KMITL Thailand General Chair: Assoc.Prof.Praiboon Pantaragphong KMITL Thailand

Message from Dean, Faculty of Science, KMITL

On behalf of the Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang (KMITL), Thailand, I would like to welcome all the keynote speakers, invited speakers, presenters and participants to the 11th IMT- GT International Conference on Mathematics, Statistics and Its Applications 2015 (ICMSA 2015).The main purpose of this conference is to provide an academic forum for researchers and academics to meet, share and exchange their research and innovative knowledge in the fields of Mathematics, Statistics, and other related fields as well as their applications.

Our Faculty is greatly honored to host this conference under the auspicious occasion of the Indonesia-Malaysia-Thailand Growth Triangle (IMT-GT). I hope this platform will give a good opportunity for all participants to strengthen and extend their academic relationships among each other. With mathematics and statistics being the foundation of most significant scientific advances, I am confident that this gathering will unleash the collective knowledge of these research findings.

Regarding the response to this conference which is overwhelming, we are glad to receive submissions from various countries all over the world. The response reflects that Mathematics and Statistics continue to be a hot topic in research. Among the participants, there are not only mathematicians and statisticians but also researchers from emerging areas such as Industrial Mathematics, Financial Mathematics, Logistics, Computer Science, and so on. I am excited to witness such development in the research scene.

Finally, I would like to thank all those who have committed to make this conference possible. I wish all the success for this conference.

Assoc.Prof.Dr. Dusanee Thanaboripat Dean, Faculty of Science, KMITL

Message from General Chair

Dear Colleagues,

I am pleased to welcome you to the 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 (ICMSA 2015) at Ambassador City Jomtien Hotel, Pattaya, Thailand during 23-25 November, 2015.

This conference was initiated by the Indonesia-Malaysia-Thailand Growth Triangle (IMT-GT) mathematicians formed in 2005. This year the conference is, for the first time, organized by the Department of Mathematics, King Mongkut’s Institute of Technology Ladkrabang (KMITL). The main purpose of the conference is to bring together researchers, professors, and everyone interested in mathematics, statistics and its applications for exchanging research ideas and innovations.

ICMSA2015 has accepted 108 abstracts and received 113 registered participants from 11 countries, totally. In addition to the 84 technical papers and 1 poster session for presentation at the conference, we are also delighted to welcome the 11 renowned keynote and invited speakers to our rich conference program.

I would like to thank Prof.Dr.Suchatvee Suwansawat, the president of KMITL and Assoc. Prof. Dr.Dusanee Thanaboripat, the dean of faculty of science, KMITL for all the support to this conference.

I would also like to thank all the international scientific committee to make this conference possible. Finally, I would like to thank the organizing committee and all staffs for their efforts and hard work.

Assoc. Prof. Praiboon Pantaragphong

General Chair, ICMSA2015

ICMSA2015 ICMSA2015 00 (2009) 000–000 www.icmsa2015.kmitl.ac.th

Advisory Committee Members: Prof.Dr.Suchatvee Suwansawat KMITL President Thailand Assoc.Prof.Dr.Dusanee Thanaboripat Dean of Faculty of Science KMITL Thailand General Chair: Assoc.Prof.Praiboon Pantaragphong KMITL Thailand

Organizing Committee Members (KMITL Thailand): Assoc.Prof.Wicharn Techitdheera Sujitra Sukonthamut Asst.Prof.Dr.Suwannee Junyapoon Asst.Prof.Dr.Wiboon Praditweangkum Assoc.Prof.Dr.Puntani Pongsumpun Dr.Vorapat Sanguanchaipaiwong Dr.Santit Narabin Assoc.Prof.Patcharin Hemchote Assoc.Prof.Dr.Pakkinee Chitsakul Assoc.Prof.Dr.Chartchai Leenawong Asst.Prof.Dr.Kanchana Kumnungkit Asst.Prof.Dr.Jaipong Kasemsuwan Asst.Prof.Dr.Nopparat Pochai Asst.Prof.Dr.Atid Kangtunyakarn Asst.Prof.Dr.Wichai Witayakittilerd Asst.Prof.Dr.Pattrawut Chansangiam Dr.Busayamas Pimpunchart

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Dr.Siripawn Hananhh Winter Dr.Kampanat Namngam Dr.Decha Samana Dr.Sukrawan Mavecha Dr.Wannaporn Sanprasert Dr.Kannanut Chamsri Dr.Thawatchai Khumprapussorn Dr.Ngarmcherd Danpattanamongkon Dr.Thurdkwun Changpuek Dr.Buddhaporn Vanishkorn Chinda Chaichuay Pornchai Chaisanit Sirikul Siriteerakul

The International Scientific Committee Prof.Dr.Herman Mawenkang USU Indonesia Prof.Dr.Dato'Rosihan Ali USM Malaysia Prof.Dr.Anton Abdul Basah Kamil USM Malaysia Assoc.Prof.Dr.Hizir Sofyan SKU Indonesia Prof.Dr.Saib Suwilo USU Indonesia Prof.Dr.Mohd.Lazim Abdullah UMT Malaysia Assoc.Prof.Dr.Putipong Bookkamana CMU Thailand Assoc.Prof.Dr.Surapong Auwatanamongkol NIDA Thailand Assoc.Prof.Dr.Kannapha Amaruchkul NIDA Thailand Asst.Prof.Dr.Winai Bhodisuwan KU Thailand

ICMSA2015 ICMSA2015 00 (2009) 000–000 www.icmsa2015.kmitl.ac.th

Program Committee Members Mathematics and Applied Mathematics: Prof.Dr.Suthep Suantai CMU Thailand Prof.Dr.Somyot Plubtieng NU Thailand Prof.Dr.Pairote Satayatham SUT Thailand Prof.Dr.Sompong Dhompongsa CMU Thailand Prof.Dr.I-Ming Tang KU Thailand Prof.Dr.Sorin V. Sabau TKU Japan Assoc.Prof.Dr.Pachara Chaisuriya MU Thailand Assoc.Prof.Dr.Utomporn Phalavonk KMUTNB Thailand Assoc.Prof.Dr.Chartchai Leenawong KMITL Thailand Assoc.Prof.Dr.Pakkinee Chitsakul KMITL Thailand Assoc.Prof.Dr.Puntani Pongsumpun KMITL Thailand Assoc.Prof.Dr.Satit Saejung KKU Thailand Assoc.Prof.Dr.Supot Witayangkurn KKU Thailand Asst.Prof.Dr.Jessada Tariboon KMUTNB Thailand Asst.Prof.Dr.Nopparat Pochai KMITL Thailand Asst.Prof.Dr.Jaipong Kasemsuwan KMITL Thailand Asst.Prof.Dr.Atid Kangtunyakarn KMITL Thailand Asst.Prof.Dr.Kanchana Kumnungkit KMITL Thailand Asst.Prof.Dr.Wichai Witayakittilerd KMITL Thailand Asst.Prof.Dr.Pattrawut Chansangiam KMITL Thailand Asst.Prof.Dr.Klot Patanarapeelert SU Thailand Asst.Prof.Dr.Boonrod Yuttanan PSU Thailand Asst.Prof.Dr.Banyat Sroysang TU Thailand Asst.Prof.Dr.Sarawut Saenkarun UBU Thailand Asst.Prof.Dr.Chaichana Jaiboon RMUTR Thailand

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Dr.Busayamas Pimpunchart KMITL Thailand Dr.Decha Samana KMITL Thailand Dr.Thawatchai Khumprapussorn KMITL Thailand Dr.Sukrawan Mavecha KMITL Thailand Dr.Kannanut Chamsri KMITL Thailand Dr.Pornsarp Pornsawad SU Thailand Dr.Chatchawan Watchararuangwit KMUTT Thailand Dr.Warisa Yomsatieankul KMUTT Thailand Dr.Pinthira Tangsupphathawat PNRU Thailand Dr.Rujira Kongnuy RMUTSB Thailand

Statistics and Operation Research: Prof.Dr.Samruam Chongcharoen NIDA Thailand Prof.Dr.Kritsana Neammanee CU Thailand Assoc.Prof.Dr.Jirawan Jitthavech NIDA Thailand Assoc.Prof.Dr.Kannapha Amaruchkul NIDA Thailand Assoc.Prof.Dr.Putipong Bookkamana CMU Thailand Asst.Prof.Dr.Manus Paitooncharoenlap KMITL Thailand Asst.Prof.Dr.Sukuman Sarikavanij KMUTT Thailand Asst.Prof.Dr.Chunchoom Pongchavalit KMUTT Thailand Asst.Prof.Dr.Jutatip Silabutra MU Thailand Asst.Prof.Dr.Wararit Panichkitkosolkul TU Thailand Asst.Prof.Dr.Supranee Lisawadi TU Thailand Dr.Piyaphon Paichit SU Thailand Dr.Kannigar Hirunkasi SU Thailand Dr.Sureerat Areeraksakul Konglok SUT Thailand Dr.Waraporn Chatanin KMUTT Thailand

ICMSA2015 ICMSA2015 00 (2009) 000–000 www.icmsa2015.kmitl.ac.th

Computer Science and Information Technology: Prof.Dr.Chidchanok Lursinsap CU Thailand Assoc.Prof.Dr.Surapong Auwatanamongkol NIDA Thailand Assoc.Prof.Dr.Veera boonjing KMITL Thailand Assoc.Prof.Dr.Jeeraporn Werapun KMITL Thailand Assoc.Prof.Dr.Chanboon Sathitwiriyawong KMITL Thailand Assoc.Prof.Dr.Nopporn Chotikakamthorn KMITL Thailand Asst.Prof.Dr.Sarun Intakosum KMITL Thailand Asst.Prof.Dr.Krisana Chinnasarn BU Thailand Asst.Prof.Dr.Anantaporn Chinnasarn KMITL Thailand Asst.Prof.Dr.Krung Sinapiromsaran CU Thailand Dr.Rungrat Wiangsripanawan KMITL Thailand Dr.Peerasak Intarapaiboon TU Thailand

Remark: BU Burapha University CMU Chiang Mai University CU Chulalongkorn University KMITL King Mongkut’s Institute of Technology Ladkrabang KMUTT King Mongkut’s University of Technology Thonburi KMUTNB King Mongkut’s University of Technology North Bangkok KU Kasetsart University MU Mahidol University NU Naresuan University NIDA National Institute of Development Administration PNRU Phranakhon Rajabhat University

ICMSA2015 ICMSA2015 00 (2009) 000–000 www.icmsa2015.kmitl.ac.th

PSU Princess of Songkla University PUT Poznan University of Technology RMUTR Rajamangala University of Technology Rattanakosin RMUTSB Rajamangala University of Technology Suvarnabhumi SU Silpakorn University SUT Suranaree University of Technology SKU Syiah Kuala University TKU Tokai University TU Thammasat University UBU Ubon Ratchathani University UK Universiti Kebangsaan UM University of Malaya UMT University of Malaya Terengganu USM Universiti Sains Malaysia USU Universitas Sumatera Utara

ICMSA2015 ICMSA2015 00 (2009) 000–000 www.icmsa2015.kmitl.ac.th

Keynote Speaker

1. Prof.Dr.Chidchanok Lursinsap Department of Mathematics and Computer ScienceFaculty of [email protected] Science, Chulalongkorn University, Thailand

Research Field: Bioinformatics and Computational Biology, Neural Networks & Machine Intelligence.

Professor Chidchanok Lursinsap received the B.Eng. degree (honors) in computer engineering from Chulalongkorn University, Bangkok, Patumwan, Thailand, in 1978 and the M.S. and Ph.D. degrees in computer science from the University of Illinois at Urbana-Champaign, Urbana, in 1982 and 1986, respectively. He was a Lecturer at the Department of Computer Engineering, Chulalongkorn University, in 1979. In 1986, he was a Visiting Assistant Professor at the Department of Computer Science, University of Illinois at Urbana-Champaign. From 1987 to 1996, he worked at The Center for Advanced Computer Studies, University of Louisiana at Lafayette, as an Assistant and Associate Professor. After that, he came back to Thailand to establish Ph.D. program in computer science at Chulalongkorn University and became a Full Professor. His major research interests include neural learning and its applications to other science and engineering areas.

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2. Prof.Dr.Samruam Chongcharoen School of Applied Statistics, [email protected] National Institute of Development Administration, Thailand

Research Field: Multivariate Statistics on High dimensional Data Order restricted statistical Inference Actuarial Mathematics (Risk Theory) Other applied Statistics

Professor Samruam Chongcharoen earned his Ph.D. in Statistics from Department of Statistics, University of Missouri-Columbia, U.S.A.1998 with mater degree in M.A.(Mathematics Actuarial Science), Central Connecticut State University, U.S.A.1994 and bachelor in B.Ed. (Mathematics), Srinakharinwirot University at Phitsanulok, Thailand,1981.His research interests include Order Restricted Statistical Inference, Statistical Modeling and currently in High dimensional statistics and modeling in Actuarial science. He has published about 25 papers in international journals.

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3. Prof.Dr.Ishak Hashim School of Mathematical Sciences, [email protected] Faculty of Science & Technology Universiti Kebangsaan, Malaysia

Fluid Dynamics & Numerical Method Thermal convection, boundary layer, thin film, CFD, chaotic convection Numerical/Mathematical methods

Professor Ishak Hashim earned his Ph.D. in Industrial Mathematics, University of Strathclyde, Glasgow, UK, March 1998 with mater degree in Mathematics of Nonlinear Models, Heriot-Watt University, Edinburgh, UK, Sept. 1994 and bachelor in Mathematics, Ohio State University, Columbus, USA, June 1992. He has published about 160 papers in prestigious international journals with very high impact.

ICMSA2015 ICMSA2015 00 (2009) 000–000 www.icmsa2015.kmitl.ac.th

4. Assoc.Prof.Dr.Chooi Wai Leong Institute of Mathematical Sciences, Faculty of Science [email protected] University of Malaya, Kuala Lumpur, Malaysia

His research interests include Linear And Multilinear Algebra (Matrix Theory, Linear and Multilinear Algebra, Geometry of Matrices, Quantum Information Science)

Nonlinear Preserver Problems on Matrix and Tensor Spaces Additive Preserver Problems on Matrix Spaces and its Applications Operators on matrices with invariance of lie products Preserver Problems on Spaces of Matrices or Operators and their Applications Some Studies on Preserver Problems on Triangular Matrices Linear preserver problems on spaces of matrices or operators

ICMSA2015 ICMSA2015 00 (2009) 000–000 www.icmsa2015.kmitl.ac.th

Invited speaker

1. Prof.Dr.Suthep Suantai Department of Mathematics, Faculty of Science, [email protected] ChiangMaiUniversity, Chiang Mai, Thailand

Professor Dr. Suthep Suantai received his Ph.D. from Chulalongkorn University, Thailand in 1993. His fields of specialization are Banach Spaces Theory, Geometry of Banach Spaces and Fixed Point Theory and Applications. During the past 20 years, he has made significant contributions to the area of fixed point theory and applications, and many of them are published in prestigious international journals with very high impact. He has also supervised more than 50 students and created a large research group in the area with more than 100 mathematicians and students. He also has been invited to be a keynote speaker at many international conferences and workshops. He is currently a member of the editorial board of many well-known journals in the field of fixed point theory and nonlinear analysis. He is currently the director of the Center for Promotion of Mathematical Research of Thailand (CEPMART).

ICMSA2015 ICMSA2015 00 (2009) 000–000 www.icmsa2015.kmitl.ac.th

2. Prof.Dr.Ryszard Pluciennik The director of Institute of Mathematics, [email protected] Poznan University of Technology, Poznan, Poland

Research Interests  Functional analysis  Integral equations  Operator theory

3.Prof. Dr. I-Ming Tang Department of Materials Science, Faculty of Science, [email protected] Kasetsart University, Thailand

B.Sc. (Physics), Ph.D. (Physics), University of Cincinnati, U.S.A. His research interests include Advanced Materials, Biological Materials, Theory and experiment of condense matter physics, Mathematical modeling. He is a head of one group to do research in nanotechnology, Thailand Center of Excellence in Physics (ThEP), the Commission on Higher Education (CHE).

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4. Prof. Dr. Sorin V. Sabau Faculty of Biological Sciences [email protected] Tokai University, Sapporo Campus, Japan

Research Interests: Differential geometry, Bioinformatics

Professor at Hokkaido Tokai University in the Computer Science Department, holding a PHD degree in Science (Tokyo Metropolitan University, Japan) and a PHD degree in Mathematics (University Al. I. Cuza, Iasi, Romania) with a number of internationally published research papers and publications. Research interests include differential geometry, particularly Higher Order Geometries, Finsler Geometry, Differential Geometry of Differential Equations and Life Science, particularly Bioinformatics, and Computational Biology. He is interesting everything concerning differential geometry, but his research interest encompasses mainly Higher Order eometries, Finsler Geometry and the Differential Geometry of differential equations. Beside these, I am also interested in Life Science, in special Bioinformatics and Mathematical Biology. He has published about 50 papers in prestigious international journals with very high impact.

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5. Prof.Dr.Anton Abdulbasah Kamil School of Mathematical Sciences, [email protected] UNIVERSITI SAINS MALAYSIA, PENANG, MALAYSIA

Research Interests Econometrics and Operation research, Stochastic Frontier Analysis, Financial Mathematics.

Dr. Anton Abdulbasah Kamil is a professor in Mathematics at Universiti Sains Malaysia (USM). He specializes in Econometrics and Financial Mathematics. He has numerous publications to his credit in journal articles and proceedings. More than hundred articles he published in the journals and proceedings. He continues to be an active researcher in his field. He strives to promote mathematics and economics at all levels. He is on the Editorial Board of three international journals. Beside that He has been appointed to hold committee positions in several international conferences and also member of international professional associations related with his field.

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6. Dr.Dusadee Sukawat Department of mathematics, Faculty of Science [email protected] King Mongkut's University of Technology Thonburi, Thailand

Dr. Dusadee Sukawat earned his Ph.D. Meteorology from Florida State University, U.S.A. 1992 with mater degree in Meteorology, University of the Philippines, Philippines 1983 and bachelor in B.S.(Mathematics), Ramkhamhaeng University, Thailand,1975. His research interests include Mathematical Atmospherics Modeling and Numerical Weather Prediction in Meteorology. He has published many papers in international journals. He has also supervised more than 20 students and created a large research group in the area with more than 30 mathematicians and students.

7. Asst.Prof.Dr.Winai Bhodisuwan Department of Statistics, Faculty of Science. [email protected] Kasetsart University, Thailand.

Some Research Articles A Statistical Analysis of Intensities Estimation on the Modeling of Non-Life Insurance Claim Counting Process A Bayesian Inference of Non-Life Insurance Based on Claim Counting Process with Periodic Claim Intensity Stochastic Orders Comparisons of Negative Binomial Distribution with Negative Binomial—Lindley Distribution The negative binomial-generalized exponential (NB-GE) distribution

He is associate Editor-in-Chief JOURNAL OF THAI STATISTICIAN ASSOCIATION.

ICMSA2015 ICMSA2015 00 (2009) 000–000 www.icmsa2015.kmitl.ac.th

ICMSA2015 Conference Program

Ambassador City Jomtien Hotel Sunday 22 November2015 16.00–17.30 Registration Room: Sattahip (C8)

Monday 23 November2015 08.30–09.00 Registration Room: Mabtapud (C10) 09.00-09.40 Opening Address by Prof.Dr. Suchatvee Suwansawat KMITL President Room: Mabtapud (C10) Report by Assoc.Prof.Dr. Dusanee Thanaboripat Dean of Faculty of Science, KMITL Special Lecture by KMITL President, “Man + Math = Mega Math” 10.00-10.30 group photography 10.30-11.00 Coffee break 11.00-11.50 Keynote Lecture: Prof.Dr.Ishak Hashim Universiti Kebangsaan, Malaysia Room: Mabtapud (C10) “Fluid flow and heat transfer problems in an enclosure with a freesurface” 12.00-13.00 LunchRoom: Laemchabang (C6)

13.00-13.50 Keynote Lecture: Prof.Dr.Chidchanok Lursinsap CU, Thailand Room: Mabtapud (C10) “The Concern for Space and Time Complexities in Large Data Analysis” 13.50-15.10 Lecture and Oral Presentations 13.50-15.10 Room: Mabtapud (C10) Room: Sattahip (C8) Room: U- tapao (C9) Room: Sriracha (C7) Pure Mathematics Applied Mathematics I Applied Mathematics II Statistics, Financial and Computer Invited Speaker: Invited Speaker: Invited Speaker: Invited Speaker: Prof.Dr.Suthep Suantai Dr.Dusadee Sukawat Prof.Dr.Ryszard Prof.Dr. Anton Abdul Pluciennik Basah Kamil Chair: Chair: Chair: Chair: Prof.Dr.Suthep Suantai Dr.Dusadee Sukawat Prof.Dr.Ryszard Prof.Dr. Anton Cochair: Cochair: Cochair: Cochair: Asst.Prof.Dr.Atid Asst.Prof.Dr. Jaipong Assoc.Prof.Dr. Assoc.Prof.Dr. Kangtunyakarn Kasemsuwan PuntaniPongsumpun ChartchaiLeenawong 15.10-15.30 Coffee break

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15.30-17.30 Oral Presentations Room: Mabtapud (C10) Room: Sattahip(C8) Room: U- tapao(C9) Room: Sriracha (C7) Pure Mathematics Applied Mathematics I Applied Mathematics II Statistics, Financial and Computer Chair: Chair: Chair: Chair: Assoc.Prof.Dr. Chooi Wai Prof.Dr. Ishak Hashim Prof.Dr. I-Ming Tang Prof.Dr. Chidchanok Leong Cochair: Cochair: Cochair: Cochair: Asst.Prof.Dr. Jaipong Asst.Prof.Dr. Asst.Prof.Dr. Kanchana Asst.Prof.Dr. Kasemsuwan WichaiWitayakittilerd Kumnungkit PattrawutChansangiam

Tuesday 24 November 2015 09.00–09.50 Keynote Lecture:Assoc.Prof.Dr.Chooi Wai Leong Univ.of Malaya, Malaysia Room: Mabtapud (C10) “Linear Preserver Problems and their Recent Developments” 09.50-10.50 Lecture and Oral Presentations 09.50-10.50 Room: Mabtapud Room: Sattahip (C8) Room: U- tapao (C9) Room: Sriracha (C7) (C10) Applied Mathematics I Applied Mathematics II Statistics, Financial and Pure Mathematics Computer Invited Speaker: Invited Speaker: Invited Speaker: Prof.Dr.Sorin V. Sabau Prof.Dr. I-Ming Tang Asst.Prof.Dr.Winai Bhodisuwan Chair:Assoc.Prof.Dr.Chooi Chair:Prof.Dr.Sorin V. Sabau Chair: Prof.Dr . I-Ming Tang Chair: Asst.Prof.Dr.Winai Wai Leong Cochair: Cochair: Bhodisuwan Cochair: Assoc.Prof.Dr. Dr. Thurdkwuan Cochair: Dr. Kampanat Namngam PakkineeChitsakul Changpuek Dr. Thawatchai Khumprapussorn 10.50-11.10 Coffee break

11.10-12.10 Oral Presentations 11.10-12.10 Room: Mabtapud (C10) Room: Sattahip (C8) Room: U- tapao (C9) Room: Sriracha (C7) Pure Mathematics Applied Mathematics I Applied Mathematics II Statistics, Financial and Computer Chair:Prof.Dr.Sorin V. Chair:Assoc.Prof.Dr.Chooi Chair:Asst.Prof.Dr. Klot Chair:Asst.Prof.Dr.Winai Sabau Wai Leong Patanarapeelert Bhodisuwan Cochair: Cochair: Cochair: Cochair: Assoc.Prof.Dr.Pakkinee Dr. Kampanat Namngam Dr. Thurdkwuan Dr. Thawatchai Chitsakul Changpuek Khumprapussorn 12.10-13.10 Lunch Room: Laemchabang (C6)

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13.10-14.00 Keynote Lecture:Prof.Dr.Samruam ChongcharoenNIDA, Thailand Room: Mabtapud (C10) “A New Test for Mean Vector in High-Dimensional Data” 14.00-15.00 Oral Presentations Poster Presentations Room: Sattahip (C8) Room: U- tapao (C9) Room: Sriracha (C7) Pure Mathematics I Pure Mathematics II Chair:Assoc.Prof.Dr.Chooi Wai Leong Chair:Dr. Rini Oktavia Chair: Cochair: Asst.Prof.Dr.Pattrawut Cochair:Dr.Sukrawan Mavecha Asst.Prof.Dr. Kanchana Chansangiam Kumnungkit 15.00-15.20 Coffee break 15.20-16.40 Oral Presentations Room: Sattahip (C8) Room: U- tapao (C9) Room: Sriracha (C7) Pure Mathematics I Pure Mathematics II Some Session/Reserved Chair:Prof.Dr.Sorin V. Sabau Chair:Dr. Rini Oktavia Chair:Prof.Dr. Anton Abdul Basah Cochair: Assoc.Prof.Dr.Pakkinee Cochair:Dr.Sukrawan Mavecha Kamil Chitsakul Cochair: Asst.Prof.Dr. Jaipong Kasemsuwan 17.30-18.30 Dinner Room: 18.30-19.30 Panel Discussion; Applied Mathematics : Today and Future Room: Mabtapud (C10) 19.30-20.00 Best Present Awards Announcement and ICMSA2105 closing Room: Mabtapud (C10)

Wednesday 25 November2015 08.30 – 09.00 Registration for excursion Room: Sattahip (C8) 09.00 – 13.00 Excursion tour -

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Map & Room Location

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Oral and Poster Presentations

Session # 1 Mon 23 Nov. 15: 13.50-15.10 Oral Presentation Room: Mabtapud (C10) Time Pure Mathematics Page Chair: Prof.Dr.Suthep Suantai Co-chair:Asst.Prof.Dr.Atid Kangtunyakarn 1 Recent Development of Fixed Point Theory and Optimization and Its 1 13.50-14.10 Applications Invited Speaker: Prof.Dr.Suthep Suantai 2 Univalent Biharmonic Mappings and linearly connected domain 2 14.10-14.30 (Zayid Abdulhadi and Layan Hajj)(4) 3 On the Algebraic Structure of Complex Twistulant Matrices 3 14.30-14.50 (Sirikanya Kittiwut and Somphong Jitman)(19) 4 THE MINIMIZING GRAPH OF EULERIAN BIPARTITE GRAPHS WITH ODD ORDER 4 14.50-15.10 (Guntaphon Tassanasophon and Khajee Jantarakhajorn)(36)

