological Spaces (B1) determined by Implicators Abha Tripathi, S.P. Tiwari Department of Mathematics & Computing, Indian Institute of Technology (ISM), Dhanbad, India [email protected]

‘is paper is towards the study of Cechˇ fuzzy interior spaces and fuzzy pretopological spaces determined by general implicators. Further, we discuss some results based on Cechˇ fuzzy interior spaces and fuzzy pretopological spaces. Also, we show that the results regarding one-to-one correspondence between fuzzy reƒexive approximation spaces and Cechˇ fuzzy interior space as well as fuzzy reƒexive approximation spaces and fuzzy pretopological spaces.

Demonstration and Proof of a Uni€e Property of Mersenne Primes (B2) Pranav Narayan Sharma Delhi Public School, Ahmedabad, INDIA [email protected]

Till date, as many as more than 50 Mersenne primes, have been discovered using GIMPS. A Mersenne prime holds unique properties which can be used in computational processing. ‘ere is only one Mersenne prime that ends with unit digit three and rest of them end with either one or seven. ‘is paper presents the unique property exhibited by Mersenne Primes using cyclicity which can be extended to double Mersenne Primes.

Data Encryption to Decryption by Using Laplace Transform (B3) B. Ramu Naidua, K.P.R. Sastryb, D.M.K. Kiranc aFaculty of Mathematics, AU PG Campus, Vizianagaram, Andhra Pradesh, India. bGVP College of Engineering (Autonomous), Visakhapatnam, Andhra Pradesh, India. cDepartment of Mathematics, Vizag Institute of Technology, Visakhapatnam, Andhra Pradesh, India. [email protected], [email protected],[email protected]

In this paper, we introduce an encryption and decryption procedure with high security by mathematical model, using Laplace transformation and Inverse Laplace Transformation for the given transforming data from one end to other end. We also give an example. Here we convert plain text to ASCII code.We take two primes as a primary key for encryption and decrypt in of the original data.

Principal Ideal in Regular Rings (B4) Anupam Rachna B.N. Mandal University Madhepura [email protected]

In this paper we have study the impact of Von-Neumann regularity of a ring on some of the other concept in a ring. ‘e impact is most pronounced in case of ideals. For rings in general, the collection of principal right ideals need not form a la‹ice, let alone a complemented la‹ice and so Von-Neumann was led to the class of regular rings, which may be described as those rings in which the collection of principal right ideals form a la‹ice under the obvious la‹ice operations. Von-Neumann showed that in a regular ring, the sum and the intersection of €nitely many principal right ideals are also principal right ideals. ‘us in any regular ring, the collection of principal right ideals forms a complemented modular la‹ice.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 48 VIT-Vellore

(B5) Notation on Rough Fuzzy Ideals in G−rings and its Properties P. Durgadevi, Ezhilmaran Devarasan Department of Mathematics School of Advanced Sciences Vellore Institute of Technology, Vellore. India. [email protected], [email protected]

Rough set theory plot a new mathematical approach to inadequate understanding. In this approach ambiguity is expressed by a boundary region of the set. Rough set concept can be de€ned by means of algebraic operator union and intersection called approximations. In this article, we de€ne the notion of rough fuzzy ideals in G−rings and proved some of its properties.

(B6) Cubic Magnified Translation on β−Subalgebras P. Muralikrishnaa, R. Vinodkumarb, G. Palanic aPG and Research Department of Mathematics, Muthurangam Government Arts College (Autonomus),Vellore-632002. India bDepartment of Mathematics, Prathyusha Engineering College, ‘iruvallur-602025. India cDepartment of Mathematics, Dr. Ambedkar Government Arts College, Chennai-600 039. India [email protected]

‘e theory of fuzzy sets introduced by Zadeh which has immense range of applications in various branches of mathematics. Jun et al. proposed a new concept called cubic sets which is applied into several algebraic structures like BF,KU & β-algebras and so on. In this article, the notion of cubic magni€ed translation on β−subalgebra is introduced and veri€ed some results of cubic β-subalgebra using the idea of cubic magni€ed translation(CMT). Also, the characteristics of cubic magni€ed translation on β−subalgebra is studied based on the fundamental operations like union and intersection.

(B7) Structure of MBJ - Neutrosophic Set applied on β-Filter Prakasam Muralikrishna, Surya Manokaran PG & Research Departement of Mathematics, Muthurangam Govt. Arts College, Vellore, TN, India. [email protected]

In 1965, Zadeh introduced Fuzzy Set and researchers developed the fuzzy sets to many kinds of fuzzy sets like intuitionistic, interval valued fuzzy set and many. And Smarandache came up with the concept of Neutro- sophic set is welcomed by the current researchers and many research work are explored using Neutrosophic Set. In recent days the study of MBJ-Neutrosophic set is investigated and is merged with some algebraic structures like BCK/BCI and β-algebra. ‘e notion of €lters was introduced by Henri Cartan in 1937. In 1991, C. S. Hoo introduced the concept of the €lters in BCI-algebras. Also in 2013, A. Rezaei and A. Bourmand intro- duced the notion of geberalized fuzzy €lters of BE-algebras. In this paper, the structure of MBJ-Neutrosophic β-subalgebra is considered and is cultivated to MBJ-Neutrosophic β-€lter. Several results such as image, preimage and levels on €lters are discussed.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 49 VIT-Vellore

A Fast Prime-Factorization of Large Integers and Its Applications to (B8) Affine Ciphers Blankson Henrya,b, Cha‹amvalli Rajana aDepartment of Mathematics, Vellore Institute of Technology, Vellore, Tamil Nadu, India bStatistics, Mathematics and Computer Studies Department, Cape Coast Technical University, Cape Coast, Ghana [email protected]

‘is paper seeks to provide an alternative and fast prime-factorization algorithm for large integers. We also considered the decryption operation in a given Ane Cipher with a modulus (m). We also assumed that the gcd (A, m) = 1. To decrypt any cipher text, we need to solve the congruence Y ≡ AX + B(mod m) for x. ‘e encryption function is of the form Y = Ek(X) = (AX + B)(mod m), where A, B ∈ Zm. −1 Consequently, the decryption function will also be of the form X = Dk(Y ) = D (Y –B)(mod m). Since gcd (A, m) = 1, A has a multiplicative inverse modulo m. It was established that the congruence will have a unique solution but it does not give us an ecient and fast method of €nding the solution. We will therefore require an ecient algorithm to do this. Furthermore, a modular arithmetic and a fast prime-factorization of large integers provided us with the ecient decryption algorithm that we seek. ‘is paper considered the application of fast prime-factorization of large integers and how to apply them to Ane Ciphers.

The G-vetex Colour Partition Algebra as a Centralizer Algebra of (B9) An × G A. Joseph Kennedy, P. Sundaresan Department of Mathematics, Ramanujan School of Mathematical Sciences, Pondicherry University, Puducherry - 605 014, India

We are going to restrict the generalized Jones result in [PK] which says that the G-vertex colored partition Pk(n, G) is the centralizer algebra of an action of the direct product of symmetric group and G Sn × G on tensor products of its permutation representation to the action of the direct product of alternating group and G An ×G. Herein, we determine a basis for the centralizer algebra and exhibit at the moment the centralizer is isomorphic to the G-Colored partition algebra. Also we do the same for Extended G-vertex colored partition algebras Pˆk(n, G).

Commutativity of Prime Rings with Symmetric Biderivations Satisfying (B10) Certain Relations C. Jaya Subba Reddya, Ramoorthy Reddyb aDepartment of Mathematics, S V University, Tirupati, India bS V Engineering College, Tirupati, India [email protected]

For any prime ring R,U be a nonzero ideal of R and B1(., .): R × R → R be a symmetric biderivation of R. In the current paper, it was showed that R is commutative if and only if it satis€es one of the following properties (i) B1(uv, w) − uv ∈ Z(R), (ii) B1(uv, w) + uv ∈ Z(R), (iii) B1(uv, w) − vu ∈ Z(R), (iv) B1(uv, w) + vu ∈ Z(R), (v) B1(u, v)D(v, w) − uw ∈ Z(R), and (vi) B1(u, v)D(v, w) + uw ∈ Z(R), for any u, v, w ∈ U.

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(B11) Some Results on the Density of Integral Sets with Missing Differences Neha Rai, Ram Krishna Pandey Department of Mathematics, Indian Institute of Technology Roorkee, India [email protected]

Let M be a set of positive integers. Motzkin posed the problem of €nding the maximal density µ(M) of the sets S of nonnegative integers in which no two elements of S are allowed to di‚er by an element of M. In 1973, Cantor and Gordon €nd µ(M) for |M| ≤ 2. Until now, there is no known general formula for µ(M) in the case |M| ≥ 3. Several partial results are known in the case |M| ≥ 3 including some results in the case when M is an in€nite set. Motivated by the earlier families M = {a, b, a + b} and M = {a, b, a + b, b − a} taken by Liu and Zhu (J. Graph ‘eory 47(2) (2004), 129-146), we study the maximal density problem for the families M = {a, b, b − a, n(a + b)} and M = {a, b, a + b, n(b − a)}. For both these families, we €nd some exact values and some bounds on µ(M). We also see the connection of parameter κ(M) with µ(M). ‘is number theory problem is also related to various chromatic number problems of the distance graphs generated by M in graph theory.

(B12) Matrices over Non-commutative Rings as Sums of Fourth Powers Deepa Krishnamurthi St Mira’s College for Girl’s , Pune [email protected]

Let R be a noncommutative ring with unity and n ≥ 2 . In this paper we prove that an n × n matrix A over R is a sum of fourth powers if and only if trace(A) is a sum of fourth powers and 2(sum of squares) and commutators modulo 4R. ‘is extends the results of S. A. Katre, Anuradha Garge in the case of commutative rings.

(B13) Connecting Monomiality estions with the Structure of Rational Group Algebras Gurmeet K. Bakshia, Gurleen Kaurb aCentre for Advanced Study in Mathematics,Panjab University, Chandigarh, India bDepartment of Mathematics, Sri Guru Gobind Singh College, Chandigarh 160019, India [email protected]

In recent times, there has been a lot of active research on monomial groups in two di‚erent directions. While group theorists are interested in the study of their normal subgroups and Hall subgroups, the interest of group ring theorists lie in the structure of their rational group algebras due to varied applications. Revisiting Dade’s celebrated embedding theorem which states that a €nite solvable group can be embedded inside some monomial group, it is proved here that the embedding is indeed done inside some generalized strongly mono- mial group. Still unresolved monomiality questions have been correlated by proving that all the classes of monomial groups where they have been answered are generalized strongly monomial. ‘e study also raises some intriguing questions weaker than those asked by Dornho‚ and Isaacs in their investigations.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 51 VIT-Vellore

asi Factorable Incidence Functions (B14) L. Madhavia, Y. Rajasekhara Gowdb aDepartment of Applied Mathematics Yogi Vemana University, Kadapa -516005 bDepartment of H & B S G. Pulla Reddy Engineering College, Kurnool - 518007 [email protected]

‘e study of multiplicative and completely multiplicative arithmetic functions constitutes an important branch of Number ‘eory. Weisner and Ward have studied arithmetical functions from La‹ice ‘eoretic point of view by generalizing the notion of an arithmetical function to that of an incidence function of a locally €- nite partially ordered set. D.A. Smith and H. Schield introduced the notion of factorable incidence function corresponding to multiplicative arithmetic function and studied the properties of factorable functions analo- gous to the well-known properties of multiplicative functions in Number ‘eory. Recently the authors have introduced the notion of completely factorable incidence function analogous to the notion of completely mul- tiplicative arithmetic function and obtained certain conditions under which a factorable incidence function is completely factorable.

D. B. Lahiri introduced the notion of quasi-multiplicative arithmetical function and studied the conditions under which a multiplicative arithmetic function is quasi-multiplicative. Haukkanen also studied quasi- multiplicative arithmetical functions of n-variables as well as quasi A-multiplicative functions of one variable. One can also €nd a discussion of quasi-multiplicative functions in Chapter XI of “Classical ‘eory of Arith- metical Functions”.

In this paper we introduce the concept of quasi-factorable incidence function of a locally €nite partially ordered set analogous to quasi-multiplicative arithmetical function and obtain conditions under which a factorable incidence function is quasi-factorable.

Commutarias and Commutator Subgroup of finite p-groups (B15) Rahul Kaushik, Manoj K. Yadhav Harish-Chandra Research Institute, Prayagraj [email protected]

Let G be a €nite group with γ2(G) its commutator subgroup and K(G) := {[x, y]|x, y ∈ G}. ‘e problem whether γ2(G) is equal to K(G) or not for a group G has been investigated for various classes of €nite groups. It was proved that if γ2(G) is an Abelian p-group, p > 3, generated by atmost 3 elements, then K(G) = γ2(G). Recently this result has been proved for €nite p-groups, by relaxing the condition of commutativity of γ2(G), i.e., if G is a €nite p-group, p > 3, and γ2(G) is generated by at most 3 elements, then K(G) = γ2(G). But such a result is not true in general for all €nite p-groups G such that γ2(G) is minimally generated by 4 more that 3 elements. In this paper I will present a classi€cation of €nite p-groups G with γ2(G) of order p and exponent p such that each element of γ2(G) is a commutator.

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Section C: Real and Complex Analysis (including Special Functions, Summability and Transforms etc) and Teaching of Mathematics

(C1) On Subclasses of Univalent Functions Defined By Opoola Differential Operator A.N. Metkaria, N.D. Sangleb, S.P. Handec aDepartment of Mathematics, Visvesvaraya Technological University, Belagavi, Karnataka-590018, India bDepartment of Mathematics, Annasaheb Dange College of Engineering and Technology, Ashta, Maharashtra-416301, India cDepartment of Mathematics, Vishwanathrao Deshpande Institute of Technology, Haliyal, Karnataka-581329, India [email protected]

‘e subclass AR (n, ρ, σ, δ, γ, µ, η) of the univalent functions with negative coecients determined by the di‚erential operator Opoola Dn has been introduced in this paper. Sharp results for coecient estimates have been obtained, Hadamard product, Bounds of closure, Bounds of distortion and some other results.

(C2) On Multiplication and Division Theorems of Entire Algebroidal Functions of their Relative Growth Indicators of Higher Index in the Light of p-adic Analysis Sanjib Kumar Da‹aa, Aditi Biswasb aProfessor, Department of Mathematics, University of Kalyani P.O. Kalyani, Nadia -741235, West Bengal, India. bAssistant Professor,Department of Mathematics, Fakir Chand College, Diamond Harbour, Diamond Harbour, South 24 Parganas-743331, West Bengal,India. sanjibda‹[email protected] ,[email protected]

Several ways of estimating of comparative growth analysis of entire algebroidal functions of their di‚erent kind of higher order relative growth indicators in the light of p-adic analysis, where p being a prime inte- ger have been elaborately studied in this paper. Some examples are provided in order to justify the results obtained here.

(C3) Bounds for Probability of the Genaralized Distribution for Certain q-starlike and q-convex Error Functions Related to Shall-Shaped Region K. Saritha, K. ‘ilagavathi School of Advanced Sciences,Vellore Institute of Technology,Vellore-632014, India. [email protected],[email protected]

‘e error function occurs widely in multiple areas of mathematics, mathematical physics and natural sciences. In this paper , using the concept of subordination and notion of q-operators, we de€ned a new subclass of q-di‚erence operator for certain classes of the Spirallike Starlike and Convex error function . Also we estimate, ‘e Fekete-Szeg¨o and Hankel determinant results associated with Shell-Shaped function for the new function.

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Boas Transform of Wavelets and their Applications (C4) Leena Kathuriaa, Nikhil Khannab aDepartment of Mathematics, Amity Institute of Applied Sciences, Amity University, Sector 125, Noida - 201313 (U.P.), India. bDepartment of Mathematics, Motilal Nehru College, University of Delhi, Delhi - 110021, India. [email protected] In 1936, Boas introduced an integral transform associated to the Hilbert transform which emerged due to the study of the class of functions having Fourier transform which vanishes on a €nite interval. Later, in 1960, Goldberg studied this transform in detail and gave some signi€cant results and properties. ‘is transform was known by Boas transform. In this talk, we introduce the notion of Boas transform of wavelets and give its applications in the form of Boas transform wavelet convolution and cross-correlation theorems to analyze Boas transform of convolved (cross-correlated) signals. Analogously to Bedrosian theorem, Boas transform product theorem is also given.

On Configurations of Five Periodic Herman Rings (C5) Gorachand Chakraborty Department of Mathematics, Sidho-Kanho-Birsha University Purulia, West Bengal, Pin-723104 [email protected] In this paper, we have studied the con€gurations of Herman rings for a special class M0 of meromorphic functions having at least one omi‹ed value. We have shown that possible number of con€gurations of a 5-periodic Herman rings of function in M0 is six. Also we have investigated that the number of 5-cycles of Herman rings of the function is at most one. We have given a result about the non-existence of a 3-periodic Herman rings and a 5-periodic Herman rings simultaneously. Few examples of transcendental meromorphic functions which do not have any Herman rings are discussed. Finally, we end up with the conclusion section which may spark new problems for future research interest.

Convolution Conditions for New Subclass of Negative Analytic (C6) Functions Associated with Polylogarithm Functions Defined by Linear Differential Operator M. ‘irucheran, C. Selvi Post Graduate and Research Department of Mathematics, L N Government College, Ponneri, Chennai - 624 302, University of Madras, Tamil Nadu, INDIA. [email protected]

n In this paper, we introduce and study some properties for the new subclass Tβ,γ,δ,b (a) of polylogarithm n P∞ function which is associated with the convolution of di‚erential operator Lλ,δf(ξ) = ξ − k=2[1 + (k − n 1+c P k 1)δ] k+c λ akξ Also, we obtain coecient inequalities, growth and distortion, partial sums and integral operator.

Obtain Subclass of Multivalant Function Connected with Convalution (C7) of Polylogarithm Functions M. ‘irucheran, A. Anand Post Graduate and Research Department of Mathematics, L N Government College, Ponneri, Chennai - 624 302, University of Madras, Tamil Nadu, INDIA. [email protected] n,p In this present work, we investigate some properties for the subclass Pβ,λ,δ,b(φ(z)) of analytic function related n,p with the linear di‚erential operator Rλ,δ f(z) de€ned by polylogarithm functions . And also, we obtain coecient inequalities, extreme points, radii of convexity and starlikeness, growth and distortion bounds for n,p the subclass Pβ,λ,δ,b(φ(z)).

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(C8) On Extension of Mittag-Leffler Function Sunil Joshi Department of Mathematics & Statistics, Manipal University Jaipur, Jaipur, India drsuneeljoshi@redi‚mail.com, [email protected]

In this paper, we study the extended Mi‹ag-Le„er function by using generalized beta function and obtain various di‚erential properties, integral representations. Further we discuss Mellin transform of these func- tions in terms of generalized Wright hypergeometric function and evaluate Laplace transform, Whi‹aker transform in terms of extended beta function. Finally, several interesting special cases of extended Mi‹ag- Le„er functions have also be given.

(C9) A Note on the Convergence of Wavelet Fourier Series Varsha Karanjgaokara, Namrata Shrivastavb aDepartment of Mathematics, Govt. N.P.G.College of Science, Raipur bDepartment of Mathematics, Govt. Kavyopadhyay Hiralal College, Abhanpur, Raipur [email protected], [email protected]

In this paper we discuss the rate of convergence of Wavelet Fourier series of periodic functions. Our result generalizes the results of Skopina,M.(Localization Principle for wavelet expansion, Self seminar systems, Dubna,(1999), 125-133) and Karanjgaokar,V.et al(communicated).

(C10) A New Subclass of Negative Multivalent Functions Involving Polylogarithm Functions M. ‘irucheran, M. Vinoth Kumar Post Graduate and Research Department of Mathematics, L N Government College, Ponneri, Chennai - 624 302, University of Madras, Tamil Nadu, INDIA. [email protected]

n,p In this current work, we introduce and study some properties for the new subclass Nβ,γ,δ,b(φ(ξ)) of polyloga- n,p rithms functions associated with the di‚erential operator Dλ,δ f(ξ). Also, we obtained coecient inequalities, integralmeans of inequalities, extreme points and distortion of the class.

(C11) On the Study of Deficiencies of Differential E€ation under the Flavour of p-adic Co-prime Polynomial Sanjib Kumar Da‹aa, Ashima Bandyopadhyayb aDepartment of Mathematics, University of Kalyani P.O.: Kalyani, Dist: Nadia, Pin: 741235, West Bengal, India. bRanaghat Brojobala Girls High School (H.S.) P.O.: Ranaghat, Dist.:Nadia, Pin: 741201, West Bengal, India [email protected]

Let K be an algebrically closed €eld of charecteristic 0, complete with respect to a p-adic absolute value and A (K) represents the K-algebra of analytic functions in K i.e, the set of power series with an in€nite radius of convergence. In this paper,we will give a brief outline on co-prime polynomial of p-adic meromorphic functions. Also we wish to investigate some properties of de€ciencies of p-adic di‚erential equation. We also discuss here about holomorphic curve in the same line. A few examples are given here to justify the result obtained.

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Few Results on Relative (k, n) Valiron Defact from the View Point of (C12) Intagrated Modult of Logarathamic Derivative of Entire and Meromorpic Functions Sanjib Kumar Da‹aa, Sukalyan Sarkarb, Ashima Bandyopadhyayc, Lakshmi Biswasd aDepartment of Mathematics, University of Kalyani P.O.: Kalyani, Dist.: Nadia, PIN: 741235, West Bengal, India bDepartment of Mathematics, Dukhulal Nibaran Chandra College P.O.: Aurangabad, Dist.: Murshidabad, Pin: 742201, West Bengal, India cRanaghat Brojobala Girls High School (H.S) P.O.: Ranaghat, Dist.: Nadia, Pin: 741201, West Bengal, India dKalinarayanpur Adarsha Vidyalaya P.O.: Kalinarayanpur, Dist.: Nadia, Pin: 741254, West Bengal, India [email protected] Xiong (1967) has shown various relations between the usual defects and the relative defects. Singh (1984) introduced the term relative defect for distinct zeros and poles and established various relations between it. (k) (k) ‘e relative (k, n) Nevanlinna defect Rδ(n)(α; f) and the relative (k, n) Valiron defect R∆(n)(α; f) of ‘α’ with respect to f (k) for k = 1, 2, 3, ...... and n = 0, 1, 2, 3, ..... are respectively de€ned as limit inferior of the ratio N r, α; f (k)
and T r, f (n)
as r → ∞ and limit superior of the ratio N r, α; f (k)
and T r, f (n)
as r → ∞ . ‘e prime target of this paper is to compare some relative (k, n) Nevanlinna defects with relative (k, n) Valiron defects from the view point of integrated moduli of logarithmic derivative of entire and meromorphic functions where k and n are any two non-negative integers.Some related examples are provided here in order to validate the result obtained.

Common Fixed Point Theorems for a Pair of Mappings in Bicomplex (C13) Valued Metric Spaces Sanjib Kumar Da‹aa, Dipankar Palb, Rakesh Sarkarc, Arghyatanu Mannad aDepartment of Mathematics, University of Kalyani, P.O.: Kalyani, Dist: Nadia, PIN-741235, West Bengal, India. bDepartment of Mathematics, Prof. Syed Nurul Hasan College, P.O.: Farakka Barrage, Dist: Murshidabad, PIN-742212, West Bengal, India. cDepartment of Mathematics, Gour Mahavidyalaya, P.O.: Mangalbari, Dist: Malda, PIN-732142, West Bengal, India dMousini Co-operative High School(H.S.), Bagdanga, Fraserganj Coastral, Kakdwip, South 24 Parganas, PIN-743357, West Bengal, India. [email protected] ‘e theory of bicomplex numbers is acknowledged as an area of active research for quite a long period of time in search of special algebra. ‘e concept of bicomplex numbers is widely used in the literature as it becomes a viable commutative alternative to the non-skew €eld of quaternions, both are four dimensional and generalizations of complex numbers. In this paper we de€ne the ‘max’ function for the partial order -i2 on a set of bicomplex numbers and study some common €xed point theorems for a pair of mappings satisfying a quasi-contraction condition in a bicomplex valued metric space. Some relevant examples are provided in support of our theorems. Our result is the generalization of the result obtained by Verma & Pathak (2013).

On g-Mellin Transform: Construction, Convexity and Applications (C14) Chandrani Basu, Pankaj Jain, Vivek Panwar Department of Mathematics, South Asian University, New Delhi, India [email protected] Integral transforms play an important part in solving many di‚erential and integral equations. Historically, in 1876, Riemann, €rst recognized the Mellin transform. In 1894, Mellin gave an elaborate discussion of the Mellin transform and its inversion formula. In the framework of g-calculus, the Mellin transform has been de€ned and studied. For the new g-Mellin transform, the appropriate convolution is de€ned and its connec- tion with the Hausdor‚ operator is pointed out. ‘e notion of pseudo-logarithmic convexity (concavity) has been introduced and it is proved that the g-Mellin transform is pseudo-logarithmically convex (concave) for a suitable pseudo-exponential function. ‘is leads to de€ning the g-gamma function. Finally, certain applica- tions of g-Mellin transform are provided, namely, solving integral equations and a Titchmarsh type theorem.

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(C15) Common Fixed Point Theorems for Three Self Mapping in Bicomplex Valued Metrix Spaces Sanjib Kumar Da‹aa, Rakesh Sarkarb, Nityagopal Biswasc, Jayanta Sahaa aDepartment of Mathematics, University of Kalyani, P.O.: Kalyani, Dist.: Nadia, Pin: 741235, West Bengal, India. bDepartment of Mathematics,Gour Mahavidyalaya, Mangalbari, Malda, West Bengal, India. cDepartment of Mathematics, Chakdaha College, Chakdaha, Nadia, West Bengal, India. [email protected]

During the last €‰y years, €xed point theories in complex valued metric spaces are emerging areas of works in the €eld of the complex as well as functional analysis. Banach’s €xed point theorem plays a major role in the €xed point theory. It has applications in many branches of mathematics. ‘e famous Banach’s theorem states that if (X, d) be a metric space and T be a mapping of X into itself satisfying d(T x, T y) ≤ kd(x, y), ∀x, y ∈ X, where k is a constant in (0, 1), then T has a unique €xed point x∗ ∈ X. In the paper we prove some common €xed point theorems for three self mappings in a bicomplex valued metric space. Our results generalize the literature due to Azam (2011) & S. K. Mahanta (2012) by using both the ideas of two weakly compatible mappings and rational contractions for a pair of mappings in bicomplex valued metric space.

(C16) Some Common Fixed Point Theorems in Bicomplex Valued Metric Spaces under both Rational type Contraction and Coupled Fixed Point Mappings Sanjib Kumar Da‹aa, Rakesh Sarkarb, Nityagopal Biswasc, Ashima Bandyopadhyayd aDepartment of Mathematics, University of Kalyani, P.O.: Kalyani, Dist.:Nadia, Pin:741235, West Bengal, India. bDepartment of Mathematics, Gour Mahavidyalaya, P.O.: Mangalbari, Malda, Pin: 732142, West Bengal, India. cDepartment of Mathematics, Chakdaha College, P.O.: Chakdaha, Nadia, Pin:741222, West Bengal, India. dRanaghat Brojobala Girls High School(H.S), Rabindra Saranii, P.O.: Ranaghati, Dist.: Nadia, Pin: 741201, West Bengal, India. [email protected]

During the past decades, enormous works by di‚erent researchers have been carried out in €xed point theory on metric spaces. ‘e theory of bicomplex numbers is also a ma‹er of active research for quite a long period of time in search of special algebra. ‘e algebra of bicomplex numbers are widely used in the literature as it becomes viable commutative alternative to the non-skew €eld of quaternions, both are four dimensional and generalizations of complex numbers. ‘e concept of the coupled €xed point was €rst introduced by Bhaskar & Laxikantham (2006). ‘e aim of this paper is to investigate some common €xed point theorems for a pair of mappings satisfying certain rational type contraction condition and having a unique common coupled €xed point in the framework of bicomplex valued metric spaces. Our results are the generalizations of existing literature of coupled €xed point theorems of Bha‹ et. al (2011) and Savitri & Hooda (2015). A few examples are provided to justify the results obtained and the course of future prospect of works as carried out is sketched in the paper.

(C17) A Study of Extended Beta function with its Applications Ekta Mi‹al Departement of Mathematics, IIS (Deemed to be University), Jaipur ekta.mi‹[email protected]

Present study is to provide a systematic analysis of new type of extended beta function and hypergeometric function using a conƒuent hypergeometric function to investigate di‚erent properties and formulas of this function such as integral representations, derivative formula, transformation formula, summation formula and much more. In addition, we also explore extended Riemann-Liouville fractional integral operator with associated properties.

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On the Location of Zeros of Transcendental Entire Functions (C18) Sanjib Kumar Da‹aa, Tanchar Mollab, Mukul SKa, Jayanta Sahaa aDepartment of Mathematics, University of Kalyani P.O.: Kalyani, Dist: Nadia, Pin: 741235, West Bengal, India. bDepartment of Mathematics, Dumkal College, P.O.: Basantapur,P.S: Dumkal, Dist.: Murshidabad, Pin: 742406, West Bengal, India. [email protected]

A function of one complex variable analytic in the €nite complex plane C is called an entire function and whenever it has an essential singularity at point at in€nity it will be transcendental. If a function f(z) is entire then it can be represented by an everywhere convergent power series like

n f (z) = a0 + a1z + ... + anz + ...

‘us the entire functions form natural generalization of polynomials.

‘e prime purpose of this paper is to derive zero free region for some transcendental entire functions of €nite order under various conditions using the coecients an’s. A few examples with related €gures are given here to justify the results obtained.

On the Generalization of Enstrom-Kakeya¨ Theorem for Entire (C19) Functions Sanjib Kumar Da‹aa, Tanchar Mollab, Mukul SKa, Tandra Sarkara aDepartment of Mathematics, University of Kalyani, P.O.: Kalyani, Dist: Nadia, Pin: 741235, West Bengal, India. bDepartment of Mathematics, Dumkal College, P.O.: Basantapur, P.S: Dumkal, Dist.:Murshidabad, Pin: 742406, West Bengal, India [email protected]

n P j ‘e classical Enstrom-Kakeya¨ theorem states that if P (z) = ajz is a polynomial of degree n with real j=0 coecients satisfying 0 ≤ a0 ≤ a1 ≤ ... ≤ an, then all the zeros of P (z) lie in the unit disk |z| ≤ 1 in the complex plane C. Many results on generalization of Enstrom-Kakeya¨ theorem by pu‹ing various conditions on the coecients of the polynomials exist. ‘e prime concern of this paper is to extend the classical Enstrom-¨ Kakeya theorem for entire functions of non zero €nite order having lacunary type power series expansion. A few examples with related €gures are given here to justify the results obtained.

Inclution Relation between Subclass of Pascu Type Harmonic Functions (C20) Based on Mittag-Lefflar Functions K. Vijaya, V. Malathi Department of Mathematics School of Advanced Sciences, Vellore Institute of Technology, Vellore. India [email protected], [email protected]

In this paper, we investigate an association between certain subclasses of harmonic univalent functions by applying certain convolution operator concerning generalized Mi‹ag-Le„er functions. To be more precise, we discuss such connections with PASCU-type harmonic univalent functions in the open unit disc D.

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(C21) Certain Subclass of Meromorphic Functions Associated with Bessel Function Santosh M. Popadea, Rajkumar N. Ingleb, P. ‘irupathi Reddyc aDepartment of Mathematics, Sant Tukaram College of Arts & Science, Parbhani - 431 401, Maharashtra, India. bDepartment of Mathematics, Bahirji Smarak Mahavidyalay, Basmathnagar - 431 512, Maharashtra, India. cDepartment of Mathematics, Kakatiya University, Warangal- 506 009, Telangana, India. [email protected]

In this paper, we introduce and study a new subclass of meromorphic univalent functions de€ned by Bessel function. We obtain coecient inequalities, extreme points, radius of starlikeness and convexity. Finally, we ∗ obtain partial sums and neighborhood properties for the class σp(η, κ, λ, ν, α, β)

(C22) On Relative Defects of Special type of Differential Polynomial in Connection with their Integrated Moduli of Logarithmic Derivative Sanjib Kumar Da‹aa, Sukalyan Sarkarb, Lakshmi Biswasc, Ashima Bandyopadhyayd aDepartment of Mathyematics, University of Kalyani P.O.: Kalyani, Dist: Nadia, Pin: 741235, West Bengal, India. bDepartment of Mathyematics, Dukhulal Nibaran Chandra College P.O.: Aurangabad, Dist: Murshidabad, Pin: 742201, West Bengal, India. cKalinarayanpur Adarsha Vidyalaya P.O.: Kalinarayanpur, Dist: Nadia, Pin: 741254, West Bengal, India. dRanaghat Brojobala Girls High School (H.S.) P.O.: Ranaghat, Dist: Nadia, Pin: 741201, West Bengal, India. [email protected]

‘e paper aims at the comparison between the relative Valiron defect and relative Nevanlinna defect of special type di‚erential polynomials from the view point of their integrated moduli of logarithmic derivative. Let f be a meromorphic function in the complex plane. We consider F = f nQ [f], Q[f] being a di‚erential polynomial in f with n = 1, 2, 3, ... and compare with the relative Valiron defect and relative Nevanlinna defect of F under the ƒavour of integrated moduli of logarithmic derivative. A few examples are provided here to validate the conclusion of the results obtained.

(C23) Bicomplexial Approch of Some Well Known Result In Complex Analysis Debasmita Du‹aa, Satavisha Deyb, Sukalyan Sarkarc, Sanjib Kumar Da‹ad aDepartment of Mathematics, Lady Brabourne College, P-1/2 Suhrawardy Avenue,Beniapukur, Dist. : Kolkata, PIN : 700017, West Bengal, India. bDepartment of Mathematics, Bijoy Krishna Girls’ College, M.G. Road,Dist. : Howrah, PIN : 711101,West Bengal, India. cDepartment of Mathematics, Dukhulal Nibaran Chandra College, P.O.: Aurangabad, Dist.: Murshidabad, PIN : 742201, West Bengal, India. dDepartment of Mathematics, University of Kalyani, P.O.: Kalyani, Dist.: Nadia, PIN :741235, West Bengal, India. [email protected]

In this paper, we explore the fundamental results of zeros and poles of a bicomplex valued function and relation between them. Moreover some well known results in complex analysis like Jenson’s Inequality as well as some results on univalent functions are proved here in the bicomplex context.

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Zalcman Conjecture and Hankel Determinant of Order Three for (C24) Reciprocal of Bounded Turning Functions and α-Convex Functions Associated with Exponential Function V. Suman Kumara, R.B. Sharmab aDepartment of Mathematics, TSMS Chigurumamidi, Karimnagar, Telangana, India. bDepartment of Mathematics, Kakatiya University, Warangal, Telangana, 506009, India. [email protected]

α In this work, we make an a‹empt to introduce two new subclasses denoted by Me and RTde which are analytic. ‘e purpose of this investigation is to determine an upper bound of H3(1) | for the functions f in these classes associated with Exponential Function. Similar outputs are obtained for the rational function and the inverse function of f.

On a Common Fixed Point Theorem in Bicomplex Valued b-metric Space (C25) Sanjib Kumar Da‹aa, Dipankar Palb, Rakesh Sarkarc, Arghyatanu Mannad aDepartment of Mathematics, University of Kalyani, P.O.: Kalyani, Dist: Nadia, PIN-741235, West Bengal, India. bDepartment of Mathematics, Prof. Syed Nurul Hasan College, P.O.: Farakka Barrage, Dist: Murshidabad, PIN-742212, West Bengal, India. cDepartment of Mathematics, Gour Mahavidyalaya, P.O.: Mangalbari, Dist: Malda, PIN-732142, West Bengal, India dMousini Co-operative High School(H.S.), Bagdanga, Fraserganj Coastral, Kakdwip, South 24 Parganas, PIN-743357. [email protected]

Segre’s introduction of bicomplex numbers has stimulated the conceptualization of the bicomplex valued metric space by the subsequent mathematicians. ‘e study of €xed point theorems within the framework of bicomplex valued metric spaces can unfold an area of research endowed with in€nite scope of growth. ‘is paper can be regarded as a humble e‚ort towards the exploration of that scope. Rao et al. (2013) de€ned the complex valued b-metric space. ‘is provided the opportunity to formulate the concept of bicomplex valued b-metric space by the researchers like Da‹a et al. (2020). ‘e main purpose of this paper is to investigate a common €xed point theorem in bicomplex valued b -metric space satisfying some rational inequalities for two pairs of weakly compatible self contracting mappings. Our result is the generalisation of the €ndings of Mitra (2015).

Some Exceptional Value Theorems of Entire Functions Under the (C26) Treatment of Bicomplex Analysis Satavisha Deya, Debasmita Du‹ab, Surajit Hazrac, Sanjib Kumar Da‹ad aDepartment of Mathematics, Bijoy Krishna Girls’ College, M.G. Road, Howrah-711101, West Bengal, India. bDepartment of Mathematics Lady Brabourne College, Kolkata-700017, West Bengal, India. cDepartment of Mathematics Ananda Mohan College, 102/1, Raja Rammohan Sarani, Kolkata-700009, West Bengal, India dDepartment of Mathematics University of Kalyani, P.O.: Kalyani, Dist: Nadia, PIN-741235, West Bengal, India. [email protected]

‘e study of exceptional values of entire functions was started with the famous theorem of Picard, one of the most important theorems of complex analysis. ‘e exceptional values may be de€ned in many sense. Picard’s theorem admits the possibility of having an exceptional value in case of an entire function like as 0 for exp z. ‘e value with this property is called Exceptional-P. ‘ere is another sense in which the value may be exceptional. An entire function may take the value a only at the points which have exponent of convergence less than the order of the function. ‘e value with this property is called Exceptional-B, i.e., in the sense of Borel. In this paper our aim is to derive a few exceptional value theorems of entire functions such as Scho‹ky’s theorem, Li‹le Picard’s theorem, Landau’s theorem etc. under the ƒavour of bicomplex analysis. Some examples are given here to validate the results obtained.

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(C27) Fractional Fourier transforms with the Flip Operator Syed Papia Nawaz, V.R. Lakshmi Gorty SVKM’s NMIMS University, MPSTME Vile Parle (W), Mumbai - 400 056. Maharashtra, India [email protected] In this paper, a modi€ed Fourier transform known as fractional Fourier transform is introduced. Di‚erent properties of the transform including shi‰ing properties and derivatives are studied in this work. Fractional Fourier transform is demonstrated with some examples. Relations with ƒip operators of Fractional Fourier transform have also been studied in this context.

(C28) Starlike Functions Associated with the Parabolic Region in the Right Half Plane Sushil Kumar Bharati Vidyapeeth’s College of Engineering, Delhi–110063, India [email protected] In this note, we consider the class of parabolic starlike functions de€ned on the open unit disk, introduced by F. Rønning. ‘ese functions are closely associated with the parabolic region in the right plane that is given by Ω = {w ∈ C : |w − 1| < <(w)}. We determine sharp estimate on Hermitian–Toeplitz determinant of third order and a bound on third order Hankel determinants for parabolic starlike functions. In addition, parabolic starlikenees radius estimate and subordination result for various functions with positive real parts are also examined.

(C29) Certain Subclass of Analytic Function with Negative Coefficients Defined by Catas Operator G.M. Birajdara, N.D. Sangleb aDepartment of Mathematics, Shivaji University, Kolhapur (M.S) India bDepartment of Mathematics, Annasaheb Dange College of Engineering & Technology, Sangli, (M.S.) India [email protected] In this paper, we investigate subclass of analytic function with negative coecient de€ned by Catas operator in the unit disc U = {z ∈ C : |z| < 1}. ‘e results included coecient estimates, closure theorem and distortion theorems of several functions belonging to this subclass. Also, we presented detailed study of uniformly convex and uniformly starlike functions..

(C30) Analytic Functions of Complex Order Involving Hadamard Product Lateef Ahmad WANI, Anbhu Swaminathan Department of Mathematics, Indian Institute of Technology, Roorkee, U‹arakhand, India [email protected]; [email protected]

Let k ≥ 0, α ∈ [0, 1), γ ∈ [0, 1] and b ∈ C \{0}. We use Hadamard product to introduce a novel function class TUMγ (g, b, k, α) consisting of normalized analytic functions f(z) with negative coecients satisfying the inequality

  0 2 00  0 2 00 1 zΦ (z) + γz Φ (z) k zΦ (z) + γz Φ (z) Re (1 − α) + − 1 > − 1 , b (1 − γ)Φ(z) + γzΦ0(z) |b| (1 − γ)Φ(z) + γzΦ0(z)

where Φ(z) = (f ∗ g)(z) for some analytic function g(z). In this paper, we solve certain coecient and radii problems, and the Silverman’s conjecture related to TUMγ (g, b, k, α). It is also shown that the class is invariant under certain well-known integral operators. Furthermore, some previously known results are obtained as special cases.

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Growth Properties of Solutions of Linear Difference E€ations with (C31) Coefficients Having Finite Logarithmic Order Nityagopal Biswas Assistant Professor, Department of Mathematics, Chakdaha College Chakdaha, Nadia, Pin: 741222, West Bengal, India. [email protected]

In this paper, we investigate the relations between the growth of entire coecients and that of solutions of complex homogeneous and non-homogeneous linear di‚erence equations with entire coecients of €nite logarithmic order by using a slow growth scale, the logarithmic order. We extend some precedent results due to Zheng and Tu (2011) (X.M. Zheng and J. Tu, Growth of meromorphic solutions of linear di‚erence equations, J. Math. Anal. Appl. 384(2011), pp. 349 − 356.) and others.

Implications of Baker Omitted Value (C32) Subhasis Ghora, Tarakanta Nayak School of Basic Sciences, IIT Bhubaneswar, Bhubaneswar, India. [email protected], [email protected]

For a transcendental meromorphic map f : C → Cb with only one essential singularity at ∞, the set of n ∞ points z ∈ Cb for which {f (z)}n=0 is de€ned and normal is called the Fatou set of f. ‘e Julia set is the complement of the Fatou set. A maximal connected subset of the Fatou set is called a Fatou component. A −1 Fatou component U is called completely invariant if f(U), f (U) ⊆ U. A value z0 ∈ Cb is called an omiˆed value of f if f(z) 6= z0 for any z ∈ C. An omi‹ed value is called a Baker omi‹ed value (bov) if each boundary component of the pre-image of every open ball containing the omi‹ed value is bounded. It is called stable if it is in the Fatou set. It is known that the bov (if exists) is the only asymptotic value also for a function with the stable bov, there is only one unbounded Fatou component which is in€nitely connected and all other Fatou components are bounded. Certain dynamical issues of meromorphic maps with the stable bov are investigated. It is shown that the bov is always a limit point of the critical values and if the bov of a function is contained in an invariant Fatou component, then the Fatou component must be completely invariant. ‘e non-existence of Baker domain of a function with the stable bov and non-existence of invariant Baker domain of a function with non-stable bov are evinced.

Existance of Entire Solutions of Difference E€ations (C33) Renukadevi Sangappa Dyavanal Department of Mathematics, Karnatak University - Dharwad, India [email protected]

‘e main objective of this paper is to investigate the problem of existence of transcendental entire solution of a di‚erence equation generated by general di‚erence polynomial of a transcendental entire function of €nite order.

Fractional Wavelet Transform in Rn (C34) Bivek Gupta, Amit K. Verma Department of Mathematics, Indian Institute of Technology Patna, Bihta, India [email protected]

In this paper, we study continuous fractional wavelet transform (CFrWT) in Rn with scaling parameter a = n (a1, a2, . . . , an) ∈ R . We derive some of its basic properties like inner product relation and inversion formula. We also characterize the range of the transform. Moreover, we also study the boundedness and the approximation property of the transform in Morrey space.

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(C35) A note on the bicomplex version of Enstrom-Kakeya¨ theorem Sanjib Kumar Da‹aa, Tanchar Mollab, Mukul Ska, Jayanta Sahaa Department of Mathematics, University of Kalyani, P.O.:Kalyani, Dist.:Nadia, Pin:741235 West Bengal, India Department of Mathematics, Dumkal College, P.O: Basantapur, P.S: Dumkal, Dist.: Murshidabad Pin: 742406, West Bengal, India [email protected]

Fundamental theorem of algebra only gives information about the number of zeros of a polynomial but not location of the zeros. All zeros of a quadratic polynomial can be derived algebraically for all possible values of its coecients. But diculty arises when degree of polynomial increases. So, it is desirable to know a region where the zeros of a polynomial lie. Classical Enstrom-Kakeya¨ theorem is a result in this direction which Pn j says that if P (z) = j=0 ajz is a polynomial of degree n with non negative real coecients satisfying non decreasing relation, then all the zeros of P (z) lie in the unit disc contained in the €nite complex plane. Bicomplex algebra is the generalization of the €eld of complex numbers. Like complex entire function, a bicomplex entire function f(z) is also represented by an everywhere convergent power series as f(z) = P∞ j j=0 αjz , where αj’s and z are bicomplex numbers. ‘us, bicomplex entire functions are the natural generalization of bicomplex polynomials. ‘e prime concern of this paper is to revisit the Enstrom-Kakeya¨ theorem with some of its consequences under the ƒavor of bicomplex analysis. Some examples with related €gures are given here to validate the results obtained.

(C36) Ine€alities for the Maclaurin’s coefficients of spiralike functions involving q-differential operator K. Amarender Reddy, G. Murugusundaramoorthy, K.R. Karthikeyan Department of Mathematics, VIT University, Vellore [email protected]

‘e main purpose of this paper is to unify, extend and discretize several results related to spiralike and strongly spiralike functions. We achieve this purpose by making use of q-analogue of the well-known di‚er- ential operator. We provide a formal extension of a bi-univalent spiralike and bi-univalent strongly spiralike functions. We obtain the inequalities for the Maclaurin’s coecients of the functions belonging to the de€ned subclasses.

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Section D: Functional Analysis, Measure ‡eory, Probability ‡eory and Stochastic Processes, and Information ‡eory

A generalization of the density zero ideal (D1) Sumit Som Department of Mathematics, National Institute of Technology Durgapur, India. [email protected]

Let F = (Fn) be a sequence of nonempty €nite subsets of ω such that limn |Fn| = ∞ and de€ne the ideal

I(F ) := {A ⊆ ω : |A ∩ Fn|/|Fn| → 0 as n → ∞} .

‘e case Fn = {1, . . . , n} corresponds to the classical case of density zero ideal. We show that I(F ) is an analytic P-ideal but not Fσ. As a consequence, we show that the set of real bounded sequences which are I(F )-convergent to 0 is not complemented in `∞.

A note on Toeplitz, Hankel and Composition operators on the Bergman (D2) space Pabitra Kumar Jena P G Department of Mathematics, Berhampur University, Bhanja Bihar, Berhampur-760007, Ganjam, Odisha, India [email protected]

In this article, we characterize the sucient conditions for Toeplitz and Hankel operators de€ned on the Bergman space to be unitary and mean of unitaries. Further, unitariness of Composition operators on the Bergman space are also studied.

Analysis of Retrial eueing System with Two Way Communication, (D3) Working Breakdown and Collision G. Ayyappana, B. Somasundaramb, G. Archanaa, S. Sankeethac aDepartment of Mathematics, Pondicherry Engineering College, Puducherry, India bDepartment of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R & D Institution of Science and Technology, Tamilnadu, India cDepartment of Mathematics, Saradha Gangadharan College, Puducherry, India [email protected]

‘is paper consider two way communication retrial queueing system with working breakdown and collision. Arriving primary incoming calls send to orbit while the server is busy. A retrial incoming calls on arrival, enter for service, if the server is found to be idle and may collide the service, if the server is busy. ‘e outgoing calls made by the server when it is idle. ‘e incoming calls is consider as a high priority call and an outgoing call is consider as a low priority call. ‘e system may become defective when it is in regular service. A‰er ge‹ing breakdown, instead of stopping service, the server will continue the service at a slower rate. ‘e incoming calls arrive to the system according to Markovian arrival process(MAP), outgoing call and service time follow phase type (PH) distribution. ‘e resulting QBD process is investigated in the steady state by using matrix-analytic method. Some of the performance measures are computed. Finally, numerical and graphical results are presented.

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(D4) Simulation of Markov Chain Monte Carlo Method for Analysis of Sunspot Cycles Shikhar Chandra School of Electronics (SENSE), VIT University, Vellore, India [email protected]

Monte Carlo methods have been in application in various €elds such as €nance modelling, weather fore- casting, chemical kinetics and nanotechnology. ‘e method uses random sampling on a probability distri- bution a‰er constructing a random process for a problem. ‘is paper covers a speci€c technique of Monte Carlo method called the Markov Chain Monte Carlo (MCMC) technique. We use particularly, the Metropolis- Hastings algorithm for the implementation of this technique. ‘e technique is further used to simulate prob- ability distribution of time series solar activity in order to €nd recurring pa‹erns and correlations in sunspot cycles. ‘e data used for simulation is the “Monthly mean total sunspot number”, for each month from Jan- uary 1749 to November 2018, publicly available by ‘World Data Center for the production, preservation and dissemination of the international sunspot number’. ‘rough simulations performed using Python program- ming, we €nd that the Markov Chain Monte Carlo technique provides a statistically accurate probability distribution model for the sunspot cycles data.

(D5) Iterative approximation of common fixed points with simulation results in Banach spaces Ashis Beraa, Ankush Chandab, Lakshmi Kanta Deya aDepartment of Mathematics, National Institute of Technology Durgapur, India bDepartment of Mathematics, Vellore Institute of Technology, Vellore, India [email protected]

In this article, we propose the Abbas-Nazir three step iteration scheme and employ the algorithm to study the common €xed points of a pair of generalized α-Reich-Suzuki non-expansive mappings de€ned on a Banach space. Moreover, we explore a few weak and strong convergence results concerning such mappings. Our €ndings are aptly validated by non-trivial and constructive numerical examples and €nally, we compare our results with that of the other noteworthy iterative schemes utilizing MATLAB 2017a so‰ware. However, we perceive that for di‚erent set of parameters and initial points, the newly proposed iterative scheme converges faster than the other well-known algorithms. To be speci€c, we give an analytic proof of the claim that the novel iteration scheme is also faster than that of Liu et al.