Session # 2 Mon 23 Nov. 15: 13.50-15.10 Oral Presentation Room: Sattahip (C8) Time Applied Mathematics I Page Chair: Dr.Dusadee Sukawat Co-chair:Asst.Prof.Dr.Jaipong Kasemsuwan 1 Mathematics of Climate Models 5 13.50-14.10 Invited Speaker: Dr.Dusadee Sukawat 2 On the use of GamboostLSS Models for Autocorrelation on interpreting 6 14.10-14.30 Sea Surface Temperature (M Miftahuddin and Sofia K)(86) 3 NUMERICAL TREATMENT TO A WATER-QUALITY MEASUREMENT MODEL IN AN 7 14.30-14.50 OPENED-CLOSED RESERVOIR WITH ANISOTROPIC BOTTOM TOPOGRAPHY (Witsarut Kraychang and Nopparat Pochai)(29) 4 MAXIMUM PRINCIPLES FOR FRACTIONAL DIFFUSION EQUATIONS WITH APPLICATIONS 8 14.50-15.10 (Mohammed Al-Refai and Yuri Luchko)(33)

ICMSA2015 ICMSA2015 00 (2009) 000–000 www.icmsa2015.kmitl.ac.th

Session # 3 Mon 23 Nov. 15: 13.50-15.10 Oral Presentation Room:U- tapao (C9) Time Applied Mathematics II Page Chair:Prof.Dr.Ryszard Pluciennik Cochair:Assoc.Prof.Dr. Puntani Pongsumpun 1 Local approach to Kadec–Klee properties in symmetric function 9 13.50-14.10 spaces Invited Speaker:Prof.Dr.Ryszard Pluciennik 2 Mathematical Simulation of a Groundwater Management in a Drought 11 14.10-14.30 Area Using an Implicit Finite Difference Method (Nattawoot Pongnoo and Nopparat Pochai)(43) 3 Geometrical Methods in the study of Insulin Evolution 12 14.30-14.50 (Sorin V. Sabau and Kazuhiro Shibuya)(40) 4 THE SAULYEV SCHEME FOR AN ADVECTION-DIFFUSION-REACTION EQUATION 13 14.50-15.10 (Pawarisa Samalerk and Nopparat Pochai)(26)

Session # 4 Mon 23 Nov. 15: 13.50-15.10 Oral Presentation Room:Sriracha (C7) Time Statistics, Financial and Computer Page Chair : Prof.Dr.Anton Abdul Basah Kamil Co-chair:Assoc.Prof.Dr.Chartchai Leenawong 1 Grouping in Homogenous Months Based on Daily Maximum Precipitation 14 13.50-14.10 in Penang, Malaysia Invited Speaker: Prof.Dr. Anton Abdul Basah Kamil (72) 2 EEG Signals Classification for Brain Computer Interfaces Using K* Classifer 15 14.10-14.30 (Yotsapat Ruangpaisarn)(85) 3 CUSTOMER LIFETIME VALUE WITH MARKOV CHAIN IN INSURANCE INDUSTRY 17 14.30-14.50 (Adilan Widyawan Mahdiyasa)(74) 4 The Examination of Statistical and Item Analysis According to the 18 14.50-15.10 Classical Test Theory on Students' Learning Trajectory in Statistics (Rini Oktavia) (65)

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Session # 5 Mon 23 Nov. 15: 15.30-17.30 Oral Presentation Room: Mabtapud (C10) Time Pure Mathematics Page Chair: Assoc.Prof.Dr.Chooi Wai Leong Co-chair: Asst.Prof.Dr.Pattrawut Chansangiam 1 The Rainbow Connection Number of Some Classes of Halin Graphs 20 15.30-15.50 (Bety Hayat Susanti, A.N.M. Salman, and Rinovia Simanjuntak)(97) 2 STABILITY OF THE GENERALIZED LOGARITHMIC EQUATIONS BY USING BRZDEK'S FIXED 21 15.50-16.10 POINT METHOD (Laddawan Aiemsomboon and Wutiphol Sintunavarat)(50) 3 A study on $(1,k)$-prime ideals 22 16.10-16.30 (Thawatchai Khumprapussorn)(112) 4 FIXED POINT THEOREMS WITH GENERALIZED ALTERING DISTANCE FUNCTIONS UNDER 23 16.30-16.50 BINARY RELATION (Kanokwan Sawangsup and Wutiphol Sintunavarat)(52) 5 Iterated functional equations related to roots of simple functions 24 16.50-17.10 (Vichian Laohakosol, Sukrawan Mavecha, and Boonrod Yuttanan)(118)

6 THE SECOND SMALLEST EIGENVALUE OF COMPLETE TRIPARTITE HYPERGRAPH 25 17.10-17.30 (Alfi Yusrotis Zakiyyah, Hanni Garminia, A.N.M Salman and Irawati)(96)

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Session # 6 Mon 23 Nov. 15: 15.30-17.30 Oral Presentation Room:Sattahip (C8) Time Applied Mathematics I Page Chair: Prof.Dr.Ishak Hashim Co-chair:Asst.Prof.Dr.Jaipong Kasemsuwan 1 Numerical Simulation of Heat and Mass Transfer of Bio-Coal Pellets in 26 15.30-15.50 The Combustion Process (Manunchaya Noowattana and Supuchara Kongnuan)(68) 2 An explanation of distorted magnetotelluric responses by using 27 15.50-16.10 synthesis-related function (Ninrat Promdee and Weerachai Sarakorn)(73) 3 A Numerical Experiment on Optimal Inverse Multiquadric RBF Shape 28 16.10-16.30 Parameter in the Dual Reciprocity Boundary Element Method for Convective-Dominated Problem (Sayan Kaennakham and Krittidej Chanthawara)(11) 4 MODIFIED COLLECTED BOTTOM LEFT (MCBL) ALGORITHM FOR TWO DIMENSIONAL 29 16.30-16.50 RECTANGLE PACKING PROBLEM (Ariya Unchai and Tawun Remsungnen)(77) 5 ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF WEAKLY DELAYED LINEAR DISCRETE 30 16.50-17.10 SYSTEMS IN R^2 (Josef Diblík, Hana Halfarová and Jan Šafařík)(101) 6 Numerical integration method based on the hyperfunction theory 31 17.10-17.30 (Hidenori Ogata and Hiroshi Hirayama)(35)

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Session # 7 Mon 23 Nov. 15: 15.30-17.30 Oral Presentation Room:U- tapao (C9) Time Applied Mathematics II Page Chair: Prof.Dr.I-Ming Tang Co-chair:Asst.Prof.Dr.Wichai Witayakittilerd 1 ON REPRESENTATION OF SOLUTIONS OF LINEAR DIFFERENTIAL SYSTEMS OF SECOND- 32 15.30-15.50 ORDER WITH CONSTANT DELAYS BY DELAYED MATRIX EXPONENTIAL (Zdeněk Svoboda, Hana Demchenko and Gabriela Vincúrová)(102) 2 ANALYSIS OF MATHEMATICAL MODELLING OF MERS 33 15.50-16.10 (Doungrat Chitcharoen, Puntani Pongsumpun and I-Ming Tang)(113) 3 First-Passage Time Model of Stock Price to a Curved Boundary 34 16.10-16.30 (Klot Patanarapeelert, Charintorn Tangngamsri, Nichaphat Patanarapeelert)(120) 4 Improved delay-range-dependent stability criteria for linear system with 35 16.30-16.50 non-differentiable interval time-varying delay and nonlinear perturbations (Presarin Tangsiridamrong and Kanit Mukdasai)(34) 5 ENHANCEMENT OF NATURAL CONVECTION HEAT TRANSFER IN A ROTATING 36 16.50-17.10 ENCLOSURE BY UTILIZING NANOLIQUID (Habibis Saleh and Ishak Hashim)(45)

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Session # 8 Mon 23 Nov. 15: 15.30-17.30 Oral Presentation Room:Sriracha (C7) Time Statistics, Financial and Computer Page Chair: Prof.Dr.Chidchanok Lursinsap Co-chair:Asst.Prof.Dr. Kanchana Kumnungkit 1 Effect of array sizes on specific humidity pattern classification using self- 37 15.30-15.50 organizing map (Natita Wangsoh, Wiboonsak Watthayu and Dusadee Sukawat)(104) 2 PHISHING WEBSITE DETECTION USING ROTATION FOREST 38 15.50-16.10 (Pumitara Ruangthong)(91) 3 SIMULATION OF QUEUING SYSTEMS TO INCREASE THE EFFICIENCY OF SERVICE IN 39 16.10-16.30 OUTPATIENT DEPARTMENT OF BANGPAKONG HOSPITAL, SAMUPRAKAN PROVICE,THAILAND (Chanin Srisuwannapa)(115) 4 CONJECTURING VIA ANALOGICAL REASONING OF CREATIVE THINKING LEVEL IN 40 16.30-16.50 CONSTRUCTING EQUATION SLICED CONE (Supratman Ahman Maedi)(107) 5 THE ROBUST TEST STATISTIC IN COMPARING TWO INDEPENDENT GROUPS USING 42 16.50-17.10 TRIMMING AND WINSORIZATION (Suhaida Abdullah, Sharipah Soaad Syed Yahaya, Zahayu Md Yusof and Faridzah Jamaluddin)(6) 6 ANISOTROPIC ADAPTIVE REGULARIZATION EFFECTS ON MOVING IMAGES 43 17.10-17.30 (Khda Bux Amur and Shakeel Ahmed Kamboh)(25)

Session # 9 Tue 24 Nov. 15: 09.50-10.50 Oral Presentation Room: Mabtapud (C10) Time Pure Mathematics Page Chair: Assoc.Prof.Dr.Chooi Wai Leong Co-chair: Dr.Kampanat Namngam 1 A NEW GENERALIZATION OF (F,f)-CONTRACTION MAPPINGS IN METRIC SPACES WITH f- 45 09.50-10.10 FIXED POINT RESULTS (Pathaithep Kumrod and Wutiphol Sintunavarat) (51) 2 Fixed Point Results for Generalized $F$-Contractions in Complete Metric 46 10.10-10.30 Spaces (Ahmed Al-Rawashdeh)(30) 3 Generalizations of Schweizer-Wolff Measure of Dependence 47 10.30-10.50 (Wasamon Jantai and Songkiat Sumetkijakan)(71)

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Session # 10 Tue 24 Nov. 15: 09.50-10.50 Oral Presentation Room:Sattahip (C8) Time Applied Mathematics I Page Chair: Prof.Dr.Sorin V. Sabau Co-chair: Assoc.Prof.Dr.Pakkinee Chitsakul 1 Geometrical Models in Biology 48 09.50-10.10 Invited Speaker: Prof.Dr.Sorin V. Sabau (41) 2 THE KANSA MESHLESS METHOD FOR CONVECTION DIFFUSION PROBLEMS USING 49 10.10-10.30 VARIOUS RADIAL BASIS FUNCTIONS (Nissaya Chuathong, Sayan Kaennakam and Wattana Toutip)(8) 3 STABILITY ANALYSIS OF FUZZY CONTROL OF AN APPROXIMATED NONLINEAR 50 10.30-10.50 SINGULARLY PERTURBED SYSTEM (Preeyaporn Waree and Wichai Witayakiattilerd)(78)

Session # 11 Tue 24 Nov. 15: 09.50-10.50 Oral Presentation Room:U- tapao (C9) Time Applied Mathematics II Page Chair: Prof.Dr. I-Ming Tang Co-chair:Dr.Thurdkwun Changpuek 1 DIFFERENTIAL EVOLUTION ALGORITHM: A METHOD FOR DETERMINING THE VALUES 51 09.50-10.10 OF THE PARAMETERS IN A MATHEMATICAL MODEL OF A BIOLOGICAL SYSTEM. Invited Speaker: Prof.Dr. I-Ming Tang 2 A POLYNOMIAL APPROACH TO OPTIMAL CONTROL SWITCHED SYSTEMS AND 52 10.10-10.30 APPLICATIONS (Mohamed Ali Hajji and Abdessamad Tridane)(42) 3 DIFFERENTIAL TRANSFORMATION METHOD FOR THE SUSPENDED STRING EQUATIONS 53 10.30-10.50 (Kamonpad Mansilp and Jaipong Kasemsuwan)(117)

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Session # 12 Tue 24 Nov. 15: 09.50-10.50 Oral Presentation Room:Sriracha (C7) Time Statistics, Financial and Computer Page Chair: Asst.Prof.Dr.Winai Bhodisuwan Co-chair:Dr.Thawatchai Khumprapussorn 1 Some recent development of zero inflated distributions 54 09.50-10.10 Invited Speaker:Asst.Prof.Dr.Winai Bhodisuwan 2 TWO-SAMPLE TESTS FOR HIGH-DIMENSIONAL REPEATED MEASURES DESIGNS WITH 55 10.10-10.30 UNEQUAL VARIANCES (Boonyarit Choopradit, Saowapa Chaipitak and Samruam Chongcharoen)(82) 3 USING PROTOCOL LEVEL PARAMETER IN WCF WITH DIFFERENT PROTOCOL 56 10.30-10.50 (Mirsat Yeşiltepe and Muhammet Kurulay)(31)

Session # 13 Tue 24 Nov. 15: 11.10-12.10 Oral Presentation Room: Mabtapud (C10) Time Pure Mathematics Page Chair: Prof.Dr.Sorin V. Sabau Co-chair: Assoc.Prof.Dr.Pakkinee Chitsakul 1 CONSTRUCTING A REAL SYMMETRIC DOUBLY ARROW MATRIX FROM ITS TWO 57 11.10-11.30 EIGENPAIRS (Wanwisa Pengudom and Archara Pacheenburawana)(55) 2 A Landsberg Moving Frames 58 11.30-11.50 (Pipatpong Chansri and Pakkinee Chitsakul)(66) 3 MAXIMAL DIAMETER SPHERE THEOREM FOR MANIFOLDS WITH NONCONSTANT RICCI 59 11.50-12.10 CURVATURE (Nathaphon Boonnam and Watsana Boonsawaeng)(88)

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Session # 14 Tue 24 Nov. 15: 11.10-12.10 Oral Presentation Room:Sattahip (C8) Time Applied Mathematics I Page Chair: Assoc.Prof.Dr.Chooi Wai Leong Co-chair: Dr.Kampanat Namngam 1 Numerical Simulation of Water-Quality Model on Flooding using Revised 60 11.10-11.30 Lax-Diffusive and Modified Siemieniuch-Gladwell Methods (Kanawoot Subklay and Nopparat Pochai)(39) 2 ANALYTICAL SOLUTIONS OF TIME FRACTIONAL NAVIER-STOKES 61 11.30-11.50 (Muhammet Kurulay and Mirsat Yeşiltepe)(92) 3 Mixed Cyclic Codes over GF(2)GF(4) 62 11.50-11.10 (Taher Abualrub)(110)

Session # 15 Tue 24 Nov. 15: 11.10-12.10 Oral Presentation Room:U- tapao (C9) Time Applied Mathematics II Page Chair: Asst.Prof.Dr. Klot Patanarapeelert Co-chair: Dr.Thurdkwun Changpuek 1 THE DETERMINATION OF THE OPTIMAL COMPONENT RATIO IN FIBER-CEMENT 63 11.10-11.30 PROFILE SHEET ROOF TILES TO REDUCE MATERIALS COST USING A MIXTURE DESIGN (Chuckaphun Aramphongphun, Kampanart Ungtawondee, Duangrudee Chaysuwan)(95) 2 A NUMERICAL SOLUTION FOR NON-UNIFORM BEAM EQUATION BY ADAPTIVE FINITE 64 11.30-11.50 DEFFERENCE METHOD (Kumponsak Boongoy and Pakkinee Chitsakul)(100) 3 COLORING TYPE II FUZZY GRAPH BASED ON FUZZY INDEPENDENT VERTEX SET 65 11.50-12.10 (Isnaini Rosyida, Widodo, Ch. Rini Indrati and Kiki.A. Sugeng)(61)

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Session # 16 Tue 24 Nov. 15: 11.10-12.10 Oral Presentation Room:Sriracha (C7) Time Statistics, Financial and Computer Page Chair: Asst.Prof.Dr.Winai Bhodisuwan Co-chair: Dr.Thawatchai Khumprapussorn 1 FORMULA FOR A CORRELATION COEFFICIENT BETWEEN UNDERLYING COMMODITY 66 11.10-11.30 PRICE AND ITS CONVENIENCE YIELD UNDER SCHWARTZ MODEL (Yamonporn Thummanusarn, Khamron Mekchay and Sanae Rujivan)(47) 2 STOCK SELECTION INTO PORTFOLIO BY FUZZY QUANTITATIVE ANALYSIS AND FUZZY 67 11.30-11.50 MULTI-CRITERIA DECISION MAKING (Satit Yodmun and Wichai Witayakiattilre)(90) 3 Performance of the modern robust test using different trimming criteria 68 11.50-12.10 in comparing two independent groups (Suhaida Abdullah, Sharipah Soaad Syed Yahaya and Zahayu Md Yusof) (62)

Session # 17 Tue 24 Nov. 15: 14.00-15.00 Oral Presentation Room:Sattahip (C8) Time Pure Mathematics I Page Chair: Assoc.Prof.Dr.Chooi Wai Leong Co-chair: Asst.Prof.Dr.Prattrawut Chansangiam 1 KRONECKER PRODUCT OF MATRICES OVER A COMMUTATIVE SEMIRING 69 14.00-14.20 (Raviwan Stangam and Prattrawut Chansangiam)(54) 2 FURTHER GENERALIZED CONTRACTION MAPPING PRINCIPLE IN PARTIAL METRIC 70 14.20-14.40 SPACES (Aphinat Ninsri and Wutiphol Sintunavarat)(49) 3 Weakly Contractive self - mapping on partially ordered quasi metric 71 14.40-15.00 space (Rahma Zuhra, Mohd Salmi Md Noorani and Fawzia Shaddad)(48)

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Session # 18 Tue 24 Nov. 15: 14.00-15.00 Oral Presentation Room:U- tapao (C9)

Chair: Dr. Rini Oktavia Co-chair: Dr.Sukrawan Mavecha 1 Complementary Dual Subfield Linear Codes over Finite Fields 72 14.00-14.20 (Kriangkrai Boonniyom and Somphong Jitman)(15) 2 ON NEW TYPES OF SIMULATION FUNCTIONS WITH FIXED POINT RESULTS IN $b$- 73 14.20-14.40 METRIC SPACES (Oratai Yamaod and Wutiphol Sintunavarat)(53) 3 On Modules over Dedekind Prime Rings 74 14.40-15.00 (Elvira Kusniyanti, Hanni Garminia and Pudji Astuti) (79)

Session # 19 Tue 24 Nov. 15: 14.00-15.00 Poster Presentation Room:Sriracha (C7) 14.00-15.00 Topics Chair: Asst.Prof.Dr. Kanchana Kumnungkit

1 Incomplete split-plot designs constructed by $\alpha$-resolvable 75 designs (Kazuhiro Ozawa)(12) 2 APPLICATION OF NEW MATHEMATICAL OPERATIONS ZERATION AND DELTATION IN 76 ALGORITHMS OF IMAGES (Konstantin Anatol'Evich Rubcov)(99) 3 The stress of undergraduate students, faculty of science King Mongkut’s 77 Institute of Technology Ladkrabang (Pornchai Laipasu) (116)

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Session # 20 Tue 24 Nov. 15: 15.20-16.40 Oral Presentation Room:Sattahip (C8) Time Pure Mathematics I Page Chair: Prof.Dr.Sorin V. Sabau Co-chair: Assoc.Prof.Dr.Pakkinee Chitsakul 1 APPLICATION OF MAMDANI FIS METHOD FOR CLASSIFICATION OF MELINJO MATURITY 78 15.20-15.40 ACCORDING TO ITS COLOUR (Hizir Sofyan, Marzuki Abubakar, Asep Rusyana and Dian Rahmat)(81) 2 The Number of Labelled Trees with r_1,r_2 End-Vertices in K_n,n 79 15.40-16.00 (Thipapat Portawin, Wannaporn Sanprasert and Decha Samana)(38) 3 SOME PROPERTIES OF ROTATIONAL RANDERS TWO-SPHERE OF REVOLUTION 80 16.00-16.20 (Rattanasak Hama)(46) 4 COMPOSITION OPERATOR ON THE GENERALIZE SEGAL-BARGMANN SPACE 81 16.20-16.40 (Tapanee Kittinatgumtorn) (64)

Session # 21 Tue 24 Nov. 15: 15.20-16.40 Oral Presentation Room:U-tapao(C9) Time Pure Mathematics II Page Chair: Dr. Rini Oktavia Co-chair: Dr.Sukrawan Mavecha 1 Skew Polynomials and Some Generalizations of Circulant Matrices 82 15.20-15.40 (Prarinya Morrakutjinda and Somphong Jitman)(14) 2 SOME INEQUALITIES VIA POWER SERIES APPROACH 83 15.40-16.00 (Presarin Tangsiridamrong and Kanit Mukdasai)(13) 3 Numerical Study of Turbulent Convection in Oblique-Ribbed Tube 84 16.00-16.20 (Somchai Sripattanapipat and Pongjet Promvonge)(75) 4 FURTHER RESULTS ON PATH-(SUPER) MAGIC TREES 85 16.20-16.40 (Tita Khalis Maryati and Otong Suhyanto)(67)

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Session # 22 Tue 24 Nov. 15: 15.20-16.40 Oral Presentation Room:Sriracha (C7) Time Applied Mathematics (Optional) Page Chair: Prof.Dr.Anton Abdul Basah Kamil Co-chair: Asst.Prof.Dr.Jaipong Kasemsuwan 1 COMPARISON BETWEEN NATURAL NEIGHBOR INTERPOLATION METHOD AND SPLINE 87 15.20-15.40 INTERPOLATION METHOD OF ARCGIS IN SALINE LEVELS IN BANDA ACEH AFTER ONE DECADE OF TSUNAMI DISASTER (Muslim , Richa Yusima Mauliza)(87) 2 THE EFFECT OF WOLBACHIA INFECTION IN DENGUE TRANSMISSION MODEL WITH 88 15.40-16.00 AGE-DEPENDENT SURVIVAL RATES (Asep K. Supriatna)(94) 3 EVALUATION OF PROCESSES GOVERNING GROUNDWATER SALINIZATION IN AN 89 16.00-16.20 EPHEMERAL COASTAL FLOOD PLAIN: GULF OF KHAMBHAT, INDIA (Pankaj Kumar, Srikantha Herath, Ram Avtar)(58) 4 EXPONENTIAL STABILITY OF AN COUPLED SYSTEM FOR THE VIBRATIONS MODELED 90 16.20-16.40 BY THE STANDARD LINEAR SOLID MODEL WITH A THERMAL EFFECTS (Octavio Vera Villagran)(108)

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Abstracts

ICMSA2015 ICMSA2015 00 (2009) 000–000 www.icmsa2015.kmitl.ac.th

The 11th IMT-GT International ConferenceonMathematics,Statisticsand Its Applications 2015 Recent Development of Fixed Point Theory and Optimization and Its Applications

Prof. Dr. Suthep Suantai

Department of Matematics, Faculty of Science, Chaing Mai University, Chiang Mai, Thailand.

Email: [email protected] Abstract A fixed point Thoery plays very important role in nonlinear analysis, theory of equations and inequalities, approximation theory, economic, engineering and physic. Many problems is science and applied sicience can be formulated in the form oe equations, inequality, sytem of equations and equalities which represent their models. Two main problems arise for solving those equations and inequalities. The first one in the existence problems, how can we know that those equations have a solution ?. Fixed point theory in several theories using to guarantee the existence of a solution of such equations, Fixed Point Theory (more than 90%) is the main tool for this. Once we know the existence of a solutions of the equation, we come to the second problem, Approximation Methods, how to find or approximate a solution of those equations. In the 15 years, Many mathematicians pay much attention on approximation methods for finding or approximation such solutions of the studied problems. Some of them are interested to comprare the rate of convergence of those approximation metheods and construct computer program for solving and approximation such solutions. In this talk, we first mention first period works in fixed point theory such as Banach Contraction Principle, and then give several directions how to generalize the Banach Contraction Principle in many ways, both for single and multi-valued mapping after that new fixed point theorems will dicussed. Then we pay attention on applications of fixed point theory in other areas such as economic, optimization, physic, engineering and computer scince. Finally, some interesting and challenging problems related to fixed point theory and its applications are posed and discussed.

ICMSA2015 ICMSA2015 00 (2009) 000–000 www.icmsa2015.kmitl.ac.th

The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 Univalent Biharmonic Mappings and linearly connected domain

Zayid Abdulhadi1

1 Department of Mathematics, and Statistics, American University of Sharjah, Sharjah, UAE

E-mail: [email protected]

Abstract A four times continuously differentiable complex‐valued function F=u+iv in a simply connected domain Ω is biharmonic if the laplacian of F is harmonic. Every biharmonic mapping F in Ω has the representation F=|z|²G+K, where G and K are harmonic in Ω. In this talk we investigate the relationship between the univalence of F and of K using the concept of linearly connected domains.

Keywords : Biharmonic mappings; univalent; linearly connected domains

References

[1] Z. Abdulhadi and Y.Abumuhanna , " Landau's theorem for biharmonic mappings," Journal of Mathematical Analysis and Applications, Vol.338. no. 1. pp. 705-709, 2008. [2] Z. Abdulhadi, Y.Abumuhanna and S. Khoury, " On Univalent Solutions of the Biharmonic Equations," Journal of Inequalities and Applications, Vol2005 Issue 5, pp.469-478, 2005. [3] Z. Abdulhadi, Y.Abumuhanna and S. Khoury, "On the univalence of the log-biharmonic mappings" Journal of Mathematical Analysis and Applications, Vol. 289, Issue 2,629-638(2004). [4] Y.Abu-Muhanna and R. M. Ali" Biharmonic Maps and Laguerre Minimal Surfaces," Journal of Abstract and Applied Analysis, Vol2013, Article ID 843156, 9 pages, 2013. [5]Y.Abu-Muhanna and G. Schober, Harmonic mappings onto convex mapping domains, Can. J. Math,XXXIX,No. 6, (1987),1489-1530.

ICMSA2015 ICMSA2015 00 (2009) 000–000 www.icmsa2015.kmitl.ac.th

The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 On the Algebraic Structure of Complex Twistulant Matrices

Sirikanya Kittiwut a,b and Somphong Jitman a, *

aDepartment of Mathematics, Faculty of Science, Silpakorn University, Nakhon Pathom 73000, Thailand

bSuratpittaya School, Meung, Suratthani 84000, Thailand

Abstract A class of z -twistulant matrices over the complex field are studied. Given a non-zero z  and a positive integer n, an n×n matrix A over is said to be z -twistulant if

a0 a 1 a 2 ann 2 a 1  za a a a a n1 0 1 n  3 n  2 A  za za a a a n2 n  1 0 n  4 n  3    za1 za 2 za 3 zan 1 a 0

n for some ( a 0 , a 1 ,..., a n  1 )  . It is not difficult to see that a z -twistulant matrix becomes a classical circulant matrix when z = 1 . Given a positive integer n and a non-zero z in the algebraic structure and properties of the set of all n×n z -twistulant matrices are studied. In the case where z  1 , the determinant of a z -twistulant matrix is determined.

Keywords : determinants; circulant matrices; twistulant matrices

References

[1] P. J. Davis. Circulant Matrices. second edition. New York : Chelesa publishing ; 1994. [2] M. Grassl, T. A. Gulliver.On circulant self-dual codes over small fields. Designs, Codes and Cryptography 2009;52:57–81. [3] I. Kra, S. R. Simanca. On circulant atrices, Notices of the AMS 2012;59(3):368–377. [4] D. C. Lay. Linear Algebra and Its Applications. second edition. New York : Addison Wesley Longman; 1997. [5] W. K. Nicholson. Linear Algebra with Applications. fourth edition. Singapore : McGraw-Hill; 2002. [6] D. Rocchesso, J. O. Smith. Circulant and elliptic feedback delay networks for artificial reverberation. IEEE Transactions on Speech and Audio Processing 1997;5(1):51–63. [7] C. Zhang, G. Dangelmayr, I. Oprea. Storing cycles in Hopfield-type networks with pseudoinverse learning rule: admissibility and network topology. Neural Network 2013;46: 283–298. [8] Y. Zheng, S. Shon. Exact inverse matrices of Fermat and Mersenne circulant matrix. Abstract and Applied Analysis 2015;2015: ID760823(10 pages).

ICMSA2015 ICMSA2015 00 (2009) 000–000 www.icmsa2015.kmitl.ac.th

The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 The Minimizing Graph of Eulerian Bipartite Graphs with Odd Order

a b,∗ Guntaphon Tassanasophon and Khajee Jantarakhajorn

a Department of Mathematics and statistics, Faculty of Science and Technology, Thammasat University, Rangsit center, Pathum Thani 12120, Thailand b Department of Mathematics and statistics, Faculty of Science and Technology, Thammasat University, Rangsit center, Pathum Thani 12120, Thailand

Abstract

Let G be a simple graph and A(G) be the adjacency matrix of G. The eigenvalues of A(G) are eigenvalues of G. A graph G is called the minimizing graph in a certain class of graph if its least eigenvalue is minimal among all graphs in a class. In this paper, we determine the minimizing graph in the class of Eulerian bipartite graph with odd order.

Keywords : Eulerian graph; eigenvalues of graph; minimizing graph

References

[1] Brighm RC, Dutton RD. Bound on graph spectra. Journal of Combinatorial Theory Series B 1984;37:228-234. [2] Das KCh, Kumar P. Some new bounds on the spectral radius of graphs. Journal of Discrete Mathematics 2004;281:149-161. [3] Hong Y. Bounds of eigenvalues of graphs. Journal of Discrete Mathematics 1993;123:65-74 [4] Hong Y, Shu JL. Sharp lower bounds of the least eigenvalue of planar graphs. Linear Algebra and its Applications 1999;296:227-232. [5] Nikiforov V. Bounds on graph eigenvalues I. Linear Algebra and its Applications 2007;420:667-671. [6] Nikiforov V. Bounds on graph eigenvalues II. Linear Algebra and its Applications 2007;427:183-189. [7] Power DL. Bounds on Graph Eigenvalues. Linear Algebra and its Applications 1989;117:1-6. [8] Constantine G. Lower bounds on the spectra of symmetric matrices with nonnegative entries. Linear Algebra and its Applications 1985;65:171-178. [9] Bell FK, Cvetkovic D, Rowlinson P, Simic SK. Graphs for which the least eigenvalue is minimal I. Linear Algebra and its Application 2008;429:234-241. [10] Bell FK, Cvetkovic D, Rowlinson P, Simic SK. Graphs for which the least eigenvalue is minimal II. Linear Algebra and its Applications 2008;429:2168-2179. [11] Fan YZ, Wang Y, Gao YB. Minimizing the least eigenvalues of unicyclic graphs with application to spectral spread. Linear Algebra and its Applications 2008;429:577-588. [12] Fan YZ, Zhang FF, Wang Y. The least eigenvalue of the complements of trees. Linear Algebra and its Applications 2011;435:2150-2155. [13] Ye ML, Fan YZ, Liang D. The least eigenvalue of graphs with given connectivity. Linear Algebra and its Applications 2009;430:1375-1379. [14] Tan YY, Fan YZ. The vertex (edge) independence number, vertex (edge) cover number and the least eigenvalue of a graph. Linear Algebra and its Applications 2010;433:790-795. [15] Wang Y, Fan YZ. The least eigenvalue of a graph with cut vertices. Linear Algebra and its Applications 2010;433:19-27. [16] Wang Y, Qiao Y, Fan YZ. On the least eigenvalue of graphs with cut vertices. Journal of Mathermatical Research & Exposition 2010; 30(6):951-956. DOI:10.3770/j.ssn:1000-341X.2010.06.001 [17] Wang Y, Fan YZ. The least eigenvalue of graphs with cut edges. Graphs and Combinatorics 2012;28:555-561. DOI:10.1007/s00373-011- 1060-z [18] Zhu BX. The least eigenvalue of a graph with a given domination number. Linear Algebra and its Applications 2012;437:2713-2718. [19] Zhu BX. A note on the least eigenvalue of a graph with given maximum degree. Electronic Journal of Linear Algebra 2012;23:514-522. [20] Nimnuch T. The least eigenvalue of eulerian graphs. Master’s thesis. Thammasat University; 2013. [21] Cvetkovic D, Rowlinson P, Simic SK. Eigenspaces of Graphs. Encyclopedia of Mathematics and its Applications. Cambridge; 1997. [22] Chartrand G, ZhangP. Introduction to Graph Theory. McGraw-Hill Higher Mathematics; 2005.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 Mathematics of Climate Models

Dusadee Sukawat

The Joint Graduate School of Energy and Environment

King Mongkut’s University of Technology Thonburi

Abstract

Climate models are the most important tools for the study of climate system and its variability. A climate model consist of an atmospheric model, an oceanic model, a land surface model and a sea ice model. The fundamental mathematical concepts of climate models are discussed in this presentation. The topics include governing equations, numerical methods and limitations of climate models.

Keywords : Climate Model, Governing Equations, Numerical Methods

ICMSA2015 ICMSA2015 00 (2009) 000–000 www.icmsa2015.kmitl.ac.th

The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 On the use of GamboostLSS Models for Autocorrelation on interpreting Sea Surface Temperature

Miftahuddin M1, Sofia K2

1Department of Mathematics and Statistics, Faculty of Mathematics and NaturalSciences, Syiah Kuala University, Banda Aceh, Indonesia E-mail: [email protected] 2Department of Environmental Health, Faculty of Medicine, Syiah Kuala University,Banda Aceh, Indonesia E-mail: [email protected]

Abstract The earth's climate system is inuenced by a large number of parameters. Sea Surface Temperature (SST) is one of them. To model SST, we proposed generalized additive models for location, scale and shape by boosting with time-autocorrelation (called gamboostLSS for time-autocorrelation). We have used the gamboostLSS models for autocorrelation and the e_ects of this provide many useful insights. The hyper-parameters such as location, scale,and shape provide more detailed information, for example, seasonal and annual e_ects in the gaps (missing observation). The proposed models have a exible structure and smoothness that incorporates many e_ects of covariates.

Keywords: modi_ed gamboostLSS models, time-autocorrelation, gaps.

References [1] F. A. Schott, S. P. Xie and J. P. McCreary, “Indian Ocean Circulation and Climate Variability, ”Reviews of Geophysics, American Geophysical Union, 47, 1-46 (2009). [2] G. R. North and M. J. Stevens, “Detecting Climate Signals in the Surface Temperature Record, ”Journal of climate, 11, 563-577 (1998). [3] C. Deser, M. A. Alexander, S. P. Xie and A. S. Phillips, “Sea Surface Temperature Variability: Patterns and Mechanisms, ”The Annual Review of Marine Science, 2, 115-143 (2010). [4] B. P. Kumar, J. Vialard, M. Lengaigne, V. S. N. Murty, M. J. McPhaden, M. F. Cronin and K. G. Reddy, “Evaluation of Air-sea Heat and Momentum Fluxes for the Tropical Oceans and Introduction of Tropflux, ” CLIVAR, 58, 1-9 (2012). [5] S. Bojinski, M. Verstraete, T. C. Peterson, C. Richter, A. Simmons and M. Zemp, “The Concept of Essential Climate Variables in Support of Climate Research, Application, and Policy, ”American Mete- orological Society, 1431-1443 (2014). [6] T. Qu, Y. Du, J. Strachan, G. Meyers and J. Slingo, “Sea Surface Temperature and Its Variability in The Indonesian Region, ”Oceanography, 18, 4, 50-61 (2005). [7] P. J. Gleckler, K. E. Taylor and C. Doutriaux, “Performance Metrics for Climate Models, ”Journal of Geophysical Research, 113, 1-20 (2008). [8] J. Rougier and M. Goldstein, “Climate Simulators and Climate Projections, ”Annual Review of Statistics and Its Application, 1, 103-123 (2014). [9] A. Mayr, N. Fenske, B. Hofner, T. Kneib, and M. Schmid, “Generalized Additive Models for Location, Scale and Shape for High Dimensional Data a Flexible Approach Based on Boosting, ”Journal of the Royal Statistical Society: Series C (Applied Statistics), 61 (3), 403-427 (2012). [10] R. A. Rigby and D. M. Stasinopoulos, “Generalized Additive Models for Location Scale and Shape, ”Journal of the Royal Statistical Society: Series C (Applied Statistics) 54 (3), 507-554 (2005). [11] D. M. Stasinopoulos and R. A. Rigby, “Generalized Additive Models for Location Scale and Shape (GAMLSS) in R, ”Journal of Statistical Software, 23 (7), 1-46 (2007). [12] B. Rigby and M. Stasinopoulos, “A flexible regression approach using GAMLSS in R, ”University of Athens, (2010). [13] P. J. Diggle and M. F. Hutchinson, “On Spline Smoothing with Autocorrelated Errors, ”Australian and new Zealand Journal Statistics, 31 (1), 166-182 (1989).

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 Numerical Treatment to a Water-Quality Measurment Model in an Opened-Closed Reservoir with Anisotropic Bottom Topography

Witsarut Kraychang1,2 and Nopparat Pochai1,2

1Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand. 2Centre of Excellence in Mathematics, Commission on Higher Education (CHE), Si Ayutthaya Road, Bangkok 10400, Thailand. E-mail: [email protected]

Abstract Measuring the water quality in water sources or the Monkey Cheeks Project with opened-closed reservoir. It can be measured by the field measurement, using the water quality monitoring tools and the water quality models consist of hydrodynamic model and dispersion model, to calculate the quality of the water. Hydrodynamic model, using the shallow water equation as a governing equation, is used to describe the water current, having source of wave maker and bottom topography as the required data, bringing about the elevation and velocities of water. Dispersion model, using the advection-diffusion equation as the governing equation, is used to describe the spread of the pollutant concentration of water, having pollutant concentration at point source and calculated water velocities from the first model as the input data, bringing the time-dependent pollutant concentration of water at any point. In this research, the three-dimensional surface fitting technique is employed, the anisotropic bottom topography data is represented by a surface function in the hydrodynamic model, in order to have a more realistic water current and water quality approximations in opened-closed reservoir.

Keywords: Water quality model, Hydrodynamic model, Dispersion model, Advection-Diffusion equation, Opened-closed reservoir;

References [1] Garzon, A., and D'Alpaos, L., A modified method of the characteristic technique combined with Gelerkin finite element method to solve shallow water mass transport problems, Proceedings 23rd International Conference in Coastal Engineering 3, 1992 3068-3080. [2] Pochai, N., A numerical computation of the non-dimensional form of a non-linear hydrodynamic model in a uniform reservoir, Journal of nonlinear analysis: Hybrid systems, 3, 2009, 463-466. [3] Pochai, N., A numerical computation of a non-dimensional form of stream water quality model with hydrodynamic advection–dispersion– reaction equations, Journal of nonlinear analysis: hybrid systems, 3, 2009, 666-673. [4] Pochai, N. and Sornsiri C., A non-dimensional form of hydrodynamic model with variable coefficients in a uniform reservoir using Lax- Wendroff method, Procedia Engineering, 8, 2011, 89-93. [5] Pochai, N., Tangmanee, S., Crane, L.J., Miller, J.J.H., A water quality computation in the uniform reservoir, Journal of Interdisciplinary Mathematics, 11(6), 2008, 803-814. [6] Pochai, N., A numerical treatment of non-dimensional form of water quality model in a non-uniform flow stream using Saulyev scheme, Mathematical Problems in Engineering, Volume 2011, 2011, Article number 491-317. [7] Pochai, N., Numerical treatment of a modified MacCormack scheme in a nondimensional form of the water quality models in a nonuniform flow stream, Journal of Applied Mathematics, Volume 2014, 2014, Article number 274-263. [8] Tabuenca, P., Vila, J. and Cardona, J., A. Samartin, Finite element simulation of dispersion in the bay of Santander, Advanced inEngineering Software, 28, 1997, 313-332. [9] Tabuenca, P. and Cardona, J., Numerical model for the study of hydrodynamics on bays and estuaries. Applied Mathematical Modeling,16(2), 1992, 78–85. [10] Pochai, N., Tangmanee, S., Crane, L.J. and Miller, J.J.H., A Finite Element Simulation of Water Quality Measurement in the OpenReservoir, Thai Journal of Mathematics, 7(2), 2009, 77–93. [11] C. Moler, Experiments with MATLAB, MathWorks, 2015. [12] C.R. Robinson, Shallow Water Equations, Syracuse University, 2011. [13] Kraychang, W and Pochai, N., “A Numerical Treatment of a Non-Dimensional From of a Water Quality Model in the Rama-nine Reservoir,” Journal of Interdisplinary Mathematics 18(2015), pp. 375-394.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 MAXIMUM PRINCIPLES FOR FRACTIONAL DIFFUSION EQUATIONS WITH APPLICATIONS

Mohammed Al-Refai1 and Yuri Luchko2

1 Department of Mathematical Sciences, UAE University, Al Ain, UAE E-mail: [email protected] 2 Department of Mathematics, Technical University of Applied Sciences, Berlin, Germany E-mail: [email protected]

Abstract In this talk, we present several new results concerning the fractional derivatives of a function at its extreme points. We then apply these results to establish several maximum principles for linear fractional di_usion equations. Existence and uniqueness results as well as stability results, for linear and nonlinear fractional initial-boundary-value problems, are presented. We consider several types of fractional derivatives such as the Riemann-Liouville fractional derivative and the fractional derivative of distributed order.

Keywords: Riemann-Liouville fractional derivative, extremum principle for the Riemann-Liouville fractional derivative, maximum principle, linear and non-linear time-fractional dif-fusion equations, existence and uniqueness of solutions.

References [1] M. Al-Refai and M. Hajji, Monotone iterative sequences for nonlinear boundary value problems of fractional order. Nonlinear Anal. 74(2011), 3531–3539. [2] M. Al-Refai, On the Fractional Derivative at Extreme Points. Elect. J. of Qualitative Theory of Diff.Eqn. 55(2012), 1– 5. [3] M. Al-Refai, Basic Results on Nonlinear Eigenvalue Problems of Fractional Order. Electronic Journal of Differential Equations 2012(2012), 1–12. [4] M. Al-Refai and Yu. Luchko, Maximum principles for the fractional diffusion equations with the Riemann- Liouville fractional derivative and their applications. Fract. Calc. Appl. Anal. 17(2014), 483–498. [5] S.D. Eidelman and A.N. Kochubei, Cauchy problem for fractional diffusion equations. J. Diff. Equat.199(2004), 211– 255. [6] R. Hilfer (Ed.), Applications of Fractional Calculus in Physics. World Scientific, Singapore (2000). [7] Yu. Luchko, Maximum principle for the generalized time-fractional diffusion equation. J. Math. Anal.Appl. 351(2009), 218–223. [8] Yu. Luchko, Boundary value problems for the generalized time-fractional diffusion equation of distributed order. Fract. Calc. Appl. Anal. 12(2009), 409–422. [9] Yu. Luchko, Some uniqueness and existence results for the initial-boundary-value problems for the generalized time- fractional diffusion equation. Comput. Math. Appl. 59(2010), 1766–1772. [10] F. Mainardi, Fractional Calculus and Waves in Linear Viscoelasticity. Imperial College Press, London (2010). [11] C.V. Pao, Nonlinear Parabolic and Elliptic Equations. Plenum Press, New York (1992). [12] I. Podlubny, Fractional Differential Equations. Academic Press, New York (1999).

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 Local approach to Kadec–Klee properties in symmetric function spaces

Maciej Ciesielski, Paweł Kolwicz, Ryszard Płuciennik

Institute of Mathematics, Poznań University of Technology, Piotrowo 3a, 60-965 Poznań, Poland

Emails: [email protected], [email protected] and [email protected]

Abstract We prove several results concerning local approach to Kadec–Klee properties with respect to global (local) convergence in measure in symmetric Banach function spaces which may be of independent interest. Moreover, we prove characterizations of these properties in the Lorentz spaces. Finally, we show applications ofHgand Hlpoints to the local best dominated approximation problems in Banach lattices.

Keywords: Symmetric spaces, Lorentz spaces, Kadec–Klee property, Hl point, Hg point, Best dominated approximation problems

References

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 Mathematical Simulation of a Groundwater Management in a Drought Area Using an Implicit Finite Difference Method

Nattawoot Pongnooa,b*, Nopparat Pochaia,b*

aDepartment of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand bCentre of Excellence in Mathematics, CHE Si Ayutthaya Rd. Bangkok 10400, Thailan

Abstract The groundwater management is required to solve the problem of lack water resources in many drought areas for agricultural usage. In this study, we propose a groundwater flow model and a groundwater management model that provide the pumping rates and the injection rates respectively. The groundwater model is providing the hydraulic head that gives the groundwater level. The implicit finite difference method is used to approximate the groundwater flow directions. The objective of groundwater flow management model is the minimum cost of injection rates. These are then subjected to optimal management of the water injection stations to achieve minimum cost. The numerical experiments are also given.

Keywords: groundwater management; groundwater model; implicit method

References [1] Olsthoorn TN, The power of electronic worksheet: Modeling without special programs, Ground Water, 1985, 23(3):381-390. [2] Hill, Mary. The practical use of simplicity in developing groundwater models, Grand Water, 2006, 44(6): 775-781. [3] Cryer CW, On the approximate solution of free boundary problems using finite difference, J Assoc Comput Mach, 1970, 17(3):397-411. [4] Bardet JP, Tobita T, A practical method for solving free-surface seepage problems, Comput Geotech, 2002, 29:451-475. [5] Ayvaz MT, Tuncan M, Karahan H, Tuncan A, An extended pressure application for transient seepage problems with a free surface, J.Porous Media, 2005, 8(6):613-625. [6] Desai CS, Li GC, A residual flow procedure and application for free surface flow in porous media, Adv Water Resour, 1983, 6:27-35. [7] Kikuchi N, An analysis of the variational inequalities of seepage flow by finite-element methods, Quarter Appl Math, 1977, 35:149-163. [8] Tatfur G, Swiatek D, Wita A, Singh VP, Case study: Finite element method and artificial neural network models for flow through Jeziorsko earthfill dam in Poland, J Hydraulic Eng, 2005, 131(6):431-440. [9] Ayvaz MT, Karahan H, Asimulation/optimization model for the identification of unknown groundwater locations and pumping rates, Hydrology, 2008: 76-92. [10] Karahan H, Ayvaz MT, Transient groundwater modeling using spreadsheets, Advance in Engineer Software, 2006, 36:374-38. [11] Baalousha H, Fundamental of groundwater modelling, In:Konig L.F and J.L., Nova Science Publishers Inc, 2008, p.149-166.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 Geometrical Methods in the study of Insulin Evolution

Sorin V. SABAU1, Kazuhiro SHIBUYA2

1Department of Mathematics, Faculty of Science, Tokai University, Sapporo, Japan E-mail: [email protected] 2 Department of Mathematics, Hiroshima University, Hiroshima, Japan E-mail: [email protected]

Abstract We study the molecular evolution of insulin from metric geometry point of view. In mathematics, and in particular in geometry, distances and metrics between objects are of fundamental importance. Using a weaker notion than the classical distance, namely the weighted quasi-metrics, one can study the geometry of biological sequences (DNA, mRNA, or proteins) space. We analyze from geometrical point of view a family of 60 insulin homologous sequences ranging on a large variety of living organisms from human to the nematode C. elegans. We show that the distances between sequences provide important information about the evolution and function of insulin.

Keywords: Finite Metric geometry, evolution, insulin.

References [1] S. V. Sabau, K. Shibuya, H. Shimada, “Metric structures associated to Finsler metrics”, Publ. Math.Debrecen, 84 (2014), no. 1-2, 89-103. [2] Y. Kunihiro, S. V. Sabau, K. Shibuya, “A geometrical perspective on the insulin evolution”, WASET, Intl. Journal of Math., Comput. Science and Engineering, Vol: 7, No: 12, 2013. [3] J. Pevnser, Bioinformatics and Functional Genomics, Second Edition, 2003.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 THE SAULYEV SCHEME FOR AN ADVECTION-DIFFUSION- REACTION EQUATION

Pawarisa Samalerk1,2 and Nopparat Pochai 1,2

Abstract The one-dimensional advection-diffusion-reaction equation is a mathematical model describing the transport and diffusion problems such as pollutants and suspended matter in a river or channel. If the velocity field is non-uniform the model cannot be theoretically manipulated, there for numerical techniques are required. The object of this research is to propose a simple advection-diffusion-reaction numerical simulation by using the Saulyev schemes. The proposed numerical technique uses an unconditionally stable method. It is the large or small of time step and/or grid size can be employed in the techniques. Among examples are calculated for three  values. The case of   0 gives a smooth solution compare to the another values. Increasing the mass decay rate affects the maximum concentration level. The numerical experiments show that the calculated results are reasonable approximations

Keywords: Advection-diffusion –reaction equation, Saulyev schemes, Non-uniform

References [1] Mehdi Dehghan, Numerical shemes for one-dimensional parabolic equations with nonstandard initial condition, Applied Mathematics and Computation, 147, 321-331(2004). [2] Halil Karahan, Unconditional stable explicit finite difference technique for the advection-diffusion equation using spreadsheets,Advances in Engineering Software, 38, 80-86 (2007). [3] Nopparat Pochai, A Numerical Treatment of Non-dimensional Form of Water Quality Model in Non-uniform Flow Stream Using Saulyev Scheme, Mathematical Problems in Engineering, 2011, 1-15 (2011). [4] Nopparat Pochai, A Numerical Treatment of Modified MacCormack Schemes in a Nondimensional Form of Water Quality Model in a Nonuniform Flow Stream , Mathematical Problems in Engineering, 2014,1-8 (2014). [5] Guoyuan Li, C, Rhett Jackson, Simple, accurate, and efficient revisions to MacCormack and Saulyev schemes: High Peclet numbers,Applied Mathematics and Computation, 186, 610-612 (2007). [6] BenitoM. Chen-Charpentire, Hristo V, Kojouharov, An unconditionally positivity preserving schem for advection-diffusion reaction equations, Mathematical and Computer Modelling, 57, 2177- 2185 (2013).

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 Grouping Homogeneous Months Based on Daily Maximum Precipitation in Penang, Malaysia

Md. Kamrul Hossaina , Anton Abdulbasah Kamilb, Habibah Latehb

aDepartment of Natural Sciences, Faculty of Science and Information Technology, Daffodil International University, Dhaka - 1207, Bangladesh bSchool of Distance Education, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia

Abstract Precipitation is triggering factor for landslide which is a recurrent problem throughout Malaysia especially in Penang. Daily maximum precipitation influenced mostly to trigger landslide. In this article, daily maximum precipitation which was recorded in eight sites of Penang has been used. The study period of daily maximum precipitation is from 2001 to 2012. The objective of the study is to categories months based on homogeneity in maximum daily precipitation using compare mean and Tukey HSD test. Results shows that highest maximum precipitation is of the sites were recorded in the month of September. For site 5105051 (KOLAM TAKONGAN at BKT PANCHOR), no significant difference is recorded within the months for daily maximum precipitation. However, in other sites, highly significant differences are recorded in between months in case of daily maximum precipitation. In most of the sites, differences in daily maximum precipitation are found in the month of January and February with the month of August, September and October. The finding of the study can be use to determine distribution of daily maximum precipitation using short available data.

Keywords: Daily Maximum Precipitation; Homogeneous Month; Tukey HSD Test; Penang

References [1] Arellano-Lara, F., & Escalante-Sandoval, C. A. (2014). Multivariate delineation of precipitation homogeneous regions for estimating quantiles of maximum daily precipitation: A case study of northwestern Mexico. Atmósfera, 27(1), 47-60. [2] Ros, F. C., Tosaka, H., Sasaki, K., Sidek, L. M., &Basri, H. (2015, May). Absolute homogeneity test of Kelantan catchment precipitation series. In International Conference on Mathematics, Engineering and Industrial Applications 2014 (ICoMEIA 2014) (Vol. 1660, p. 050028).AIP Publishing. [3] Ahmad, N. H., &Deni, S. M. (2013).Homogeneity test on daily precipitation series for Malaysia. MATEMATIKA, 29, 141-150. [4] Kang, H. M., & Yusof, F. (2012). Homogeneity Tests on Daily Precipitation Series. Int. J. Contemp. Math. Sciences, 7(1), 9-22. [5] J.B. Wijngaard, A. M. G. Kleink Tank, G. P. Konnen, Homogeneity of 20th Century European Daily Temperature and Precipitation Series. Int. J. Climatol, 23(2003), 679-692.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 EEG Signals Classification for Brain Computer Interfaces Using K* Classifier

Yotsapat Ruangpaisarn1 and Saichon Jaiyen2

1Department of Computer Science, Faculty of Science,King Mongkut's Institute of Technology Ladkrabang,Thailand 2Department of Computer Science, Faculty of Science,King Mongkut's Institute of Technology Ladkrabang,Thailand

Abstract Electroencephalograph (EEG) signals analysis is an important and necessary work in neuroscience. It is a part of the brain computer interfaces that human can control the computer by thinking. Currently, EEG signals classification plays significant roles in the brain computer interface. In addition, it can be applied to various applications such as classifying diseases, controlling robots, and helping people with disabilities. In this paper, we adopt k* algorithm to classify the 14 channel raw EEG signals for eye opening or closing status. The dataset from the UCI Repository is used in the experiments. The dataset contain EEG signals of the frequency range of Theta waves (4-8 Hz). The performance of the proposed method is evaluated and compared to C4.5 classifier, Radial Basis Function Networks classifier, K-Nearest Neighbors classifier, and k* classifier. The experimental results show that the k* algorithm can achieve the highest accuracy of classification at 97.30%.