(D6) The Mean Deviation Generating functions and a New Measure of Dispersion Rajan Cha‹amvelli Department of Mathematics, VIT University, Vellore, Tamil Nadu 632014 rajan.cha‹[email protected]

‘e mean deviation (MD), also called average absolute deviation (AAD), is a popular measure of dispersion used in several applied science €elds. ‘e population MD is not easy to €nd for some distributions, as it requires meticulous arithmetical work. Most of the graduate courses in biostatistics, mathematical statistics, econometrics and management sciences devote minimal discussion on MD. ‘e purpose of this paper is to derive new expressions for the mean absolute deviation from the mean and median. ‘is formulation is not only of interest to students and teachers in various €elds, but also useful to professionals and practitioners when explicit expressions for MD are unknown, but the tail sums are easy to €nd. ‘ese results are used to form new combinatorial identities and a new measure of dispersion that has potential for generalizing to higher dimensions.

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Ine€ality for Maximum Modulus of Rational Functions (D7) D. Tripathi, Deepa Arora Department of Mathematics, Manav Rachna University, Faridabad-121001, INDIA [email protected]

In this paper, we establish some inequalities for rational functions with prescribed poles and restricted zeros in the sup-norm on the unit circle in the complex plane. Some generalizations and re€nements of rational function inequalities of Xin Li et.al [Some Rational Inequality Inspired by Rahman’s Research;Progress in Approximation Œeory and Applicable Complex Analysis, Springer 2017 ] are obtained.

Associate space of grand Bochner Lebesgue spaces without (D8) Radon-Nikodym´ property Monika Singh Lady Shri Ram College for Women, (University of Delhi), Lajpat Nagar, New Delhi - 110024 [email protected]

‘e Bochner Lebesgue space, denoted by Lp(Ω, µ; X), is the collection of all X-valued µ-measurable €nite almost everywhere (a.e.) functions f i.e., k.kX value is €nite a.e., such that

1 Z  p 1 p kfkLp(Ω,µ;X) := kf(t)kX dµ(t) < ∞, µ(Ω) Ω where µ(Ω) < ∞. In, Kokilashvili, Meskhi and Rafeiro introduced grand Bochner Lebesgue spaces (GBLS) on €nite measure space and studied its associate space assuming Radon-Nikodym´ property on X.

In this paper presentation our aim is to talk about the associate space of GBLS without Radon-Nikodym´ property on X.

Rubio de Francia Extrapolation Theorem in Variable Lebesgue Spaces (D9) Arun Pal Singh Dyal Singh College, (University of Delhi), Lodhi Road, New Delhi - 110003 [email protected]

In this paper presentation, we shall talk about the Rubio de Francia extrapolation results for pair of non- increasing functions with Bp(·)-weights. And, mention an application to obtain the extrapolation result in p(·) the framework of variable exponent Lebesgue space Lw with Luxemburg norm.

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(D10) Analysis of MMAP/P H1,PH2/1 Pre-emptive Priority Retrial eueing System under Constant Retrial Policy with Orbital Search, Standby Server, Vacation, Impatient Behavior of Customers, Breakdown and Repair G. Ayyappan, K. ‘ilagavathy Department of Mathematics, Pondicherry Engineering College, Pillaichavady, Puducherry, India [email protected], [email protected]

In this article, we consider a single server queue in which two types of heterogeneous customers arrive according to the marked Markovian arrival process and their corresponding service based on phase-type(PH) distribution. While the main server is o‚ering service to the high/low priority customer who may be struck with breakdown immediately go for repair meanwhile, standby server would interrupt and take over service up to the main server rejuvenated from repair and return to the service station. Whenever the main server becomes idle due to completion of the repair, vacation and service times who may do an orbital search of low priority customers but in the case of standby server who do an orbital search when become idle due to completion of service to high/low priority customers. Using the Matrix-Analytic method, we investigated the expected number of high priority customers in the system as well as number of low priority customers in the orbit with the aid of steady-state probability vector. We examined the stability condition, a busy period of the system, cost analysis and characteristics of some performance measures of the system are discussed. Numerical results are tabulated and graphical representations are provided for a clear view of our model.

(D11) Fractals in Controlled Hausdorff Metric Space C. ‘angaraj, D. Easwaramoorthy Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore – 632 014, Tamil Nadu, India [email protected]

‘is paper explores a new fractal space called Controlled Hausdor‚ Metric Space by using the controlled metric, which is extended from b-metric. ‘en the Hutchinson–Barnsley Operator(HB Operator) is de€ned by using the Iterated Function System (IFS) of contractions on a controlled complete metric space. It is proved that, the HB Operator of IFS is contraction on a controlled Hausdor‚ metric space and also assured that it has a unique €xed point in a controlled Hausdor‚ metric space, called Controlled Fractal.

(D12) New Generalized ‘Useful’ Entropies using Weighted asi-linear Mean with Utility Aakanksha Singhal, D.K. Sharma Jaypee University of Engineering and Technology, Raghogarh, Dist. Guna, India [email protected]

Renyi´ entropy was the €rst generalized entropy derived using the concept of quasi-linear mean. Various other generalized entropies were later analyzed and expressed as the quasi-linear mean of elementary or generalized information. On similar lines, was introduced a generalized entropy: supra-extensive entropy. It was initially perceived that supra-extensive entropy may not be expressed as quasi-linear mean of infor- mation. In this paper, supra-extensive entropy is demonstrated as quasi-linear mean of generalized infor- mation for the €rst time. A new concept of weighted quasi-linear mean with utility is introduced and used to derive few existing generalized ‘useful’ information measures. Using the introduced concept of weighted quasi-linear mean with utility, new generalized ‘useful’ information measures based on generalized entropies namely: Tsallis, Sharma-Mi‹al and supra-extensive are de€ned. ‘e concept de€ned can be used to €nd the generalized ‘useful’ information measure corresponding to any generalized information measures which are quasi-linear means of elementary or generalized information.

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An Application of Intuitionistic Fuzzy Multisets in an Investment (D13) Decision Making Problem V. Inthumathi, A. Gnanasoundar Department of Mathematics, Nallamuthu Gounder Mahalingam College, Pollachi – 642001. [email protected].

Making decisions on investment is certainly the most important task of an investor. ‘e aim of this paper is to show how the concept of intuitionistic fuzzy multisets plays an important role in making good decisions using various distance measures.

∆m-Statistical Convergence of Order α of generalized difference (D14) se€ences in Probabilistic Normed Spaces Gursimran Kaur, Meenakshi Department of Mathematics, Chandigarh University, Mohali, Punjab, India. [email protected]; [email protected]

In the captioned paper, we de€ne ∆m-statistical convergence of order α of generalized di‚erence sequences in Probabilistic Normed Spaces and give their characterization. We also de€ne the notion of ∆m-statistical Cauchy of order α for these types of sequences in Probabilistic Normed Spaces. We have also given few examples which demonstrates that this notion is more generalized in the Probabilistic Normed Spaces.

Distance functions (π, β) and a fixed point result in ordered metric (D15) spaces Amit Sharmaa, Reeta Bhardwaja, Kamal Kumara, Naveen Manib aDepartment of Mathematics, Amity University, Haryana, India bDepartment of Mathematics, Sandip University, Nashik, India [email protected]

In present work, we derived a common €xed point result in an ordered complete metric space by using distance functions (π, β). Our main result, improves and unify the results of Yan et al. [Fixed Point ‘eory and Applications. 2012 (2012)] and Gupta and Mani [J. Fixed Point ‘eory Appl. 19 (2017), 1251 − 1267]. An example has been given in support of our €ndings.

Bulk service €eueing system with multiple vacation and remaining (D16) service by standby server during the breakdown period S. Karpagam Department of Mathematics, Vel Tech Rangarajan Dr.Sagunthala R&D Institute of Science and Technology, Chennai, India [email protected]

‘e purpose of this article is to bring out certain silent features of an M [X]/G(a, b)/1 queueing model with multiple vacation and remaining service by standby server for the service interrupted batch due to break- down. For this model, some important performance measures are obtained and the stability conditions are derived. Finally, numerical results of the proposed model are presented.

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(D17) I O I O Analysis of MAP1 , MAP2 /P H1 ,PH2 /1 Retrial eue with Single Vacation, Closedown, Setup, Optional Service, Balking and Two Way Communication G. Ayyappana, G. Archanaa, S. Sankeethab aDepartment of Mathematics, Pondicherry Engineering College, Puducherry, India bDepartment of Mathematics, Saradha Gangadharan College, Puducherry, India [email protected]

In this paper we consider a single server constant retrial queueing system with close down, vacation, setup, optional service and balking. ‘ere are two types of arrivals namely incoming calls which are made by the customers and outgoing calls which are made by the server during the idle period. If server is idle, the arriving incoming call will be served immediately. If server is busy, the arriving incoming call will send the orbit. A‰er the service completion the server become idle. During the idle time, the server will make the outgoing calls for their popularizing various schemes. ‘e server goes vacation only if the system is empty. Before takes the vacation server will be close down the system and a‰er the completion of vacation the server will set up the system for ready to give the service. ‘e server will give optional service for incoming calls if its need additional service. ‘e arriving incoming call may leave without entering the system, if server is busy. ‘e incoming calls and outgoing calls follows the Markovian Arrival Process (MAP ) and service times of incoming and outgoing calls follow the Phase-type distribution and the rest of the random variables are exponentially distributed. ‘e resulting QBD process is investigated in the steady state by employing matrix-analytic method. We have also done the busy period analysis of our model and discussed about the waiting time distribution of our system. Some of the performance measures of the system are derived and illustrated graphically/numerically.

(D18) Best approximations, distance formulas and orthogonality in C∗-algebras Priyanka Grover, Sushil Singla Department of Mathematics, Shiv Nadar University, India [email protected]

‘e length of the perpendicular in a right-angled triangle is always less than or equal to the length of the hypotenuse. In an inner product space H, if v ∈ H and W is a subspace of H, then v is orthogonal to W if and only if kvk ≤ kv − wk for all w in W . ‘is characterization of orthogonality to a subspace in an inner product space is taken as the de€nition of orthogonality of an element to a subspace in a normed space, called Birkho‚-James orthogonality. We characterize Birkho‚-James orthogonality of an element a ∈ A to a subspace B of A. We prove that that a is Birkho‚-James orthogonal to B if and only if there exists a state φ on A such that φ(a∗b) = 0 for all b ∈ B and φ(a∗a) = kak2. And we will see many known results which follow as corollary to this result.

(D19) A study on MAP/P H1,PH2/2 €eue with unreliable servers and vacation G. Ayyappan, R. Gowthami Department of Mathematics, Pondicherry Engineering College, Puducherry, India [email protected]

In this article, we discuss about a two heterogeneous classical queueing model with working breakdown and Bernoulli vacation for server-1 and starting failure with single vacation for server-2. Customers arrive to the system by following Markovian Arrival Process(MAP) and service times follow Phase-type(PH) distribution. We have studied our model by using matrix analytic method. We have provided practical application for our model. We have done the busy period analysis and also derived the waiting time distribution for our system. To the end, some numerical and graphical exempli€cations are provided.

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MAP/P H(1),PH(2)/2 with interaction, multiple vacation and repair (D20) G. Ayyappana, S. Sankeethab, Archana Gurulakshmia aDepartment of Mathematics, Pondicherry Engineering College, India bDepartment of Mathematics, Saradha Gangadharan College, India [email protected]

In this paper we consider two types of servers namely main and regular, the main server will be interrupted when he is providing service to the regular server customers. Inter arrival time of the system follows Marko- vian Arrival Process (MAP), the service time follows phase type distribution under the rest of the random variables are exponentially distributed. ‘is system has been modeled into a QBD process investigating steady state using matrix analytic technique where the block elements of the generated matrix have €nite dimensions. We have also discussed the busy period, waiting time distribution for our model. Performance measures of the system are derived and illustrated numerically/graphically.

On Existence Results of Generalized Evolution E€ation with (D21) Non-Instantaneous Impulses over the Banach space Haribhai R. Katariaa, Prakashkumar H. Patela, Vishant Shahb aDepartment of Mathematics, Faculty of Science, ‘e M. S. University of Baroda, Vadodara - 390 002, India bDepartment of Applied Mathematics, Faculty of Technology and Engineering, ‘e M. S. University of Baroda, Vadodara - 390 001, India [email protected], [email protected], [email protected]

‘is article established sucient conditions for the existence of mild solution for the generalized impulsive evolution equation with non-instantaneous impulses with local and non-local conditions. Conditions for existence of mild solution of evolution equations with local conditions are established through Banach €xed point theorem while, with non-local condition is established through Krasnoselkii’s €xed point theorem. Finally, an illustration is added to validate derived results.

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Section E: Di‚erential, Integral and Functional Equations

(E1) First-Order Nonlinear Dynamic Initial Value Problems Martin Bohnera, Sanket Tikareb, Iguer Luis Domini dos Santosc aDepartment of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409-0020, USA. bDepartment of Mathematics, Ramniranjan Jhunjhunwala College, Ghatkopar, Mumbai, India. cDepartamento de Matematica,´ Faculdade de Engenharia de Ilha Solteria, UNESP-Univ Estadual Paulista, Rua Rio de Janeiro, 266, Ilha Solteria, Sao˜ Paulo CEP 15385-000, Brazil. [email protected]

We prove three existence theorems for solutions of €rst-order dynamic initial value problems, including cor- responding continuous and discrete cases. ‘e main tools are €xed point theorems and dynamic inequalities. Two more results are given that discuss dependence of solutions on the initial conditions as well as conver- gence of sequences of solutions.

(E2) An Uncountable, Measure Zero, Dense Set of Non-monotone Points of Continuous Functions V. Murugan, R. Palanivel Department of Mathematical and Computational Sciences, National Institute of Technology, Karnataka, Suarthkal, Mangalore- 575 025, India [email protected]

In this paper, we present a continuous function which has every Cantor ternary point as its non-isolated non- monotone points. ‘e union of all the sets of non-isolated non-monotone points of iterates of the function have the desired properties.

(E3) Stability and Boundedness Criteria for Impulsive Fractional Differential E€ations in Caputo Sense with Initial Time Difference Pallvi Mahajan Beant College of Engineering & Technology, Gurdaspur, Punjab, India [email protected]

In the past few decades, fractional di‚erential equations have gained considerable importance and recently researchers are ge‹ing more interest in impulsive fractional di‚erential equations due to its widespread appli- cations in various €elds of science and engineering. In the present work, an impulsive fractional di‚erential equation in Caputo sense is investigated with initial time di‚erence for the €rst time and some novel crite- ria has been derived to investigate their stability and boundedness behaviour. ‘e stability with respect to initial time di‚erence is the generalization of the basic stability concept in the literature. ‘e investigations are carried out by perturbing Lyapunov function and by using comparison results. A generalized piecewise Lyapunov function has been used to obtain the desired results. ‘e results that are obtained to investigate the stability signi€cantly depend on the moment of impulses.

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Classification of Delay Differential E€ations with Constant (E4) Coefficients to Solvable Lie Algebras Jervin Zen Lobo Department of Mathematics, St. Xavier’s College, Mapusa, Goa - 403507, India [email protected]

In this paper, we shall apply symmetry analysis to €rst and second order delay di‚erential equations with constant coecients. ‘e determining equations of the admi‹ed Lie group are constructed in a manner di‚erent from that of the existing literature for delay di‚erential equations. We de€ne the standard Lie bracket and make a complete classi€cation of linear delay di‚erential equations with constant coecients, to solvable Lie algebras. We also classify some non-linear delay di‚erential equations with constant coecients, to solvable Lie algebras.

A Study of the Reproducing Kernel Hilbert Space Method for Poor (E5) Nutrition in the Life Cycle Gautem Patel, Kaushal Patel Department of Mathematics, Veer Narmad South Gujarat University, Gujarat, India [email protected]

In this work, the reproducing kernel Hilbert space method is applied for solving the mathematical model of the poor nutrition in the life cycle in the form of non linear system of ordinary di‚erential equations. ‘e exact solution of the system has been obtained in terms of a convergent series. ‘e results in €gure show that the proposed method is e‚ective for solving such non linear system of ordinary di‚erential equations as compare to numerical methods.

Existence Assertion of Solution in the Space `p, p > 1 for Fractional (E6) Infinite System of Integral E€ations of Nonlinear Type Vijai Kumar Pathak, Lakshmi Narayan Mishra Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632 014, Tamil Nadu, India [email protected], [email protected]

‘is article deals with existence assertion of solution in the space `p, p > 1 of fractional in€nite system of integral equations of nonlinear type via measure of noncompactness (MNC) together with generalized Meir- Keeler €xed point theorem. ‘e obtain result of existence assertion of solution is proved under rather general hypotheses. Some examples are given to illustrate the natural appreciations of our results presented in this work. We analyze the existence assertion of solution of the system of nonlinear fractional integral equations. Finally, we will bring up an example to show the advantage of our results. We use the homotopy perturbation method together with Adomian decomposition technique to obtain our existence assertion.

Periodic Boundary Value Problem for System of Caputo Se€ential (E7) Differential E€ations of Fractional Order Jagdish A. Nanware Department of Mathematics, Shrikishna Mahavidyalaya, Gunjoti, Dt.Osmanabad (M.S) India jag skmg91@redi‚mail.com

Monotone method coupled with lower and upper solutions is developed for periodic boundary value problem for system of Caputo sequential di‚erential equations of fractional order. Method is successfully applied to obtain existence and uniqueness results for periodic boundary value problem for system of Caputo sequential di‚erential equations of fractional order.

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(E8) Solutions of Rossby Waves with Dissipation through Symmetries Amlan K. Haldera, C.T. Dubab, P.G.L. Leachc,d aDepartment of Mathematics, Pondicherry University, Kalapet - 605014, Puducherry, India bSchool of Computer Science and Applied Mathematics, University of Witwatersrand, Johannesburg, South Africa cInstitute For Systems Science, Durban University of Technology, Durban, South Africa dSchool of Mathematics, Statistics and Computer Science, University of KwaZulu - Natal, Durban, South Africa [email protected]

‘e Lie symmetry analysis method is applied to (1 + 1) and (1 + 2)−dimensional Rossby wave with a dis- sipative term in the f and β−plane. We employ the canonical coordinates to obtain certain new reductions and equations which are generally devoid of any point symmetries. Some symmetry reductions leads to an Abel’s equation of the €rst kind and maximally symmetric second-order ordinary di‚erential equation. ‘e dispersion relation points that the (1 + 1)−dimensional Rossby wave propagation and energy trans- portation is in both the directions and the presence of dissipation coecient reduces the speed whereas the energy transportation increases for the viscous case in the β- plane. From the dispersion relation for the (1 + 2)−dimensional Rossby equation, it can be deduced that there are two waves propagating at the same time one in the eastward and the other westward, as evident from the values of the phase and group veloc- ities. Moreover, the energy propagation is towards the east and it remains consistent throughout the ƒow. For a particular symmetry, the graphical representations of the solutions for various values of the parameter β, presents a pictorial observations of Rossby wave on the Sun. We also present a comparative study with the inviscid case to prove our €ndings.

(E9) Optical Solitons with Generalized Third-order Nonlinear Schrodinger¨ E€ation via Lie Symmetry Analysis Sachin Kumar, Sandeep Malik Department of Mathematics and Statistics, Central University of Punjab, Bathinda–151001, Punjab, India [email protected]

In this article, we investigate the generalized third order nonlinear Schrodinger¨ equation (NLSE), which is utilized in optical €bers to model pulses of ultra-short. By the implement of Lie symmetry analysis, we derive optical solutions of this model. ‘ese optical solutions are received in the form of dark, bright, and singular soliton solutions.

(E10) A Novel Techni€e for Solving the Higher-dimensional System of Nonlinear Coupled Partial Differential E€ation Kumbinarasaiah S Department of Mathematics, Bangalore University, Bengaluru-560056, India [email protected]

In this study, we propose an e‚ective numerical algorithm to €nd numerical solutions to the system of partial di‚erential equations. ‘is algorithm includes the collocation method and the truncated Laguerre wavelet series. Here, we reduce the system of (2+1) dimensional partial di‚erential equations into a set of algebraic equations that have unknown Laguerre wavelet coecients. Some numerical examples are solved to validate the proposed technique’s eciency and, also, discussed the comparison between the present method and other methods of solutions with the exact answer. ‘e obtained results reveal that the current algorithm provides a be‹er result than other methods.

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A Result on the Approximate Controllability of Fractional (E11) Differential E€ations of Order 1 < r < 2 M. Mohan Raja, V. Vijayakumar, R. Udhayakumar Department of Mathematics, School of Advanced Science, Vellore Institute of Technology, Vellore 632 014, Tamil Nadu, India [email protected]

‘is manuscript is mainly focusing on approximate controllability for fractional di‚erential evolution equa- tions of order 1 < r < 2 in Hilbert spaces. We consider a class of control systems governed by the fractional di‚erential evolution equations. By using the results on fractional calculus, cosine and sine functions of op- erators, and €xed-point approach, a new set of sucient conditions are formulated which guarantees the approximate controllability of fractional di‚erential evolution systems. ‘e results are established under the assumption that the associated linear system is approximately controllable. Lastly, we present the applica- tions to support the validity of the study.

Existence and Uni€eness of Classical and Mild Solutions of Impulsive (E12) Fractional Evolution E€ations Jaita Sharmaa, Vishant Shaha, Raju K. Georgeb aDepartment of Applied Mathematics, Faculty of Technology and Engineering, ‘e M. S. University of Baroda, Vadodara, India bDepartment of Mathematics, Indian Institute of Space Science and Technology, Trivendrum, Kerala, India [email protected]; [email protected]; [email protected]

In this article, we are deriving a set of sucient conditions for existence and uniqueness of classical and mild solutions of fractional semi-linear evolution equation with and without impulses on the Banach spaces by generalizing the concept of semigroup in terms of generators and using generalized €xed point theorem. ‘e conditions for the existence and uniqueness of classical and mild solutions obtained using this concept of generators are weaker than previously derived conditions. We also derived conditions under which mild solution becomes a unique classical solution. Illustrations are provided to validate our results.

On Approximate Controllability of a Class of Neutral Hilfer (E13) Fractional Stochastic Differential Systems by using Wright Function C. Dineshkumar, R. Udhayakumar, V. Vijayakumar Department of Mathematics, Vellore Institute of Technology, Vellore - 632 014, India [email protected]

‘is article mainly focusing approximate controllability of a class of neutral Hilfer fractional stochastic di‚er- ential systems. By applying some ideas about the semi-group theory and fractional calculus, the main results of this article are proved. At €rst, the investigation about the existence of mild solution and then we study about the approximate controllability of the considered equation. Next, we extend our study to system with non-local conditions. Finally, a theoretical application is presented for proving the validity of controllability results obtained.

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(E14) An Effective Iterative Method and Existence Result for a Class of Second-order Four-point Nonlinear BVPs Nazia Urus, Amit Kumar Verma Department of Mathematics, Indian Institute of Technology Patna, India [email protected]

In this article, we develop a monotone iterative technique (MI-technique) with upper and lower solutions for a class of four-point nonlinear boundary value problems (NLBVPs). ‘e nonlinear source term is dependent on the derivative of the solution. To study the existence of a solution, we construct iterative sequences for the corresponding linear problem. We use quasilinearization to construct these iterative sequences. We prove maximum and anti-maximum principle to establish monotonicity of sequences of lower solutions (ln(x))n and upper solution (un(x))n such that ln(x) ≤ un(x) as well as ln(x) ≥ un(x), ∀n ∈ N. ‘en under certain assumptions, we prove that these sequences converge uniformly to the solution in the speci€c region. ‘e motivation for this work came from many recent investigations on MI-technique for four-point NLBVPs. To demonstrate that the proposed technique is impressive, we compute the solution of the NLBVPs which may not be computed e‚ortlessly. We have also plo‹ed upper and lower solutions for the test examples and have shown that under some sucient conditions, the derived upper and lower solutions are monotonic in nature.

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Section F: Geometry and Topology

Some ξ-Pre-Continuous Maps (F1) Nazir Ahmad Ahengar, J.K. Maitra Department of Mathematics and Computer Sciences, R.D. University, Jabalpur M.P. INDIA [email protected], kmrdvv@redi‚mail.com

In this paper the concept of ξ-pre-continuous and ξ-regular continuous maps in ξ-topological spaces are introduced and all the possible relationships of these maps have been discussed and established. Further we introduce and study ξ-pre-generalized closed sets and ξ-pre-generalized continuity in ξ-topological spaces and investigate various relationship by making the use of some counter examples.

p∗-Continuous Maps and its Generalization via Ideal (F2) Rajesh Kumar Tiwari, J.K. Maitra Department of Mathematics and Computer Science, Rani Durgawati University, Jabalpur, India [email protected]; jkmrdvv@redi‚mail.com

A collection of sets which are derived from topological space with respect to generalized topology is said to be the p∗-open sets. In this paper the de€ne p∗-continuity on topological space with respect to generalized ∗ ∗ topology in sense of p -open set. Also using the ideal in p -open set, we presented Ip∗ -open sets. On the basis of Ip∗ -open sets, we propose to de€ne Ip∗ -continuity and weakly Ip∗ -continuity on topological space with respect to generalized topology via ideal. Further, classical properties of P ∗-continuity, P ∗-continuity and weakly Ip∗ -continuity are presented on topological space with respect to generalized topology.