Keyword: BCI; EEG; Eye State; Classification; K*;

REFERENCES [1] A. Khasnobish, S. Bhattacharyya, A. Konar, D.N.Tibarewala and A.Nagar, “A Two-fold classification for composite decision about localized arm movement from EEG by SVM and QDA techniques,” Proceedings of International Joint Conference on Neural Networks, USA,2011. [2] R. Ebrahimpour, K. Babakhani and M. Mohammad-Noori, “EEG-based Motor Imagery Classification using Wavelet Coefficients and Ensemble Classifiers,” The 16th CSI International Symposium on Artificial Intelligence and Signal Processing, 2012. [3] L.A.P. Marquez and G.R. Muñoz, “A nalysis and Classification of Electroencephalographic Singnals(EEG) to Identify Arm Movements,” 10th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE), Mexico, 2013. [4] M. Jahan, Y.U. Khan and B.B. Sharma, “Classification of EEG Signals Based on Imaginary Movement of Right and Left Hand Wrist,” International Conference on Medical Imaging, m-Health and Emerging Communication Systems (MedCom), 2014. [5] A.E. Selim, M.A. Wahed and Y.M. Kadah, “Machine Learning Methodologies in P300 Speller Brain-Computer Interface Systems,” 26th National Radio Science Conference(NRSC), 2009. [6] K. Rittikun, P. Boonpramuk and P. Prechaprapranwong, “A study of data reduction for P300 speller system,” Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology (ECTI-CON), 2014. [7] Z. Huang, “Combining AR filter and Sparse Wavelet representation for P300 speller,” IEEE International Conference on Bioinformatics and Biomedicine, 2014.

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[8] E.D. Ubeyli, "Least square support vector machine employing modelbased methods coeffiients for analysis of EEG signals," Expert System with Applications, 2010. [9] K. Polat, and S. Gunes, "Classifiation of epileptiform EEG using a hybrid system based on decision tree classifir and fast Fourier transform," Applied Mathematics and Computation, 2007. [10] L. Guo, D. Rivero,1. A Seoane and A. Pazos,"Classifiation of EEG signals using relative wavelet energy and artifiial neural networks," GCE, 2009. [11] A. Subasi,"EEG signal classifiation using wavelet feature extraction and a mixture of expert model," Expert System with Applications, 2007. [12] S. Chandaka,A Chatterjee and S. Munshi, "Cross-correlation aided support vector machine classifir for classifiation of EEG signals," Expert System with Applications, 2009. [13] Siuly, Y. Li, and P. Wen, “Analysis and classifiation of EEG signals using a hybrid clustering technique,” Interntional Conference on Complex Medical Engineering (CME), Australia, 2010. [14] O. Fukuda, T. Tsuji, and M. Kaneko, "Pattern classification of EEG signals using a log-linearized Gaussian mixture neural network," International Conference on Neural Networks, Aust, 1995. [15] T. Wang, S.U. Guan, K.L. Man and T.O. Ting, “Time Series Classification for EEG Eye State Identification based on Incremental Attribute Learning,” International Symposium on Computer, Consumer and Control (IS3C), 2014. [16] R. Ade and P. R. Deshmukh, “An incremental ensemble of classifiers as a technique for prediction of student’s career choice,” International Conference on Networks & Soft Computing(ICNSC), 2014. [17] R. Ade and P.R. Deshmukh, “Classification of Students by Using an Incremental Ensemble of Classifiers,” INTERNATIONAL CONFERENCE on. Reliability, Infocom Technologies and. Optimization (ICRITO), India, 2014. [18] T. Iliou and G. Paschalidis, “Using an Automated Speech Emotion Recognition Technique to Explore the Impact of Bullying on Pupils Social Life,” Panhellenic Conference on Informatics (PCI), 2011. [19] C. Lakshmi Devasena, “Adeptness Evaluation of Memory Based Classifiers for Credit Risk Analysis,” International Conference on Intelligent Computing Applications, 2014. [20] Cleary, John G. and Leonard E. Trigg, “K*: An instance based learner using an entropic distance measure.” International Conference on Machine Learning (ICML), 1995. [21] O. Roesler. (2013). UCI Machine Learning Repository. [Online].Available: http://archive.ics.uci.edu/ml/datasets [Accessed: Mar. 10, 2015]

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 Customer Lifetime Value With Markov Chain In Insurance Industry

Adilan Widyawan M1, Udjianna S.Pasaribu2

1 Master Student, Faculty of Mathematics and Natural Sciences, Bandung Institut of Technology Bandung, Indonesia E-mail: [email protected] 2 Statistics Research Division, Faculty of Mathematics and Natural Sciences, Bandung Institut of Technology Bandung, Indonesia E-mail:[email protected]

Abstract Nowadays competition between insurance companies become more competitive. This causes insurance companies try to maintain good relationship with customers who have high potential and value for the companies. One method that can be used to determine the value of customers is Customer Lifetime Value (CLV). CLV is present value of expectation from profit or loss that will be obtained by the company during the transaction with the customers [1]. In this paper, the important thing is study about CLV based on Markov Chain stochastic process that devoloped by [2], but with dynamic interest rate. Beside that, also explained algorithm for calculate CLV in health insurane.

Keyword : Customer Lifetime Value (CLV), markov chain , stochastic process, insurance

Reference [1] Berger, Nasr,1998. Customer lifetime value: Marketing models and applications. Journal of Interactive Marketing Volume 12, Number 1, Winter. [2] Pfeifer and Carraway.,2000. Modeling customer relationships as marcov chain. Journal of Interactive Marketing 14(2), Spring. p.43-55 [3] F. Buttle. 2009. Customer Relationship Management Concepts and Technologies, 2nd ed. USA : Elsevier Ltd [4] D. Permana, U.S. Pasaribu, S.W. Indratno,2014.Study of Behaviour and Determination of Customer Lifetime Value using Markov Chain Model.. AIP Conf. Proc. 1589, p.456-459 [5] Ross S.M. 1996. Stochastic Processes, 2nd ed. Canada : John Wiley & Sons [6] Stephen G. Kellison. 2009. The Theory of Interest, 3rd ed. Singapore :Mc Graw Hill [7] Blattberg, Deighton, 1996. Manage marketing by the customer equity. Harvard Business Review, p136-144. [8] Dwyer,1997. Customer lifetime value to support marketing decesion making. Journal of Direct Marketing, Volume 11 Number 4. [9] Gupta S., Lehman D. R., Stuart J. A., 2004. Valuing customers. Jurnal of Marketing Research, p 7-18. [10] M. E. Gookeh, M. J. Tarokh, 2013. Customer lifetime value models: A literature survey. International Journal of Industrial Enginering & Production Research Vol 24, No 4.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 The examination of item analysis according to the classical test theory on students’ learning trajectory in statistics

Rini Oktaviaa*

aSyiah Kuala University, Kopelma Darussalam, Banda Aceh 23111, Indonesia

Abstract This study provides empirical evidence on how students develop their understanding of statistical concepts and investigation. Using the Guidelines for Assessment and Instructions of Statistics Education (GAISE) Framework [1], we developed and administered an instrument to measure students' developmental levels and learning trajectory in statistics. The administration took place in Central Texas, USA where 797 students participated by responding to the 40 items in the instrument that measure students’ understanding on four statistical process components: formulating questions, collecting data, analyzing data, and interpreting results. Some items in the instrument also measure students' understanding on the nature of variability and the focus on variability. In this article we will report the main descriptive and item analysis results according to the classical test theory (CTT). The results explain how students develop their understanding on the four process components and the concepts of variability. The item analysis results describe the effectiveness of test items in the instrument and some aspects of the validity of test scores for explaining students' developmental levels in learning statistics. These results complement some other validity aspects of the test scores that have been discussed in [2].

Keywords: the classical test theory (CTT); the Guidelines for Assessment and Instructions of Statistics Education (GAISE); item analysis; learning trajectory.

References [1] C. Franklin, G. Kader, D. Mewborn, J. Moreno, R. Peck, M. Perry and R. Sceaffer, "Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report: A Pre-K-12 Curriculum Framework," American Statistical Association, Alexandria, VA, 2007. [2] R. Oktavia and M. A. Sorto, "Confirmatory and exploratory factor analysis of students' developmental level in learning statistics," in Sustainability in Statistics Education. Proceedings of the Ninth International Conference on Teaching Statistics (ICOTS9), Flagstaff, AZ, 2014. [3] Conference Board of the Mathematical Sciences, The Mathematical Education of Teachers, Providence, RI; Washington D. C.: American Mathematical Society; Mathematical Association of America, 2001. [4] J. Utts, "Unintentional lies in the media: don’t blame journalists for what we don’t teach," in Proceedings of the Eighth International Conference on Teaching Statistics (ICOTS8, July, 2010), Voorburg, The Netherlands, 2010. [5] J. Utts, "What Educated Citizens Should Know about Statistics and Probability," The American Statistician, pp. 57, 74–79, 2003. [6] National Council of Teachers of Mathematics (NCTM), Principles and Standards for School Mathematics, Reston, VA: NCTM, 2000. [7] R. Peck, G. Kader and C. Franklin, "Shaping K-12 statistics education in the United States," in Proceedings of the ICMI Study 18 and 2008 IASE Round Table Conference: Joint ICMI/IASE Study, Voorburg, The Netherlands, ICMI, IASE, & ISI, 2008. [8] D. Clements and J. Sarama, "Learning trajectories in mathematics education," Mathematics Thinking and Learning, 6(2), pp. 81-89, 2004. [9] P. Daro, F. A. Mosher and T. Corcoran, "Learning trajectories in mathematics: A foundation for standards curriculum, assessment, and instruction," Consortium for Policy Research in Education (CPRE), Philadelphia, PA, 2011. [10] National Governors Association Center for Best Practices, Council of Chief State School Officers, Common Core State Standards- Mathematics, Washington D. C. : National Governors Association Center for Best Practices, Council of Chief State School Officers, 2010. [11] C. Franklin, G. Kader, D. Mewborn, J. Moreno, R. Peck, M. Perry and R. Sceaffer, Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report: A Pre-K-12 Curriculum Framework, Alexandria, VA: American Statistical Association, 2007. [12] R. Nemirovsky, "A functional approach to algebra: Two issues that emerge," in Approaches to algebra: Perspectives for research and teaching, Boston, MA, Kluwer Academic Publishers., 1996, pp. 295-313. [13] S. Embretson and S. P. Reise, Item Response Theory for Psychologists, Mahwah, NJ: Lawrence Erlbaum Associates, 2000. [14] M. McAlpine, "Principles of assessment. Bluepaper Number 1. February 2002. Robert Clark Centre for Technological Education," The CAA Centre, Glasgow, Scotland, 2002.

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[15] T. J. B. Kline, Psychological Testing: A Practical Approach to Design and Evaluation, Thousand Oaks, CA: Sage Publication, Inc., 2005. [16] E. G. Carmines and R. A. Zeller, Reliability and Validity Assessment, London: SAGE Publications, Inc. , 1979.

[17] L. Shu and R. Schwarz, "IRT Estimated reliability for tests containing mixed item formats," in Presented at the National Council on Measurement in Education May 2010, Denver, CO, 2010. [18] L. J. Crohnbach, "Coefficient alpha and the internal structure of test," Psychometrika, 16(3), pp. 297-334, 1951.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 THE RAINBOW CONNECTION NUMBER OF SOME CLASSES OF HALIN GRAPHS

Bety Hayat Susanti 1 , A.N.M. Salman 2 and Rinovia Simanjuntak 3

1,2,3Combinatorial Mathematics Research Group Faculty of Mathematics and Natural Sciences Institut Teknologi Bandung Jl. Ganesa 10 Bandung 40132 Indonesia E-mail: [email protected] , [email protected] , [email protected]

Abstract Let G be a nontrivial connected graph on which is defined an edge-coloring c : E(G) → {1, 2, ..., k}, k ∈ , where adjacent edges may be colored the same. A path in G is called rainbow if there are no two edges of it has the same color. An edge-coloring graph G is rainbow connected if every two vertices are connected by a rainbow path. An edge-coloring under which G is rainbow connected is called a rainbow coloring. The smallest number of colors in a rainbow coloring of G is called the rainbow connection number of G, denoted by rc(G). In this paper, we determine the rainbow connection number of some classes of Halin graphs.

Keywords : halin graph, rainbow connection number, rainbow path

References [1] S. Chakraborty, E. Fischer, A. Matsliah, R. Yuster,\Hardness and algorithms for rainbow connectivity. Journal of Combinatorial Optimization 21, (2011) 330{347. [2] G. Chartrand, G.L. Johns, K.A. McKeon, P. Zhang,\Rainbow connection in graphs. Mathematica Bohemica.133, (2008) 85{98. [3] Susilawati N. and A.N.M. Salman, \The rainbow connection number of rocket graphs, to appear. [4] Syafrizal Sy, G.H. Medika, and L. Yulianti, \The rainbow connection number of fan and sun, Appl. Math. Sci. 7 (2013), 3155{3160.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 STABILITY OF THE GENERALIZED LOGARITHMIC EQUATIONS BY USING BRZDEK’S FIXED POINT METHOD

Laddawan Aiemsomboon 1 , Wutiphol Sintunavarat 2

1 Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathumthani 12121, Thailand E-mail: [email protected] 2 Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathumthani 12121, Thailand E-mail: [email protected], poom [email protected]

Abstract

The aim of this work is to study the stability problem of the generalized logarithmic functional equation :

ab fxy( )  afx ( )  bfy ( ), ab ,  0 where f : \  0   is mapping, by using the Brzdek’s fixed point method as main tool.

Keywords : Brzd¸ek’s fixed point theorem, Hyers-Ulam stability, logarithmic functional equation.

References [1] J. Brzd_ek, \Stability of additivity and _xed point methods," Fixed Point Theory and Applications 2013, 2013:285.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 A study on (1, k)-prime ideals

Thawatchai Khumprapussorn

Department of Mathematics, Faculty of Science King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand [email protected]

Abstract In this paper, we study a generalization of prime ideal of a ring R. Let k be a natural number. A proper ideal I of R is called a (1, k)-prime ideal of R if for every left ideal A of R and right ideal B of R, ARBk ⊆ I implies A ⊆ I k or B ⊆ . Note that = {x ∈ R | x ∈ I}. Our inspiration come from an observation that a prime number in a ring of integers is equivalent with respect to a prime ideal in a ring. We use only basic knowledge in ring theory to obtain that a prime number power of k in a ring of integers is equivalent with respect to a (1, k)-prime ideal in a ring.

Keywords : (1, k)-prime ideals; (R, S)-modules; (1, k)-fully prime (R, S)-submodules; (1, k)-fully multiplication systems

References

[1] T. Khumprapussorn, S. Pianskool and M. Hall, (R; S)-modules and Their Fully prime and Jointly prime Submodules, International Mathematical Forum, 7, 2012, 1631 1643. [2] T. Khumprapussorn, Generalization of jointly prime (R; S)-submodules, Proceedings of 19th Annual Meeting in Mathematics (AMM2014), 2014, 101-107

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 FIXED POINT THEOREMS WITH GENERALIZED ALTERING DISTANCE FUNCTIONS UNDER BINARY RELATION

Kanokwan Sawangsup 1 , Wutiphol Sintunavarat 2

1 Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathumthani 12121, Thailand E-mail: [email protected], [email protected] 2 Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathumthani 12121, Thailand E-mail: [email protected], [email protected]

Abstract

The aim of this work is to prove a new fixed point theorem in metric space endowed with binary relation by using generalized altering distance functions. Our result deduces fixed point theorems in metric space endowed with several relations such as reflexive, irreflexive, symmetric, antisymmetric, transitive, connected, weakly connected and partially ordered set (main results in [1]). Moreover, coupled/ tripled/ quadrupled and multidimensional fixed point theorems are derived from our main results.

Keywords : binary relation; generalized altering distance function; complete metric space 2010

References

[1] Y. Su, “Contraction mapping principle with generalized altering distance function in ordered metric spaces and applications to ordinary di_erential equations,” Fixed Point Theory and Applications, 2014, 2014:227.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 Iterated functional equations related to roots of simple functions

Vichian Laohakosola, Sukrawan Mavechab, and Boonrod Yuttananc

aDepartment of Mathematics, Faculty of Science, Kasetsart University, Bangkok 10900, Thailand. bDepartment of Mathematics, Faculty of Science, King Mongkut's Institute of Technology Ladkrabang, Bangkok 10520, Thailand cDepartment of Mathematics and Statistics, Faculty of Science, Prince of Songkla University, Songkhla 90112, Thailand e-mail: [email protected], [email protected], [email protected]

Abstract. An exposition about polynomial-like iterative functional equations is given. Emphases are placed upon equations of the form fq(x) = g(x), for a given function g and a positive integer q, de_ned over two kinds of domain, non-discrete and discrete. In addition to historical developments, one of our recent results is presented.

Keywords: iterative functional equations, cycles. 2010 Mathematics Subject Classi_cation: 39B12, 11B99

References

[1] Allouche, J.-P., Rampersad, N., Shallit, J.O.: On integer sequences whose _rst iterates are linear. Aequationes Math. 69(1-2), 114-127 (2005). [2] Berg, L.: Iterative functional equations. Rostock. Math. Kolloq. 64, 3-10(2009). [3] Jarczyk, W.: On an equation of linear iteration. Aequationes Math. 51, 303-310(1996). [4] Kuczma, M., Choczewski, B. and Ger, R.,Iterative Functional Equations, Encyclopedia of Mathematics and Its Applications, Vol. 32, Cambridge Univ. Press, Cambridge, 1990. [5] Kulczycki, M. and Tabor, J.: Iterative functional equations in the class of Lipschitz functions. Aequationes Math.64, 24-33(2002). [6] Laohakosol, V. and Yuttanan, B.: Iterates of increasing sequences of positive integers. Aequationes Math. 87, 89-103 (2014). [7] Matkowski, J. and Zhang, W.: On linear dependence of iterates. J. of Appl. Anal. 6(1), 149-157(2000). [8] Matkowski, J. and Zhang, W.: On the polynomial-like iterative functional equation. Th. M. Rassias (Ed.) Functional Equations and Inequalities. 145-170(2000). [9] Propp, J.: Problem proposal 474. Crux Math. 5, 229 (1979). [10] Propp, J.: Solution by G. Patruno. Crux Math. 6, 198 (1980). [11] Sarkaria, K.S.: Roots of translations. Aequationes Math. 75, 304-307 (2008). [12] Yang, D. and Zhang, W.: Characteristic solutions of polynomial-like iterative equations. Aequationes Math. 67, 80-105(2004).

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 THE SECOND SMALLEST EIGENVALUE OF COMPLETE TRIPARTITE HYPERGRAPH

1 1 1 1 Alfi Yusrotis Zakiyyah , Hanni Garminia , Salman msalman , Irawati irawati

1Institut Teknologi Bandung,Indonesia,[email protected]

Abstract In the terminology of hypergraph, there is a relation with the terminology graph. In the theory of graph, the edges connected two vertices. In otherwise, in hypergraph, the edges can connect more than two vertices. There are representation matrix of graph such as adjacency matrix, Laplacian matrix and incidence matrix, see [2]. Adjacency matrix is symmetry matrix so that all eigenvalues is real. This matrix is nonnegative matrix. The all diagonal entry from adjacency matrix is zero so that the trace is zero. Another representation matrix of graph is Laplacian matrix. Laplacian matrix is symmetry matrix and semidefinit positif so that all eigenvalues are real and nonnegative. According to the spectral study in the graph, some that result is generalized to hypergraph. A hypergraph can be represented by a matrix such as adjacency, incidence and Laplacian matrix, see[1,3]. Throughout for this term, we use Laplacian matrix to represent a complete tripartite hypergraph. The aim from this research are determine second smallest eigenvalues from this matrix and find a relation this eigenvalues with the connectivity of that hypergraph.

Keywords: algebraic connectivity,graph,hypergraph,Laplacian matrix

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 Numerical Simulation of Heat and Mass Transfer of Bio-Coal Pellets in The Combustion Process

Manunchaya Noowattanaa and Supuchara Kongnuanb; aDepartment of Mathematics and statistics, Faculty of Science, Thammasat University, Pathum Thani, Thailand e-mail : [email protected] bDepartment of Mathematics and statistics, Faculty of Science, Thammasat University, Pathum Thani, Thailand e-mail : [email protected]

Abstract In this research, a mathematical model is developed to simulate the distribution of heat and mass transfer in the combustion process of a bio-coal pellet. Heat and mass transfer inside the particle are described by the heat transfer equation couple with mass balance equation with appropriate initial and boundary conditions. In this study, we present numerical simulation of heat and mass transfer of bio-coal pellets in the combustion process by using algorithm base on the ﬁnite element method in the commercial software of COMSOL Multiphysics. The results of the heat and mass transfer are feasible and reasonable. Moreover, the parameters such as thermal conductivity and speciﬁc heat capacity of several materials are studied.

Keywords : bio-coal pellet; heat transfer; mass transfer; combustion

References [1] Babu BV, Chuarasia AS. Modeling for pyrolysis of solid particle kinetics and heat transfer effects. Energy Conversion and Management, 2002;44:2251-2275. [2] Babu BV, Chuarasia AS. Pyrolysis of biomass:improved models for simulataneous kinetics and transport of heat, mass and momentum. Energy Conversion and Management, 2003;45:1297-1327. [3] Brito AG, and Melo LF. Mass transfer coefficients within anaerobic biofilms: effects of external liquid velocity. Wat.Res, 1999;33:3673- 3678. [4] Dupont C, Chiriac R, Gauthir G, and Toche F. Heat capacity measurement of various biomass types and pyrolysis residues.Fuel, 2014;115:644-651. [5] Ferrero F, Malow M, Berger A, and Krause U. Modelling the coupled heat and mass transfer during fires in stored biomass,coal and recycling deposits. Berlin: Germany; 2007. [6] GuoW, Lim JC, Sokhansanj S, and Melin S. Determination of effective thermal conductivity and specific heat capacity of wood pellets. Fuel, 2013;103:347-366. [7] Gupta M, Yang J, and Roy C. Specific heat and thermal conductivity of softwood bark and softwood char particle. Fuel, 2003;82:919-927. [8] Jalan PK, Srivastava VK. Studies on pyrolysis of single biomass cylindrical pellet-kinetic and heat transfer effects. Energy Conversion and Management, 1999;40:467-494. [9] Lu H, Robert W, Peirce G, Ripa B, and Baxter LL. Comprehensive study of biomass particle combustion. Energy Fuels, 2008;22:2826-2839. [10] Ojolo SJ, Osheku CA, and Sobamowo MG. Analytical investigation of kinetic and heat transfer in slow pyrolysis of a biomass particle. Int. Journal of Renewable Energy Development, 2013;2(2):105-115. [11] Peng JH, Bi HT, Sokhansanj S, and Lim JC. A study of particle size effect on biomass torrefaction and densification. Energy Fuels, 2012;26:3826-3839. [12] Porterio J, Miguez JL, Granada E, and Moran JC. Mathematical modelling of the combustion of a single wood particle. Fuel Processing Techonology, 2006;87:169-175. [13] Prakash N, and Karunanithi T. Advances in modelling and simulation of biomass pyrolysis. Asian Journal of Scienctific Research, 2009;2(1):1-27. [14] Sadhukhan AK, Gupta P, and Saha RK. Modelling and experimental studies on pyrolysis of biomass particles. Journal of Analytical and Applied Pyrolysis, 2008;81:183-192.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 An explanation of distorted magnetotelluric responses by using synthesis-related function

Ninrat Promdeea, Weerachai Sarakornb*

aDepartment of Mathematics, Faculty of Science, Khon Kaen University, Khon Kean, Thailand

bDepartment of Mathematics, Faculty of Science, Khon Kaen University, Khon Kean, Thailand

Abstract Magnetotelluric (MT) Modeling describes the phenomena of the electromagnetic (EM) wave that interact with both of the earth’s sphere and earth’s subsurface. Solving MT Modeling using either analytical or numerical methods yields the synthetic earth’s responses defined by the apparent resistivity and phases. Usually, when the resistivity structure of the earth is assumed to be uniform or layered and any topography are not present, the obtained apparent resistivity are identical to its structures. How ever, when the topography are presented, the calculated responses are distorted. In this research, the obtained distorted responses with the presence of some simple topographies are studied. The synthetic functions are selected to describe the distortion and the ir included parameters are estimated using the Randomized Neighbourhood Search (RNS) to fit the synthetic data. The obtained results indicate that the selected synthetic functions can describe the distortion of responses quite well: the root mean squ are errors are between 0.13545 and 3.0278. Furthermore, the topographic functions are the kernel of the selected synthetic functions and the estimated parameters are varied by the frequency of EM wave.

Keywords: Magnetotelluric responses, topography, distortion;

References [1] Key K., and Weiss C., Adaptive finite-element modeling using unstructured grids: The 2D magnetotelluric example. Geophysics; 2006 71(6): G.291-G299. [2] Khyzhnyak M., Geoelectric strike and its application in magnetotellurics. North American Actuarial Journal [B.Sc.thesis in Earth science]: University of Iceland [3] Myung Jin Nam, Hee Joon Kim, Yoonho Sing, Tae Jong Lee, and Jung Hee Suh., Three-dimensional topography corrections of magnetotelluric data. Geophysics Journal International; 2008, p. 305-350. [4] Sarakorn W., Three-dimensional electromagnetic modeling and inversion, [Ph.D. Thesis in Mathematics]: University of Mahidol; 2001. [5] Sarakorn W., and Siripunvaraporn W., solving 2-D magnetotelluric forward modeling using finite element methods with unstructured quadrilateral mesh, the 22-nd Electromagnetic Induction Workshop. [6] Schwalenberg K., Edward R.N., the effect of seafloor topography in magnetotelluric fields: and analytical formulation confirmed with numerical results. Geophysical Journal International; 2004 159: 607-621. [7] Boonta S., Sattayatham A., and Sattatatham.P., Estimation of weibull parameters using a randomized neighborhood search for the severity of fire accidents. Journal of Mathematics Statistic; 2013, p. 12-17. [8] Worzewski T., Jegen M. and Swidinsky A., Approximations for the 2-D coast effect in marine magnetotelluric data. Geophysics; 2012, 189:357-368. [9] Wannamaker E., Stodt A., and Rijo L., Two-dimensional topographic responses in magnetotellurics modeled using finite elements. Geophysics; 1986, 51(11): 2131-2144.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 A Numerical Experiment on Optimal Inverse Multiquadric RBF Shape Parameter in the Dual Reciprocity Boundary Element Method for Convective-Dominated Problem

a Sayan Kaennakhama *, Krittidej Chanthawarab,

aSchool of Mathematics, Institute of Science, Suranaree University of Technology, NakhonRatchasima and 30000, Thailand bDepartment of mathematics , faculty of science, Ubonratchathani Rajabat University , Ubonratchathani and 34000, Thailand

Abstract

This work focusses on two main challenges; the development of the dual reciprocity boundary element method (DRBEM) to problems categorized as convective-diffusive, and the search for optimal shape parameter when utilizing the inverse Multiquadric radial basis function (IMQ-RBF). There are only a few works carried out on applications of DRBEM to convective-diffusive problems and even less when it comes to phenomenon when the convective force becomes dominant, due to its well-known difficulties. Unlike the linear form of RBF where it remains the most popular choice, the IMQ-RBF has received some doubt. This is due to the lack of information on choosing the best shape parameter available in nowadays literature, forcing the user having to make an ‘ad-hoc’ decision. Recent numerical experiments available in literature nevertheless, IMQ-RBF has shown great potential when dealing with coupled form of PDE’s in two dimensions if an adequate shape value is provided. It is, therefore, great of our interest to expand the experiment to the problem governed by the convection-diffusion equation in the hope to shed some more light on the topic and also provide a piece of useful information for future scientists and engineers.

Keywords: Inverse Multiquadric; Radial Basis Function; Boundary Element Method; Convection Diffusion Problems. References [1] Brebbia, CA, Butterfield, RL. Formal equivalence of direct and indirect boundary element methods. Applied Mathmatical Modelling 1978; 2:132-134. [2] Chanthawara K, Keannakham S, Toutip W. The dual reciprocity boundary element method(DRBEM) with Multiquadric radial basis function for coupled burgers’ equation. International Journal of Multiphysics 2014; 8:123-143. [3] Chanthawara K, Keannakham S, Toutip W. Inverse Multiquadric RBF in the Dual Reciprocity Boundary Element Method(DRBEM) for Coupled 2D Burgers’ Equations at high Reynolds numbers. Proceeding of the 19th international annual symposium on computational science and engineering; 2015 Jun 17-19; Ubon Ratchathani, Thailand. [4] Djidjeli K, Chinchapatnam PP, Nair PB, Price WG. Global and compact meshless schemes for the unsteady convection-diffusion equation. Proceedings of the international symposium on health care and biomedical research interaction; 2004 Oct 08-09; Oujda, Morroco. [5] Ikeuchi M, Onishi K. Boundary element solutions to steady convective diffusion problem. Journal of Computational and Applied Mathematics 1983; 12-13:381-389. [6] Ikeuchi M, Sakakihara M. Boundary element in steady convective diffusion equation. Applied Mathematical Modelling 1985; 7:115-118 [7] Partridge PW, Brebbia CA, Wrobel LC. The dual reciprocity boundary element method. Southampton: Computational Mechanics Publications; 1992. [8] Boztosun I, Charafi A. An analysis of the linear advection-diffusion equation using mesh-free and mesh-dependent methods. Engineering Analysis with Boundary Elements 2002; 26:889-895. [9] Powell MJD. The uniform, convergence of thin plate splines in two dimensional. Numerische Mathematik 1994: 68:107-128. [10] Junpou Nee, Duan J. Limit set of trajectories of the coupled viscous Burger equation. Applied Mathematics Letters 1998; 11:57-61. [11] Dehghan D, Mohebbi A. High-order compact boundary value method for the solution of unsteady convection-diffusion problems. Math Comput Simul 2008; 79:683-699. [12] Gu YT, Liu GR. Meshless techniques for convection dominated problems. Comput Mech 2006; 38: 171-182. [13] Chanthawara K, Kaennakham S, Toutip W. The Numerical Study and Comparison of Radial Basis Functions in Applications of the Dual Reciprocity Boundary Element Method to Convection-Diffusion Problems. The international conference on Progress in Applied Mathematics in Science and Engineering (PIAMSE), 2015, Indonesia. Accepted for oral presentation and published in a SCOPUS indexed journal.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 Modified collected bottom left (MCBL) algorithm for two dimensional rectangle packing problem

Ariya Unchaia*, Tawun Remsungnen

Department of Mathematics, Faculty of Science, KhonKaen University, KhonKaen, Thailand Department of Mathematic, 2Faculty of Applied Science and Engineering, Nong Khai Campus Khon Kaen University, Nong Khai, Thailand

Abstract

Keywords: Inverse Multiquadric; Radial Basis Function; Boundary Element Method; Convection Diffusion Problems.

References [1] Hochbaum D, Maass W. An approximation Schemes for covering and packing problems in image processing and VLSI. Journal of Computing Machinery 1985; 32: 130-136. [2] Hopper E, Turton BCH. An empirical investigation of meta-heuristic and heuristic algorithms for a 2D packing problem. European Journal of Operational Research 2001; 128: 34-57. [3] Hadjiconstantinou E, Christofides N. An exact algorithm for general, orthogonal, two-dimensional knapsack problem. European Journal of Operational Research 1995; 83: 39-56. [4] Jakob S. On genetic algorithms for the packing of polygons. European Journal of Operational Research 1996; 88: 165-181. [5] Lui D, Teng H. An improve BL for genetic algorithms of the orthogonal packing of Rectangles. European Journal of Operational Research 1999; 112: 413-420. [6] He K, Huang W, Jin Y. An efficient deterministic heuristic for two-dimensional rectangular packing. Computer and Operations Research 2012; 39: 1355–1363. [7] Unchai A, Remsungnen T. Collected bottom left algorithm for 2D rectangle packing problem. Annual Meeting in Mathematics 2014; 19: 63- 70. [8] Storn R, Price K. Differential evolution simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 1997; 11: 341-359. [9] Unchai A, Remsungnen T. Vertical-horizontal cross points (VHCP) algorithm for 2D rectangle packing problem. Annual Meeting in Mathematics 2015; 20: 399-405. [10] Yi-chao H, et al. Differential evolution algorithm with position-order encoding for solving traveling salesman problem. Journal of Computer Applications, 2007;3: 039.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF WEAKLY DELAYED LINEAR DISCRETE SYSTEMS IN R2

Josef Diblik1,Hana Halfarova2 and Jan Safarik3

1Central European Institute of Technology, and Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Brno,Czech Republic E-mail: [email protected], [email protected] 2Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Brno University of Technology, Brno, Czech RepublicE- mail: [email protected] 3Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Brno, Czech Republic E- mail: [email protected]

Abstract Two-dimensional linear discrete systems n l

x k1  Ax (k)  B xll k  m , k  0 l1 1 n are analyzed, where m12,,, m mn are constant integer delays, 0m12  m   mn , A , B , , B are constant ll 2 22 matrices, A aij,B  B ij  , i , j  1,2, l  1,2, , n and x: mnn ,  m  1,  R . Under the assumption that the system is weakly delayed, the asymptotic behavior of its solutions is studied. Asymptotic formulas describing the solutions are derived as well as sucient conditions for conditional stability and asymptotic conditional stability. The theoretical background for derived results can be found in [1-3].

Keywords: asymptotic behavior, discrete system, stability, weakly delayed system

References [1] Dibl´ık J., Khusainov D., Sˇmarda Z., “Construction of the general solution of planar linear discrete systems with constant coefficients and weak delay,” Advances in Difference Equations, 2009, Art. ID784935, doi:10.1155/2009/784935, 1-18 (2009). [2] Dibl´ık J., Halfarov´a H., “General explicit solution of planar weakly delayed linear discrete systems and pasting its solutions,” Abstract and Applied Analysis, 2014, doi:10.1155/2014/627295, 1-37 (2014). [3] Dibl´ık J., Halfarov´a H., “Explicit general solution of planar linear discrete systems with constant coefficient and weak delays,” Advances in Difference Equations, 2013, Art. number: 50, doi:10.1186/1687-1847-2013-50, 1-29 (2013).

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015

NUMERICAL INTEGRATION METHOD BASED ON THE HYPERFUNCTION THEORY

Hidenori Ogata 1 and Hiroshi Hirayama 2

1 Department of Communication Engineering and Informatics, Graduate School of Informatics and Engineering, The University of Electro-Communications, Chofu, Japan E-mail: [email protected] 2 Department of Vehicle System Engineering, Faculty of Creative Engineering, Kanagawa Institute of Technology, Atsugi, Japan E-mail: [email protected] Abstract

b In this study, we examine a numerical integration method proposed by Hirayama [2]. We consider an integral f()() x w x dx , a where fx() is a given real analytic function on [a, b] and wx() is a weight function, that is, a function such that wx( ) 0 except for a finite number of zero points. In his method, we transform the integral into the complex loop integral bb1wx ( ) (1) f()()()()() x w x dx f z z dz with z dx a2i  C  a z x where C is a loop in the complex plane such that C encircles the interval [a; b] in the positive sense and fz() is analytic on C and in its inside. Then, we obtain an approximation of the integral by applying the trapezoidal rule to the complex integral in (1). We expect that the above method gives an accurate approximation since the trapezoidal rule is very efficient for integrals whose integrands are periodic analytic functions, and, in fact, a theoretical error analysis shows an exponential convergence of the method. Numerical examples show the efficiency of the method especially for integrals with so strong end- point singularities that the DE rule [3] does not work for them. In addition, the above method is closely related to the hyperfunction theory [1] in the sense that (1) is the integral of f()() x w x which is regarded as a hyperfunction and, in the method, we approximate the complex integral which defines the desired integral as a hyperfunction integral.

Keywords: numerical integration, complex analysis, hyperfunction

References [1] U. Graf, \Introduction to Hyperfunctions and Their Integral Transforms | An Applied and Computational Approach |, Birkh•auser, Basel, 2010. [2] H. Hirayama, \A numerical integration rule by the contour integral transformation", Abstract of the 44-th Numerical Analysis Symposium, 21- 24 (2015) (in Japanese). [3] H. Takahasi, M. Mori, \Double exponential formulas for numerical integrations", Pulb. RIMS, Kyoto Univ., 9, 721-741 (1974).

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015

ON REPRESENTATION OF SOLUTIONS OF LINEAR DIFFERENTIAL SYSTEMS OF SECOND-ORDER WITH CONSTANT DELAYS BY DELAYED MATRIX EXPONENTIAL

Zdenek Svoboda 1, Hana Demchenko 2 and Gabriela Vincurova 3

1 Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Brno, Czech Republic E-mail:[email protected] 2 Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Brno, Czech Republic E-mail: [email protected] 3 Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Brno, Czech Republic E-mail: [email protected]

Abstract

In the presentation will be considered n-dimensional second-order linear di_erential equation with delay 2 x''()2 t Ax '( t  )  A x ( t  2) where A is an constant matrix and   0 . A new representation of solutions to initial problem is given utilizing what is called a At delayed matrix exponential e defined by theformula t/1  s At s (ts ( 1) )

eA   s0 s! where . is the floor integer function. The theoretical background for derived results can be found in [1]- [4].

Keywords: representation of solutions, delay, matrix delayed functions

References [1] Khusainov D.Ya., Shuklin G.V., \Linear autonomous time-delay system with permutation matrices solving," Stud. Univ. _Zilina, Math. Ser. 17 (2003), 101-108. [2] Khusainov, D.Ya., Shuklin, G.V., \Relative controllability in systems with pure delay," (English. Russian original) Int. Appl. Mech. 41, No. 2, 210{221 (2005), translation from Prikl. Mekh., Kiev 41, No. 2, 118{ 130 (2005). [3] Medved' M., Posp___sil M., \Su_cient conditions for the asymptotic stability of nonlinear multidelay differential equations with linear parts de_ned by pairwise permutable matrices," Nonlinear Anal.-Theor.75 (2012), 3348{3363. [4] Posp___sil M., \Representation and stability of solutions of systems of functional di_erential equations with multiple delays," Electron. J. Qual. Theory Di_er. Equ. 4 (2012), 1{30.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015

ANALYSIS OF MATHEMATICAL MODELLING OF MERs

1 2 3 Doungrat Chitcharoen , Puntani Pongsumpun , and I Ming Tang

1 Department of Mathematics, Faculty of Science, Chandrakasem Rajabhat University Bangkok, Thailand E-mail: [email protected] 2 Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok, Thailand E-mail: [email protected] 3 Department of Materials Science, Faculty of Science, Faculty of Science, Kasetsart University Bangkok, Thailand E-mail: [email protected]

ABSTRACT

Middle East respiratory syndrome (MERS) is a viral respiratory disease caused by a novel coronavirus (MERS-CoV) that was first identified in Saudi Arabia in 2012 and has since spread to several other contries. MERS has raised global public health concerns regarding the current situation and its future evolution. A virus is studied by formulating a SEIQR (susceptible, exposed, infected, quarantine, and recovered) model and analyze the model properties.

Keywords: a SEIQR model; Middle East respiratory syndrome 2010 Mathematics Subject Classi_cation: 05C15, 05C55, 05D10

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 First-Passage Time Model of Stock Price to a Curved Boundary

a a b Klot Patanarapeelert ,*, Charintorn Tangngamsri , Nichaphat Patanarapeelert

a Department of Mathematics, Facluty of Science, Silpakorn University, Nakorn Pathom 73000, Thailand b Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand

Abstract

In finance literature, the first-passage time (FPT) distribution of the firm value process is necessary in analyzing the structure of credit spread and widely used in the context of complicated option pricing. In this paper, we focus on the derivation of the FPT distribution of the Geometric Brownian Motion (GBM) which often represents the simple model of stock price. By using the transformation technique we derive the first-passage time densities for the case of exponential boundary and the case of stochastic boundary. In order to generate sample data sets from the concrete model, we perform on data of stock price of a company selected from SET50 that can be fit with the GBM. The results from simulations coincide with analytical formulas.

Keywords: First-Passage time; Geometric Brownian Motion; Stock price.

References [1] Kijima M. Stochastic processes with applications to finance. Chapman & Hall/CRC; 2003. [2] Joshi M. The concepts and practice of mathematical finance. Cambridge University Press; 2003. [3] Valenti D, Spagnolo B, Bonanno G. Hitting time distributions in financial markets. Physica A 2007; 382: 311-320. [4] Paul W, Baschnagel J. Stochastic processes from Physics to Finance. Springer-Verlag; 1999. [5] Dominé M. First passage time distribution of a Wiener process with drift concerning two elastic barriers. Journal of Applied Probability 1996; 33 (1):164-175. [6] Williams D. An appendix to Durbin’s paper. Journal of Applied Probability 1992; 29: 302-303. [7] Malone SW. Alternative price processes for Black-Scholes: Emperical evidence and theory. Monograph date April; 2002:19. [8] Kijima M, Suzuki T. The pricing of options with stochastic boundaries in a Gaussian economy. Journal of the Operations Research Society of Japan 2007; 50(2): 137-150. [9] Pinsky MA, Karlin S. An introduction to stochastic modeling. 4th ed. Academic Press; 2011.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 Improved delay-range-dependent stability criteria for linear system with non-differentiable interval time-varying delay and nonlinear perturbations

Presarin Tangsiridamrong1 and Kanit Mukdasai2;¤

1Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand E-mail: [email protected] 2Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand E-mail: [email protected] ¤Corresponding author. E-mail : [email protected]

Abstract

In this paper, we investigate the problem of delay-range-dependent stability analysis for linear system with interval time-varying delay and nonlinear perturbations. The restriction on the derivative of the interval time-varying delay is removed, which means that a fast interval time-varying delay is allowed. The method combining descriptor model transformation, Leibniz-Newton formula, improved integral inequalities, utilization of zero equation and new Lyapunov-Krasovskii functional has been adopted to study. New delay-range-dependent stability criteria for considered system are established in terms of linear matrix inequalities (LMIs). A numerical example has shown significant improvement over some existing results.

Keywords: stability, linear system, linear matrix inequality, Lyapunov method, descriptor model transformation

References [1] Chen Y, Xue A, Lu R, Zhou S. On robustly exponential stability of uncertain neutral systems with time-varying delays and nonlinear perturbations. Nonlinear Anal, 68(8); 2008,p. 2464-2470 [2] Fridman E. Stability of linear descriptor systems with delays: a Lyapunov-based approach. J Math Anal Appl, 273; 2002, p. 24-44 [3] Fridman E, Shaked U. A descriptor system approach to H1 control of linear time-delay systems. IEEE Trans on Automat Control, 47(2); 2002, p. 253-270 [4] Gu K, Kharitonov V L, Chen J. Stability of time-delay systems. Berlin: Birkh¨auser; 2003.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 Enhancement of Natural Convection Heat Transfer in a Rotating Enclosure by Utilizing Nanoliquid

a, a a,b Habibis Saleh *, Ammar Alsabery , Ishak Hashim

aSchool of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 Bangi, Malaysia bSolar Energy Research Institute, Universiti Kebangsaan Malaysia, 43600 Bangi, Malaysia

Abstract Natural convection heat transfer in a rotating enclosure is studied theoretically in this paper. The enclosure is filled with Cu- water nanoliquid and it executes a steady uniform counterclockwise angular velocity about its longitudinal. The governing equations are in velocity, pressure and temperature formulation and solved using the staggered grid arrangement together with MAC method. We found that total heat transfer rate enhances by increasing the nanoparticles concentration.

Keywords : Nanoliquid; Natural convection; Rotating enclosure

References [1] Choi SUS. Enhancing thermal conductivity of fluids with nanoparticles. ASME Fluids Eng Div 1995;231:99-105. [2] Khanafer K, Vafai K, Lightstone M. Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids. Int J Heat Mass Transf 2003;46:3639-3653. [3] Ogut EB. Natural convection of water-based nanofluids in an inclined enclosure with a heat source. Int J Thermal Sci 2009;48:2063-2073. [4] Rashmi W, Ismail AF, Khalid M, Faridah Y. CFD studies on natural convection heat transfer of Al2O3-water nanofluids. Heat and Mass Transfer 2011;47:1301-1310 [5] Ho CJ, Chen MW, Li ZW. Numerical simulation of natural convection of nanofluid in a square enclosure: Effects due to uncertainties of viscosity and thermal conductivity. Int J Heat Mass Transf 2008;51:4506-4516. [6] Fattahi E, Farhadi M, Sedighi K, Nemati H. Lattice Boltzmann simulation of natural convection heat transfer in nanofluids. International Journal of Thermal Sciences 2012;52;137-144.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 Effect of array sizes on specific humidity pattern classification using self-organizing map

Natita Wangsoha, Wiboonsak Watthayua, Dusadee Sukawatb,*

aDepartment of Methematics, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand bJoint Graduate School of Energy and Environment, King Mongkut’s University of Technology Thonburi,Bangkok 10140, Thailand

Abstract Specific humidity patterns over southern Thailand during summer monsoon between the years 2000 and 2009 are classified by self-organizing map (SOM). Three different SOM array sizes of 3×3 (9 patterns), 4×4 (16 patterns) and 5×5 (25 patterns) are determined in the study. Gaussian function with power series learning rate is selected for the training algorithm. Frequency of occurrence is used for the analysis of SOM. All cases of SOM array sizes give the same results with two major distinguish patterns. The two patterns are the days with dry air and the days with moist air. However, the 3×3 SOM array size provides the best classification of the dry pattern and the moist pattern in terms of the frequency of occurrence. Therefore, it is appropriate for the classification of pattern of specific humidity.

Keywords: Self-organizing map; specific humidity; southern Thailand

References [1] Loo YY, Billa L, and Singh A. Effect of climate change on seasonal monsoon in Asia and its impact on the variability of monsoon rainfall in Southeast Asia. Geoscience Frontiers xxx 2014;1-7. [2] Bação F, and Lobo V. Introduction to Kohonen’s self-organizing maps. Retrieved Aug 24, 2015, from universitat Jaume I website: http://edugi.uji.es/Bacao/SOM%20Tutorial.pdf [3] Cavazos T. Using self-organizing maps to investigate extreme climate events: an application to wintertime precipitation in the Balkans. J. Climate 2000;13:1718-1732. [4] Hewiton BC, and Crane RG. Self-organizing maps: applications to synoptic climatology. Clim Res 2002;22:13-26. [5] Cassano EN, Koslow RM, Thornbrugh C, and Lynch HA. Classification of synoptic patterns in the western Arctic associated with high wind events and temperature trends at Barrow, Alaska. J. Climate 2003;1-38. [6] Gutiérrez JM, Cano R, Cofiño AS, and Sordo C. Analysis and downscaling multi-model seasonal forecasts in Peru using self-organizing maps. Tellus 2005;57:435-447. [7] Tymvios F, Savvidou K, and Michaelides SC. Association of geopotential height patterns with heavy rainfall events in Cyprus. Adv. Geosci 2010;23:73-78. [8] Saha S, Moorthi S, Pan H, Wu X, Wang J, Nadiga S, Tripp P, Kistler R, Woollen J, Behringer D, Liu H, Stokes D, Grumbine R, Gayno G, Wang J, Hou YT, Chuang H, Juang HH, Sela J, Iredell M, Treadon R, Kleist D, Delst PV, Keyser D, Derber J, Ek M, Meng J, Wei H, Yang R, Lord S, Dool H, Kumar A, Wang W, Long C, Chelliah M, Xue Y, Huang B, Schemm JK, Ebisuzaki W, Lin R, Xie P, Chen M, Zhou S, Higgins W, Zou CZ, Liu Q, Chen Y, Han Y, Cucurull L, Reynolds RW, Rutledge G, and Goldberg M. The NCEP climate forecast system reanalysis. BAMS 2010;91:1015-1057. [9] Schuenemann KC, Cassano JJ, and Finnis J. Synoptic forcing of precipitation over Greenland: climatology for 1961-99. Journal of Hydrometeorology 2008;10:60-78. [10] Wangsoh N, Watthayu W, and Sukawat D. Appropriate Learning Rate and Neighborhood Function of Self-Organizing Map (SOM) for Specific Humidity Pattern Classification over Southern Thailand. International conference on applied physics and mathematics 2015, submitted. [11] Stefanovič P, and Kurasova O. Visual analysis of self-organizing maps. Nonlinear Anal. Model. Control 2011;16:488-504. [12] Gabrielsson S, and Gabrielsson S. The use of self-organizing maps in recommender systems. Retrieved Aug 24, 2015, from movsom research lab website: http://www.rslab.movsom.com/paper/somrs/somrs.pdf [13] Pölzlbauer G. Survey and Comparison of Quality Measures for Self-Organizing Maps. Retrieved Aug 24, 2015, from information & software engineering group website: http://www.ifs.tuwien.ac.at/~poelzlbauer/publications/Poe04WDA.pdf

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 Phishing Website Detection using Rotation Forest

Pumitara Ruangthong and Saichon Jaiyen

Department of Computer Science, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok, Thailand E-mail: [email protected], [email protected]

Abstract Phishing websites [1-3] are critical cybercrime for deceiving the internet users. This fraudulence conceals itself by imitating an actual website that requires users to complete identity verification before making any transaction. If the phishers are able to extract your personal data, they can use this data to commit many forms of crimes such as financial identity theft. Additionally, the damage may occur to major service providers such as banking, education, government agencies. The purpose of this research is to most accurately detect phishing websites in order to prevent these sites from emulating actual websites and obtain important data. Inspection and protection in advance are most useful in this situation. Information in this research determines abnormalities of phishing websites at each mark such as the length of URL. When determining each mark, it will prove whether each mark is phishing, legitimate, or suspicious. In the experiments, algorithms that provide high accuracy are in Tree group and Decision Tree Ensemble. From experimental results, Rotation Forest can achieve higher accuracy than normal Decision Tree and generates the most accurate detection with the result of 97.15%.

Keywords: Decision Tree, Rotation Forest, Principal Component, Phishing Website, Random Forest

References [1] Mohammad R., McCluskey T.L., Thabtah F. An Assessment of Features Related to Phishing Websites using an Automated Technique. In: International Conferece For Internet Technology And Secured Transactions, London: IEEE;2012, p. 492-497. [2] Mohammad R., Thabtah F., Abdeljaber, McCluskey T.L. Predicting phishing websites based on self-structuring neural network. In: Neural Computing and Applications, 2014, p. 443-458. [3] Mohammad R., McCluskey T.L., Thabtah Abdeljaber F. Intelligent Rule based Phishing Websites Classification. In: IET Information Security, 2014, p. 153-160. [4] Wardman B., Warner G. Automating phishing website identification through deep MD5 matching. In: eCrime Researchers Summit, Atlanta GA: IEEE; 2008, p. 1-7. [5] Aburrous M., Hossain M.A., Thabatah F., Dahal K. Intelligent Phishing Website Detection System using Fuzzy Techniques. In: Information and Communication Technologies, Damascus: IEEE; 2008, p. 1-6 [6] Ee Hung C., Kang Leng C., San Nah S., Wei King T. Phishing Detection via Identification of Website Identity. In: IT Convergence and Security (ICITCS), Macao: IEEE; 2013, p.1-4. [7] Barraclough P., Sexton G. Phishing website detection fuzzy system modelling. In: Science and Information Conference (SAI), London: IEEE; 2015, p.1384-1386. [8] Ramanathan, V., Wechsler H. Phishing website detection using Latent Dirichlet Allocation and AdaBoost. In: Intelligence and Security Informatics (ISI), Arlington: IEEE; 2012, p.102-107. [9] Weiwei Z., Qingshan J., Tengke X. An Intelligent Anti-phishing Strategy Model for Phishing Website Detection. In: Distributed Computing Systems Workshops (ICDCSW), Macau: IEEE; 2012, p.51-56. [10] Fatt J.C.S., Kang Leng C., San Sze N. Phishdentity: Leverage Website Favicon to Offset Polymorphic Phishing Website. In: Availability, Reliability and Security (ARES), Fribourg: IEEE; 2014, p.114-119. [11] Hotelling, H. Analysis of a complex of statistical variables into principal components. In:Journal of Educational Psychology, 1933, p.417– 441, p.498–520. [12] Fukunaga, Keinosuke. Introduction to Statistical Pattern Recognition, 1990 [13] Jonathon S. A Tutorial on Principal Component Analysis. [14] Roweis S. EM Algorithms for PCA and SPCA. Advances in Neural Information Processing Systems. Ed. In: Michael I. Jordan, Michael J. Kearns, and Sara A. Solla The MIT Press, 1998. [15] Warmuth M. K., Kuzmin D. Randomized online PCA algorithms with regret bounds that are logarithmic in the dimension. In: Journal of Machine Learning Research, 2008 p.2287–2320 [16] Opitz, D., Maclin, R., Popular ensemble methods: An empirical study. In: Journal of Artificial Intelligence Research, 1999, p.169–198. [17] Eberly College of Science URL:https://onlinecourses.science.psu.edu/stat505/node/51. [18] Rodriguez J. J., Kuncheva L. I., Alonso C. J., Rotation Forest: A New Classifier Ensemble Method, In: IEEE Transactions on Pattern Analysis and Machine Intelligence,2006, p. 1619-1630.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 SIMULATION OF QUEUING SYSTEMS TO INCREASE THE EFFICIENCY OF SERVICE IN OUTPATIENT DEPARTMENT OF BANGPAKONG HOSPITAL, SAMUPRAKAN PROVICE,THAILAND

Chanin Srisuwannapa1*, Kasidit Samaisut1, Jamjuri Srihormkrin1, Natpong Kaewchoe1, Metta Doksantae1

1 Department of Statistics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok, Thailand *E-mail: [email protected]

ABSTRACT This research purpose was to study and solve the problem of patient’s long waiting time in queue in a outpatient department of Bangpakong hospital, Samuprakan province, Thailand. The 4 weeks-related data from 8.30 a.m.-16.30 p.m. of Monday – Wednesday each week in November 2557 were collected. Then a simulation model was created using Arena software. Mean, standard deviation and t -test at significance level of 0.05 were used to analyze data using a statistical software package. The results were follows. A suitable solution to improve the system is to add nurse’s more service time at the point of interview by starting at 07.30 a.m. as the old one at 08.30 a.m., and that of one doctor room at 08.00 a.m. as the old one at 08.30 a.m. and starting at 9:00 a.m. for 3 rooms remaining. The average service time of each patient decreased from 126.08 minutes to 69.21 minutes or 45.11% significantly at 0.05.