Intuitionistic Fuzzy Almost Generalized e-continuous Mappings (F3) Chandra Prakash Rathor Department of Mathematics and Computer Science, Rani Durgawati University, Jabalpur, India [email protected]

In this paper, we introduce and study the concept of Intuitionistic fuzzy almost generalized e-continuous mappings. Several interesting properties of these mappings are also given. Examples and counter examples are also given to illustrate the concepts introduced in this paper. We also introduce the concept of Intuition- istic fuzzy T 1 e-space. It is seen that a Intuitionistic fuzzy almost generalized e-continuous mapping from a 2 Intuitionistic fuzzy T 1 1 e-space to another Intuitionistic fuzzy topological space becomes Intuitionistic fuzzy 2 almost continuous mapping.

Kaehlerian Spaces Admitting in H-Projective Vector Field with (F4) Constant Scalar Curvature U.S. Negi H.N.B. Garhwal (A Central) University, S.R.T. Campus Badshahithaul, Tehri Garhwal - 249199, (U.K.), India. [email protected]

Ishihara (1959) has studied holomorphically projective changes and their groups in an almost complex man- ifold and also proved on holomorphic planes. Obata (1965) has de€ned and studied Riemannian manifolds admi‹ing a solution of a certain system of di‚erential equations. In this paper, we have de€ned and studied Kaehlerian spaces admi‹ing in H-projective vector €eld with constant scalar curvature and several theo- rems have been proved. Also, then €nd necessary and sucient conditions for such a Kaehlerian space to be isometric to a complex projective space with Fubini-Study metric.

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(F5) Lower Bounds for Regular Genus and Gem-complexity of PL 4-manifolds with Boundary Biplab Basak, Manisha Binjola Department of Mathematics, Indian Institute of Technology Delhi [email protected]

Let M be a connected compact PL 4-manifold with boundary. In this article, we have given several lower bounds for regular genus and gem-complexity of the manifold M. In particular, we have proved that if M is a connected compact 4-manifold with h boundary components then its gem-complexity k(M) satis€es the following inequalities:

k(M) ≥ 3χ(M) + 7m + 7h − 10 and k(M) ≥ k(∂M) + 3χ(M) + 4m + 6h − 9,

and its regular genus G(M) satis€es the following inequalities:

G(M) ≥ 2χ(M) + 3m + 2h − 4 and G(M) ≥ G(∂M) + 2χ(M) + 2m + 2h − 4,

where m is the rank of the fundamental group of the manifold M. ‘ese lower bounds enable to strictly im- prove previously known estimations for regular genus and gem-complexity of a PL 4-manifold with boundary. Further, the sharpness of these bounds has also been shown for a large class of PL 4-manifolds with boundary.

(F6) On Some Intuitionistic p−Sets and Intuitionistic q−Sets Poonam Agrawal, J.K. Maitra Department of Mathematics and Computer Science, Rani Durgawati University, Jabalpur (M.P.) India poo [email protected]

In 2002, ‘angavelu and Chandrasekhara Rao introduced a new class of sets, namely p−sets in topologi- cal space. Also they have introduced a new class of set, namely q−sets in topological space. ‘ey have studied some basic properties of p−sets and q−sets in topological space. In this paper we have introduced intuitionistic p−sets and intuitionistic q−sets in intuitionistic toplogical spaces and obtained its signi€cant properties. We have constructed some examples which are quite useful in theory of intuitionistic p−sets and intuitionistic q−sets.

(F7) Comprehensive asi-Einstein Spacetime with Application to General Relativity Punam Gupta Department of Mathematics & Statistics, School of Mathematical & Physical Sciences, Dr.Harisingh Gour University, Sagar- 470 003, M.P., INDIA [email protected]

‘e aim of this work is to introduce and investigate geometric and physical properties of the comprehensive quasi Einstein spacetime C(QE)n under certain conditions. Firstly, we prove the existence of C(QE)n by constructing non trivial examples. Finally, we study conformally ƒat comprehensive quasi Einstein space- times and homogeneous, isotropic, relativistic two-ƒuid comprehensive quasi Einstein spacetimes.

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On W2-Curvature Tensor of the Projective Semi-Symmetric Connection (F8) T. Raghuwanshia, S.K. Pandeyb, M.K. Pandeya, A. Goyala aDepartment of Mathematics, U.I.T. R.G.P.V. Bhopal, M.P., India bDepartment of Mathematical Sciences, A. P. S. University, Rewa, M. P., India,, India [email protected]

We study the curvature conditions of semi-symmetry type on an SP -Sasakian manifold admi‹ing a projective semi-symmetric connection. It is shown that an SP -Sasakian manifold satisfying the conditions R˜ · W˜2 = 0 and W˜2 · R˜ = 0 is a quasi Einstein manifold.

On Selection of Generalized Continuous Multifunctions (F9) Pankaj Jain, Chandrani Basu, Vivek Panwar Department of Mathematics, South Asian University, Akbar Bhawan, Chanakya Puri, New Delhi-110021, India. [email protected]

Continuity of functions is an important property. However, o‰en, we encounter functions with discontinu- ities of various types. In the past many decades, people have classi€ed discontinuous functions in weaker classes of continuous functions, e.g., quasi continuity, semi continuity, B-continuity, B∗-continuity, and many more.

Very recently the authors have obtained and studied new classes of weak continuity, namely, weak B∗- continuity, contra B∗-continuity and slight B∗-continuity.

‘e notion of weaker (or generalized) continuity also exist in the case of multifunctions or multivalued map- pings. ‘e question arises that can we obtain a continuous selection for these multifunctions?

In 1956, Michael showed that a closed convex valued continuous multifunction F : X → Y from a para- compact space X to a Banach space Y admits a continuous selection. A‰er that several authors obtained continuous selections for non-convex valued multifunctions in Banach spaces. Carbone showed that not al- ways continuous selection exists. In this direction, many authors have studied the problems of existence of various types of selections for generalized continuous multifunctions.

In this presentation, we discuss about the existence of quasicontinuous selection for slightly B∗-continuous multifunctions.

On Somewhat Pairwise Fuzzy β Continuous Map (F10) Lalita Verma, J.K. Maitra Department of Mathematics and Computer Science, Rani Durgawati University, Jabalpur, M.P. 482001 [email protected], jkmrdvv@redi‚mail.com

In this paper we have de€ned and characterized the concept of somewhat pairwise fuzzy β-continuous map and somewhat pairwise fuzzy β-open map in fuzzy bitopological spaces. We have obtained signi€cant prop- erties of it and constructed basic examples.

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(F11) On Nonempty Intersection Properties in Metric Spaces Ajit Kumar Gupta, Saikat Mukherjee Department of Mathematics, National Institute of Technology Meghalaya, India [email protected] ‘e classical Cantor’s intersection theorem states that in a complete metric space X, the intersection of every decreasing sequence of nonempty closed bounded subsets, with diameter approaches zero, has exactly one point. In this article, we deal with decreasing sequences {Kn} of nonempty closed bounded subsets of a metric space X, for which the Hausdor‚ distance H(Kn,Kn+1) tends to 0, as well as for which the excess of Kn over X \ Kn tends to 0. We achieve nonempty intersection properties in metric spaces. ‘e obtained results also provide partial generalizations of Cantor’s theorem.

(F12) On Interval Type-2 Fuzzy Rough Sets and their Topological Structures Shambhu Sharan Department of Mathematics & P.G Center, College of Commerce, Arts & Science, Patna-800020 Patliputra University, Patna [email protected] ‘e present paper studies the relationship between interval type-2 (IT2) fuzzy rough sets and interval type-2 fuzzy topologies (IT2F-topologies) induced by IT2 fuzzy relations. Speci€cally, we establish some notable results: (i) any serial IT2 fuzzy relation induces an IT2F-topology (ii) any reƒexive IT2 fuzzy relation and its transitive closure induce the same IT2F-topology. Subsequently, we obtain the interior and closure IT2 fuzzy operators of IT2F-topology induced by reƒexive IT2 fuzzy relation and investigate their connection with IT2 fuzzy relation. Finally, the corresponding results are obtained when the relation is a similarity IT2 fuzzy relation.

(F13) Space-time Admitting Generalized Conharmonic Curvature Tensor S.P. Maurya, S.K. Pandey, R.N. Singh Department of Mathematical Sciences, A.P.S. University, Rewa–486003, India [email protected] ‘e object of the present paper is to study Space-time Admi‹ing Generalized Conharmonic Curvature Tensor. In this paper we have studied the basic algebraic properties of generalized conharmonic curvature tensor. Next, it is proved that a 4-dimensional relativistic generalized conharmonic ƒat space-time is an Einstein space-time and it is of constant curvature. Moreover, it is of O-type. It is also observed that in a 4-dimensional relativistic perfect ƒuid generalized conharmonically ƒat space-time following Einstein’s €eld equation in the absence of cosmological constant, energy momentum tensor is covariant constant. Finally, it is proved that a 4-dimensional relativistic conservative generalized conharmonic space-time M with constant scalar function ψ is a GRW space-time.

(F14) Some Geometric Estimates on Warped Product Lightlike Submanifolds of Indefinite Kaehler Manifolds Sangeet Kumar Department of Mathematics, SGTB Khalsa College, Sri Anandpur Sahib - 140118, Rupnagar, India [email protected] ‘e purpose of present paper is to investigate SCR-lightlike warped product submanifolds of inde€nite Kaehler manifolds and to €nd geometrical estimates arising in such warped products. We derive several geometric characterizations for squared norm of the second fundamental form of SCR-lightlike warped product submanifolds in an inde€nite Kaehler manifold. ‘en we €nd a sharp estimate for the squared norm of the second fundamental form in terms of Hessian of the warping function, for SCR-lightlike warped product submanifolds in an inde€nite complex space form. Finally, we present a geometric inequality for the existence of SCR-lightlike warped product submanifolds in inde€nite complex space forms.

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Screen Generic Lightlike Submanifolds of Indefinite Nearly Kaehler (F15) Manifolds Megha, Sangeet Kumar Department of Mathematics, SGTB Khalsa College, Sri Anandpur Sahib - 140118, Rupnagar, India [email protected]

In the process of generalization from Riemannian to semi-Riemannian manifolds, there is a natural exis- tence of lightlike submanifolds and for which the local and global geometry is completely di‚erent than non-degenerate case. ‘e main di‚erence between the lightlike submanifolds and non-degenerate subman- ifolds is that the tangent bundle intersects with the normal bundle. ‘e concept of lightlike submanifolds has perceived several important contributions in complex and contact semi-Riemannian geometries and has been successfully applied in di‚erential geometry and mathematical physics, particularly, in theory of gen- eral relativity. Considering the growing importance of lightlike submanifolds and interesting geometrical and topological properties inde€nite nearly Kaehler manifolds, we study screen generic lightlike submani- folds of inde€nite nearly Kaehler manifolds. We prove the existence of screen generic lightlike submanifolds in inde€nite nearly Kaehler manifolds of constant holomorphic sectional curvature c and of constant type α. Further, we derive several characterizations for the integrability of distributions associated with such sub- manifolds. Finally, we discuss totally umbilical screen generic lightlike submanifolds and minimal screen generic lightlike submanifolds of inde€nite nearly Kaehler manifolds.

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Section G: Numerical Analysis, Approximation ‡eory and Computer Science

(G1) A Fitted Galerkin Finite Element Method for Singularly Perturbed Differential E€ations with a Small Negative Shift N. Sathya Kumar, R. Nageshwar Rao Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore – 632 014, Tamil Nadu, India. [email protected]

In this paper a €‹ed Galerkin €nite element method is presented for the boundary value problem of singularly perturbed di‚erential equations with a small negative shi‰ in the convection term. A €‹ing parameter is introduced in the Galerkin €nite element scheme and is obtained from the theory of singular perturbations. ‘e resultant 3-term recurrance relation is solved by ‘omas algorithm. Numerical results are obtained for test problems, which demonstrate the eciency of the method.

(G2) Numerical Solution for Fractional Variable-order Differential E€ation with Delay Sarita Nandala,b, Dwijendra N. Pandeya aTechnology Studies Department, Woosong University, South Korea bDepartment of Mathematics, Indian Institute of Technology Roorkee, India [email protected]

In this paper, we propose a new ecient numerical approach for fractional variable-order di‚erential equa- tion with delay. ‘e topic of variable-order fractional di‚erential equations has not been explored extensively using delay, and to augment the order of convergence. Noting that O(h4) and O(τ 1−α) are the best conver- gence orders achieved in the spatial and temporal dimensions respectively, our aims are to improve the spatial convergence order to 4.5 and temporal order to 2, and to provide rigorous proof of solvability, convergence and stability of the proposed method. In the existing literature, a few work is available to construct higher- order numerical methods for the variable-order fractional di‚erential equations with delay. Construction of a mathematical approach for such equations involves the more numerical analysis. Here, we propose to use parametric quintic spline in the spatial dimension and L2 − 1σ formula for time dimension. ‘e stability, convergence, and solvability will be proved using discrete energy method. ‘e proposed numerical approach will improve the convergence in both aspects (spatial-dimension and time-dimension). Numerical simulation will be carried out using the MATLAB so‰ware to demonstrate the e‚ectiveness of numerical scheme.

(G3) A Fixed Point Approach to the Existence-Uni€eness of Coupled-Elliptic Nonlinear Partial Differential for Convection in Porous Media Saginta Dey, B.V.R. Kumar Department of Mathematics and Statistics,IIT-Kanpur

‘e problem of convection in a porous media, which is topic of great interest for researchers all over the world, is governed a system of coupled elliptic nonlinear partial di‚erential equations. While the model, based on experimental validation, has been widely used the fundamental question of existence-uniqueness has not been addressed so far. In this study, we prove the existence-uniqueness of a coupled non-linear elliptic partial di‚erential equation system using Feado-GalerkinMethod, compactness theorems and Brouwer’s €xed point theory.

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On Fuzzy Contra g∗β-Continuous Functions (G4) Madhulika Shuklaa, J.K. Maitrab aDepartment of Applied Mathematics, Gayan Ganga Insitude of Technology and Sciences Jabalpur (M.P.) 482011 India, bDepartment of Mathematics and Computer Science, R.D. University, Jabalpur 482001. [email protected], jkmrdvv@redi‚mail.com

‘e notion of fuzzy sets was introduced by L. A. Zadeh in 1965. C. L. Chang has extended the concept of topol- ogy by taking a collection of fuzzy sets instead of crisp sets and developed the theory of Fuzzy Topological spaces. N. Levine introduced the concepts of generalized closed sets in general topology in the year 1970. In 2006, Eradal and Etienne introduced the notation of fuzzy contra continuous mapping. S. S. Benchalli and G. P. Siddapur introduced the notation of generalized pre-closed sets in fuzzy topological space in 2011. Recently M. Shukla introduced the concept of fuzzy contra g∗p-continuous, fuzzy contra g∗s-continuous and fuzzy contra g∗α-continuous in fuzzy topological space.

In this paper we introduce and study the new class of mappings called fuzzy contra g∗β-continuous and fuzzy almost contra g∗β-continuous functions in fuzzy topological spaces. Also we de€ne the relation between of fuzzy contra g∗β-continuous and fuzzy almost contra g∗β-continuous spaces and study some of their properties.

Generalized Differential adrature Method for Vibration Analysis (G5) of Non-homogeneous Orthotropic Thin Rectangular Plates Renu Saini Department of Mathematics, Maharaja Agrasen College, University of Delhi, India. [email protected]

In present paper generalized di‚erential quadrature method (GDQM) is used to analyze the vibration charac- teristics of non-homogeneous orthotropic rectangular plates. It is assumed that the non-homogeneity arises due to the exponential variation in young’s moduli, shear modulus and density of the plate material along the direction of orthotropy. In GDQM the derivative of a function with respect to space variable at a given grid point is approximated as the weighted linear sum of function values at all the grid points in the computational domain of that variable. Based on Kirchho‚’s plate theory, the governing di‚erential equation for such a plate model is derived. ‘e solution procedure by means of GDQM has been implemented in a MATLAB code. ‘e Numerical results are computed for CCCC boundary condition for €rst three modes of vibration. ‘e e‚ect of various plate parameters on natural frequencies is analyzed and presented graphically. A comparison of results with other methods available in the literature is presented. A close agreement of results shows the versatility of the present method.

Power Series Convergence Method for an Operator Based on (G6) Multivariate q-Lagrange Polynomials Rahul Shukla, Pursho‹am Narain Agrawa Department of Mathematics, Indian Institute of Technology Roorkee, India [email protected]

Let C(I), k.k
be the Banach space of all continuous functions on I = [0, 1] with the sup-norm. Motivated by the work of Erkus et al.(Appl. Math. Comput. 182(2006), 213–222), for f ∈ C(I), Behar et al.(J. Math. Anal. Appl., 491(2) (2020), 1–24) de€ned the following class of operators

( r n) ∞  β(1),...,β(r) Y  (k) n X X n n n Bn,q (f(s); x) = 1 − xβn q (q ; q)l1 (q ; q)l2 ...(q ; q)lr

k=1 p=0 l1+l2+···+lr =p (1) (2) (r) (β )l1 (β )l2 ...(β )lr  [l ]   n n n f r q xp, (q; q)l1 (q; q)l2 ...(q; q)lr [n + lr − 1]q

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and studied the approximation properties of the bi-variate and GBS(Generalized Boolean Sum) operators as- sociated to the above operators in the terms of the partial moduli of continuity and the mixed modulus of smoothness, respectively.

In the present work, using multivariate q-Lagrange polynomials, we construct an integral type generalization of the above linear positive operator. We prove some interesting inequalities concerning to the moments and the central moments. Further, we study the convergence of our operator by means of Power series convergence method. In this quest, we prove a non-trivial Korovkin type theorem to show the convergence of the proposed operator. It is worth to mention that the power series convergence method is more general form of classical convergence.

(G7) A Novel Two Steps Numerical Method to Solve Non-linear E€ations Jogendra Kumar Department of Mathematics, School of Physical Sciences DIT University, Dehradun, U‹arakhand-248009, India, [email protected] Present work proposes a numerical method of order three based on fundamental theorem of calculus and composite Simpson rule for solving nonlinear equations. ‘e accuracy of method is shown with the help of numerical examples and a comparative study is done with some well-known existing numerical schemes.

(G8) A Numerical Scheme based on Haar Wavelet Nonstandard Finite Difference Method for the Solution of a Class of Generalized Burgers’ E€ation Mukesh Kumar Rawani, Amit Kumar Verma Department of Mathematics, Indian Institute of Technology Patna, India [email protected] Solving Burgers’ equation always posses challenges for small values of viscosity. Here we propose a method to compute the numerical solution for a class of generalised Burgers’ equation based on the Haar wavelet (HW) coupled with nonstandard €nite di‚erence (NSFD) method. In the solution process, the time derivative is discretised by nonstandard €nite forward di‚erence and spatial derivatives are approximated by Haar wavelet. ‘e quasilinearization process is used to tackle the non-linearity in the equation. Accuracy and eciency of the method are assessed by computing L∞ and L2-error norms. It is observed that the proposed method produces accurate results and quite easy to implement.

(G9) An Effective Numerical Techni€e to Solve Lane-Emden E€ations based on the Galerkin Finite Element Method Biswajit Pandit, Amit Kumar Verma Department of Mathematics, Indian Institute of Technology Patna, Patna–801106, Bihar, India. [email protected] Lane-Emden type equations arise various physical phenomena in mathematical and astrophysics like stellar structure, thermionic currents, thermal explosions, radiative cooling, CTC, etc. In this work, we consider a model by considering the equation

( 0 xβy0(x)
+ xβf(x, y) = 0, 0 < x < 1, & 0 0 y (0) = 0, b1y(1) + a1y (1) = c1.&

Here, we apply continuous Galerkin €nite element method (CGFEM) by choosing the Lagrange linear and quadratic polynomials as a test and trial functions. We approximate the integral value of nonlinear function 1 by using trapezoidal and Simpson’s 3 rule. We compare the numerical results with other numerical results computed by various methods. Residue table shows that our proposed techniques are ecient, convenient and promising in the existing literature.

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Application of Haar Wavelet on a Class of System of Coupled (G10) Lane-Emden E€ation Narendra Kumar, Amit K. Verma Department of Mathematics, Indian Institute of Technology Patna, India [email protected]

Coupled Lane-Emden equation appears in several branches of science and engineering such as catalytic di‚u- sion reactions, dusty ƒuid models, and in the study of concentrations of Carbon Dioxide and Phenyl Glycidyl Ether. In this work, we consider a system of Coupled Lane-Emden equations with boundary conditions. We propose an ecient numerical technique based on the Haar wavelets collocation method together with the Newton-Raphson approach to solve the above di‚erential equation. In this technique, we use the Haar wavelets collocation method and get the system of nonlinear equations. ‘en, we solve the system of nonlin- ear equations using the Newton Raphson method to get the solution of the system of Lane-Emden equations. We discuss some test problems based on it. We compare our results with the other existing methods such as the Adomian decomposition method, Taylor series solution, Successive iteration technique etc. and check the accuracy and eciency of the proposed method.

Contour based Analysis for Image Classification (G11) Ezilmaran D, Vinoth Indira D Vellore Institute of Technology, Vellore [email protected], [email protected]

Image processing has trending research in current decades. It contains lots of research challenges to increase results of the images. Classi€cation behave major role for image processing to solve the challenges. Contour segmentation helps us to €nd the detecting edges of the images. ‘e contrario approach, the starting point is de€ning the conditions where contours should not be detected so‰ gradient regions contaminated by noise. Ion mobility spectrometry (IMS) increase the peal clarity of di‚erent measurement and it signi€es signal to noise ratio. So in this article, we will approach the contour technique and IMS classsi€cation to cluster the image through that this article make an analysis of the image.

Exact and Nonstandard Finite Difference Schemes for the Generalized (G12) Form of Burgers Fisher E€ation Sheerin Kayenat, Amit K. Verma Department of Mathematics, Indian Institute of Technology Patna, India [email protected]

We consider a generalized form of Burgers Fisher (BF) equation subject to certain initial and boundary condi- tions. We propose an explicit exact €nite di‚erence (EFD) scheme for the BF equation using its solitary wave solution. Furthermore, a non-standard €nite di‚erence (NSFD) scheme is also proposed. ‘e properties like positivity and boundedness is proved to be preserved by the proposed NSFD scheme. ‘e method is shown to be stable under certain conditions and the local truncation error is calculated. ‘e principal part of the local truncation error of NSFD scheme is O (∆x + ∆t) . Approximate solutions of the BF equation is obtained using the proposed NSFD scheme. We have compared our result with two methods. First is compact €nite di‚erence (CFD) method in which a combination of a sixth-order CFD scheme in space and a low-storage third-order total variation diminishing Runge-Ku‹a scheme in time have been used and second is Adomian decomposition method. Comparisons indicate the supremacy of our proposed NSFD method. It gives encour- aging result for various di‚erent parameters. Also the proposed NSFD scheme is very easy to handle and the computation work takes very less time. Moreover it gives accurate result for relatively bigger values of step size.

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Section H: Solid Mechanics, Fluid Mechanics, Astrophysics and Relativity, and related areas

(H1) A Study of Unsteady Magnetohydrodynamic Flow of An Incompressible, Viscous, Electrically Conducting Fluid Bounded By Two Non-Conducting Vertical Plates in Presence of Inclined Magnetic Field Mrinmoy Goswami, Krishna Gopal Singha Kaziranga University, Assam, India, Pragya Academy Junior College, Assam [email protected]

‘e present article addresses the e‚ect of unsteady MHD ƒow of an incompressible, viscous ƒuid bounded by two no-conducting parallel plates placed vertically in presence of uniform inclined magnetic €eld. One of the plates is considered to be in motion with constant velocity whereas the other plate is adiabatic. Using transformation associated with decay factor, we have deduced a set of ordinary di‚erential equations which are solved analytically for the ƒow €eld, temperature €eld and induced magnetic €eld for di‚erent values of MHD ƒow parameters. ‘e results obtained for velocity, temperature and induced magnetic €eld are discussed and analyzed graphically.

(H2) Nonlinear evolution of weak discontinuity waves in Darcy-type porous media Mithilesh Singh Department of Applied Science, Rajkiya Engineering College, Sonbhadra-231206, INDIA [email protected]

‘e propagation of nonlinear waves in one dimensional space, unsteady and compressible ƒow in Darcy-type porous media is analyzed. It is assumed that the weak discontinuity propagates long the characteristic path using the characteristics of the governing quasilinear system as the reference coordinate system. Evolution equation in the characteristic plane is derived. As an application of the theory the breaking point at the wave front is determined. It is assessed as to how the porosity of the medium a‚ects the process of steepening and ƒa‹ering of acceleration waves with planar, cylindrical, and spherical symmetry. ‘e critical amplitude of the initial disturbance has been determined such that any compressive disturbance with initial amplitude greater than the critical one always grows into a shock wave, while the initial amplitude less than the critical one always decays.

(H3) On Swirling Flows Near Rotating Disks Bikash Sahoo Department of Mathematics, National Institute of Technology Rourkela, India. [email protected]

In this paper we have discussed about di‚erent kind of revolving ƒows near rotating disks. ‘ese ƒow prob- lems have immense technical and industrial applications. ‘ough most of the ƒow problems admit self-similar solutions, it is dicult to €nd closed form analytic solutions even for the simplest of these problems. ‘e mathematical and computational challenges arising due to such ƒow problems will be discussed. ‘e chal- lenges become worse if one considers non-Newtonian ƒuids, speci€cally viscoelastic ƒuids. ‘e higher order derivatives present in the constitutive equations give rise to momentum equations, whose order exceeds the number of available boundary conditions. Finally, we will focus on a speci€c ƒow problem, namely the prob- lem arising due to the ƒow of a viscous Newtonian ƒuid near an in€nite rotating disk with rough surface. ‘e no-slip boundary conditions are replaced by partial slip boundary conditions. Simple mathematical analysis will be used to prove the existence of the solution before proceeding for the numerical computation of the self-similar equations.

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Heat and Mass Transfer Effects on Linearly Accelerated Isothermal (H4) Inclined Plate J.L. Ramaprasada, K.S. Balamuruganb, B. Rushi Kumarc aDepartment of Mathematics, PB Siddhartha College of Arts and Science, Vijayawada, Andhra Pradesh, India bDepartment of Mathematics, RVR & JC College of Engineering, Guntur, Andhra Pradesh, India cDepartment of Mathematics, School of Advanced Sciences, VIT University, Vellore, Tamilnadu, India [email protected]

Current work reports heat and mass transfer e‚ects on unsteady free convection ƒow past a linearly acceler- ated isothermal inclined plate with variable temperature and mass di‚usion with thermal radiation. ‘e ƒuid is gray and non-sca‹ering medium. When time t > 0, the plate is accelerated with velocity u0t, the plate temperature is raised linearly with respect to time and the mass is di‚used from the plate linearly with time. ‘e Mathematical equations represent the present ƒow problem are solved by Laplace transform method. ‘e inƒuences of signi€cant involved parameters on velocity, temperature and concentration are tested. ‘e rate of heat transfer in terms of Nusselt number and the rate of mass transfer in terms of Sherwood number have also been computed and their impacts for various parameters are discussed through the graphs.

MHD Three-dimensional Flow of Powell Eyring Fluid over a (H5) Bidirectional Non-linear Stretching Surface with Temperature Dependent Conductivity, Heat Absorption/generation R. Meenakumari, P. Lakshminarayana Department of Mathematics, SAS, VIT, Vellore-632014, India [email protected]

‘e Present work addresses the MHD three-dimensional boundary layer ƒow of Powell Eyring ƒuid over a bidirectional non-linear stretched surface in the presence of thermal radiation and heat generation/absorption. We also considered the temperature dependent thermal conductivity. ‘e governing ƒow partial di‚erential equations are transmuted into ordinary di‚erential equations with the help of suitable similarity transfor- mations. ‘e resultant non-linear coupled system is solved numerically by shooting technique. ‘e e‚ects of various pertinent parameters on the present ƒow are presented graphically and explained in detail. ‘e numerical values of heat transfer coecient on various parameters are tabulated and analyzed.

Finite Difference Computation of Free Magneto-Convective (H6) Powell-Eyring Nanofluid Flow over a Permeable Cylinder with Variable Thermal Conductivity G. Kumaran, R. Sivaraj Department of Mathematics, SAS, VIT, Vellore-632014, India [email protected]

In this paper, a theoretical examination is implemented to analyze the impact of thermal conductivity varia- tion and thermal radiation on chemically reacting, free convective Powell-Eyring nanoƒuid ƒow over a cylin- der. ‘e nanoscale e‚ects are accounted by employing the Buongiorno model. ‘e transformed governing equations are numerically solved by using Keller box method under suitable boundary conditions. ‘e com- parison results reveal that the obtained results €nd an excellent match with the results in the literature. ‘e graphs and tables elucidate the impacts of various pertinent parameters on thermo-solutal transport charac- teristics. It is to be noted that amplifying thermal conductivity variation rises ƒuid velocity and temperature. Magnifying the radiation corresponds to weak radiative ƒux and stronger thermal conduction which decrease the heat transfer whereas the mass transfer is increased.

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(H7) Coupled Radiative and Convective Heat Transfer in Enclosures N. Rajaa, S. Saravananb aDepartment of Mathematics, KPR Institute of Engineering and Technology, Coimbatore, India bDepartment of Mathematics, Bharathiar University, Coimbatore, India. [email protected]

‘e combined e‚ect of surface radiation and buoyancy induced convection in a closed enclosure is investi- gated numerically. A vertical walls of the enclosure are cooled at a constant temperature whereas horizontal ones are perfectly insulated. Two discrete heaters with higher constant temperature are placed either side by side or one above the other inside the enclosure. ‘e surfaces of the enclosure walls and the heaters are assumed to be opaque, gray and di‚use emi‹ers and reƒectors of thermal radiation. Air is considered as a working ƒuid which is radiatively non-participating under moderate temperatures conditions. ‘e nonlinear partial di‚erential equations for the resulting ƒow were solved by the €nite volume method on a uniform staggered grid system. ‘e ƒuid ƒow and energy distribution inside the enclosure is studied for di‚erent pos- sible values of Rayleigh number, Ra and the emissivity, , of the surfaces concerned. It was found that, when the heaters remains side by side, the surface radiation plays a prominent role in altering the ƒow pa‹ern. On the other hand the e‚ect of surface radiation is minimal when the heaters are placed one above the other.

(H8) Impact of Inclined Magnetic Field on the Peristaltic Flow of a Couple Stress Fluid with Heat Transfer R. VijayaKumara, Nirmalab, P. Ratchagarc aDepartment of Mathematics, Annamalai University, Tamilnadu, India bDepartment of Mathematics, Periyar Government Arts College, Cuddalore, Tamilnadu, India cDepartment of Mathematics, Annamalai University, Tamilnadu, India. [email protected]

‘e aim of the present paper is to investigate the mathematical study of peristaltic transport of an incom- pressible couple stress ƒuid in an asymmetric channel under the inƒuence of an inclined magnetic €eld and heat transfer. ‘e channel walls contains inner and outer tube are rigid and sinusoidal wave and it is de€ned in cylindrical coordinate. ‘e non-dimensional governing di‚erential equations have been tackled under the assumption of long wave approximation and low Reynolds number. ‘e velocity equation is solved analyt- ically by utilizing the perturbation technique and exact solutions are computed from temperature equation. Impact of various parameters on ƒow characteristic have been analysed by plo‹ing graphs and discussed numerically in details. ‘e study exposes that the ƒow is appreciably inƒuenced by the presence of a inclined magnetic €eld and it is contributed in biomedical engineering such as transport phenomenon in peristaltic micro pumps.

(H9) On the Azimuthal Shear Instability of Inviscid Incompressible Swirling Flows S. Prakash, M. Subbiah Department of Mathematics, Pondicherry University, Kalapet, Puducherry-605014, India. [email protected]

Bounds on Complex Eigenvalues corresponding to unstable azimuthal normal mode disturbances of inviscid incompressible variable density swirling ƒows are obtained.

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Numerical Study of an Electrically Conducting three-dimensional (H10) Casson Fluid Flow over Porous Elastic Sheet with Non-Uniform Heat Source/Sink and Soret Effect. L. Padmavathia, S. Venkateswarlub, M. Suryanaryana Reddy c aDepartment of Mathematics, Jawaharlal Nehru Technological University Anantapur, Ananthapuramu 515002, A.P, India bDepartment of Mathematics , RGM college of Engg &Tech, Nandyal 518501, A.P, India cDepartment of Mathematics , JNTUA college of Engineering, Pulivendula 516390, A.P, India [email protected]

‘e three-dimensional ƒow of Casson ƒuid over a porous Elastic sheet in the presence thermal radiation , non- uniform heat source/sink, soret e‚ect and €rst ordered chemical reaction with the di‚usion slip condition. ‘e governing set of partial di‚erential equations is converted into the set of nonlinear ordinary di‚erential equations using suitable similarity transformations and they are solved numerically by using bvp4c shooting technique. For an analysis of the problem, velocity, temperature and concentration €elds are demonstrated graphically and also skin friction, Nusselt number, and Sherwood number are represented through tables. ‘e current results are compared to the previous results in an excellent agreement.

Effect of Viscoelasticity and Internal Current on Wave Attenuation (H11) Shyam Sunder Iyer, M.J. Vedan Department of Computer Applications, CUSAT, Cochin [email protected]

Wave a‹enuation on a viscoelastic sea bed in the presence of internal current is studied. ‘e sea bed charac- teristic is seen to have a signi€cant inƒuence on wave a‹enuation. ‘is and the inƒuence of internal current are investigated both analytically and numerically. ‘is study is related to the modelling of the phenomenon of mud bank formation observed in the south-west coast of India

Mathematical Model of MHD Flow and Heat Transfer between a Solid (H12) Rotating and Stationary Permeable Disk Maraika Alexander, Sreedhara Rao Gunakala, Victor M. Job Department of Mathematics and Statistics, ‘e University of the West Indies, St. Augustine, Trinidad and Tobago. [email protected]

‘is study examines some of the velocity and temperature characteristics of the steady MHD ƒow of a viscous incompressible ƒuid between a rotating disk and a stationary permeable disk, the depth of which is equal to that of the free ƒuid. ‘e ƒow is conceptually divided into two layers, including: a free ƒuid region; and the porous layer (where the ƒow is naturally restricted). ‘e Navier-Stokes and Brinkman equations are used to model the ƒow in the respective layers. ‘e solution strategy involves the use of a series expansion method to approximate the velocity distributions and temperature e‚ects. ‘e velocity pro€les are sketched for variations in the Reynolds number Darcy parameter, and Hartmann number; while temperature pro€les are sketched for variations in Reynolds number, Darcy parameter and thermal conductivity ratio. ‘e inƒuence of the above mentioned parameters on streamlines is also discussed.

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(H13) Radiative Newtonian Carreau Nanofluid through Stretching Cylinder Considering First Order Chemical Reaction Nasru Sivakumara, B. Rushi Kumarb, P. Durgaprasadc aDepartment of Mathematics, SRM IST,Ka‹ankuluthur, India. bDepartment of Mathematics, SAS, VIT, Vellore,India cDivision of Mathematics, VIT, Chennai, India [email protected] A Mathematical model of MHD radiative Carreau nanoƒuid is investigated for laminar, steady and incom- pressible ƒow. ‘e power law under the inƒuence of heat generation/absorption and radiation is taken into consideration. ‘e geometrical model comprises the e‚ects of thermophoresis and Brownian motion. ‘e governing conservation ƒow equations are converted into non-linear ordinary di‚erential equations by suit- able similarity transformations. ‘e emerging nonlinear governing equations are tackled by numerical tech- nique Runge-Ku‹a method of fourth order. ‘e insight of the physical signi€cances of the problem is pre- sented graphically using MATLAB So‰ware BVP4C. ‘e interference impacts of Carreau nanoƒuid ƒow char- acteristics are presented in the formation of velocity €eld, temperature €eld and concentration €eld distribu- tions. ‘e non-dimensional physical parameters, magnetic parameter, radiation parameter, ‘ermophoresis parameter, Brownian motion parameter, Weissenberg parameter and chemical reaction parameter are ana- lyzed. ‘is investigation outlined that the ability of Magnetic €eld slow down the momentum of Carreau nanoƒuid to reduce the governing ƒow.

(H14) Bioconvective Flow of Eyring-Powell Fluid Suspended with Microorganisms in the Presence of Non-linear Thermal Radiation, Activation Energy and Variable Thermal Conductivity A. Sumithra, R. Sivaraj Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore – 632014, India. [email protected] ‘e dynamics of Eyring-Powell nanoƒuid suspended with microorganisms on a plate, wedge and stagnation point is explored. ‘e ƒow €eld is subject to non-linear thermal radiation, activation energy, variable thermal conductivity, chemical reaction, and bioconvection. ‘e governing equations are modi€ed into a system of ordinary di‚erential equations via similarity transformation which are solved numerically through Runge- Ku‹a (R-K) shooting technique.‘is study addresses the inƒuence of numerous pertinent parameters on the ƒuid ƒow, mass and heat transfer characteristics and the solutions obtained are elucidated through graphs and tables. It is witnessed that the Eyring-Powell ƒuid material parameters (λ1) and (λ2) exhibit a contrary nature on the velocity pro€le. Improved values of Prandtl number aids in heat transfer. Larger values of Schmidt number weaken the concentration boundary layer. In addition, the density of micro-organisms depreciates for growing values of Peclet number and bioconvective Schmi‹ number.

(H15) Numerical Simulation of Blood Nanofluid Flow over Three Different Geometries by Means of Gyrotactic Microorganisms: Applications to the Flow of a Circulatory System H. ‘ameem Basha, R. Sivaraj Department of Mathematics, Vellore Institute of Technology, Vellore 632014, India [email protected] ‘is work is performed to express the signi€cance of the induced magnetic €eld and gyrotactic microorgan- isms on the ƒow of tangent hyperbolic nanoƒuid over a plate, wedge and stagnation point of plate. Suitable self-similarity variables are employed to convert the ƒuid transport equations into ordinary di‚erential equa- tions which have been computed with the use of the Runge-Ku‹a-Fehlberg (RKF) approach. ‘e impacts of active parameters on ƒow €eld are illustrated with graphs and tables. ‘e growing magnetic parameter lessens the blood nanoƒuid velocity over three di‚erent geometries. Blood nanoƒuid has a higher heat trans- fer rate over a stagnation point than a wedge and plate. Blood nanoƒuid temperature augments by upli‰ing the thermophoresis parameter. Peclet number shows a high impact on microorganisms density in a blood nanoƒuid. ‘is exploration can provide a clear view regarding the heat and mass transfer behavior of blood ƒow in a circulatory system and various hyperthermia treatments like the treatment of cancer.

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Cross diffusion and heat source effects on a three dimensional MHD (H16) flow of Maxwell nanofluid over a stretching surface with chemical reaction M. Vinodkumar Reddy, P. Lakshminarayana Department of Mathematics, Vellore Institute of Technology, Vellore 632014, India [email protected] ‘is paper investigates the three-dimensional magnetohydrodynamic (MHD) ƒow of an upper convected Maxwell (UCM) nanoƒuid with the thermal radiation, cross-di‚usion and heat source e‚ects along a stretch- ing sheet. ‘e e‚ects of chemical reaction, thermophoresis and Brownian motion are also studied. We have applied proper similarity variables and transformed the governing boundary layer equations into a system of non-linear ordinary di‚erential equations. ‘e present problem is solved numerically by R-K based shooting technique. ‘e variations of temperature and concentration pro€les are shown graphically and discussed in detail. ‘e numerical results of Nusselt and Sherwood numbers are presented in tabular form for di‚erent physical parameters. We noticed that the Dufour and thermal radiation parameters decrease the temperature €eld and increase the concentration €eld. Heat source and chemical reaction parameters decrease the Nus- selt number and increase the Sherwood number. Also, noticed that the Dufour and Soret numbers raise the Nusselt number, but they decline the Sherwood number.

Similarity Solutions of One-dimensional MHD Shock Wave in a Non-Ideal (H17) Gas with the Effect of Viscosity Narsimhulu Dunnaa, Ravilise‹y Revathib aDepartment of Statistics and Applied Mathematics, School of Mathematics and Computer Sciences, Central University of Tamil Nadu, Neelakudi, ‘iruvarur - 610 005, Tamil Nadu, India. bDepartment of Mathematics, Birla Institute of Technology and Science Pilani, Hyderabad - 500078, Telangana, India. [email protected] ‘e interaction of shock waves with viscosity into a di‚erent medium is one of the most important problems in the regime of compressible gas ƒow. ‘e e‚ect of viscosity and non-idealness parameter on unsteady cylindrical strong magnetohydrodynamic (MHD) shock wave driven out by a piston moving with the time n according to a power law [vp ∝ (t/t0) ] in a non-ideal gas for both adiabatic and isothermal ƒows are investigated. ‘e governing equations considered are reduced into a set of ordinary di‚erential equations (ODEs) by using similarity transformations. To obtain distinct features of shock propagation, it is assumed that the dusty gas ƒow is the mixture of real gas and small solid particles which are uniformly distributed in the medium and the equilibrium ƒow condition is maintained. Numerical calculations have been performed to obtain the pro€les of ƒow variables between the piston (η = ηp) and shock front (η = 1) using Runge- Ku‹a method of 4th order. It is found that the ƒow variables have distinct e‚ects in perfect gas, dust-free gas, and a mixture of perfect gas and small solid particles by increasing values of non-idealness parameters in the presence of viscosity. ‘ese e‚ects are more signi€cant in the case of isothermal ƒow when compared with adiabatic ƒow. ‘e €ndings con€rmed that the viscosity and non-idealness parameters have major e‚ect on the ƒow variables and shock strength.

Gravity Effects on the Onset of Transient Convection in a Porous (H18) Medium S. Vigneshwaran, S. Saravanan Department of Mathematics, Bharathiar University, Coimbatore - 641 046, Tamil Nadu, India [email protected] ‘is study is concerned with the onset of transient convection in a ƒuid saturated horizontal porous layer heated uniformly from below. ‘e layer is subjected to a gravity gradient along its height. Bo‹om heating is imposed suddenly that can introduce temperature gradients within the layer, in particular adjacent to the bo‹om surface. A linear stability analysis is carried out employing the propagation theory. ‘e resulting eigenvalue problem is solved using the shooting technique. ‘e conditions representing the onset of transient convection are obtained in terms of critical Rayleigh-Darcy number and critical wave number.

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(H19) A Study with Magnetic field on Stenosed Artery of Blood flow Sarfraz Ahmed, Biju Kumar Du‹a Department of Mathematics, School of Basic Sciences, Assam Kaziranga University, Jorhat- 785006

‘e present study and its mathematical modelling was done to decide the impact of the magnetic €eld on blood moving through a pivotally asymmetric but radially symmetric atherosclerotic conduit. Herschel- Bulkley ƒuid model condition has been taken to non-Newtonian character of blood ƒow in the presence of applied magnetic e‚ect. ‘e mathematical model is analyzed graphically and numerically. It was revealed that within the sight of applied magnetic €eld, blood didn’t de€nitely change the stream designs, yet caused an apparent decline in the shear stresses and a marginally lower protection from stream. ‘is hypothetical demonstration to cardiovascular infections is considered in our study.

(H20) Soret and Heat Generation Effects on an Unsteady Free Convective Flow Past an Exponentially Accelerated Plate with Constant Mass Flux

J. Prakasha, R. Swethab, S. Vijaya Kumar Varmac aDepartment of Mechanical Engineering Science Faculty of Engineering and ‘e Built Environment University of Johannesburg, Auckland Park Kingsway Campus Johannesburg,South Africa bDepartment of Mathematics, Gudalvalleru Engineering College, Gudlavalleru,521356, A.P. India. cDepartment of Mathematics, S. V. University, Tirupati (A.P.), India. [email protected]

Closed form analytical analyzation has been accomplished to examine the consequences of Soret and heat ab- sorption on a free unsteady convective ƒow with mass and heat transfer of a viscous, electrically conducting and incompressible ƒuid over a vertical plate which is exponentially accelerated. ‘e plate is accelerated ex- at ponentially in its plane with a velocity u = u0e at time t > 0 and at the same time, the level of temperature near the plate raises to TW with constant mass ƒux. ‘e Boussinesq’s dimensionless equations are €gured out by the method of Laplace transforms in closed form. ‘e results of these ƒow parameters on pro€les of tem- h ∂u i perature,concentration, velocity are presented in graphs and the e‚ects of velocity gradient ∂y ,surface y=0 h ∂θ i h ∂c i heat transfer rate tables. ∂y and surface mass transfer rate ∂y are discussed through tables. y=0 y=0

(H21) Dufour and Soret Effects on MHD Flow of Cu − water and Al2O3 − water Nanofluid Flow over a Permeable Rotating Cone Padmaja K, B. Rushi Kumar Department of Mathematics,School of Advanced Sciences, VIT, Vellore-632014, Tamil Nadu, INDIA. [email protected]

In this paper, we investigate numerically the nanoƒuid ƒow about a permeable, vertical rotating cone with Dufour and Soret e‚ects in the presence of thermal radiation, magnetic €eld and chemical reaction. ‘e heat and mass transfer of a MHD nanoƒuid about a porous vertical rotating cone is analysed. ‘e ƒuid ƒow considered is steady, laminar and incompressible. A uniform suction/injection of the ƒuid is present on the surface of the cone. ‘e cone is symmetric about the axis of rotation and is rotating with an angular rotating velocity. ‘e governing equations pertinent to the ƒuid ƒow and the thermophysical properties of the nanoƒuid are nonlinear partial di‚erential equations (PDEs). Using similarity transformation variables, these partial di‚erential equations are converted into ordinary di‚erential equations (ODEs). MATLAB’s bvp4c solver is used to solve the converted system of ODEs. To achieve a clear understanding about the physical insights of the problem, the two nanoƒuids- copper in water and alumina in water are analysed. ‘e graphical representations of tangential, normal, circumferential velocity pro€les, temperature pro€les and concentration pro€les with respect to various ƒuid ƒow parameters are investigated. ‘e Dufour and Soret numbers and the thermal radiation parameter have signi€cant impact on the rates of heat and mass transfer.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 91 VIT-Vellore

Entropy Generation on EMHD Stagnation Point Flow of Hybrid (H22) Nanofluid over a Stretching Sheet: Homotopy Perturbation Solution Shaik Jakeer, P. Bala Anki Reddy Department of Mathematics,School of Advanced Sciences, VIT, Vellore-632014, Tamil Nadu, INDIA. [email protected]

‘e intention of this article is to explore the entropy generation in EMHD hybrid nanoƒuid on a stagnation point in the presence of slips, heat generation and viscous dissipation. ‘e ƒuid in the enclosure is water containing hybrid nanoparticles Ag-Cu. Suitable self-similarity variables are employed to transform the non- linear di‚erential systems into an ordinary di‚erential system, which computed via homotopy perturbation method (HPM). ‘e comparison with the homotopy perturbation method (HPM) gives an accurate and reli- able result than the numerical method (Runge-Ku‹a method). ‘e graphical results are expressed for velocity, temperature, entropy generation, Bejan, skin friction and Nusselt number with an impact of active parame- ters. ‘e higher values of electric €eld enhancing the velocity whereas the opposite nature for a magnetic €eld parameter. ‘e entropy generation rises for higher values of a magnetic parameter, Eckert number and α1. In the magnetic €eld and electromagnetic €eld plays an important role in biomedical applications especially radiofrequency ablation (RFA), magnetic resonance imaging (MRI), cancer therapy, tumor therapy, malaria infection. ‘is theoretical investigation may be pro€table in biomedical engineering, especially cardiology, cure of skin disorders and treat tumors in Uterus.

Natural Convection in a Nanofluid Saturated Porous Medium under (H23) Time-Periodic Gravity Modulation M. Kousalya, S. Saravanan UGC DRS Centre for Di‚erential Equations and Fluid Dynamics, Department of Mathematics, Bharathiar University, Coimbatore 641 046, Tamil Nadu. [email protected]

Time-periodic gravitational €eld is of immense importance in space laboratory experiments involving crystal growth and other related €elds. Hence the e‚ect of time-periodic gravity modulation on the onset of natural convection in a nanoƒuid saturated porous medium is investigated. In particular, water based nanoƒuids containing conventional metallic and metal oxide particles are considered. ‘e Khanafer-Vafai-Lightstone model with more realistic empirical correlations for the physical properties will be used. ‘e medium is assumed to be heated uniformly from below and a stability analysis is carried out on this con€guration with the help of the Floquet theory. ‘e emerging instabilities of synchronous and subharmonic types and the transition between them will be examined. ‘e applications of the results of the present study in physical problems will be addressed.

Soret and Dufore Effects on MHD Flow through the Porous Medium (H24) about a Rotating Vertical Cone in Presence of Thermal Radiation M. Chitra, S. Jeevitha Department of Mathematics, ‘iruvalluvar University, Vellore- 632115 [email protected]

‘e objective of this paper is to analysis the Soret and Dufour e‚ect with heat and mass transfer on MHD ƒow through a porous medium of a binary ƒuid mixture about a vertical rotating cone along with thermal radiation. ‘e governing equations are nonlinear partial di‚erential equations and so by using similarity transformation. ‘ey are converted into ordinary di‚erential equations. Matlab’s built in solver bvp4c is employed to solve numerically the ordinary di‚erentials equations. ‘e e‚ect of various parameter on the Velocity, Temperature and Concentration pro€les are computed and discussed through graphs.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 92 VIT-Vellore

(H25) Effective Thermal Conductivity and MHD Convection Flows of Non Newtonian Nanofluid from Horizontal Circular Cylinder P. Vijayalakshmi a, R. Sivarajb aDepartment of Mathematics, Muthurangam Government arts college, Vellore, Tamilnadu, India. bVIT University, Vellore, India [email protected] , [email protected]

‘is paper illustrates the combined magneto hydrodynamic (MHD) ƒows of casson viscoplastic nanoƒuid from a horizontal isothermal circular cylinder in non-Darcy porous medium. ‘e e‚ect of Brownian motion and thermophoresis are studied and validated. ‘e overall heat and mass transfer shape are enhanced for improving the thermal and solutal dispersion e‚ect. ‘e governing partial di‚erential equations are turned into nonlinear ordinary di‚erential equations using appropriate non similarity transformation and are solved numerically using Keller-Box €nite di‚erence technique. Numerical results for velocity, temperature, con- centration along with skin friction coecient, heat and mass transfer rate computed for di‚erent values of physical parameters. It is identi€ed that velocity, heat and mass transfer rate are increased with increasing casson ƒuid parameter whereas temperature, concentration and skin friction are e‚ectively decreased. Also observed that velocity is decreased with increasing Forchheimer parameter whereas temperature and nano- particle concentration are enhanced. ‘e temperature pro€les are enhanced for thermal dispersion coecient and concentration pro€les are enhanced for increasing solutal dispersion coecient.