Keywords: Simulaiton; Hospital, outpatient department

REFERENCES [1] Kornchanok Suwanmajo. 2548. “Simulation model of outpatient service system of Phumipol Uduldech hospital”. Master degree on major of information technology management, University of the Thai Chamber of Commerce. [2] Chatpot Keatjarulsiri etc. 2554. “Simulation of queuing problem servicing outpatient at general department of Bangple hospital”. Special problem of Bechelor degree on major of applied statistics, Faculty of science, King Mongkut’s Institute of Technology Landkrabang. [3] Natpol Chawasiri. 2554. “Development of service efficiency of heart department’s patient using simulation: a case study of Queen Sirikit National Institute of Child Health”. Bangkok: Kasertsat University. [4] Tanat Prajongjad , et.al. 2556. “Simulation of service queuing problem of general department, Tamaka hospital”. Special problem of Bechelor degree on major of applied statistics, Faculty of science, King Mongkut’s Institute of Technology Landkrabang. [5] Patchatkan Bamrung, et.al. 2556. “Simulation of service queuing problem of general department, Puttasotorn hospital”. Special problem of Bechelor degree on major of applied statistics, Faculty of science, King Mongkut’s Institute of Technology Landkrabang. [6] Pimpimol Sittiyuno. 2555. “Queuing development: a case study of diabetes clinic, Tasala hospital. Nakornratchasima”, Reference and education communication center, Walailuk University. [7] Sirijan Tongprasert. 2542. “Simulation”. Bangkok: Chulalongkorn printing. [8] Kiataramkul, C. 2553. “Simulation of the Queueing System for Venepuncture Service at Ramathibodi Hospital”. Nakhonpathom : Mahidol University. [9] Kelton ,D.W., Sadowski , R.P. and Sturrock D.T., 2003, “Simulation with Arena”-3rd ed., International Edition, McGraw-Hill, The McGraw- Hill Company, Inc. [10] Maria, A., 1997, “Introduction to model and simulation”, Proceeding of the 1997 Winter simulation Conference ed. S. Andradottir, K.J. Healy, D.H. Withers, and B.L.Nelson.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 CONJECTURING VIA ANALOGICAL REASONING OF CREATIVE THINKING LEVEL IN CONSTRUCTING EQUATION SLICED CONE

Supratman Ahman Maedi

Mathematics education, the Faculty of Education University of Siliwangi Tasikmalaya Postcode 46115, West Java, Indonesia

Abstract The purpose of this study was to reveal in detail the process of conjecturing via analogical reasoning in the creative thinking stage of students to build a cone equation. Conjecturing via analogical reasoning in the stage of creative thinking, it is based adaptation framework of Piaget. Context problems analogy used to assess the occurrence of conjecturing via analogical reasoning. The research method used to think aloud, supported by interesting findings and interviews. Conjecturing via analogical reasoning of creative thinking stages for construct equation conic sections, it revealed through sequential steps, when students construct some form of conic equation.

Keywords: conjecturing, analogical reasoning, creative thinking, construction of new knowledge, Piaget‟ adptation framewoek.

References [1] Anthony, G. Active learning in a constructivist framework. Educ. Stud. Math. 31(4), 1996, p. 349–369. ME 2002c.01837 [2] Oxford, R. Constructivism: shape-shifting, substance, and teacher education applications. Peabody Journal of Education 72(1), 1997, p. 35– 66 [3] Stacey, K, Mason, J and Burton. L. Thinking Mathematically Pearson Education Limited. 2010, Second edition published [4] Polya, G.. Mathematics and plausible reasoning; volume 1. Princeton: Princeton University Press. 1954 [5] Vinner, S. The pseudo-conceptual and the pseudo-analytical thought processes in mathematics Learning. Educ. Stud. Math. 34(2), 1997, p. 97–129. ME 2002c.01839 [6] Subanji. R and Supratman. A. M. The Pseudo-Covariational Reasoning Thought Processes in Constructing Graph Function of Reversible Event Dynamics Based on Assimilation and Accommodation Frameworks. J. Korean Soc. Math. Educ., Ser. D, Res. Math. Educ. Vol. 19, No. 1, March 2015, 55–73 [7] Van De Walle, J.A.. Elementary aand Middle School Mathematics. Library of congress Cataloging-in-Publication Data. 2010 [8] NCTM (National Council of Teacher of Mathematics).. Principle and standards for the school mathematics, RestonVA; 1989. NCTM [9] Canadas, M. C., Deulofeu, J., Figueiras, L., Reid, D., & Yevdokimov, A. The conjecturing process: Perspectives in theory and implications in practice. Journal of Teaching and Learning, 5 (1), 2007. p. 55–72 [10] English LD. Mathematical and analogical Reasoning of Young Learners. New Jersey London Lawrence Erlbaum Associates Publisher Mahwah 2004. [11] Lee, K.H. & Sriraman, B. 2010. Conjecturing via reconceived classical analogy. Educational Studies in Mathematics, 76 . 123-144 [12] Alexander, P.A., White, C.S., Daugherty, M. Children‟ s use of analogical reasoning in early mathematics learning in English LD. Mathematical Reasoning; analogies metaphor and Images (pp. 117-147) . Mahwah, New Jersey Lawrence Erlbaum Associates Publisher 1997 [13] Holyoak, K.J dan Thagard, P. 1989. Analogical Mapping by Constraint Satis-faction, Cognitive Science 13, 295-355 [14] White & Alexander, Effects of training on four year-olds ability to solve geometric analogy problems, Cognition and Instruction, 3(3), 1986. 261-268. [15] Alexander, P.A., Wilson, V.L., White, C. S & Fuqua,J.D. Analogical reasoning in Young Children. Journal of Educational Psycology, 79. 1987. 401-408. [16] White C.S, Alexander, P.A., and Daugherty, M. The Relationship between young children‟ s analogical reasoning and mathematical learning. Mathematical Cognition 4(2). 1998. p.103-123. [17] Krulik, S., Rudnick, J. & Milou, E. Teaching Mathematics in Middle School. Boston, MA: Allin and Bacon 2003. [18] Amabile, T. M.. The Social Psychology of Creativity. New York, Springer Verlag 1983. [19] Parkins, D. N. (1984). Creativity by Design. Educational Leadership 42(1), 18–25 [20] Bybee R.W. Piaget for Educators, Charles E Merri Publising. co Colombus Ohio. 1982. [21] Yevdokimov, O. 2005. About A Constructivist Approach for Stimulating Stu-dents' Thinking to Produce Conjectures and Their Proving in Active Learning Of Geometry, Kharkov State Pedagogical University, Ukraine, Proceedings of CERME 4 [22] Varberg, D., Purcell, E., and Rigdon, S. Calculus 9th editions. Pearson Publisher 2006 [23] Supratman. Piaget‟ s Theory in the Development of Creative Thinking, Journal the Korean Society Mathematical Education, Series D, Res. Math. Educ. Vol. 17, No. 4, December 2013, p.291–307

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[24] Gentner, D., Holyoak, K. J.,& Kokinov, B. (Eds.). 2001. The analogical mind: Perspectives from cognitive science. Cambridge, MA: MIT Press. [25] Lincoln, Yvona S and Egon G. Guba. Naturalistic Inqury. Baverly Hills: Sage Publications. 1985.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 The Robust Test Statistic in Comparing Two Independent Groups using Trimming and Winsorization

Suhaida Abdullah, Sharipah Soaad Syed Yahaya, Zahayu Md. Yusof, Faridzah Jamaludin

School of Quantitative Sciences, Universiti Utara Malaysia, 06010 Sintok, Kedah, Malaysia

Abstract The classical independent t-test is often in jeopardy when there is violation of normality or homogeneity of variances. The performance of the test is worsened when these violations occur simultaneously. Alexander-Govern test offers the alternative solution to the classical t-test when dealing with heterogeneous variances conditions. However, it produces good control of Typ I error rates only if the data are normally distributed, which is a known fact that normality is hardly achieved in real life situation. As a remedy, in this study, Alexander-Govern test was modified by using trimmed mean and Winsorized mean as the location measures. Generally the modified test using trimmed mean enhanced the performance of the original test in terms of Type I error rates. However, the test using Winsorized mean failed to perform well under most condition considered.

Keywords: t-test; Alexander-Govern test; trimmed mean; Winsorized mean

References [1] Lix, L. M., & Keselman, H. J. (1998). To trim or not to trim: Tests of location equality under heteroscedasticity and nonnormality. Educational and Psychological Measurement, 58(3), 409-429. [2] Alexander, R. A., & Govern, D. M. (1994). A new and simpler approximation for ANOVA under variance heterogeneity. Journal of Educational Statistics, 19(2), 91-101. [3] Schneider, P. J., & Penfield, D. A. (1997). Alexander and Govern's approximation: Providing an alternative to ANOVA under variance heterogeneity. Journal of Experimental Education, 65(3), 271-287. [4] Myers, L. (1998). Comparability of the James' second-order approximation test and the Alexander and Govern A statistic for non-normal heteroscedastic data. Journal of Statistical Computational Simulation, 60, 207-222. [5] Reed III, J. F & Stark, D. B, Hinge estimator of location: Robust to asymmetry. Computer methods and programming in biomedicine, 1996, 49, 11-17. [9] Bradley, J. V. (1978). Robustness? British Journal of Mathematical and Statistical Psychology(31), 144-152. [6] Wilcox, R. R. (2005). Introduction to robust estimation and hypothesis testing (Second ed.): California: Academic Press. [7] Keselman, H. J. (1976). A power investigation of the Tukey multiple comparison statistic. Educational and Psychological Measurement, 36(97), 97-104. [8] Wilcox, R. R & Keselman, H. J. (2003). Modern robust data analysis methods : Measures of central tendency. Psychological Methods, Vol 8, No. 3, 254 – 274. [9] Keselman, H. J., Wilcox, R. R., Lix, L. M., Algina, J., & Fradette, K. (2007). Adaptive robust estimation and testing. British Journal of Mathematical and Statistical Psychology, 60, 267-293.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 ANISOTROPIC ADAPTIVE REGULARIZATION EFFECTS ON MOVING IMAGES

1 2 K..B AMUR , SHAKEEL AHMED KAMBOH

1Department of Mathematics and Statistics Quaid-A-Awam Unversity of Engineering, Science and Technology Sindh, Pakistan E-mail: [email protected] 2Department of Mathematics and Statistics Quaid-A-Awam Unversity of Engineering, Science and Technology Sindh, Pakistan E-mail: [email protected]

Abstract It is observed from the general practice that the quadratic regularization does not perform very well in the neighbourhood of discontinuities like edges in the moving images. To observe the dense flow vector with sharp hyper-surfaces in the neighborhood of moving pixels in the images where the practitioners think of a regularization approach, with which one can cope with the discontinuities and regularized solution of ill-posed problems simultaneously. Though some nonlinear energy minimization methods have such diffusion properties like discontinuity preservation but the ambiguities like contradiction in smoothness and the reaction terms are still remaining to cope with. The novel idea of regularization was appeared as ([1-4],[16]) , which seems to be more appropriate in such ambiguous situations. Extending the idea of ([1], [16]) we propose an anisotropic adaptive process to observe the regularization effects in the solution of a nonlinear variational model considered as a regularize version of the total variation approach. Our solution strategy is based on the P1 finite elements where the computational domain will be considered as triangular grid.

Keywords: Regularization, Optic flow, Variational Methods, Finite Elements, Mesh Adaption, Numerical Algorithm, Partial Differential Equations.

References [1] Amur K. B Contrôle adaptatif, techniques de régularisation et applications en analyse d’images. PhD thesis LMAM University of Metz France (2011). [2] Amur K. B. Some regularization Strategies for an Ill-Posed Denoising Problem. International Journal of Tomography and Statistics, 19 (1): 46-59(2012) [3] Amur K. B. A Posteriori Control of Regularization for Complementary Image motion Problem. Sindh Univ. Res. Jour. (Sci. Ser.), 45 (3): 546- 552 (2013). [4] Amur K. B., M. S. Chandio, E. Ali. A Novel Mesh adaptation Technique for the computation of Stereo Depth Using Texture less Simple Stereo Pairs. Sindh Univ. Res. Jour (Sci. Ser.), 45 (4): 737-742 (2013). [5] Amur K. B, E. Buriro, A. H. Jalbani, W. A. Sheikh, A. Ali Ghoto. Local and Adaptive selection of optimal Parameters for TV regularization model and the FEM Based Stereo-Vision Simulation. QUEST Research Journal, 12 (2): 9-13 (2013). [6] Amur K. B, A. L. Memon, and S. Qureshi. FEM based Approximations for the TV Denoising Optimization Problem. Mehran University Research Journal of Engineering & Technology, Vol. (33): No. 1, 121-128 (2014). [7] Aubert, G., R. Derriche, P. Kornprobst. Optic flow estimation while preserving its discontinuities a variational approach, In Proc. Second Asian Conference on Computer Vision, vol 2, singapore 290-295 and Springer 1996 Lecture Notes in Computer Science ISBN 3-540-60793-5, 1995. [8] Aubert, G., R. Deriche, P. Kornprobst . Computing optical flow via variational techniques, SIAM Journal on Applied Math., 60 (1), 156- 182,1999. [9] Brenner S. C and L. R. Scott . The mathematical theory of finite element methods. Third Edition, Springer Science, Business Media, LLC, 233 Spring Street, New York, NY 10013, USA, 1994. [10] Engl, H., M. Hanke, A. Neubauer. Regularization of Inverse Problems. Kluwer Acad. Publ. Dordrecht ets 1996. [11] Hecht F. New development in FreeFem++ . Journal of Numerical Mathematics. VOLUME 20 pp: 3-4(2012), [12] Horn, B., B. Shunk . Determining Optical flow. Artificial Intelligence, 1981, Vol.17, 185-203. [13] Strong D. M.. Adaptive Total Variation Minimizing Image Restoration. CAM Report , University of California, Los Angeles. 1997, 97-38. [14] Alvarez, L., J. Esclarin, M. Lefebure, and J. Sanchez . A PDE model for computing the optic flow In . XVI Congreso de Ecuaciones Diferenciales y aplicationes, Las Palmas de Gran Canaria, Spain, 1999, 1349-46. [15] Anandan P. A computational framework and an algorithm for the measurement of visual motion. International Journal of Computer Vision, 2000, vol. 39(1), 41-56. [16] Belhachmi Z. and F.Hecht (2011). Control of Effects of the regularization on Variational optic flow computations. J.Mathematical imaging and vision, 40 (1):1-19.

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[17] Bruhn A.. Variational Optic Flow Computation, accurate modeling and efficient numerics. PhD thesis in computer Science Saarbrcken, Germany. Saarland University(2006). [18] Bruhn, A., J. Weickert, Christophschnorr. Lucas/Kanade meets Horn/Schunck: Combining Local and Global Optic flow methods, International Journal of computer vision 61(3),211-231(2005). [19] Robert A. Adams and John J. F. Fourier. Sobolev spaces. Academic press, Elsevier, second edition, printed in Netherlands (2003). [20] Tikhonov A. N. Solution of incorrectly formulated problems and the regularization method. Soviet Mathematics Doklady, 4, 1035- 1038(1963). [21] Verfurth R. A Review of a posteriori error Estimation and Adaptive mesh refinement Techniques. Advances in Numerical Mathematics, Wiely and Teubner (1996). [22] Zimmer, H. Andres Bruhn, Jaochim Weickert, Levi Valgaerts,Agustin Salgado,Bodo Rosenhahn, and Hans-Peter Seidel. Complementary optic flow. 7th International Conference, EMMCVPR, Bonn, Germany, 24-27 and Springer, Lecture Notes in Computer Science Volume 5681, 2009, pp 207-220.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 A NEW GENERALIZATION OF (F,  )- CONTRACTION MAPPINGS IN METRIC SPACES WITH  -FIXED POINT RESULTS

Pathaithep Kumrod 1 , Wutiphol Sintunavarat 2

1Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Pathumthani, Thailand E-mail: [email protected] 2Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Pathumthani, Thailand E-mail: [email protected], [email protected]

Abstract

In 2014, Jleli et al. [1] introduced the concepts of  -fixed points1 and (F, )-contraction mappings In this work, we study a new generalization of (F, )-contraction mappings in metric spaces and establish some existence results of -fixed point for such mappings. Our results are extension of the results of Jleli et al. [1] and references therein. Also, the obtained results are used to deduce some fixed point theorems in partial metric spaces.

Keywords:  -fixed points; (F, )-contraction mappings; partial metric space.

References [1] M. Jleli, B. Samet, C. Vetro, “Fixed point theory in partial metric spaces via -fixed point's concept in metric spaces, Journal of Inequalities and Application, 2014:426 (2014).

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 Fixed Point Results for Generalized F-Contractions in Complete Metric Spaces

Ahmed Al-Rawashdeh

Department of Mathematical Sciences UAE University, 15551, Al Ain, UAE E-Mail: [email protected]

Abstract In 2012, D. Wasrdowski defined the concept of F-contraction and deduced a new fixed point result, which is a generalization of the Banach contraction principle. In this paper, we first recall the results concerning the F-contraction mappings. Then owing the concept of F- contraction, we introduce new types of contractions and we deduce new fixed point results. We define two new classes of functions M(S, T ) and N(S, T ) and we prove some new fixed point results for single-valued and multivalued mappings in complete metric spaces. We also introduce the concept of a modified F-contraction via _-admissible pairs of mappings. We provide several common fixed point results for such type pairs of contractive mappings in the setting of metric spaces. Our results extend, generalize and unify several known results in the literature.

Keywords: Fixed point; F-contraction; _-admissible pairs of mappings

References [1] A. Ahmad, A. Al-Rawashdeh, A. Azam, Fixed point results for {α, ξ}-expansive locally contractive mappings, Journal of Inequalities and Applications, 2014:364 (2014). [2] R. Batra, S. Vashistha, Fixed points of an F -contraction on metric spaces with a graph, International Journal of Computer Mathematics, 91, 1-8 (2014). [3] M. Cosentino, P. Vetro, Fixed point results for F-contractive mappings of Hardy-Rogers-type, Filomat 28:4, 715-722 (2014). [4] N. V. Dung and V. T. L. Hang, A fixed point theorem for generalized F -contractions on complete metric spaces, Vietnam J. Math., DOI:10.1007/s10013-015-0123-5 (2015). [5] S. Shuklaa, S. Radenovi´c, Some common fixed point theorems for F -contraction type mappings in 0- complete partial metric spaces, J. Ineq. Appl. (2014). [6] D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces. Fixed Point Theory Appl. 2012, 94 (2012).

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 Generalizations of Schweizer-Wolff measure of dependence

Wasamon Jantaia*, Songkiat Sumetkijakanb

aDepartment of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand bDepartment of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand

Abstract A measure of dependence indicates the level of dependence between two random variables. Adjusting some of Rényi's postulates for measures of dependence, Schweizer and Wolff proposed a measure of dependence  (,)XY of continuous random 1 variables X and Y defined as the normalized L -norm of Cx,y  where Cx,y is the copula of X, Y and  is the independent copula. We investigate some generalizations of Schweizer-Wolff measure of dependence, all of which are copula- based measures of dependence of continuous random variables. The first measure is defined as the normalized L1- norm of ()Cx,y  . We give a sufficient condition on  for  to be a measure of dependence in the sense of * * Schweizer and Wolff. We then define the measure  (X, Y) as the supremum of  (f(XY ),g( )) over all injective Borel measurable functions f,g It turns out that  is a measure of dependence in the sense of Rényi.

Keywords: measure of dependence; Schweizer-Wolff; Rényi's postulates

References [1] Chou S. H., Nguyen T. T., On Frechet theorem in the set of measure preserving functions over the unit interval. International Journal of Mathematics and Mathematical Sciences; 1990, 13(2): 373-378. [2] Darsow W. F., Olsen E. T., Characterization of idempotent 2-copulas. Note di Matematica; 2010, 30: p. 147-177. [3] Embrechts P., Hofert M., A note on generalized inverses. Mathematical Methods of Operations Research; 2013, 77(3): p. 423-432. [4] Nelsen R. B., An Introduction to Copulas. 2nd ed. New York: Springer; 2006. [5] Olsen E. T., Darsow W. F., Nguyen B., Copulas and markov operators. IMS Lecture Notes - Monograph Series; 1996, 28: p. 244-259. [6] Rényi A., On measure of dependence. Acta Mathematica Academiae Scientiarum Hungarica, 1959, 10(3): p. 441-451. [7] Ruankong P., Santiwipanont T., Sumetkijakan S., Shuffles of copulas and a new measure of dependence. Jounal of Mathematical Analysis and Applications; 2013, 398(1): p. 392-402. [8] Schweizer B., Wolff E. F., On nonparametric measures of dependence for random variables. The Annals of Statistics; 1981, 9: p. 879-885. [9] Siburg K. F., Stoimenov P. A., A measure of mutual complete dependence. Metrika; 2010, 71(2): p. 239-251.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 Geometrical Models in biology

Sorin V. SABAU

Department of Mathematics, Faculty of Science, Tokai University, Sapporo, Japan E-mail: [email protected]

ABSTRACT A powerful mathematical method for the investigation of the properties of dynamical systems is represented by the Kosambi- Cartan-Chern (KCC) theory. In this approach the time evolution of a dynamical system is described in geometric terms, treating the solution curves of a dynamical system by geometrical methods inspired by the geodesics theory of Finsler spaces. In the present talk we will present this method and show some applications in biology.

Keywords: ODE, curvature, stability.

References [1] S. V. Sabau, \Systems biology and Deviation curvature tensor", Nonlinear Analysis: Real World Appli-cations, 6 (2005), 563-587. [2] T. Harko, S. V. Sabau, \Jacobi stability of the vacuum in the static spherically symmetric brane world models", Physical Review D, 77 (10) (2008). [3] C. G. Bohmer, T. Harko, S. V. Sabau, \Jacobi stability analysis of dynamical systems - applications in gravity and cosmology", Adv. Theor. Math. Phys. 16 (2012), 1145-1196.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 The Kansa meshless method for convection diffusion problems using various radial basis functions

Nissaya Chuthonga, Sayan Kaennakamb,*, Wattana Toutipa

aDepartment of Mathematics, Faculty of Science, Khon Kaen University, Muang, Khon Kaen 40000, Thailand bSchool of Mathematics, Institute of Science, Suranaree University of Technology, NakhonRatchasima 30000, Thailand

Abstract

Two main purposes of this work are to study the numerical solution of convection diffusion equations in two dimensions using the Kansa’s meshless method and to investigate and compare the effectiveness of different well-known Radial Basis Functions (RBF), providing effectively useful information for numerical method users in selecting optimal RBF. The performance and accuracy of this method are demonstrated with some test problems both steady and time-dependence state. The results obtained are validated against the exact ones and other corresponding numerical work where available. These experiments show that the method is capable of producing accurate solution for convection diffusion equations. Moreover, it is found that the best results of these problems can be obtained by applying Multiquadric and Inverse Quadratic type of radial basis functions. However, there are still several factors affecting the accuracy of this method and therefore, truly deserves further investigation.