(H26) Cattaneo-Christov Heat Flux Model for MHD Sakiadis Flow of a Carrearu Fluid Subject to artic Autocatalysis Chemical Reaction V. Nagendramma Deparment Of Mathematics, Presidency University, Banglore-560064 [email protected]

‘is paper explored the heat and mass transfer characteristics in magnetohydrodynamic Sakiadis ƒow of a Carreau ƒuid in the presence of autocatalysis chemical reaction. Ca‹aneo-Christov heat ƒux model is con- sidered to develop the energy equations. ‘e governing partial di‚erential equations of motion were reduced to a system of ordinary di‚erential equations with the aid of local similarity variables. ‘ese ordinary di‚er- ential equations were further solved by using the Runge-Ku‹a Fourth order method with BVP5C technique. ‘e thickness of the thermal boundary layer increases with increasing values of magnetic €eld parameter and Weissenberg number while a reduction is noticed with power law index and thermal relaxation parame- ters and Prandtl number. Concentration distribution decreases for higher values of strength of homogeneous reaction parameter K. Strength of heterogeneous reaction parameter ks results in the enhancement of con- centration.

(H27) Significance of Nanoparticle Aggregation of Nanofluid flow in an Irregular Channel Sandra Jestine, B Mahanthesh Department of Mathematics, CHRIST (Deemed to be University), Bangalore 560029, Karnataka, India [email protected]

‘e study of incompressible unsteady laminar ƒow and free convective heat transfer of nanoƒuid between a vertical long wavy wall and a parallel ƒat wall is carried out. For the investigation, Ethylene glycol-based nanoƒuid with titania nanoparticles were used. ‘e study examines the role of nanoparticles aggregation e‚ect under the inƒuence of applied magnetic €eld, thermal radiation and internal heat absorption. E‚ective properties of the nanoƒuid are measured by mixture theory and e‚ective medium theory. ‘e semi-analytical solution of the problem is obtained by regular perturbation method. E‚ect of di‚erent physical parameters on the velocity pro€le and temperature pro€le have been studied. In addition, the skin friction and Nusselt number are also examined and presented graphically.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 93 VIT-Vellore

Effects of MHD and Electro-Magnetic Fields in Nanofluid over a (H28) Stretching Sheet G. Lakshmi Devi, H. Niranjan Department of Mathematics, School of Advanced Sciences Vellore Institute of Technology, Vellore-632014, India. [email protected]

‘e present paper targets to explode the e‚ects of Electro-magnetic €elds and heat transfer in a nanoƒuid over a stretching sheet near a stagnation point. In this mathematical model hires the electric €eld, thermophoresis, Brownian motion and magnetic €eld of the system is explode. ‘e governing partial di‚erential equations are non-dimensionalized via related similarity transformation and the results are solved numerically. ‘e impression of some governing ƒow constants on the temperature, velocity, and concentration of nanoparti- cles are described through graphs. ‘e variation of engineering quantities such as the Nusselt number and Sherwood number are calculate

The Study of Rayleigh-Benard´ Convection in Vertically Oscillating (H29) Hybrid Nanoli€ids Gayathri, S. Pranesh Department of Mathematics, CHRIST (Deemed to be University), Bangalore, India [email protected]

Rayleigh-Benard´ convection in vertically oscillating hybrid nanoliquids is studied in this paper. ‘e gravity modulation e‚ect is studied on €‰een di‚erent hybrid nanoliquids by carrying out linear and non-linear analysis. Venezian approach is used to obtain the expression for the correction Rayleigh number and wave number. Fourier series method is used in the non-linear analysis to obtain the expression for Nusselt number. It is observed that with the increase in amplitude of modulation, average Nusselt number decreases and with the increase in frequency of modulation, average Nusselt number increases.

Analysis of Fluid Flow in Triangular Cavity using FEM (H30) Mariya Helen Mercy JK, V. Prabhakar Department of Mathematics, Vellore Institute of Technology, Chennai, India [email protected]

In the present work the temperature distribution and distortion of ƒuid ƒow inside a triangular cavity is validated using ANSYS. ‘ree cases are dealt here. Case 1: ‘e vertical wall is insulated, bo‹om wall heated up and the inclined wall is kept cold. Case 2: ‘e vertical wall is hot, the bo‹om wall insulated and the inclined wall is kept cold. Case 3: ‘e vertical wall is cold, the bo‹om wall insulated and the inclined wall is heated. ‘e penalty €nite element method is applied to solve the residuals of the non-dimensional form of the governing di‚erential equation. Di‚erent types of ƒuids from air to engine oil is studied. ‘e solid within which the ƒuid ƒows also was varied and analyzed. A no slip boundary condition is applied. ‘e laminar nature of the ƒuid is desired with a di‚erent combination of ƒuids and solids. ‘e same model can be extended for a €eld problem like plastic injection mould ƒow with objective function with the results and a mathematical model can be developed.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 94 VIT-Vellore

(H31) The Effect of The Viscosity of ohe Porous Solid on ohe Parallal Plate Channal Flow of Ree-Eyring Li€id when the Dividers are Provided with Non-Erodible Porous Lining R.L.V. Renuka Devi Department of Mathematics, Sri Venkateswara University, Tirupati, Andhra Pradesh [email protected]

In this analysis the e‚ect of the viscosity of the porous solid on the parallel plate channel ƒow of Ree-Eyring liquid when the dividers are provided with non-erodible porous lining is contemplated. ‘e governing partial di‚erential equations are changed to ordinary di‚erential equation by utilizing non-dimensional quantities and solved it analytically. ‘e e‚ects of governing parameters on the liquid velocity are showed graphically.

We researched the stream in the free stream area and permeable stream districts by utilizing Darcy law and Ree-Eyring liquid model respectively.

(H32) Wall Slip Effects on Nanofluid Flow in a Porous Channel A. Subramanyam Reddya, S. Srinivasb aDepartment of Mathematics, VIT, Vellore -632 014, Tamil Nadu, India. bDepartment of Mathematics, VIT-AP University, Amaravati- 522237, Andhra Pradesh, India. [email protected]

‘e present analysis deals with the nanoƒuid ƒow in a porous channel with slip e‚ects. In this work, blood is considered as a Newtonian ƒuid and gold (Au)/copper (Cu) as nanoparticles. System of nonlinear ordinary di‚erential equations is derived from the governing ƒow equations and is solved with the aid of homotopy analysis method. Convergence of series solutions is analysed. ‘e inƒuence of nanoparticle volume fraction, wall expansion ratio and slip parameters on the various ƒow variables have been discussed in detail.

(H33) Effect of Heat Transfer in a Micropolar Fluid on the Onset of Rayleigh-Benard-Chandrasekhar´ Convection with Porous Medium under Time Periodic Boundary Temperature and Internal Heat Source Maria Anncy , Joseph T V , Pranesh S Department of Mathematics, CHRIST (Deemed to be University), Bangalore, India [email protected]

‘e impact of heat transfer rate over a surface containing voids whose temperature at the boundaries are modulated in a micropolar ƒuid is investigated to understand the thermal instability of the system exposed to magnetic €eld and internal heat source. ‘e heat transfer rate within the system with respect to time is found using Lorentz model. ‘e outcome of the study conveys that as the internal heat of the system is increased the heat transfer rate within the system also increases indicating that the thermal instability is destabilized. Moreover, increase in Chandrasekhar number shows a decrease in heat transfer rate this is because, the impact of strong magnetic €eld is to reduce the rate of heat transport.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 95 VIT-Vellore

MHD Combined Convection Flow over a Moving Non-Isothermal Vertical (H34) Plate with Soret and Dufour Effects and Viscous Dissipation A. Neerajaa, R.L.V. Renuka Devib, N. Bhaskar Reddyb aAditya College of Engineering, Surampalem, East Godavari Dt. Andhra Pradesh, India bSri Venkateswara University, Tirupati, Andhra Pradesh, India [email protected]

‘is paper focuses on the numerical solution of a steady MHD combined convection ƒow of a viscous incom- pressible electrically conducting ƒuid along a moving, non-isothermal vertical plate in the presence of mass transfer, Soret and Dufour e‚ects and viscous dissipation. ‘e governing boundary layer equations have been transformed to a two-point boundary value problem in similarity variables and the resultant problem is solved numerically using the fourth order Runge-Ku‹a method along with shooting technique. ‘e inƒuence of various governing parameters on the ƒuid velocity, temperature, concentration, skin-friction coecient, Nusselt number and Sherwood number are computed and discussed in detail.

Triple Diffusive Convection in Temperature and Electric Field (H35) Dependent Variable Viscosity in a Newtonian Dielectric Li€id with Internal Heat Source S. Pranesh, P.G. Siddheshwar, Ansa Mathew Department of Mathematics, CHRIST (Deemed to be University), Bangalore. [email protected]

‘e linear and non-linear analysis of the triple di‚usive convection in a temperature and electric €eld variable viscosity dielectric Newtonian liquid with internal heat source (or sink) are studied analytically. ‘e strength of heat source and electric €eld are characterised by internal Rayleigh number and electric Rayleigh number respectively. ‘e linear stability analysis shows that the increase in variable viscosity and internal heat source is to stabilize the system. ‘e e‚ect of internal Rayleigh number, electric Rayleigh number and variable viscosity on heat and mass transfer is investigated by deriving the generalized Lorenz model and solving it numerically. It is found the e‚ect of increase of all these parameters increases the heat and mass transfer.

Linear and Non-Linear Analysis of Internal Heat Modulation on (H36) Rayleigh-Benard´ Convection in Ferromagnetic Li€ids with Couple Stress Meghana J, Pranesh S Department of Mathematics, CHRIST (Deemed to be University), Bangalore, India [email protected]

Rayleigh–Benard´ convection in ferromagnetic liquids with couple stress in the presence of internal heat modulation is studied using linear and non-linear analysis. A non-autonomous Lorenz model for the problem is derived and both linear and nonlinear analyses are performed using this Lorenz model. ‘e expression for the critical Rayleigh number and the correction Rayleigh number is found from the linearized Lorenz model. ‘e Lorenz system of equations is solved for the amplitude to arrive at the Nusselt number which quanti€es the heat transport. ‘e inƒuence of various non-dimensional parameters on the onset of convection and heat transfer are analysed. ‘e study reveals that Couple stress parameter stabilizes the system and decreases the heat transfer. It is also found that square wave type of internal heat modulation is more stable compared to other wave types of internal heat modulation.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 96 VIT-Vellore

(H37) Linear and Nonlinear Analysis of Two-fre€ency Time-periodic Boundary Temperature on Rayleigh-Benard´ Convection Ansa Mathew, S. Pranesh, P.G. Siddheshwar Department of Mathematics, CHRIST (Deemed to be University), Bangalore. [email protected]

‘e paper analyses the e‚ect of two-frequency temperature modulation at the onset of convection and heat transfer in a Newtonian ƒuid by carrying out a linear and non-linear analysis. ‘e Venezian approach is assented encompassing the correction Rayleigh number and wave numbers for meagre amplitude two- frequency temperature modulation ‘e Lorenz model is derived and is solved numerically to quantify the heat transport through Nusselt number. ‘e e‚ects of various combinations of sinusoidal and non-sinusoidal waveforms have been studied on the onset of convection and on heat transfer. On comparison with no- modulation and single-frequency temperature modulation, it is seen that two-frequency temperature mod- ulation delays the onset of convection and decreases the heat transport with increase in mixing angle. It is observed that temperature modulation results in sub-critical motion however out-of-phase temperature modulation is more stable compare to others.

(H38) Nonlinear Rayleigh-Benard´ Convection in Variable Viscosity Ferromagnetic Li€ids Prakash Ra, Jayalatha Ga, Siddheshwar P.Gb,Sekhar G.Nc aDepartment of Mathematics, RV College of Engineering, Bengaluru 560059, Karnataka, India bDepartment of Mathematics, CHRIST (Deemed to be University), Bengaluru 560029, Karnataka, India cDepartment of Mathematics, BMS College of Engineering, Bengaluru 560019, Karnataka, India [email protected]

‘e paper deals with linear and nonlinear stability subjected to thermal convection of a variable viscosity Newtonian ferromagnetic liquid in the existence of uniform vertical magnetic €eld. ‘e truncated Galerkin expansion is employed to study the perturbations in the system due to external constraints. ‘e nonlinear stability is based on truncated Fourier series. ‘e modi€ed Lorenz model together with variable viscosity parameter is €rst derived and then it is used to describe both linear and nonlinear analyses of the system. ‘e expressions for the critical Rayleigh number, R, Nusselt number (Nu) is found by solving the Lorenz system of equations. ‘e e‚ects of di‚erent parameters on the heat transport, thermal convection have been discussed. ‘e results obtained agree truly with those of limiting cases.

(H39) Analytic Solution of Bloch E€ation for a Time Varying Magnetic Field in the Transverse Direction Parameswaran Ra, M.J. Vedanb aDepartment of Mathematics, Amrita School of Arts & Sciences, Kochi.Amrita Vishwa Vidyapeetham bDepartment of Computer Applications, Cochin University of Science & Technology [email protected]

A solution for Bloch Equation in the case of time varying magnetic €eld in the transverse direction is ob- tained. For this, purely analytical techniques with fundamental matrix generally used in solving a system of di‚erential equations with non constant coecients is employed. When the magnetic €eld increases expo- nentially, magnetization vector satis€es a second order di‚erential equation which has the form of a Sturm Liouville equation. ‘e solution in this case is also obtained.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 97 VIT-Vellore

Stability of Microscopic Body Cosmological Model in Barber (H40) Self-Creation Theory of Gravitation J.S. Wath, A.S. Nimkar Shri Dr. R.G. Rathod Arts and Science College, Murtizapur, Dist. Akola (M.S.) India. [email protected], [email protected]

In this paper, we have studied stability of cosmological model in Ruban’s background in the context of Barber Self-Creation theory of gravitation in the presence of macroscopic body. Exact solutions are obtained by using relation between metric coecients and radiation. Also, we discuss the features of the obtained model.

Bianchi Type-III Cosmological Model Barber Self-Creation Theory of (H41) Gravitation A.M. Pund , P.M. Lambat Department of Mathematics, Shri Shivaji Education Society Amravati’s Science college, Congress Nagar, Nagpur (M.S.) India. ashokpund64@redi‚mail.com

In this paper, we have investigated the self-creation theory of cosmology proposed by Barber with wet dark ƒuid as a source of ma‹er in Bianchi type-III space time. ‘e solution of €eld equation and cosmological model is obtained by using relation between metric coecients and radiation universe. Also, we have discussed some Physical and kinematical properties of the obtained model.

Exact solution for Cosmological constant problem, Variable (H42) Gravitational Constant Problem and other Cosmological Problems and the Continuity between Anisotropic and Isotropic Cosmology with Single type of Scalar Field and Scale Factor Shouvik Sadhukhana, Alokananda Karb aIndian Institute of Technology , Kharagpur, West Bengal , India. bUniversity of Calcu‹a , Kolkata , West Bengal , India. [email protected], [email protected]

We have derived exact solutions for several cosmological problems in case of both Isotropic and Anisotropic cosmology. We have established the direct mapping between the anisotropic Bianchi Type I model and a 2 a Isotropic FRW model. We have assumed cosmological constant as Λ = 3α a β a which helps us to solve some cosmological problems in generalized way. We have established all the cosmological phases with our derived generalized scale factor. In our last few papers we had given some predictions about anisotropy as well as viscosity and here we have derived those predictions true. At last we have de€ned intessence scalar €eld dependent potential and its time evolution using a special type of canonical transformation technique. We have also predicted a direct transition between dark energy and baryonic ma‹ers. One of the most im- portant areas of this paper is the derivation of Hyperinƒation in Friedmann model.

We get time evolution of G, Λ, viscosity η and anisotropic shearing constant σ which are controlling the phases and its transformations with time. We derived that both shearing scaler and cosmological con- stant are decreasing function of time whereas coecient of viscosity and gravitational constant are partly decreasing and partly increasing and this fact caused the graceful exit as well as reheating phase in cos- mic evolution. ‘e most interesting and new part of this research. So the Hyperinƒationary model is as a = a0 exp((H0 exp(bt))t). We also derived the inƒation which matched completely with well known inƒa- tion solution but we proved that inƒation is not a phenomena at w = −1. It happened just a‰er a while of this point. Finally we got Scalar €eld vs Field potential relation that helped us to plot the following graphical representation.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 98 VIT-Vellore

(H43) Bianchi Type VI0 String Cosmological model in Lyra’s Manifold S.R. Hadole, A.S. Nimkar Shri Dr. R.G. Rathod Arts and Science College, Murtizapur, Dist. Akola (M.S.) India. [email protected], [email protected]

A solution of €eld equations has been obtained for a Bianchi Type VI0 space-time with cosmic string in Lyra’s Manifold by using relation between metric coecients and Reddy string. Certain physical and kinematic properties of the model have been examined.

(H44) Wet Dark Fluid Cosmological Model In Barber Self-Creation Theory Of Gravitation S.C. Wankhade, A.S. Nimkar Shri Dr. R.G. Rathod Arts and Science College, Murtizapur, Dist. Akola (M.S.) India. [email protected], [email protected]

In this paper, we investigate a Bianchi type VIII cosmological model with wet dark ƒuid in Barber Self- Creation theory of gravitation. To get the determinate model of the universe, we have assumed the relation between metric coecients R and S i.e S = Rn Also, the behavior of the model in radiation universe and physical implications of the model are discussed in detail.

(H45) Stability of Bianchi Type-IX Cosmological Model in Brans -Dicke Theory of Gravitation A.S. Nimkar Shri Dr. R.G. Rathod Arts and Science College, Murtizapur, Dist. Akola (M.S.) India. [email protected]

In this paper ,we have investigated stability of Bianchi Type-IX cosmological model in the presence of energy momentum tensor for ma‹er and the holographic dark energy in the framework of scalar tensor theories of gravitation proposed by Brans-Dicke(1961) . To obtain the exact solution we have used variation law for Hubble parameter. Also, we discuss the physical and kinematical properties of the model.

(H46) Hamiltonian Formalism of Bianchi Type 1 Model for Different types Cosmic Fluid and Effect of Bulk Viscosity on intessence Model and Scalar Field Potential Alokananda Kara, ShouvikSadhukhanb aDepartment of Physics, University Of Calcu‹a, Kolkata, India. bDepartment of Physics, Indian Institute of Technology, Kharagpur, India. [email protected],[email protected]

We have proposed the Hamiltonian formalism of Bianchi type-1 cosmological model for di‚erent types of cosmic ƒuids including both viscous and non-viscous cases. We have used generalized equation of state (EOS) parameter ω and the cosmological constant Λ. We have proposed a Lagrangian for the anisotropic Bianchi type-1 model in view of a variable mass-system moving in a variable potential. We have considered a canonical transformation from expanding scale factor to scalar €eld ϕ, which gives a proper transition from classical theory to €eld theory of cosmology. At the end we have derived Wheeler-DeWi‹ equation from the Hamiltonians in operator form and predicted the coupling of Coecient of viscosity and anisotropy. We have also predicted the time variation of scalar €eld potential with coecient of viscosity. We have also de€ned the e‚ect of bulk viscosity on intessence model and scalar €eld potential as well as on classical €eld. In the derivation we have also shown the possibility of time dependent evolution of gravitational constant G. ‘e evolution pro€le for anisotropy has also been shown. It is observed that viscosity doesn’t modify the relationship between scalar €eld potential V (φ) and Scalar €eld φ in case of viscous ƒuid of universe.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 99 VIT-Vellore

Propagation Of Stoneley Waves In Non-Local Elastic Medium (H47) Ajmeera Chandulal Department of Mathematics, National Sanskrit University, Tirupati – 517 507, [email protected]

In particular, the non–local continuum is formulated and developed by Kunin, Edelen and Eringen. ‘is theory is physically valid because we can compare this theory with classical and molecular theories. In this paper, the propagation of stoneley waves in non–local elastic medium is considered. ‘e period equation is derived and it is used to draw the stoneley boundary curves, taking two limiting cases. ‘e nature of stoneley wave in non–local elastic medium is found to be dispersive unalike the non–dispersive nature of the stoneley waves in classical elasticity. ‘e two limiting cases of the period equation are obtained. ‘ese two equations are solved numerically for ratios of densities and rigidity moduli of two elastic half–spaces. Using these results, the stoneley boundary curves are drawn.

Remarks On The Dynamic Responce Of Irregular Orthotropic (H48) Viscoelastic Half-Sace Sunjected To a Moving Line Load M.K. Pal, A.K. Singh Department of Mathematics & Computing, IIT(ISM) Dhanbad - 826004, India. [email protected]

In this paper, we analyse that e‚ect of induced stresses (compressive, shear and tensile) due to moving line load on irregular functionally graded orthotropic viscoelastic half-space. ‘e expressions for said induced stresses are deduced in closed-form by using analytical approach. ‘e e‚ect of various physical parameters viz. maximum depth of irregularity, functionally gradedness, irregularity factor, and frictional coecient on induced stresses for the considered model has been investigated. For numerical computation, the half-space are comprised with Carbon-€ber and Prepreg materials. Moreover, some notable characteristics have been outlined and delineated through graphs by using Matlab so‰ware.

Investigation of thermal excitation induced by laser pulses and (H49) thermal shock in the half space medium with variable thermal conductivity Rakhi Tiwari Department of Mathematics, Nitishwar Mahavidyalaya, A Constituent Unit of Babasaheb Bhimrao Ambedkar Bihar University, Muza‚arpur, India [email protected]

‘e present study is concerned with the investigation of the transient responses of a half-space medium with the variable material properties in the context of dual phase lag thermo -elasticity. Boundary of the medium is subjected to a thermal shock. Further, the bounding surface is considered to be heated by a non- Gaussian laser beam. Kirchho‚ transformation and Laplace transform technique have been adopted to obtain the analytical solutions. Graphical results of the €eld-components – non-dimensional conductive tempera- ture, non-dimensional displacement as well as non-dimensional stress have been achieved and illustrated for the di‚erent values of time and variable thermal conductivity. Signi€cant results are obtained and it is believed that these results may support in designing the structures heated by a non-Gaussian laser beam in engineering.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 100 VIT-Vellore

(H50) Investigation on SH-wave propagation in a porous piezoelectric composite with mechanically and electrically perfect interfacial boundaries Sharmistha Rakshita, Anirban Lakshmana, Kshitish Ch. Mistrib aDepartment of Mathematics, IIIT Kalyani, Kalyani,741235 bDepartment of Mathematics, Chandrapur College, Purba Burdwan 713145 sharmistha [email protected]

‘e propagation of shear horizontal(SH) waves in tri-layered structure consisting of a perfectly bonded porous piezoelectric layer sandwiched by two isotropic layer is studied analytically in this paper. With the aid of constitution equation for a porous piezoelectric structure, the solution of mechanical displacement and electric potential is explored. Dispersion relation is derived for electrical-mechanical boundary conditions at the free surface and interface, solved numerically and illustrated by means of graphs. ‘e e‚ect of porosity, width ratio on the dispersion curve are studied extensively.PZT-5H materials is considered for validation of numerical procedure and further investigation of results .‘e €ndings of this mathematical schema can be used for designing and developing of underwater acoustic devices for sensing, non-destructive testing and health monitoring devices.

(H51) Study of torsional problem in Micro-isotropic, Micro-elastic solid E. Rama Department of Mathematics Osmania University, Hyderabad, Telangana. [email protected]

In the present paper torsional problem in a Micro-isotropic, Micro-elastic solid is studied and obtained the components of displacement, microrotation, stress and couple stress and shown them graphically.

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Section I: Mathematical Modelling, Bio-Mathematics, Operations Research

Bifurcation and Chaos in a Discrete Predator-Prey Model with Holling (I1) Type-III Functional Response and Harvesting Effect Anuraj Singh, Preeti Deolia ABV-Indian Institute of Information Technology and Management Gwalior, M.P.,India [email protected], [email protected] Nowadays, due to the indiscrete and unconventional harvesting of biotic assets, over-exploitation of biolog- ical resources is becoming a topic of much concern among researchers. In this study, a discrete resource- consumer model with Holling type III functional response and harvesting e‚ort is investigated. Bifurcation theory and center manifold theorem are used to establish the conditions for the existence of various bifur- cations of codimension 1 such that Neimark-Sacker bifurcation, transcritical bifurcation and ƒip bifurcation. Numerical simulation is performed to demonstrate the analytical €ndings.

Nonlinear Dynamical Behaviour of an SEIR Mathematical Model: (I2) Effect of Information, Saturated Treatment and Time Delay Tanuja Dasa, PK Srivastavaa, Anuj Kumarb aDepartment of Mathematics, Indian Institute of Technology Patna, Patna 801103, India bSchool of Mathematics, ‘apar Institute of Engineering and Technology, Patiala 147004, India. [email protected] When the disease spreads in a population, individuals tend to change their behaviour due to presence of information about disease prevalence. ‘erefore, the infection rate is a‚ected and the incidence term in the disease model should be appropriately modi€ed. In addition, it will be also interesting to see how limitation of medical resources have their impact on the dynamics of the disease. In this work, we propose and analyse an SEIR epidemic model which accounts for the information induced non-monotonic incidence function and saturated treatment function. ‘e model analysis is carried out and it is found that when the basic reproduc- tion number is below one, the disease may or may not die out due to the saturated treatment (i.e a backward bifurcations may exist and cause multi-stability). Further, we note that in this case disease extinction is possible if the medical resources are available for all. When basic reproduction number exceeds one, there is possibility of existence of multiple endemic equilibrium points. ‘ese multiple equilibrium points give rise to rich and complex dynamics by showing various bifurcation and oscillations (via Hopf-bifurcation). A global asymptotic stability of unique endemic equilibrium (when it exists) is established under certain para- metric conditions. An impact of information is shown and also sensitivity analysis of model parameters is performed. Further, a corresponding delay mathematical model is proposed and analysed incorporating delay in incubation. ‘e delay model is analysed and existence of periodic oscillations in population is established via Hopf-bifurcation. Various cases are considered numerically to provide the insight of model behaviour mathematically and epidemiologically. Our study underlines that saturation in treatment i.e. limitation of medical resources may cause bi (multi)-stability in the model system. Also, information plays signi€cant role and gives rise a rich and complex dynamical behaviour of the model. Delay in incubation, may cause oscillations in the populations.

Painleve Property Analysis of Self Interacting Four Species Food Chain (I3) Mathematical Model and its Generalization to N-Species B.V. Baby 3/88, Jadkal Post,Udupi District, Karnataka [email protected] Long time scale dynamics of self interacting two types of Four Species Food Chain Mathematical Models and their generalization to N-species model are studied. It is found that, more than two species models are always of non Painleve‘ types and so they have erratic dynamics and that may lead to chaos in long time scale. Models are extended to N-species, where N is any €nite integer greater than two.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 102 VIT-Vellore

(I4) The Role of Media on the Dynamics of Zika Outbreak: A Modeling Approach Naba Kumar Goswamia, B. Shanmukhab aDepartment of Mathematics, University of Mysore, Mysuru, India bDepartment of Mathematics, PES College of Engineering, Mandya, India. [email protected]

A non-linear mathematical model has been proposed and analysed for the impact and role of media on the spread of Zika virus disease during the epidemic. First, we investigated the epidemiological feasible equilibrium points and the threshold parameter, basic reproduction number R0 is computed using the next- generation matrix method. ‘e infected mosquito biting rate and the rate of human to human sexual trans- mission are the main parameters of the basic reproduction number. ‘e stability of di‚erent equilibria of the model is studied and backward bifurcation is discussed, which suggests that merely reducing R0 less than one is not enough to make disease-free equilibrium globally stable. We present the sensitivity analysis based on the parameters involved in the basic reproduction number and identify some of the key parameters which can be regulated to control the transmission dynamics of the Zika virus. Secondly, we integrate time depen- dent control measures into the model and then examine the conditions that are requisite for the disease to be controlled optimally by employing Pontryagin’s Maximum Principle. Finally, e‚ects of the deterministic and optimal control model witnessed by using numerical simulations.

(I5) Mathematical Model of Corona Virus (COVID-2019) with Limited Resources: A Case Study of India Akhil Kumar Srivastav School of Advances Sciences, Vellore Institute of Technology, Chennai Campus, India [email protected]

‘e COVID-19 is now one of the deadliest pandemic in human history and has had tragic consequences af- fecting millions of people worldwide. In this paper, we propose a mathematical model where we classify the infective into two subcategories: asymptomatic and symptomatic. In the developing country like India, medical resources is very limited for this kind of pandemic situation, So in this model we have incorporated treatment factor with limited resource. We analyse the model and also exploit the available data for assess- ing the pa‹ern and future prediction. We calibrate the proposed model to €t the four data sets, viz. data for the states of Maharashtra, Tamil Nadu, Delhi and overall India, and estimate the transmission rate of symptomatic individuals and recovery rate of quarantined individuals. We also estimate basic reproduction number for the regions under study. Our simulations predict that the infective population will be on increas- ing curve for Maharashtra and India whereas we can see the se‹ling of active cases for Tamil Nadu and Delhi. Sophisticated techniques of sensitivity analysis are employed to determine the impacts of model parameters on basic reproduction number and symptomatic infected individuals. Further, we perform stability analysis and established local stability of both disease free and endemic equilibrium.

(I6) Effect of Catheter on Unsteady Fluid Flow through an Inclined Stenosed Artery Chhama Awasthi Department of Mathematics, Harcourt Butler Technical University Kanpur-208002, U‹ar Pradesh, India [email protected]

In the epidemic situation of COVID-19, patients su‚ering from cardiovascular diseases are at high risk of this disease. ‘erefore, it’s necessary and signi€cant to understand the hemodynamic properties of the rhe- ology of blood by developing a mathematical model on it. ‘e non-linear di‚erential equations along the suitable boundary conditions governing the ƒuid ƒow of the above mathematical model have been solved by the Perturbation method. In this study, the catheterization process is used that uses a long ƒexible tube called a catheter. ‘is process determines the location and the percentage of blockage of the stenosis in an artery. Stenosis develops due to the invasion and deposition of fats and cholesterol and it obstructs partially

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 103 VIT-Vellore or completely the blood ƒow in arteries.

‘e combined e‚ect of catheterization, body acceleration, slip, pressure gradient, yield stress, stenosis height, and inclination has been optimized and analyzed with the help of MATLAB. ‘e graph shows that the axial velocity and ƒow rate increases with the increase in body acceleration, inclination angle, and slip velocity while axial velocity diminishes on increasing the catheter radius. Wall shear stress increases with the increase in catheter radius and body acceleration but the presence of slip velocity reduces the wall shear stress. E‚ec- tive viscosity diminishes on increasing body acceleration and inclination angle, whereas slightly augmented in the non-inclined stenosed artery.

ICU domain adaptation on survival prediction models built with neural (I7) networks Lintu M.K.a, Asha Kamathb, Sudarsan N.S. Acharyaa aManipal School of Information Sciences, Manipal Academy of Higher Education, Manipal, Karnataka, India bDepartment of Data Science, Manipal Academy of Higher Education, Manipal, Karnataka, India [email protected]

Understanding the relationship between di‚erent disease factors and survival time in the presence of cen- soring is the core concept of survival analysis. ‘e conventional survival approaches include the Kaplan- Meier method, the Cox proportional hazards model, and extended Cox models. With the availability of large medical datasets, deep learning approaches are emerging to compete with conventional survival techniques, especially in clinical healthcare applications. PhysioNet challenge 2012 provided one such dataset with adult patients from ICU where the survival methodology is applicable. Rather than predicting the usual mortality, an a‹empt to analyze the survival aspect of the PhysioNet data is made in this paper. ‘e dataset consists of the heterogeneous population from di‚erent ICU domains that form di‚erent sub-populations. ‘e concept of domain adaptation was suggested recently to overcome this problem and make the predictions more ac- curate with minimal mismatch in training and testing sets that leads to improved patient care. In this study, di‚erent readily available deep survival methods are implemented to the ICU data to address the bene€ts of the domain adaptation.

Analysis of a Modified Fractional Predator-Prey Model with Disease (I8) Infection Chandrali Baishya Department of Studies and Research in Mathematics Tumkur University, Karnataka, India [email protected]

In order to depict a situation of possible spread of infection from prey to predator a fractional-order model is developed and its dynamics is surveyed in terms of boundedness, uniqueness and existence of the solu- tions. We introduce several threshold parameters to analyze various points of equilibrium of the projected model and in terms of these threshold parameters we have derived some conditions for the stability of these equilibrium points. Novelty of this model is that fractional derivative is incorporated in a system where sus- ceptible predators get the infection from prey while predating as well as from infected predators and both infected preys and predators do not reproduce. ‘e occurrences of transcritical bifurcation for the proposed model are investigated. By €nding the basic reproduction number, we have investigated whether the disease will become prevalent in the environment. We have shown that the predation of more number of diseased prey allows to eliminate the disease from the environment, otherwise the disease would have remained en- demic within the prey population. We notice that the fractional-order derivative has a balancing impact and it assists in administering the co-existence among susceptible prey, infected prey, susceptible predator and infected predator populations. Numerical computations are conducted to strengthen the theoretical €ndings.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 104 VIT-Vellore

(I9) Analysis of effect of Social Status on Depression by using Logistic regression Ishika Ahuja a,K Karthikeyanb aSchool of Computer Science and Engineering, VIT Vellore, Tamil Nadu, Vellore. bDepartment of Mathematics, School of Advanced School, VIT Vellore, Tamil Nadu, Vellore [email protected]

Depression has recently gained the a‹ention of researchers and people are €nally paying a‹ention to mental health. Numerous studies have shown that the e‚ect of various things on di‚erent age groups is di‚erent. ‘is paper uses binomial logistic regression to analyze the impact of age and social status on depression in the case of villagers. In this paper, we concentrate on farmers. Most of the studies regarding psychological disorders are performed on educated people who are aware of these mental health issues. On the other hand, farmers from small villages who are not aware of such problems, naturally stand at a di‚erent stance compared to these people, are not considered for such analysis yet. ‘us I have used regression analysis to €nd the inƒuence of social status and age on the mental health of farmers. Upon inspecting the data, it indicated that a binomial logistic regression model would be a good €t in all cases. In examining this relationship, we included variables such as age, education level, saved asset, and living expenses. ‘e results showed evidence of a signi€cant e‚ect of age, education level, saved assets, and living expenses on the probability of a farmer su‚ering from depression.

(I10) Mathematical Modeling of COVID-19 Pandemic Dynamics with Non-pharmaceutical Interventions as Control Strategy Amit Sharmaa, Bhanu Guptaa, Sanjay K. Srivastavab aDepartment of Mathematics, JC DAV College Dasuya, Punjab, India bDepartment of Applied Sciences, B.C.E.T., Gurdaspur, Punjab, India [email protected]

Despite the major advances in the medical sciences, infectious diseases continue to cause signi€cant mor- bidity and mortality in human populations worldwide. ‘e new virus is normally responsible for an annual epidemic. Currently, we are facing COVID-19 (corona virus) outbreak, already accounted 4.5 crore infected and 11.8 lakh deaths worldwide. In this paper, we tries to build various mathematical models for studding dynamics of COVID-19 pandemic with quarantine, hospitalized and non-pharmaceutical interventions as control strategies. As, mathematical models and computer simulations are useful in determining important biological thresholds because experiments with infectious disease spread in human populations are o‰en expensive, unethical and sometimes impossible.

(I11) Stabilty Analysis of a Predator-Prey System with S€are Root Functional Response Md Golam Mortujaa, Mithilesh Kumar Chaube,a, Santosh Kumarb aDiscipline of Mathematics, International Institute of Technology, Naya Raipur, India bDepartment of CSE, International Institute of Technology, Naya Raipur, India [email protected]

In this paper, we discuss the stability of predator-prey system with square root functional response in the presence non-linear harvesting in prey and group defence. We analyze the boundedness of the solutions, existence and stability conditions of the equilibrium points of the system. ‘e results provide that, when hunting the prey or predator for economic interest, the harvesting rate must be chosen at a suitable value not smaller than the maximum sustainable yield to maintain the coexistence of both populations to maintain ecological balance. To verify our analytical results, several numerical simulations are carried out.

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A Mathematical Study on Corona Virus Model with two Infectious (I12) States Naga Soundarya Lakshmi V.S.V, A. Sabarmathi Department of Mathematics, Auxilium College, Vellore Department of Mathematics, Auxilium College, Vellore

A SIR model is formulated for COVID-19 with initial and secondary states. Existence and uniqueness of solutions, stability of the model and basic reproduction number were derived. Here the vulnerability of COVID-19 in Tirupathur district, Tamilnadu, India is discussed to exhibit the ƒow of variables of the model using numerical simulations. Also analysis of recovered is explored for Siddha and allopathy treatments.

Dynamical Behaviors of Fuzzy Prey Predator in SIR Epidemic Model (I13) P. Vinothini, K. Kavitha Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore [email protected], [email protected]

‘e aim of this paper is to study and analyze a fuzzy prey predator in SIR epidemic model. We have formulated a simple SIR type epidemic model in the presence of virus and we have discussed the dynamical behavior of the system. Further we analyze the fuzzy system and interpretation of SIR fuzzy model. Finally we €nd the existence and stability analysis of the fuzzy prey predator in SIR model system.

Dynamics of Fractional Illicit Drug Consumption Model with Holling (I14) Type-III Functional Response Sindhu J Achar, Chandrali Baishya Department of Studies and Research in Mathematics, Tumkur University, Tumkur-572103, Karnataka, India; [email protected]

In this paper we suggest a fractional di‚erential equation describing the intake of illegal drugs in a population made up of drug consumers and non-users. ‘e model describes the dynamics of non-users, experimental users, recreational users and addicts within a population. ‘is is an e‚ort by analogy to the traditional multi- species predator-prey models to suggest a model that considers non-users as prey, experimental users and recreational users as predators as well as preys and addicts as predators. Growth of non-user population is represented by logistic law and pa‹ern of inƒuence of various categories of drug users on non-users as well as users are represented by Holling type-III functional response. ‘e proposed model is analysed in terms of boundedness, existence and uniqueness, positivity of solutions. Sucient conditions are derived for existence and stability of points of equilibrium. We have used the data from Hanley to forecast the marijuana drug consumption in the states of Colorado and Washington and analysed how incorporation of fractional derivatives a‚ect the outcome of the model. ‘e theoretical results are then validated by numerical simulation. Our results suggest that fractional can be a fantastic tool for a deeper understanding of illegal drug use.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 106 VIT-Vellore

(I15) A Robust Techni€e for Brain Tumor Detection Using Type-II Fuzzy Logic Ananya Das, Subhashis Cha‹erjee Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad, India [email protected]

Detection of brain tumor in an automated way paves a signi€cant advancement in the space of medical image processing. Classi€cation is one of the signi€cant and crucial step in the detection of brain tumor to help precise treatment. Nonetheless, manual recognition with the assistance of human translation is time taking and furthermore subject to erroneous conclusion. Owing to these limitations, an automated brain tumor classi€cation algorithm is proposed in this article. ‘e current work is categorized into the following stages, viz. pre-preparing, clustering or segmentation, extraction of features, selection of key features, ranking of the chose features and lastly classi€cation of the segmented tumor. ‘ree major categories of features, viz. the Gray Level Co-occurrence Matrix, Law’s Texture and Mass E‚ect features, are extracted from the tumor and selection of features is implemented from each type followed by the ranking of the individual feature types. ‘e concluding step comprises of the classi€cation algorithm where a three phase classi€er utilizing Type-II Fuzzy Inference System is developed to classify the segmented tumor into benign or malignant class. Finally, the work is tested and validated using BRATS dataset and performance comparison is showcased between the proposed work and Type-I Fuzzy Inference System.

(I16) Dynamics in a Prey-Predator Model with Susceptible-Infected-Recovered (SIR) Epidemic Disease in the Prey Divya B, Kavitha K Department of Mathematics,School of Advanced Sciences, Vellore Institute of Technology Vellore, India [email protected], [email protected]

‘is paper proposes a non-linear mathematical model to study the dynamics of disease transmission among the prey population. We have formulated the SIR model with prey and used the Holling type II functional response and the equilibrium points are determined.‘e stability analysis of the system is analysed using the Jacobian matrix and the next generation matrix method.

(I17) The Difference E€ation Based Mathematical Model for Life-Cycle of Host-Parasitoid Systems Suresh Rasappan Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R & D Institution of Science and Technology, Tamilnadu, India [email protected]

‘e Host-Parasitoiod life cycle is modeled under di‚erence equation concept. A two-species model in which both species have a number of lifecycle stages that include eggs, larvae, pupae, and adults is considered for this analysis. An adult female parasitoid €nds a host on which to deposit its eggs. ‘e larval parasitoids consume and eventually kill their host. A novel mathematical model is constructed under the di‚erence equation concept. ‘e dynamical properties and stability of the Host-Parasitoid cycle is analyzed.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 107 VIT-Vellore

Dynamics of IGP System with Provision of Additional Food to both Prey (I18) and Predator M.S. Bhuvaneswari, B.S.R.V. Prasad Department of Mathematics, Vellore Institute of Technology, Vellore, India [email protected]

Intraguild predation (IGP) explores the predatory interaction between heterospeci€c species that use similar, o‰en limiting, resources and thus are potential competitors. Intraguild predation is claimed to be ubiquitous in nature. Intraguild predation has important implications for diversity maintenance in the €elds of biologi- cal control, community ecology, wildlife management programs, and spatial ecology. Most of the theoretical studies pertaining to biological control consider natural enemies as a specialist in nature and ignores the competitive interactions faced by these predators. However, experimental works carried out in biological control reveals that the natural enemies are not specialists always, and hence IGP is inherent in systems. In this work, we investigate the intraguild predation system, when the predators and prey are provided with supplementary food, and investigate the role of IGP in suppressing pests population. ‘e predatory inter- actions of the proposed system are modeled by using Holling-II functional form with supplementary food. Here, we assume that the system has indirect competition between prey and predator due to the presence of alternative food. We further assume that the prey population is a‚ected by the intraspeci€c competition. A detailed mathematical analysis is carried out to study the stability, permanence, and various bifurcation of the considered system. We examined the conditions for the coexisting state and the prest-free state. ‘e global dynamics of the system are studied through the local and global bifurcation curves plo‹ed in three- dimensional control parametric region consisting of additional food quality towards predator(α1), prey(α2) and the quantity of additional food (ξ). Numerical simulations are performed to validate the theoretical €nd- ings. ‘e €ndings of current studies caution the eco-manager on the choice of supplementary food quality and quantity to achieve successful biological control.

Describing Tumour Growth through Mathematical Modelling (I19) Keshav Kumar K Department of Mathematics, Jawaharlal Nehru Technological University, Hyderabad. [email protected]

Cancers are a large family of diseases that involve abnormal cell growth with the potential to invade or spread to other parts of the body. Indian Council of Medical research (ICMR) report estimates that there will be 15.7 lakh cases of cancer in India by 2025 and nearly 27.1 percent of India’s all cancer cases will be tobacco related. Cancer biology is incredibly complicated, as illustrated by the diculties surrounding the diagnosis and treatment of cancer. However, Mathematical modeling has the potential to mediate this complexity by abstracting the system using simplifying assumptions into a mathematical framework that can be analyzed and/or solved numerically to gain biological insight. ‘e growth and development of solid tumours occurs in two distinct stages-the avascular growth phase and the vascular growth phase. ‘is paper will present several mathematical models which deal with the various stages of growth and development of solid tumours.

Ring Construction for Error Correcting Codes using Jacobson Radical: (I20) A Coding Theoretic Model for Genetic Se€ence Analysis Rajrupa Singh, Selvakumar R Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India [email protected]

A novel coding model for the genetic sequence analysis is proposed in our work. One of the basic structures of the theory of rings is the ideal, in which we de€ne the Jacobson radical. In the classic polynomial ring, it coincides with the nilradical. In this presentation we study the Jacobson radical of the polynomial rings with endomorphism, R[x, σ]. We are interested to study some of the questions on the coded region of a DNA sequence that are answered using the classical polynomial rings but speci€cally in the context of Jacobson Radical of polynomial rings. In particular, here we study the conditions required for the nilradical of such

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 108 VIT-Vellore

rings that coincides with the Jacobson radical in order to identify the coding region in a DNA sequence. ‘ese results strongly suggest that some deterministic rules must be involved in the genetic code origin. In the cellular level, the information in DNA is transformed into proteins. ‘e transmission of genetic information is done by a sequence of bases like Adenine(A), ‘ymine(T), Guanine(G) and Cytosine(C) in any DNA structure which can be considered as digital codes. Further, the working of our coding model is demonstrated through an example.

(I21) Compartment Modelling and eigenvalue Expansion to Study the Drug Concentration in Capillary and Tissue Regions Surrounding the Malignant Tumour M.A. Khanday Department of Mathematics, University of Kashmir, Srinagar, 190006 Jammu and Kashmir, India. [email protected]

‘e drug transport mechanism in the biological tissue can be modelled for its e‚ective and ecient perfor- mance. Mathematics is playing a key role in almost all biomedical research problems including drug kinetics. A mathematical model based on reaction-di‚usion equation has been formulated to understand the drug transport and its di‚usion in a cancerous tissue. ‘e eigenvalue expansion has been used to obtain the so- lution of the ordinary di‚erential equations concerning the rate of change of drug concentration in di‚erent compartments including capillary and tissue regions surrounding the malignant tumour cells. ‘e graphs were plo‹ed to illustrate the variation of drug concentration with respect to time using MATLAB so‰ware. It has been observed from the graphs that the drug concentration decreases in the €rst compartment and gradually increases in the second compartment to some value and then decreases again in association with the concentration of the drug. Moreover, the behaviour of the tumour cells with changing drug concentration is simulated with respect to time and the results were compared and veri€ed with the empirical data of Unni and Seshaiyer.

(I22) Forecasting Electric Energy Consumption in India using Univariate Time-Series Analysis D. Karthika, K. Karthikeyan Department of Mathematics, SAS, VIT Vellore, Tamil Nadu, India [email protected]

Modelling electric energy consumption is useful in planning generation and distribution by power utilities. Univariate time-series analysis has been used for modeling and forecasting domestic electric energy con- sumption in India. Autoregressive integrated moving average (ARIMA) models were developed using data from 1990 to 2017 and evaluated on forecasting new data for ten years. Compared to Holt’s model and Simple Exponential Smoothing model developed on the same data, ARIMA models require less data, have fewer co- ecients, and are more accurate. ‘e optimum ARIMA model forecasts yearly data for ten years with Mean Absolute Percentage Error (MAPE) of 1.4260%. ‘e proposed ARIMA models are used to provide a ten-year forecast of the electricity demands in India.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 109 VIT-Vellore

Analysis of Lap Times in Formula-1 Motorsport due to Regulation (I23) Changes using Polynomial Regression ‘ejineaswar Guhana, K. Karthikeyanb aSchool of Information Technology and Engineering, Vellore Institute of Technology Vellore. bDepartment of Mathematics, School of Advanced Sciences, Vellore Institute of Technology Vellore [email protected], [email protected]

In the motorsport of Formula 1 engine regulation changes are quite common and when a change occurs the sport evolves by adapting to the new regulations. However, this transition from one regulation to another are not always uniform. So, we study how an engine regulation change a‚ects the performance of the car by comparing the lap times and predict future performance due to new regulations passed using polynomial regression. For this study, we compare data spanning over 3 engine eras-V10, V8 and V6-during a 25 year- time period. As mentioned, the performance of these engines is analyzed and predicted using the lap times: it is the time taken in seconds to cover the entire track once. A lap time which is relatively smaller in a speci€c track, indicates be‹er performance of the car in that track.

An EPQ Model for Delayed Deteriorating Items with Time Dependent (I24) Cubic Demand and Shortages R. Pavithra, K. Karthikeyan Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology Vellore [email protected], [email protected]

An economic production quantity model plays a dominant role in production and manufacturing components. In this article, an EPQ model is proposed for delayed deteriorating items with time dependent cubic demand in before deterioration and a‰er deterioration the demand is constant. In this inventory model shortages are allowed and it is partially backordered. A mathematical model is developed and the best cycle length which optimizes the total inventory cost and an economic production quantity. Finally, numerical example and sensitivity analysis of the developed model are presented to see the e‚ect of changes in some parameter in the inventory system.

Hexadecagonal Fuzzy Transportation Problem (I25) R. Saravanana, M. Valliathalb aNIFT-TEA College of Knitwear Fashion, Tirupur bChikkaiahNaicker College, Erode

Transportation problem is one of the sub classes of linear programming problem. ‘e objective of the trans- portation problem is to minimize the transportation cost or maximize the pro€t. Fuzzy set theory has been applied in many €elds of Science, Engineering and Management. In this article, a Hexadecagonal fuzzy number is ranked by using Robust ranking method. Fuzzy transportation problem is transformed into crisp transportation problem and solved by MODI method. A numerical example is presented and the optimal solution obtained by using proposed method.

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(I26) Tandem Fluid Model Driven by an MX/M/1 eue Subject to Balking and Vacations M. Deepa, K. Julia Rose Mary Nirmala College For Women, Red Fields, Coimbatore, Tamilnadu - 641018, INDIA [email protected], [email protected]

Generally, balking is an impatient customer’s behavior who refuses to enter the queue on arrival. ‘is paper studies the bulk arrival of a tandem ƒuid queue with multiple exponential vacations subject to balking. To provide greater ƒexibility on control of net input rate when ƒow is high, we introduce a bulk arrival ƒuid model with multiple exponential vacations and balking. We derive explicit expression for the stationary bu‚er content by using Laplace transform. ‘en the performance measures such as mean of the bu‚er content is obtained and it is found to be independent of the vacation parameter θ. Finally, the e‚ect of vacation and balking parameters on the mean bu‚er content is also illustrated by sensitivity analysis.