Keywords: Meshless method, Radial basis function, Convection diffusion problems;

References [1] Djidjeli K, Chinchapatnam PP, Nair PB, Price WG. Global and compact meshless schemes for the unsteady convection-diffusion equation. Proceedings of the international symposium on health care and biomedical research interaction; 2004 Oct 08-09; Oujda, Morroco. [2] Belytschko T, Lu YY, Gu L. Element-free Galerkin methods. Int J Numer Methods Eng 1994; 37: 229-256. [3] Sladek V, Sladek J, Atluri SN, Van Keer R. Numerical integration of singularities in meshless implementation of local boundary integral equations. Comput Mech 2000; 25: 394-403. [4] Sarra SA, Kansa EJ. Multiquadric radial basis function approximation methods for the numerical solution of partial differential equations. Adv Computl Mech 2009; 2. [5] Kansa EJ. Multiqudrics a scattered data approximation scheme with applications to computational fluid dynamics I: Surface approximations and partial derivative estimates. Comput Math Appl 1990; 19: 127-145. [6] Kansa EJ. Multiquadrics a scattered data approximation scheme with applications to computation fluid dynamics-II: Solution to parabolic, hyperbolic and elliptic partial differential equations. Comput Math Appl 1990; 19: 147-161. [7] Fasshauer GE. Meshfree Approximation Methods with MATLAB. Singapore: World scientific publishers; 2007. [8] Libre NA, Emdadi A, Kansa EJ, Shekarchi M, Rahimian M. A fast adaptive wavelet scheme in RBF collocation for near singular potential PDEs. Comput Model Eng Sci 2008; 38: 263-284. [9] Kansa EJ, Hon YC. Circumventing the ill-conditioning problem with multiquaddric radial basis functions. Comput Math Appl 2000; 39:123- 137. [10] Wendland H. Piecewise polynomial, positive definite and compactly supported radial function of minimal degree. Adv Comput Math 2000; 4: 389-396. [11] Wu Z. Compactly supported positive definite radial functions. Adv Comput Math 1995; 4: 283-292. [12] Buhmann MD. A new class of radial basis functions with compact support. Math Comput 2000; 70: 307-318. [13] Chuathong N, Kaennakham S, Toutip W. Numerical solutions of 2D nonlinear PDEs using Kansa’s meshless method and the search for optimal radial basis function. Proceeding of the 19th international annual symposium on computational science and engineering; 2015 Jun 17-19; Ubon Ratchathani, Thailand. [14] Gu YT, Liu GR. Meshless techniques for convection dominated problems. Comput Mech 2006; 38: 171-182. [15] Jiang Y, Zhengfu X. Parametrized maximum principle preserving limiter for finite difference WENO schemes solving convection-dominated diffusion equations. SIAM J Sci Comput 2013; 35: A2524-A2553.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 STABILITY ANALYSIS OF FUZZY CONTROL FOR AN APPROXIMATED NONLINEAR SINGULARLY PERTURBED SYSTEM

Preeyaporn Waree1 , Wichai Witayakiattilerd2

1,2Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabangm Bangkok, 10520, Thailand Email: [email protected] Corresponding Author The financial support *for this study was from King Mongkut’s Institute of Technology Ladkrabang

ABSTRACT

In this paper, we study a fuzzy control system with singular perturbation in a fast-slow system. The reduced system is introduced and an approximated solution of the system is defined. Moreover, a stability analysis method for the approximated system with Takaki-Sugeno fuzzy logic controllers is presented. In this research we provides some sufficiently stability conditions and proves asymptotically stable in the sense of Lyapunov (ISL) for the fuzzy control system. An example is established to explain the stability analysis method.

Keywords: fuzzy control system, stability analysis, Lyapunov, Takaki-Sugeno fuzzy logic controllers

References [1] M. Sugeno, “Fuzzy Control,” North-Holland, (1988) [2] K. Mehran,” Takagi-Sugeno Fuzzy Modeling for Process Control,” Industrial Automation, Robotics and Artificial Intelligence,(2008) [3] M-L Tomescu ,S Preitl, R-E Precup , J-K Tar, “Stability Analysis Method for Fuzzy Control Systems Dedicated Controlling Nonlinear Processes,” Acta Polytechnica Hungarica ,Vol. 4, No. 3,(2007) [4] C. Zhou, “Fuzzy-Arithmatic-Based Lyapunuv synthesis in the design of stable fuzzy controllers : A computing-with-words approach,” Journal of applies mathematic science, Vol.12, No.3,411421(2002). [5] K. Mukdasai, “Stability of Dynamical Systems with Delay,” Journal of Applied Science, Vol.11, No.1, 94-102(2012). [6] M. Corless, L. Glielmo, “On the Exponential Stability of Singularly Perturbed Systems” Journal of Control and Optimization, Vol.30, No. 6, pp.1338-1360 (1992). [7] H. O. Wang, K. Tanaka, “An LMI-based Stable Fuzzy Control of Nonlinear Systems and its Application to Control of Chaos,”IEEE 0-7803- 3645-3/96, 1433-1438(1996). [8] B. Bede, S. G. Gal, “Generalizations of the differentiability of fuzzy-number-valued function with application to fuzzy differential equation,” Fuzzy Sets and Systems, 151(2005), 581-599. [9] K. Tanaka, H. O. Wang,”Fuzzy Control Systems Design and Analysis,”Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach, ISBNs: 0-471-32324-1,(2001). [10] P. Garrett, “Normed and Banach Space,” http://www.math.umn.edu/garrett/, (2005). [11] C-C Ku, P-H Huang, W-J Chang,” Passive Fuzzy Controller Design for Perterbed Nonlinear Drum-Boiler System with Multiplicative Noise,” Journal of Marine Science and Technology,Vol. 18, No. 2, pp. 211-220 (2010).

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 DIFFERENTIAL EVOLUTION ALGORITHM: A METHOD FOR DETERMINING THE VALUES OF THE PARAMETERS IN A MATHEMATICAL MODEL OF A BIOLOGICAL SYSTEM

I-Ming Tang

Senior Research Fellow, Department of Material Science Faculty of Science, Kasetsart University

ABSTRACT

The solutions of the differential equations which are the mathematical description of any biological systems often contain parameters whose values are not known exactly are suppose to simulate the behavior of the system. Because of the uncertainties in the values of the parameters, the simulated behavior can not be expected to duplicate the actual behavior. Differential Evolution Algorithm which attempts to mimic nature is used to find the parameters values which would Yield simulated behaviors of the system more closely matching the true behavior. Like Nature, stochastic (random) changes are incorporated into the algorithm which would generate more correct parameter values.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 A POLYNOMIAL APPROACH TO OPTIMAL CONTROL SWITCHED SYSTEMS AND APPLICATIONS

Mohamed Ali Hajji1, Abdessamad Tridane 2

1;2Department of Mathematical Sciences, College of Science, UAE University, Al Ain, United Arab Emirates E-mail: [email protected], [email protected]

ABSTRACT

Switched systems are systems that model phenomena whose dynamics is controlled by a continuous control signal(s). An optimal control problem for a switched system is the problem of finding the optimal trajectory of a constrained switched system. In this talk we present a polynomial approach based on the theory of moments for solving optimal control problems for nonlinear switched systems. The main idea is to transform the nonlinear switched system into an equivalent non-switched system using polynomial representation. Then the method of moments is used to convexify the new control variable to obtain semi definite programs (SDP) which can be solved by SDP solvers. An important application of optimal control switched system in the modelling of epidemics will be discussed.

Keywords: Switched Systems, Method of Moments, Semi definite Programs

References [1] E. Mojica-Nava, N. Quijano and N. Rakoto-Ravalontsalama, \A polynomial approach for optimal control of switched nonlinear systems," International Journal of Rubust and nonlinear Control, 24, 17971808(2014). [2] M. Jaberi-Doraki and S. M. Moghadas, \Optimal control of vaccination Dynamics during an inuenza epidemic," Mathematical Biosciences and Engineering, 11(5), 1045-1063(2014). [3] J.B. Lasserre, \Global optimization with polynomials and the problem of moments," SIAM Journal on Optimization, 11(3), 796-817(2001). [4] J. B. Lasserre, \Semide_nite programming vs. LP relaxations for polynomial programming," Mathematics of Operational Research, 27(2), 347-360(2002).

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 DIFFERENTIAL TRANSFORMATION METHOD FOR THE SUSPENDED STRING EQUATIONS

Kamonpad Mansilp , Jaipong Kaseamsuwan

Department of Mathematics , Faculty of Science, King Mongkut’s Institute of Technology [email protected] , [email protected]

Abstract The purpose of this paper is to show the derivation of new theorem for the cubic transformation of the differential transformation method (DTM) and apply this method to find the approximated solution for the initial boundary value problem of the suspended string vibrating equation. The suspended string with non-uniform densities is solved easily by this method. The nonlinear external force, with damping term and without damping term of this problem is also investigated. keyword: suspended string equation , differential transformation method , suspended string , dimensional differential transform method

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 Some recent development of zero inflated distributions

W. Bodhisuwan

Department of Statistics, Faculty of Science, Kasetsart University, Chatuchak, Bangkok, 10900, Thailand

Abstract Zero inflated (ZI) distributions are the model for count data with many zeros. The basic idea of the zero-inflation model is a degenerate at zero with baseline distributions such as the Poisson and negative binomial distributions. This work will introduce some recent development of zero inflated distributions such as the zero inflated Waring distribution (ZIW) (Bodhisuwan, W. (2011), Zero inflated Waring distribution and its application, In the 37th Congress on Science and Technoloby of Thailand), the zero inflated negative binomial-generalized exponential (ZINB-GE) distribution (Aryuyuen, S., Bodhisuwan, W. and Supapakorn, T. (2014), the zero inflated negative binomial-generalized exponential distribution and its applications, Songklanakarin Journal of Science & Technology), the zero inflated negative binomial-Crack (ZINB-CR) distribution (P. Saengthong, W. Bodhisuwan and A. Thongteeraparp, to be appear) and the zero inflated negative binomial-beta exponential (ZINB-BE) distribution. Many applications of ZI are appeared in many fields including manufacturing, econometrics, public health, epidemiology, sociology, psychology, engineering, agriculture.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 Two-Sample Tests for High-Dimensional Repeated Measures Designs with Unequal Variances

Boonyarit Choopradita,*, Saowapa Chaipitakb, Samruam Chongcharoenc

aFaculty of Sciences and Industrial Technology, Prince of Songkla University, Surat Thani Campus, Surat Thani 84000, Thailand bDepartment of Statistics, Faculty of Science, Kasetsart University, Bangkok 10900, Thailand cSchool of Applied of Statistics, National Institute of Development Administration, Bangkok 10240, Thailand

Abstract In this paper, the analysis of repeated measures designs when the data are multivariate normal distribution which the dimension, p, the sample sizes, ni i.e. p ni , i 1,2, is considered. Under equal sample sizes and unequal variance-covariance matrices assumption, two-sample statistics for testing null hypotheses of the interaction effect and the time effect based on standardizing quadratic forms of linear functions between two-sample mean vectors are developed. The performance of the proposed statistics is studied via simulations technique. The application to real data are also given with male Wistar rats datasets having equal sample sizes of n 10 and p22.

Keywords: Variance-covariance matrix; Asymptotic distribution; Multivariate normal distribution; Hypothesis testing

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 USING PROTOCOL LEVEL PARAMETER IN WCF WITH DIFFERENT PROTOCOL

Mirsat Yeşiltepe1 , Muhammet Kurulay2

1 Department of Mathematic Engineering, Faculty Of Chemical And Metallurgical, Yıldız Technical University, İstanbul, Turkey E-mail: [email protected] 2 Department of Mathematic Engineering, Faculty Of Chemical And Metallurgical, Yıldız Technical University, İstanbul, Turkey E-mail: [email protected]

ABSTRACT Today, with the increasing importance of computing in the cloud boundary has emerged the concept of environment can not be fully calculated. In this environment, the client and server are communicating with each other in an environment where they don‘t know where their partner are[1]. Sometimes the client act as the server, the server can act as the client. In this study, the level of security mechanism prepared for use by programmers who do not want to deal with the details of security mechanisms will be tested on different protocols. The most appropriate protocol for the protection level mechanism will be chosen.

Keywords: Signature, TCP, unsecure, yield.

REFERENCES [1] Velte, Toby, Anthony Velte, And Robert Elsenpeter. Cloud Computing, A Practical Approach. Mcgraw-Hill, Inc., 2009. [2] Information On Https://Msdn.Microsoft.Com/Tr-Tr/Library/Aa347692(V=Vs.110).Aspx [3] Lowy, Juval. Programming WCF Services: Mastering WCF And The Azure Appfabric Service Bus. " O'Reilly Media, Inc.", 2010. [4] Grobauer, Bernd, Tobias Walloschek, And Elmar Stöcker. "Understanding Cloud Computing Vulnerabilities." Security & Privacy, IEEE 9.2 (2011): 50-57. [5] Rescorla, Eric. "Http Over Tls." (2000). [6] De Figueiredo, Jorge CA, And Lars M. Kristensen. "Using Coloured Petri Nets To Investigate Behavioural And Performance Issues Of TCP Protocols." Department Of Computer Science, Aarhus University. 1999. [7] Forouzan, Behrouz A. TCP/IP Protocol Suite. Mcgraw-Hill, Inc., 2002. [8] Vicisano, Lorenzo, Jon Crowcroft, And Luigi Rizzo. "TCP-Like Congestion Control For Layered Multicast Data Transfer." INFOCOM'98. Seventeenth Annual Joint Conference Of The IEEE Computer And Communications Societies. Proceedings. IEEE. Vol. 3. IEEE, 1998.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 Constructing of a Real Symmetric Doubly Arrow Matrix from Its Two Eigenpairs

Wanwisa Pengudoma and Archara Pacheenburawanab

a,b Department of Mathematics and Statistics, Faculty of Science and Technology,

Thammasat University, Rangsit Center, Pathum Thani 12120, Thailand

Abstract

An inverse eigenvalue problem of constructing a real symmetric doubly arrow matrix from its two eigenpairs is proposed. The necessary and sufficient conditions for the existence of a unique solution are derived in this paper. Furthermore, a numerical algorithm and some examples are presented.

Keywords : doubly arrow matrices; inverse eigenvalue problem; eigenpair

References [1] Biegler-Knig FW. A newton iteration process for the inverse eigenvalue problems. Numer. Math. 1981;37:349–354. [2] Gladwell GML. The inverse problem for the vibrating beam, Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences 1984; v393, n1805: 277–295. [3] Boley D and Golub GH. A survey of matrix inverse eigenvalue problems. Numerical Analysis Project; 1987, p. 595– 622. [4] Chu MT and Golub GH. Inverse eigenvalue problems: Theory, Algorithms and Applications. New York: Oxford; 2005. [5] Rau´ l D Jime´nez. The reconstruction of a periodic structure from its dynamical behaviour. Proyecciones Journal of Mathematics 2011;30:91–109. [6] Holtz O. The inverse eigenvalue problem for symmetric anti-bidiagonal matrices. Linear Algebra and Applications 2005;408:268–274. [7] Wang Z, Zhong B. An inverse eigenvalue problem for jacobi matrices. Mathematical problem in engineering 2011; ID 571781: 1–11 . [8] Nazari AM, Beiranvand Z. The inverse eigenvalue problem for symmetric quasi anti-bidiagonal matrices. Applied mathematics and Computation 2011;217:9526–9531. [9] Ega n˜ a JC and Soto RL. On the numerical reconstruction of a spring-mass system from its natural frequencies. Proyec- ciones 2000;19:27–41. [10] Gladwell GML. Inverse Problems in Vibration. 2nd ed. Kluwer Academic Netherlands: Dordrecht; 2004. [11] Kinser J. Python for Bioinformatics. 2nd ed. Jones. Bartlett Publishers: Burlington; 2009. [12] Peng J, Hu XY, Zhang L. Two inverse eigenvalue problems for a special kind of matrices. Linear Algebra and Appli- cations 2006;416: 336–347. [13] Pickmann H, Egan˜ a J, Soto RL. Extremal inverse eigenvalue problem for bordered diagonal matrices. Linear Algebra and Applications 2007;427:256–271. [14] Wang Z, Dai H. On the construction of a real symmetric ﬁve-diagonal matrix from its three eigenpairs. Applied mathematics and Computation 2006;175:597–608. [15] Pickmann H, Egan˜ a J, Soto RL. Two inverse eigenproblems for symmetric doubly arrow matrices. Linear Algebra Society 2009;18:700– 718. [16] Liu Z, Wang K, Xu C. Extremal inverse eigenvalue problem for Symmtric doubly arrow matrices. Appl. Math Comput 2014;45:151–164.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 A Landsberg Moving Frames

Pipatpong Chansri 1 , Pakkinee Chitsakul 2

1 Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok, Thailand E-mail: [email protected] 2 Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok, Thailand E-mail: [email protected]

Abstract In this paper,We consider 3−dim manifold Σ with tangent space Tm Σ at m and cotangent space Tm ∗ Σ at m. Wessume Σ is indicatrix of the Finsler structure (M, F ), then Σ has a finslerian adapted{ω1 , ω2 , ω3 } satisfying the structure equation of (M, F ). On the other hand, We can assume that Σ is a Riemannian manifold (M, g) and here it has a Riemannian adapted coframe {α1 2 3 ∗ , α , α } satisfying the structure equation of (M, g). This mean that on the cotangent space Tm 1 2 3 1 2 3 ∗ M we have 2 basis: {ω , ω , ω } and {α , α , α }. Since Tm M is a linear space there exist a 3 × 3 matrix for changing basis {ωi } to {αi } that is ω = A · α.We will study about property of matrix A in case the Finsler structure (M, F ) is the Landsberg.

Keywords : tangent space; cotangent space; coframe, indicatrix; Finsler; Riemannian, Landsberg

References [1] S.V. Sabau, K. Shibuya, H. shimada, \On the existence of generalized unicorns on surfaces," Di_erential Geometry and its Application,, 406- 435 (2010). [2] S.V. Sabau, K. Shibuya, H. shimada, \Moving frames on generalized Finsler structures," J. Korean Math,, 12291257(2012).

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 Maximal diameter sphere theorem for manifolds with nonconstant Ricci curvature

Nathaphon Boonnama*, Watsana Boonsawaengb

a,bDepartment of Applied Mathematics and Informatics, Faculty of Science and Industrial Technology, Prince of Songkla University, 31 Moo 6 Surat-Nasarn Rd., Makhamthea, Muang Surat Thani, Surat Thani 84000, Thailand

Abstract Sphere theorem has always been a central theme in global differential geometry. Many tools and concepts that are now fundamental for comparison geometry have been developed in this context. In our work, we interest the maximal diameter sphere theorem by means of the Ricci curvature. We prove that for an n-dimensional complete connected Riemannian manifold M having a Ricci curvature at a base point p bounded from below by 1 and the diameter of M equals π, then M is isometric to the unit n-sphere.

Keywords: maximal diameter sphere theorem; volume comparison theorem; Ricci curvature

References [1] Boonnam N. Maximal diameter sphere theorem for manifolds with nonconstant radial curvature. Tokyo J. Math. 2015; 38: 145–151. [2] Cheeger J, Ebin DG. Comparison Theorems in Riemannian Geometry. North-Holland: Amsterdam and New York; 1975. [3] Cheng SY. Eigenvalue comparison theorems and its geometric applications. Math. Z. 1975;143:289–297. [4] Grove K, Peterson P. Comparison Geometry. Cambridge; New York; 1992. [5] Sakai T. Riemannian Geometry. Trans. of Math. Monographs. 149. Amer. Math. Soc.; 1992.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 Numerical Simulation of Water-Quality Model on Flooding using Revised Lax-Diffusive and Modified Siemieniuch-Gladwell Methods

Kanawoot Subklaya,b,* and Nopparat Pochaia,b

aDepartment of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand bCentre of Excellence Mathematics, Commission on Higher Education(CHE), Si Ayutthaya Road, Bangkok 10400, Thailand

Abstract In 2011, Thailand has been confronted a largest flooding. The mass of water has been drenched from many main and branch rivers to cover wide areas. The residents who lived in the flooding area have to build a manmade sandbag dike to protect their village. The flooding has been taken for a long time meanwhile the flooding water becomes contaminated. There are some residents in their flooding area want to drain their contaminated water to a nearest area. They have been destroyed their sandbag dike. Consequently, the dispute among residents is occurred.In this research, a mathematical simulation of a water-quality on a long period flooding using a couple of two models is proposed. The first model is the one-dimensional shallow water equations that provide the water elevation and velocity. The second model is a one-dimensional advection-dispersion equation that provides the water pollutant concentrations after the sandbag dike has been destroyed. A revised Lax-diffusive is used to approximate the solution of the first model. Consequently, the numerical solutions of the second model are obtained by using the traditional and modified Siemieniuch-Gladwell schemes.

Keywords: Finite differences, Lax-diffusive scheme, Revised Lax-diffusive scheme, One-dimensional, Dam-break model, Shallow water equations, Dispersion model, Advection-dispersion equation.

References [1] F. Benkhaldoun, M.Seaid, “A simple finite volume method for the shallow water equations,” Journal of Computational and AppliedMathematics, 234, 58-72(2010). [2] M. Dehghan, “Weighted finite difference techniques for the one-dimensional advection-diffusion equation,” Applied Mathematics and Computation, 147, 307-319 (2004). [3] P.Garcia-Navarro, A. Fras,I. Villanueva, “Dam-break flow simulation: some results for one dimension models of real cases,” Journal ofHydrology, 216, 227-247 (1999) [4] G.Gottardi, M. Venutelli, “Central scheme for two-dimensional dam-break flow simulation,” Advances in Water Resources, 27, 259-268 (2004) [5] M. Pirotton, S. Erpicum, B.J. Dewals, P.Archambeau, “Dam break flow computation based on an efficient flux vector splitting,” Journal of Computational and Applied Mathematics, 234, 2143-2151 (2010) [6] A. Baghlani, “Simulation of dam-break problem by a robust flux-vector splitting approach in Cartesian grid,” Scientia Iranica, 18(5),1061- 1068, (2011) [7] H.M. Kao, T.J. Chang, K.H. Chang, M.H. Hsu, “Numerical simulation of shallow-water dam break flows in open channels using smoothed particle hydrodynamics,” Journal of Hydrology, 408, 78-90, (2011) [8] R. Touma, S. Khankan, “Well-balance unstaggered central schemes for one and two-dimensional shallow water equation system,” AppliedMathematics and Computation, 218, 5948-5960, (2012) [9] C. Berthon, F. Foucher, “Efficient well-balanced hydrostatic schemes for shallow-water equations,” Journal of Computational Physics,231, 4993-5015, (2012) [10] G. Akbari, B. Firoozi, “Implicit and Explicit Numerical simulation of Saint-Venent Equations for Simulating Flood Wave in NaturalRivers,” 5th National Congress on Civil Engineering, Mashhad, Iran, (2010) [11] M. Dehghan, “Weighted finite difference techiques for the one-dimensional advection-diffusion equation,” Applied Mathematics andComputation, 147, 307-319, (2004) [12] G. Li, C.R. Jackson, “Simple, accurate, and efficient revisions to MacCormack and Saulyev schemes: High Peclet numbers,” Applied Mathematics and Computation, 186, 610-622, (2007) [13] N. pochai, “A Numerical Treatment of Nondimensional Form of Water Quality Model in a Nonuniform Flow Stream Using Saulyev Scheme,” Hindawi Publishing Corporation Mathematical Problem in Engineering, Volume 2011

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 Analytical Solutions Of Time Fractional Navier-Stokes Equations

Muhammet Kurulaya, Mirsat Yeşiltepea

aYildiz Technical Univercity - Davut Paşa Campus, Faculty Of Chemical And Metallurgical, Esenler/Istanbul – Turkey

Abstract The major purpose of this paper is to illustrate an effcient applicability of the homotopy analysis method (HAM) to time-fractional Navier Stokes equations written in polar coordinates with some initial conditions. Using HAM we obtain convergent power series solutions of Navier Stokes equations which are considered as exact and analytical solutions. We also present some computational figures regarding the solutions for different values of fractional derivatives that are employed in the Caputo meaning.

Keywords: Time fractional Navier{ Stokes equation; Caputo fractional derivative; Homotopy analysis method;Maple.

References [1] F. C. Klebaner and R. Liptser, Asymptotic analysis and extinction in a stochastic lotka-volterra model, The Annals of Applied Probability,11(4), 1263-1291, 2001. [2] A. Dobrinevski and E. Frey, Extinction in neutrally stable stochastic Lotka-Volterra models, arXiv:1001.5235, 2010. [3] A. Keller, Stochastic delay Lotka-Volterra system to interacting population dynamics, ASM'11 Proceedings of the 5th international conference on Applied mathematics, simulation, modelling, 191-196. [4] K. V. I. Saputra, Semi-global analysis of Lotka-Volterra systems with constant terms, Ph.D. thesis, La Trobe University, 2008. [5] X. Ding, H. Liu and F. Wang, Periodic Solutions for Gause-Type Ratio-Dependent Predator-Prey Systems with Delays on Time Scales,Discrete Dynamics in Nature and Society, Volume 2013 (2013), Article ID 368176.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 Mixed Cyclic Codes over GF(2)GF(4)

Taher Abualrub

American University of Sharjah, United Arab Emirates

Abstract In this paper, we are interested in studying the structure of cyclic codes over the _ mixed alphabet GF(2) GF (4) where 2 2 GF(2) = {0,1} and GF(4) {0,1, , } where10   . This class of codes generalizes the class of binary codes over GF(2) and the class of nonbinary cyclic codes over GF(4) . We will also show that this class of codes has some other applications such as applications in the football pool problem over mixed alphabets. We will give the definition of these codes over the mixed alphabet .Then, we will give the mathematical structure of these codes over . In particular,we will give the generator polynomials of these codes. Finally, we will present a mapping that maps cyclic codes over to binary codes.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 The Determination of the Optimal Component Ratio in Fiber- Cement Profile Sheet Roof Tiles to Reduce Materials Cost Using a Mixture Design

Chuckaphun Aramphongphuna, Kampanart Ungtawondeeb

aDepartment of Industrial Engineering, Faculty of Engineering, Kasetsart University, Chatuchak, Bangkok 10900, Thailand bGraduate Program in Engineering Management, Department of Industrial Engineering, Faculty of Engineering, Kasetsart University, Chatuchak, Bangkok 10900, Thailand

Abstract

This research aims to reduce the materials cost of non-asbestos type fiber-cement profile sheet roof tiles by at least 10% by optimizing the component ratio in the mixture while the properties still comply with Thai Industrial Standard (TIS 1407- 2540). Two experimental sets were studied in this research. First, a three-component mixture of (i) virgin natural pulp or fiber, (ii) synthetic fiber and (iii) cement was studied while the amount of calcium carbonate was kept constant. Second, an additional material, recycled natural pulp from recycled paper, was used in the mixture. The four-component mixture was then studied. Constrained mixture design was applied to design the two experimental sets above. The experimental data were then analyzed to build both the mixture model and the materials cost model. These two mathematical models were then employed to optimize the component ratio of the fiber-cement profile sheet. In the three-component mixture, it was found that the optimal component ratio was as follows: 3.14% virgin natural fiber, 1.20% synthetic fiber and 75.67% cement while the materials cost was reduced by 12%. In the four-component mixture, it was found that the optimal component ratio was as follows: 3.00% virgin natural fiber, 0.50% recycled natural fiber, 1.08% synthetic fiber, and 75.42% cement. The materials cost was reduced by 14%. The confirmation runs of 30 experiments were also analyzed statistically to verify the results.