(I27) An Economic Production antity Model for Three Levels of Production with Weibull Distribution Deterioration and Shortage under Inflation G. Viji, K. Karthikeyan Department of Mathematics, SAS, VIT Vellore. Tamil Nadu, India. [email protected], [email protected]

An EPQ model has a wide range of scope in production and manufacturing sectors. ‘is article presents three levels of economic production inventory model for deterioration items with three di‚erent levels of produc- tion. Inƒation and the rate of deterioration are also considered along with this inventory model which follows two parameter Weibull distributions. ‘is article has a great inƒuence in achieving minimum quantum stock of manufacturing items at the initial stage through which holding cost will be reduced at great extent. ‘is article facilitates production organization in achieving reduced total cost, desired productivity and earning potential pro€t along with customer satisfaction. ‘e objective of this article is to €nd the optimal solution for reducing total production cycle time so that total cost of the whole production cycle will be minimized. Eventually numerical example and sensitivity analysis on parameters are made to validate the results of the proposed inventory system.

(I28) Recent Trends of Applications of Business Analytics using Operations Research Gunda Srinivasa Rao Department of Mathematics, CMR university, Bangalore

Supply chain has long been an area where advanced analytics such as statistics and optimization were used for forecasting, planning, network design, inventory optimization, routing, warehouse slo‹ing etc. Data science and data analytics are at the core of every modern globalized industry. Working in today’s technology-centric workforce not only requires superior leadership skills, but the ability to translate data problems into the big- ger picture for the organization. Business Analytics is the science of data-driven decision making. ‘e use of analytics across industries for decision-making, automation of business processes, products, and solutions driven by analytics makes it an essential skill for every student graduating from management and engineering disciplines. Many organizations generate solutions to their problems using analytics and innovation in many companies is driven by analytics. Analytics is used as a competitive strategy by many successful companies. Organizations such as Amazon, Apple, Facebook, Google, IBM and Wall mart have created solutions using analytics. Amazon has created solutions such as recommender systems and Amazon go that are driven by an- alytics. Apples predictive keyboard is another example of solutions driven by analytics. Analytics is relevant not only to pro€t-making companies but also for government and nongovernment organizations(NGOs).‘e Akshaya patra foundation, an NGO based out of Bangalore, has used several analytics models for e‚ective management of its free meal program which provides free meals to about 1.5 million school children in India. Analytics is not just about number crunching. It has evolved into a competitivestrategy that drives innovation

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 111 VIT-Vellore across several organizations. Business analytics is a set of statistical and operations research techniques, Ar- ti€cial intelligence, Information technology and management strategies used for framing a business problem, collecting data, and analyzing the data to create value to organizations. Business Analytics can be broken into 3 components: 1)Business context, 2)Technology and 3)Data Science.IT is used for data capture, data storage, data preparation, data analysis and data share. An important output of analytics is automation of actionable items derived from analytical models; automation of actionable items is usually achieved using IT. Data science is the most important component of analytics, it consists of statistical and Operations research techniques, machine learning and deep learning algorithms.

Solving Open Travelling Salesman Subset-Tour Problem through a (I29) Hybrid Genetic Algorithm Jayanth Kumar ‘enepallea, Purusotham Singamse‹yb aDepartment of Science and Humanities, Sreenivasa Institute of Technology and Management Studies, Chi‹oor-517127, Andhra Pradesh, India. bDepartment of Mathematics, School of Advanced Sciences, VIT, Vellore-632014, Tamil Nadu, India. [email protected], [email protected] In open travelling salesman subset-tour problem (OTSSP), the salesman needs to traverse a set of out of cities and a‰er visiting the last city, the salesman does not necessarily return to the central depot. ‘e objective is to minimize the overall traversal distance of covering cities. ‘e OTSSP model comprises two kinds of problems such as subset selection and permutation of the cities. Since a salesman’s tour, do not contain all the cities, the problem of selection takes place. Another problem is to €nd the optimal sequence of the cities from the selected subset of cities. To solve this problem eciently, a hybrid nearest neighbour technique based crossover-free Genetic algorithm (GA) with complex mutation strategies is proposed. To best of the author’s knowledge, this is the €rst ever hybrid GA for the OTSSP. As there are no existing benchmark instances for OTSSP, a set of test instances is generated by using TSPLIB. ‘e extensive computational experiments show that the proposed algorithm is having great potential in achieving be‹er results for the OTSSP. Our proposed GA being the €rst evolutionary-based algorithm for OTSSP, which will help as the baseline for future research on OTSSP.

Analysis of Intuionistic Fuzzy Transportation Problem (I30) K.R. Sobha Sree Ayyappa College for Women, Chunkankadai. [email protected] ‘e objective of this paper is €nd out the optimum cost (maximum pro€t) of the intuionistic fuzzy transporta- tion Problem. Using Yager’s ranking method fuzzy quantities are transformed in to crisp quantities. Finally a numeric illustration is given to check the validity of the proposal.

An Economic Order antity model with Reverse Logistics inventory (I31) model in circular economy S. Vennila, K. Karthikeyan Department of Mathematics, SAS, VIT Vellore, Tamil Nadu, India. [email protected], [email protected] ‘e Economic Order antity (EOQ) model has developed enormously over long time on the quality of in- corporating realistic factors. Reverse Logistics is the strategy for managing gathering or assembling back the pre-owned items from a de€nitive customer. It can take any structures with di‚ering expenses and advan- tages to the business. ‘e return products in an e‚ort to recycling, reusing, repairing is measured by circular economy to recover assets. In this article we developed a reverse logistics economic order quantity inventory model in circular economy. ‘e inventory issues is formed by the product was return to company when to request, how much amount to arrange where there is reverse ƒow of products into the system is manipulated into the form of optimal pro€t maximisation. To exist the result to optimal solution of the model by using non-linear Karush Kuhn-Trucker conditions for the objective functions are introduced.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 112 VIT-Vellore

(I32) Review Article on eueing Inventory Models P. Indumathi, K. Karthikeyan Department of Mathematics, SAS, VIT Vellore, Tamil Nadu, India. [email protected]

A eueing inventory system has been extensively studied because of their widespread applications in the real world. ‘e goal of this paper is to provide sucient information about the queueing inventory theory. In this paper, we discuss di‚erent components of queueing systems along with the inventory models such as queueing systems with production inventory, queueing inventory systems with stochastic, queueing inven- tory systems with perishable products, queueing inventory systems with di‚erent types of demands, general queueing inventory systems with di‚erent service times, and deteriorating inventory systems.

(I33) Bargaining of a Wholesale Price for an Optimal Manufacturer with a Retailer in a One-Channel Supply Chain K. Valli, P. Rajendran Department of Mathematics, SAS, VIT Vellore, Tamil Nadu, India. [email protected], [email protected]

In this paper we investigate the ideal planning when a manufacturer bargains with a dealer price with a retailer in one – channel supply chain that comprises of the manufacturer and the retailer. To identify the problem, we consider the decision-making method in which the manufacturer can sell the products directly to the retailer and€nally to the consumers. We assume that the manufacturer decides the direct retail price by the one channel through the retailer. ‘e manufacturer gets the highest pro€t by bargaining the wholesale price with the retailer. If manufacturer shows the one channel supply chain for practical decision making by using the multi-criterion decision making method [MCDMM], then the pro€t increases to a greater extent. To show the e‚ectiveness of the MCDMM, we provide numerical examples. ‘is paper presents the methodology, €ndings and conclusions with the scope for further research.

(I34) Modelling of Deteriorating Systems Using Fuzzy Warranty Cost with Preventive Repairs M. Mubashir Unnissa, D. Kalpanapriya Department of Mathematics, SAS, VIT Vellore, Tamil Nadu, India. [email protected], [email protected]

‘is paper studies a repairable deteriorating. In order to minimize the operating cost of the system and to improve system availability, a preventive repair, not as good as new, is adopted during the warranty period. A cost model has been developed to show the importance of fuzzy preventive repairs during warranty period. Also the paper focuses on the various warranty expenses for the above model. Numerical illustrations have also been provided to show the importance of fuzzy repair times during warranty.

(I35) Rough Hesitant Bipolar Neutrosophic Linear Programming Problem E.R. Meena Kumaria, M. ‘irucheranb aDepartment of Mathematics, Bharathi Women’s College, Chennai 108. bDepartment of Mathematics, L.N. Govenment College , Ponneri - 601 204. [email protected], [email protected]

In this paper, we have proposed a bipolar rough hesitant neutrosophic number to solve the neutrosophic linear programming problem which is a most powerful technique in decision making. A new ranking function is proposed to convert the neutrosopic linear programming problem to crisp linear programming problem. Solve this crisp linear programming problem using a standard method to get the optimal solution. We have compared this proposed method with the existing methods to prove the optimality of the solution.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 113 VIT-Vellore

Lexi-Search approach for the Three Index Assignment Problem (I36) Sumathi Pa, Viswanatha Reddy Gb,Purushotham Sc aDepartment of Mathematics, College of Agricultural Engineering (ANGRAU), Madakasira, A.P, India bDepartment of Mathematics, Sri Venkateswara University,Tirupati, A.P, India cDepartment of Mathematics, School of Advanced Sciences,VIT, Vellore, Tamilanadu, India [email protected]

‘e classical assignment problem is to €nd a one-one correspondence between a set of persons and a set of machines with the least weight. ‘e 3-index assignment problem is an NP-complete problem which is a generalization of classical assignment problem. Let there be three n−disjoint sets which denote the set of persons, machines and facilities. Let C(i, j, k) be the cost associated to each triplet (i, j, k) i.e. the weight is carried on working ith person on jth machine by utilizing kth facility. ‘e 3-index assignment problem is to €nd a combination of n−triplets which covers the union of the three sets with least weight in such a way that no i, j, k is repeated.

‘e 3-index assignment problem is expressed as a zero-one programming problem. In order to obtain the optimal combination of triplets among n3, a deterministic lexi-search algorithm is developed. ‘e algorithm searches feasible solutions systematically and then moves towards the optimal solution with the help of e‚ective backtracking and bounding strategies. ‘e problem is explained with a suitable numerical example. ‘e algorithm is coded in PYTHON programming language and computational results are tabulated. ‘e computational experiments over a large set of random data sets exhibited that the proposed LSA requires fairly less CPU runtime to €nd the ecient solutions. Based on this experience, we strongly feel that the proposed algorithm is fairly ecient in resolving higher dimensional problems also.

Bipolar Vague ELECTRE 1 method for MCDM problems (I37) Venkata Kalyani U, T. Eswarlal Department of Mathematics, Koneru Lakshmaiah Education Foundation, Vaddeswaram, AP,India [email protected], [email protected]

In numerous aspects dealing with bipolar information is essential. Elimination and choice translating reality (ELECTRE 1) is a widely used method to solve multi-criteria decision making problems. We established and proposed the Elimination and choice translating reality (ELECTRE 1) with bipolar Vague sets to solve such problems.We veri€ed the proposed method with a numerical example which shows the e‚ectiveness of the method with a decision graph.

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 114 VIT-Vellore

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS Author Index

A. Anand, 53 B. Maheswari, 44 A. Arul Devi, 41 B. Ramu Naidu, 47 A. Elamparithi, 43 B. Rushi Kumar, 85, 88, 90 A. Gnanasoundar, 67 B. Shanmukha , 102 A. Goyal, 77 B. Somasundaram, 63 A. Joseph Kennedy, 49 B. Sury,1 A. Neeraja, 95 B.S.R.V. Prasad, 107 A. Sabarmathi, 105 B.V. Baby, 101 A. Subramanyam Reddy, 94 B.V. Rathish Kumar, 19 A. Sumithra, 88 B.V.R. Kumar, 80 A.K. Singh , 99 Bhanu Gupta, 104 A.M. Pund , 97 Bhaskar Bagchi, 16 A.N. Metkari, 52 Biju Kumar Du‹a, 90 A.S. Nimkar, 97 Bikash Chakraborty, 31 A.S. Nimkar , 98 Bikash Sahoo, 84 Aakanksha Singhal, 66 Biplab Basak, 76 Abha Tripathi, 47 Biswajit Pandit, 82 Abhijit Sutradhar, 18 Bivek Gupta, 61 Aditi Biswas, 52 Blankson Henry, 49 Agnieszka Wylomanska,´ 27 Ajit Kumar Gupta, 78 C. Dineshkumar, 73 Ajmeera Chandulal , 99 C. Dominic, 45 Akhil Kumar Srivastav, 102 C. Jaya Subba Reddy, 44, 49 Alokananda Kar, 97, 98 C. Sankari, 45 Amartya Kumar Du‹a, 24 C. Selvi, 53 C. ‘angaraj, 66 Amit K. Verma, 61, 83 C.S. Aravinda, 25 Amit Kumar Verma, 74, 82 C.T. Duba, 72 Amit Sharma, 67, 104 Chandra Prakash Rathor, 75 Amlan K. Halder, 72 Chandrali Baishya, 103, 105 Amruta Shinde, 46 Chandrani Basu, 55, 77 Ananya Das, 106 Cha‹amvalli Rajan, 49 Anbhu Swaminathan, 60 Chhama Awasthi, 102 Anirban Lakshman, 100 Anish Ghosh,6 D. Easwaramoorthy, 66 Ankit Pal, 34 D. Kalpanapriya, 112 Ankush Chanda, 64 D. Karthika, 108 Ansa Mathew, 95, 96 D. Tripathi, 65 Anuj Kumar, 101 D.K. Sharma, 66 Anupam Rachna, 47 D.M.K. Kiran, 47 Anuraj Singh, 101 Debasmita Du‹a, 58, 59 Archana Gurulakshmi, 69 Deepa Arora, 65 Arghyatanu Manna, 55, 59 Deepa Krishnamurthi, 50 Arun Pal Singh, 65 Dinesh Khurana,6 Asha Kamath, 103 Dipankar Pal, 55, 59 Ashima Bandyopadhyay, 54–56, 58 Divya Antoney, 45 Ashis Bera, 64 Divya B, 106 Avinash Sathaye, 24 Dwijendra N. Pandey, 80

B Mahanthesh, 92 E. Rama, 100

115 IMS - 2020 116 VIT-Vellore

E.R. Meena Kumari, 112 K.R. Sobha, 40, 111 Ekta Mi‹al, 56 K.S. Balamurugan, 85 Ezhilmaran Devarasan, 48 K.S. Charak, 13 Ezilmaran D, 83 K.U. Sreeja, 40 Kalyani Desikan, 43 G. Archana, 63, 68 Kamal Kumar, 67 G. Ayyappan, 63, 66, 68, 69 Kanchana M, 43 G. Kumaran, 85 Kaushal Patel, 71 G. Lakshmi Devi, 93 Kavitha K, 43, 106 G. Murugusundaramoorthy, 62 Keshav Kumar K, 107 G. Palani, 48 Khinal Parmar, 31 G. Radhakrishnamacharya, 18 Krishna Gopal Singha, 84 G. Viji, 110 Kshitish Ch. Mistri, 100 G.M. Birajdar, 60 Kumbinarasaiah S, 72 Gautem Patel, 71 Gayathri, 93 L. Madhavi, 51 Gorachand Chakraborty, 53 L. Padmavathi, 87 Gunda Srinivasa Rao, 110 Lakshmi Biswas, 55, 58 Gurleen Kaur, 50 Lakshmi Kanta Dey, 64 Gurmeet K. Bakshi, 50 Lakshmi Narayan Mishra, 34, 71 Gursimran Kaur, 67 Lalita Verma, 77 Lateef Ahmad WANI, 60 H. Niranjan , 93 Leena Kathuria, 53 H. ‘ameem Basha, 88 Lintu M.K, 103 Harald Upmeier,4 Haribhai R. Kataria, 69 M. Chandramouleeswaran, 41 Harish Seshadri, 23 M. Chitra, 91 M. Deepa, 110 Iguer Luis Domini dos Santos, 70 M. Kousalya, 91 Ishika Ahuja, 104 M. Mohan Raja, 73 M. Mubashir Unnissa, 112 J. Prakash, 90 M. Nalliah, 42–44 J.K. Maitra, 40, 75–77, 81 M. Reddappa, 44 J.L. Ramaprasad, 85 M. Subbiah, 86 J.S. Wath, 97 M. Suryanaryana Reddy, 87 Jaban Meher, 20 M. ‘irucheran, 53, 54, 112 Jagdish A. Nanware, 71 M. Valliathal, 109 Jagmohan Tanti,9 M. Vinodkumar Reddy, 89 Jaita Sharma, 73 M. Vinoth Kumar, 54 Javaid Ahmad Shah, 40 M.A. Khanday, 108 Jayalatha G, 96 M.D. Srinivas,8 Jayanta Saha, 56, 57, 62 M.J. Vedan, 87, 96 Jayanth Kumar ‘enepalle, 111 M.K. Pal, 99 Jervin Zen Lobo, 71 M.K. Pandey, 77 Jogendra Kumar, 82 M.R. Raksha, 45 Joseph T V , 94 M.S. Bhuvaneswari, 107 M.S. Raghunathan,4 K. Amarender Reddy, 62 M.S. Sriram, 26 K. Julia Rose Mary, 110 Madhulika Shukla, 81 K. Karthikeyan, 104, 108–112 Mahender Singh, 22 K. Kavitha, 105 Manab Kundu, 31 K. Saritha, 52 Manisha Binjola, 76 K. Srinivas, 21 Manisha Chowdhury, 34 K. ‘ilagavathi, 52 Manoj K. Yadhav, 51 K. ‘ilagavathy, 66 Manoj Kumar Patel, 30 K. Valli, 112 Maraika Alexander, 87 K. Vijaya, 57 Maria Anncy , 94 K.P.R. Sastry, 47 Mariya Helen Mercy JK, 93 K.R. Karthikeyan, 62 Martin Bohner, 70

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 117 VIT-Vellore

Md Golam Mortuja, 104 Pabitra Kumar Jena, 63 Meena Pargaei, 19 Padmaja K, 90 Meenakshi, 67 Pallvi Mahajan, 70 Megha, 79 Panchatcharam Mariappan, 28 Meghana J, 95 Pankaj Jain, 55, 77 Mithilesh Kumar Chaube, 104 Parameswaran R, 96 Mithilesh Singh, 84 PK Srivastava, 101 Monika Singh, 65 Poonam Agrawal, 76 Mrinmoy Goswami, 84 Pradip Majhi, 12 Mukesh Kumar Rawani, 82 Prakasam Muralikrishna, 48 Mukti Acharya, 41, 45 Prakash R, 96 Mukul SK, 57 Prakashkumar H. Patel, 69 Mukul Sk, 62 Pranav Narayan Sharma, 47 Murali K. Srinivasan, 16 Pranav Sharma, 30 Pranesh S, 94, 95 N. Bhaskar Reddy, 95 Preeti Deolia, 101 N. Raja, 86 Priyanka Grover, 68 N. Sathya Kumar, 80 Punam Gupta, 76 N.D. Sangle, 52, 60 Pursho‹am Narain Agrawa, 81 Naba Kumar Goswami, 102 Purushotham S , 113 Naga Soundarya Lakshmi V.S.V, 105 Purusotham Singamse‹y, 44 Namrata Shrivastav, 54 Purusotham Singamse‹y , 111 Narendra Kumar, 83 Narsimhulu Dunna, 89 R. Angelin Suba, 40 Nasru Sivakumar, 88 R. Balakrishnan, 16 Naveen Mani, 67 R. Gowthami, 68 Nazia Urus, 74 R. Meenakumari, 85 Nazir Ahmad Ahengar, 75 R. Nageshwar Rao, 80 Neela Nataraj,6 R. Padma, 20 Neha Rai, 50 R. Palanivel, 70 Nikhil Khanna, 53 R. Pavithra, 109 Nirmala, 86 R. Saravanan, 109 Nithya Sai Narayana, 45 R. Shankar, 42 Nityagopal Biswas, 56, 61 R. Sivaraj, 85, 88, 92 Nivedha Baskar, 41 R. Swetha, 90 P. Bala Anki Reddy, 91 R. Udhayakumar, 73 P. Durgadevi, 48 R. Vignesh, 43 P. Durgaprasad, 88 R. VijayaKumar, 86 P. Indumathi, 112 R. Vinodkumar, 48 P. Jaish, 43 R.B. Sharma, 59 P. Lakshminarayana, 85, 89 R.B. Yadav,9 P. Muralikrishna, 48 R.L.V. Renuka Devi, 94, 95 P. Muthu, 19 R.N. Singh, 78 P. Prakash,8 Rahul Kaushik, 51 P. Rajendran, 112 Rahul Shukla, 81 P. Ratchagar, 86 Raisa Dsouza, 22 P. Reddaiah, 35 Rajan Cha‹amvelli, 64 P. Sundaresan, 49 Rajendra M. Pawale, 17 P. ‘irupathi Reddy, 58 Rajesh Kumar Tiwari, 75 P. Vijayalakshmi, 92 Rajkumar N. Ingle, 58 P. Vinothini, 105 Rajrupa Singh, 107 P.B. Ramkumar, 40 Raju K. George, 73 P.B. Vinodkumar, 40 Rakesh Kumar Tripathi, 40, 41 P.G. Siddheshwar, 95, 96 Rakesh Sarkar, 55, 56, 59 P.G.L. Leach, 72 Rakhi Tiwari, 99 P.K. Sahu, 36 Ram Krishna Pandey, 50 P.M. Lambat, 97 Ramesh Kasilingam, 22 P.V.S.N. Murthy, 18 Ramoorthy Reddy, 49

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 118 VIT-Vellore

Ranganatha Dasappa, 33 Sharad S. Sane, 17 Ravi P. Agarwal, 12 Sharmistha Rakshit, 100 Ravilise‹y Revathi, 89 Shayathri Linganathan, 44 Reeta Bhardwaj, 67 Sheerin Kayenat, 83 Renu Saini, 81 Shikhar Chandra, 64 Renukadevi Sangappa Dyavanal, 61 Shouvik Sadhukhan, 97 Rishikesh Yadav, 31 ShouvikSadhukhan, 98 Rupal C. Shro‚, 33 Showkat Ahmad Bhat, 41 Shyam Sunder Iyer, 87 S. Devi Yamini, 42 Siddheshwar P.G, 96 S. Gurunathan, 42 Sindhu J Achar, 105 S. Jeevitha, 91 Sivaram Ambikasaran, 28 S. Karpagam, 67 Sourav Shil, 35 S. Nivetha, 41 Sreedhara Rao Gunakala, 87 S. Prakash, 86 Stephan Baier, 20 S. Pranesh, 95, 96 Subhash Mallinath Gaded, 45 S. Pranesh , 93 Subhashis Cha‹erjee, 106 S. Rajkumar, 44 Subhasis Ghora, 61 S. Sankeetha, 63, 68, 69 Sudarsan N.S. Acharya, 103 S. Santhiya, 32 Sudarshan Tiwari, 27 S. Saravanan, 12, 86, 89, 91 Sujeet Kumar Chaturvedi, 40 S. Srinivas, 94 Sukalyan Sarkar, 55, 58 S. Sundar, 28 Sumathi P, 113 S. Venkateswarlu, 87 Sumit Kumar, 37 S. Vennila, 111 Sumit Som, 63 S. Vigneshwaran, 89 Sunil Joshi, 54 S. Vijaya Kumar Varma, 90 Surajit Hazra, 59 S.C. Wankhade, 98 Suresh Rasappan, 106 S.K. Pandey, 77, 78 Surya Manokaran, 48 S.P. Hande, 52 Sushil Kumar, 60 S.P. Maurya, 78 Sushil Singla, 68 S.P. Tiwari, 13, 47 Syed Papia Nawaz, 60 S.R. Hadole, 98 T. Divya, 42 Sachin Kumar, 72 T. Eswarlal, 113 Sachin Shaw, 18 T. Raghuwanshi, 77 Saginta Dey, 80 T. Yogalakshmi, 42 Saikat Mukherjee, 78 Tabitha Agnes Mangam, 41, 45 Samares Pal, 13 Tanchar Molla, 57, 62 Sandeep Malik, 72 Tandra Sarkar, 57 Sandra Jestine, 92 Tanuja Das, 101 Sangeet Kumar, 78, 79 Tarakanta Nayak, 61 Sanjay K. Srivastava, 104 ‘ejineaswar Guhan, 109 Sanjib Kumar Da‹a, 52, 54–59, 62 ‘omas Goetz, 27 Sanket Tikare, 70 Sanoli Gun,6 U.S. Negi, 75 Santosh Kumar, 104 Santosh M. Popade, 58 V. Inthumathi, 67 Sarfraz Ahmed, 90 V. Malathi, 57 Sarita Kumari, 37 V. Murugan, 70 Sarita Nandal, 80 V. Nagendramma , 92 Satavisha Dey, 58, 59 V. Prabhakar , 93 Sayantan Guha, 36 V. Priyadharshini, 43 Sekhar G.N, 96 V. Suman Kumar, 59 Selvakumar R, 107 V. ‘iruveni, 41 Shaik Jakeer, 91 V. Vijayakumar, 73 Shakir Ali, 14 V.R. Lakshmi Gorty, 60 Shambhu Sharan, 78 Varsha Karanjgaokar, 54 Shanta Laishram, 20 Venkata Kalyani U, 113

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS IMS - 2020 119 VIT-Vellore

Venketeswara Pai R, 25 Victor M. Job, 87 Vijai Kumar Pathak, 71 Vimala Ramani, 22 Vinod Kumar Jatav, 35 Vinoth Indira D, 83 Vishant Shah, 69, 73 Viswanatha Reddy G, 113 Vivek Panwar, 55, 77

Y. Rajasekhara Gowd, 51 Y.M. Borse, 46

Organized by Dept. of Mathematics, SAS, VIT-Vellore and IMS