Keywords: Mixture design; Design of experiments; Statistical analysis; Materials cost reduction; Fiber-cement profile sheets

References [1] Savastano Jr H, Warden PG, Coutts RSP. Brazilian waste fibres as reinforcement for cement-based composites. Cement & Concrete Composites 2000; 22 (5): 379-84. [2] Bezerra EM, Joaquim AP, Savastano Jr H, John VM and Agopyan V. The effect of different mineral additions and synthetic fiber contents on properties of cement based composites. Cement & Concrete Composites 2006; 28 (6): 555-63. [3] Moslemi A. Technology and market considerations for fiber cement. Fiber Composites Conference 2005; 5: 113-29. [4] Khorami M, Ganjian E. The effect of limestone powder, silica fume and fibre content on flexural behaviour of cement composite reinforced by waste Kraft pulp. Construction and Building Materials 2013; 46: 142-9.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 A numerical solution for non-uniform beam equation by finite difference method

Kumponsak Boongoy1, Pakkinee Chitsakul2

1Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok, Thailand 2Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok, Thailand

Abstract In this work, we used finite difference method with the error Oh()4 for the deflection of the beam y(,) x t at any point and any time of the non-uniform beam equation with the Robbins condition. Some numerical results are compared to the exact solution.

Keywords: non-uniform beam equation, Robbins condition, finite difference method

References [1] A.S. Ackleh , H.T.Banks, G.A. Pinter. A Nonlinear Beam Equation. Applied Mathematics Letters 15 (2002);381-387. [2] Chung-Yau Lam. Applied Numerical Methods for Partial Differential Equations. Singapore: Prentice Hall; 1994. [3] Dennis G. Zill, Michael R. Cullen. Advanced Engineering Mathematics. 2nded. Sudbury: Jones and Bartlett Publishers; 2000. [4] Gere, James M. Mechanics of materials. London : Chapman & Hall; 1991. [5] K. S. Thankane, T. Stys. Finite Difference Method for Beam Equation with Free Ends Using Mathematica. Southern Africa Journal of Pure and Applied Mathematics Volume 4;61-78(2009). [6] S Rao Gunakala, D.M.G.Comissiong, K.Jordan, Alana Sankar. A Finite Element Solution of the Beam Equation via MATLAB.International Journalof Applied Science and Teachnology Vol 2.No.8;2012.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 COLORING TYPE II FUZZY GRAPH BASED ON FUZZY INDEPENDENT VERTEX SET

Isnaini Rosyida,1 Widodo, Ch. Rini Indrati,2 and K.A. Sugeng3

1Department of Mathematics, Gadjah Mada University, Indonesia 1Department of Mathematics, Semarang State University, Indonesia e-mail : [email protected] 2Department of Mathematics, Gadjah Mada University, Indonesia e-mail : widodo [email protected], [email protected] 3Department of Mathematics, University of University, Indonesia e-mail : [email protected]

Abstract A type II fuzzy graph is a graph consisting a fuzzy vertex set and a fuzzy edge set. In this paper, we give the concept of fuzzy independent vertex set of type II fuzzy graph depending on   (0,1] Further, the concept of  -fuzzy independent vertex set is used to define coloring type II fuzzy graph and the concept of fuzzy chromatic number of type II fuzzy graph is given. Based on the properties of the fuzzy chromatic number, we construct a fuzzy chromatic algorithm for type II fuzzy graph. Finally, a numerical example is given to illustrate the proposed fuzzy chromatic algorithm and an application of the fuzzy chromatic number of type II fuzzy graph.

Keywords : Type II fuzzy graph; fuzzy graph coloring; fuzzy independent vertex set; fuzzy chromatic number.

References [1] A. Dharwadker, The Independent Set Algorithm, Amazon, 2011. [2] A. Kaufmann, Introduction a la theorie des sous-ensembles ou, Masson Paris, 1, 41-189, 1973. [3] A. Kishore and M.S. Sunitha, Chromatic number of fuzzy graphs, Annals of Fuzzy Mathematics and Informatics 7(4), 543-551, 2014. [4] A. Rosenfeld, Fuzzy grap, In: L.A. Zadeh, K.S. Fu and M.Shimura, Eds.,Fuzzy sets and Their Applications to Cognitive and Decission Processes, 7795,1975. [5] C.R. Bector and S. Chandra, Fuzzy Mathematical Programming and Fuzzy Matrix Games, Springer Verlag, 2005. [6] G. Wang, Q. Zhang, X. Cui, The Discrete Fuzzy Numbers on a Fixed Set With Finite Support Set, in: Proceedings of IEEE Conference on Cybernetics and Intelligent Systems, Chengdu, 812-817, 2008. [7] I. Rosyida, Widodo, Ch.R. Indrati , and K. A. Sugeng , A New Approach For Determining Fuzzy Chromatic Number of Fuzzy Grap, Journal of Intelligent & Fuzzy Systems, 28(5), 2331-2341, 2015. [8] L.A. Zadeh, Fuzzy Set, Information and Control, 33, 338-353, 1965. [9] L.S. Bershtein and A.V. Bozhenuk , Maghout Method for Determination of Fuzzy Independent, Dominating Vertex Sets and Fuzzy Graph Kernels, International Journal of General Systems, 30(1), 45-52, 2001. [10] M.S. Sunitha, Studies on Fuzzy Graphs, Ph.D. Dissertation, Cochin University of Science and Technology, 2001. [11] N. Biggs, Algebraic Graph Theory, Cambridge University Press, 1993. [12] P.S. Nair, Perfect and Precisely Perfect Fuzzy Graph. Proceedings of North American Fuzzy Information Processing Society, NewYork, 245-248, 2008. [13] V. Cioban, On Independent Sets of Vertices of Graph, Studia Univ. BabesBolyai Informatica L.II 1, 97-100, 2007. [14] W.B.S. Kandasamy, Smarandache Fuzzy Algebra, American Research Press, 2003.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 Formula Formula for a correlation coefficient between underlying commodity price and its convenience yield under Schwartz model

Yamonporn Thummanusarna*, Khamron Mekchaya, Sanae Rujivanb

1Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok, 10330, Thailand 2Department of Mathematics, School of Science, Walailak University, Nakhon Si Thammarat, 80160, Thailand

Abstract Commodity is a marketable item produced to satisfy wants or needs. We usually use it as inputs in productions of other goods such as crude oil, agricultural good, gold, etc. The price of commodity for each country usually depends on demand and supply of people in that country. However, there is a factor that effects the commodity price in economic called convenience yield, which is used to describe the benefit of holding a physical good, rather than the derivative product. The theory of storage tells us that the convenience yield varies inversely with the inventory of commodity, thus, finding the covariance between commodity price and convenience yield can imply the inventory of commodity, which is an important factor for government to make policy and decision in commodity price. This paper will offer a closed-form formula for a correlation coefficient between underlying commodity price and its convenience yield, which can be used to determine the inventory that is not observable from commodity market.

Keywords: convenience yield; commodity; Schwartz’s two-factor model.

References [1] Schwartz, E.S., 1997. The stochastic behavior of commodity prices: implications for valuation and hedging, The Journal of Finance, pp.923- 973. [2] Klebaner, F.C. 2005. Introduction to stochastic calculus with application, Second Edition. London, UK : Imperial College Press. [3] Gibson, R. and Schwartz, E.S., 1980. Stochastic convenience yield and the pricing of oil contingent claims, The Journal of Finance, pp. 959- 976. [4] Ross, Sheldon M., 2010. A first course in probability, Eight Edition. Prentice-Hall, New Jersey. [5] David,H. and Martin, S. 2000. Martingales versus PDEs in Finance: An equivalence result with examples. Journal of applied probability, pp947-957. [6] Oksendal, B.K., 2003. Stochastic differential equation, Sixth Edition. Springer-Verlag Berlin Heidelberg New York.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 STOCK SELECTION INTO PORTFOLIO BY FUZZY QUANTITATIVE ANALYSIS AND FUZZY MULTI-CRITERIA DECISION MAKING

Satit Yodmun1, Wichai Witayakiattilred2

1,2 Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok, Thailand E-mail: [email protected] 2Corresponding Author *The financial support for this study was from King Mongkut’s Institute of Technology Ladkrabang.

ABSTRACT This article presents a stock selection approach assisted by fuzzy procedures. In this approach, stocks are classified into groups according to business types. Within each group, the stocks are screened and then ranked according to their investment weight obtained from fuzzy quantitative analysis. Groups were also ranked according to their group weight obtained from fuzzy analytic hierarchy process (FAHP) and technique for order preference by similarity to ideal solution method (TOPSIS). The overall weight for each stock were then derived from both of these weights and used for selecting a stock into the portfolio. As a demonstration, our analysis procedures were applied to a test set of data.

Keywords: Fuzzy logic, Quantitative Analysis, Fundamental Analysis, Multi Criteria Decision Making, FAHP, TOPSIS, Stock Selection

REFERENCES [1] CT Chan, “Extension of TOPSIS for group decision –making under fuzzy environment,” Fuzzy Sets and Systems 114 (2000) 1-9. [2] J J Buckley, T Feuring, Y Hayashi, “Fuzzy hierarchical analysis revisited,” European Journal of Operational Research 129 (2001) 48-64 [3] Juan Aguaron, Jose Maria Moreno-Jimenez, “The geometric consistency index: Approximated threholds,”European Journal of Operational Research 147 (2003) 137-145. [4] J Aguaron, J M M Jimenez, “The geometric consistency index: Approximated thresholds,” European Journal of Operational Research, 147 (2003) 137-145 [5] Kazutomo Nishizawa, Iwaro Takahashi, Nihon University, Tsukuba University, “Weighted and Logarithmic Least Square Methods for Mutual Evaluation Network System Including AHP and ANP,” Journal of The Operations Research, Society of Japan ,Vol. 52, No. 3 , 221-244 , 2009. [6] Serkan Balli, Serdar Korukoglu, “Operation System Selection Using Fuzzy AHP and TOPSIS Methods,” Mathematical and Computational Application, Vol. 14, No. 2, pp.119130, 2009. [7] J Ramik, “Consistency of pair-wise comparison matrix with fuzzy elements,” School of Business Administration in Karvina, FSA-EUSFLAT 2009 [8] J Ramik, P Korviny “Inconsistency of pair-wise comparison matrix with fuzzy elements based on geometric mean,” Fuzzy Sets and Systems 161 (2010) 1604-1603. [9] Martin Gavalec, Jaroslav Ramil, Karel Zimmermann, “Decision Making and Optimization,” Lecture Notes in Economics and Mathematical Systems 677, (2015) DOI 10.1007/978-3-319-08323-0. [10] P.Bumlungpong, R.Chinarak, A.Thaimai, W.Witayakiatilerd, “Fuzzy Quantitative Analysis of The Property and Construction Industrial Group in The Stock Exchange of Thailand,” Special Problem, King Mongkut’s Institute of Technology Ladkrabang, 2015.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 Performance of the Modern Robust Test Using Different Trimming Criteria in Comparing Two Independent Group

Suhaida Abdullah, Sharipah Soaad Syed Yahaya, Zahayu Md. Yusof

School of Quantitative Sciences, Universiti Utara Malaysia, 06010 Sintok, Kedah, Malaysia

Abstract This paper presents a new approach of testing the equality of independent groups based on different trimming criteria using modified one step M estimator. The existence independent groups test such as t-test and analysis of variance currently suffer from deviation of normality or heterocedasticity or the worst is when both occur simultaneously. In real life, data that is normally distributed with equal variance is not always available. Alexander-Govern test is modern robust test statistic which handle problem of heteroscedasticity in comparing independent groups. However this method has problem in controlling the Type I rate when deal with non-normal data distribution. Therefore a conjunction of the Alexander-Govern test with the modified one step M estimator is proposed using different trimming criteria which refer to three robust scale estimators that are MADn, Sn and Tn. The performances of the proposed methods are evaluated based on the ability of controlling the Type I error rates. The method is considered robust if it Type I error rates lie between 0.025 and 0.075 for confidence level fixed to be 0.05. The results show that the tests which use modified one step M estimator outperform the original test where it robust in all conditions regardless the shape of distribution. The original test found to be not robust under skewed distribution. Among the three scale estimators, the MADn provide the best performance with robust in all conditions with stringently robust under normal tailed data. While the Sn and Tn have comparable performance but still better than the original test.

Keyword: Alexander Govern test; robust estimator; scale estimator; Type I error rate

References [1] Wilcox, R. R. (2005). Introduction to robust estimation and hypothesis testing: San Diego: Academic Press. [2] Alexander, R. A., & Govern, D. M. (1994). A new and simpler approximation for ANOVA under variance heterogeneity. Journal of Educational Statistics, 19(2), 91-101. [3] Schneider, P. J., & Penfield, D. A. (1997). Alexander and Govern's approximation: Providing an alternative to ANOVA under variance heterogeneity. Journal of Experimental Education, 65(3), 271-287. [4] Myers, L. (1998). Comparability of the James' second-order approximation test and the Alexander and Govern A statistic for non-normal heteroscedastic data. Journal of Statistical Computational Simulation, 60, 207-222. [5] Lix, L. M., & Keselman, H. J. (1998). To trim or not to trim: Tests of location equality under heteroscedasticity and nonnormality. Educational and Psychological Measurement, 58(3), 409-429. [5] Welch, B. L. (1951). On the comparison of several mean values: An alternative approach. Biometrika, 38, 330-336. [6] James, G. S. (1951). The comparison of several groups of observations when the ratios of the population variances are unknown. Biometrika, 38, 324-329. [7] Wilcox, R. R. (1997). A bootstrap modification of the Alexander-Govern ANOVA method, plus comments on comparing trimmed means. Educational and Psychological Measurement, 57(4), 655-665. [8] Wilcox, R. R. (2002). Understanding the practical advantages of modern anova methods. Journal of Clinical Child and Adolescent Psychology, 31(3), 399-412. [9] Keselman, H. J., Wilcox, R. R., Taylor, J., & Kowalchuk, R. K. (2000). Tests for mean equality that do not require homogeneity of variances: Do they really work? Communications in Statistics, 29, 875-895. [10] Wilcox, R. R., & Keselman, H. J. (2003). Modern robust data analysis methods: measures of central tendency. Psychological Methods, 8(3), 254-274. [11] Rousseeuw, P. J., & Croux, C. (1993). Alternatives to the median absolute deviation. Journal of American Statisical Association, 88(424), 1273-1283. [12] Syed Yahaya, S. S., Othman, A. R., & Keselman, H. J. (2006). Comparing the “Typical Score” Across independent groups based on different criteria for trimming. Metodološki zvezki, 3, 49-62. [13] Hoaglin, D. C. (1985). Summarizing shape numerically: The g-and-h distribution. In D. C. Hoaglin, F. Mosteller & J. W. Tukey (Eds.), Exploring Data Tables, Trends, and Shapes (pp. 461-513). New York: John Wiley & Sons. [14] Efron, B., & Tibshirani, R. J. (1993). An Introduction to the Bootstrap. New York: Chapman & Hall, Inc. [15] Bradley, J. V. (1978). Robustness? British Journal of Mathematical and Statistical Psychology(31), 144-152.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 Kronecker product of matrices over a commutative semiring

Raviwan Stangama, Pattrawut Chansangiamb,*

aDepartment of Mathematices,Faculty of Science, King Mongkut’s Institute of Technology Lardkrabang, Bangkok, 10520, Thailand e-mail : [email protected] bDepartment of Mathematices,Faculty of Science, King Mongkut’s Institute of Technology Lardkrabang, Bangkok, 10520, Thailand e-mail : [email protected]

Abstract In this paper, we investigate algebraic properties of the Kronecker product of matrices over a commutative semiring. It turns out that this matrix product has a rich and pleasing algebra. These algebraic properties include the associativity, the distribution over the addition and the compatability with other matrix operations. We also discuss the relationship between the Kronecker product and a kind of vector operation, namely, the vector operator.

Keywords: Kronecker product; commutative semiring; vec operator

References [1] Baccelli FL, Cohan G, Olsder GJ, Quadrat JP. Synchronization and Linearity. J. Wiley and Sons. Chichester. New York; 1992. [2] Brouwer RK. A method of relational fuzzy clustering based on producing feature vectors using FastMap. Inform. Sci 2009;179: 3561- 3582. [3] B utkovi P. Max-algebra: the linear algebra of combinatorics. Linear Algebra Appl 2003;367: 313-335. [4] Cechla rova K, Pla vka J. Linear independence in bottleneck alebras. Fuzzy Sets Syst 1996;77: 337-348. [5] Chang CC. Algebraic analysis of many valued logics. Tran. Amer. Math Soc 1958;88: 467-490. [6] Cignoli RLO, D’ottaviano IML, Mundici D. Algebraic Foundation of Many-Valued Reasoning. Kluwer Academic Publishers Dordrecht; 2000. [7] Cuninghame-Green RA. Minx algeimba r a . Lecture Notes in Econom. and Math. System. Springer. Berlin 1979;166. [8] Cuninghame-Green RA, Butkovi P. Bases in max-algebra. Linear Algebra Appl 2004;389:107-120. [9] Di Nola A, Lettieri A, Perfili eva I, Novak V. Algebraic analysis of fuzzy systems. Fuzzy Sets Syst 2007;158: 1-22. [10] Ghosh S. Matrices over semiring. Inform. Sci 1996;90: 221-230. [11] Golan JS. Semirings and their Applications. Kluwer Academic Publishers. Dordrecht; 1999. [12] Gondran M, Minoux M. Graphsoids Di and Semirings. Springer; 2008. [13] Henderson HV, Searle SR. The vec-per mutation matrix, the vec operator and Kronecker products: a review. Linear and Multilinear Algebra 1981;9:271-288. [14] Hyland DC, Collins EG. Block Kronecker products and block norm matrices in large-scale systems analysis. SIAM J. Matrix Anal. Appl 1989;10:18-29. [15] Huhtanen M. Real linear Kronecker product operations. Linear Algebra Appl 2006;148: 347-361. [16] Kim KH, Roush FW. Generalized fuzzy matrices. Fuzzy Sets Syst 1980;4: 293-315. [17] Koning RH, Neudecker H, Wansbeek T. Block Kronecker products and the vecb operator. Linear Algebra Appl 1991;149: 165-184. [18] Lancaster P, Tismenetsky M. The Theory of Matrices: with Applications,Academic Press. New York. NY. USA; 1985. [19] Neudecker H, Liu S. A Kronecker matrix inequality with a statistical application. Econometric Theory 1995;11: 655. [20] Poplin PL, Hartwig RE. Determinantal identities over commutative semirings. Linear Algebra Appl 2004;387: 99-132. [21] Rao CR, Rao MB. Matrix Algebra and Its Applications to Statistics and Econometrics. World Scientific. Singapore; 1998. [22] Reutenauer C, Straubing H. Inversion of matrices over a commutative semiring. J. algebra 1984;88: 350-360. [23] Tracy DS, Jinadasa KG, Partitioned Kronecker products of matrices and applications,Canada J. Statist 1989;17: 107-120. [24] Trenkler G. A Kronecker matrix inequality with a statistical application. Econometric Theory 1995;11: 654-655. [25] Visick G. An algebraic relationship between the Hadamard and Kronecker product with some applications. Bull. Soc. Math. Belgique 1990;42: 275-283. [26] Wei Y, Zhang F. Equivalence of a matrix product to the Kronecker product. Hadronic J. Suppl 2000;15: 327-331. [27] Zhang H, Ding F. On the Kronecker products and their applications. J. Appl. Math 2013;DOI 10.1155/2013/296185. [28] Zhao S, Wang X- P. Base in semulinear spaces over join-semirings. Fuzzy Sets Syst 2011;182:93-100. [29] Zhao S, Wang X-P. Invertible matrices and semilinear spaces over commutative semiring. Inform. Sci 2010;180:5115-5124. [30] Zimmermann U. Linear and combinatorial optimization in orders algebraic structures. Annals of Discrete Mathematics 1981;10

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 FURTHER GENERALIZED CONTRACTION MAPPING PRINCIPLE IN PARTIAL METRIC SPACES

Aphinat Ninsri 1 and Wutiphol Sintunavarat 2

1 Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathumthani, Thailand E-mail: [email protected] 2 Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathumthani, Thailand E-mail: [email protected], poom [email protected]

Abstract In this work, we will de_ne the new class of generalized contraction mappings in partial metric spaces and establish the existence theorem of fixed points for mappings in this class in partial metric spaces. Our main results generalize, extend and unify the main results of Su et al. [1] and references therein.

Keywords: fixed point theorems, generalized contraction mappings, partial metric spaces

References

[1] Y. Su, J. C. Yao, “Further generalized contraction mapping principle and best proximity theorem in metric spaces,” Fixed Point Theory and Applications, 2015:120 (2015).

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 Weak – Contraction Self – Mapping principle in partially ordered Quasi Metric Space

Rahma Zuhraa,1 , Mohd Salmi Md Noorania , Fawzia Shaddadb

a School of Mathematical Sciences, Faculty of Science and Technology University Kebangsaan Malaysia, Selangor Darul Ehsan and 43600, Malaysia Department of Mathematics Sana’a University, Yemen

Abstract In this paper, fixed point theorems of a self - mapping in partially ordered quasi metric space are presented. This theorem generalize results from fixed point on weakly - contractive that uses altering distance function which have proved in the references. We also give an example that satisfies the theorems.

Keywords: Weakly-contractive; altering distance function; fixed point; quasi metric space.

References [1] Khan MS, Swaleh M, Sessa S. Fixed point theorems by altering distances between the points. Bull Austral. Math Soc 1984;30(1):1 - 9. [2] Rhoades BE. Some theorems on weakly contractive maps. Nonlinear Anal.2001;47:2683 - 2693. [3] Dutta PN, Choudhury BS. A generalization of contraction principle in metric spaces. Fixed Point Theory and Appl. 2008;2008:1 - 8. [4] Dutta PN, Choudhury BS. A generalization of contractions in partially ordered metric spaces. Appl. Anal. 2008;87:109 - 116. [5] Rhoades BE, Pathak HK, Mishra SN. Some weakly contractive mapping theorems in partially ordered spaces and applications. Demonstratio Mathematica 2012;45 (3):621 - 636. [6] Harjani J, Sadarangani K. Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations. Nonlinear Analysis 2010;72:1188 - 1197. [7] Gordji ME, Baghani H, Kim GH. A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations. Discrete Dynamic in Nature and Society 2012;2011:1- 8. [8] Yan F, Su Y, Feng Q. A new contraction mapping principle in partially ordered metric spaces and applications to ordinary differential equations. Fixed Point Theory and Applications 2012;152:1 - 13. [9] Su Y. Contraction mapping principle with generalized altering distance function in ordered metric spaces and applications to ordinary differential equations. Fixed Point Theory and Applications 2014;227:1 - 15. [10] Shaddad F, Md Noorani MS, Alsulami SM, Akhadkulov H. Coupled point results in partially ordered metric spaces without compatibility. Fixed Point Theory and Appl. 2014:204:1 - 18.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 Complementary Dual Subfield Linear Codes over Finite Fields

Kriangkrai Boonniyoma and Somphong Jitmana,*

aDepartment of Mathematics, Faculty of Science, Silpakorn University, Nakhon Pathom 73000, Thailand

Abstract 2 Two families of complementary codes over finite fields Fq are studied, where q = r is square: i) Hermitian complementary dual linear codes, and ii) trace Hermitian complementary dual subfield linear codes. Necessary and sufficient conditions for a linear code (resp., a subfield linear code) to be Hermitian complementary dual (resp., trace Hermitian complementary dual) are determined. Constructions of such codes are given together their parameters. Some illustrative examples are provided as well.

Keywords: Complementary dual codes; Hermitian inner product; trace Hermitian inner product; subfield linear codes

References [1] M. F. Ezerman, S. Jitman, S. Ling, D. V. Pasechnik. CSS-like constructions of asymmetric quantum codes. IEEE Trans. Inf. Theory 2013;59:6732–6754. [2] R. Lidl, H. Niederreiter, Finite Fields. Encyclopedia of Mathematics and its Applications. vol. 20. Cambridge: Cambridge Univ. Press; 1997. [3] J. L. Massey. Linear codes with complementary duals. Discrete Mathematics 1992;106/107:337–342. [4] G. Nebe, E. M. Rains, and N. J. A. Sloane. Self-Dual Codes and Invariant Theory. Berlin:Springer; 2006. [5] E. Sangwisut, S. Jitman, S. Ling, P. Udomkavanich. Hulls of cyclic and negacyclic codes over finite fields. Finite Fields and Their Applications 2015;33:232–257. [6] X. Yang, J. L. Massey. The condition for a cyclic code to have a complementary dual. Discrete Math 1994;126:391–393. [7] R. J. Faudree, R. H. Schelp, Path-path Ramsey-type number for the complete bipartite graph. Journal of Combinatorial Theory Series B 1975;19(2):161-173. [8] W. Goddard, M. A. Henning, O. R. Oellermann. Bipartite Ramsey number and Zarankiewicz. Journal of Discrete Mathematics 2000; 219:85-95. [9] L. Maherani, G.R. Omidi, G. Raeisi, M. Shahsiah, O. R. Oellermann. On three-color Ramsey number of paths. Graphs and Combinatorics 2015;DOI 10.1007/s00373-014-1507-0. [10] J.H. van Lint. Introduction to Coding Theory. Berlin:Springer; 1965.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 ON NEW TYPES OF SIMULATION FUNCTIONS WITH FIXED POINT RESULTS IN b-METRIC SPACES

Oratai Yamaod 1 and Wutiphol Sintunavarat 2

1 Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathumthani 12121, Thailand E-mail: oratai [email protected] 2 Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathumthani 12121, Thailand E-mail: [email protected], poom [email protected]

Abstract Recently, Khojasteh et al. [1] introduced the concept of simulation function and Z-contraction with respect to simulation function. In this work, we extend the concept of simulation function and introduce several types of simulation functions. We also study some properties of theses types and prove some _xed point theorems along with new type of simulation functions in b-metric spaces.

Keywords: simulation functions, b-metric spaces, _xed points

References

[1] F. Khojasteh, S. Shukla, S. Radenovic, “A New Approach to the Study of Fixed Point Theory for Simulation Functions,” Filomat, 29:6, 1189-1194(2015).

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015

On Modules over Dedekind Prime Rings

Elvira Kusniyanti 1 , Hanni Garminia 2

1,2 Institut Teknologi Bandung, Indonesia E-mail: [email protected] , [email protected]

Abstract This research studies an interconnection between finitely generated uniform modules and Dedekind prime rings. The characterization of modules over Dedekind prime rings that will be investigated is an adoption of Noetherian and hereditary concept. Dedekind prime rings are Noetherian and hereditary rings This property of Dedekind prime rings is a background of the idea of adopting arises. In Noetherian area, it was known that a ring R is Noetherian ring if and only if every finitely generated R-module is a Noetherian module. Similar to that result, a characterization of hereditary ring is related to its projective modules. That is, a ring R is hereditary ring if and only if every projective R-module is a hereditary module. Due to the above two results, we suppose that characterization of a Dedekind prime ring can be analyzed from finitely generated modules over it. We propose a conjecture: a ring R is a Dedekind prime ring if and only if every finitely generated uniform R-module is Dedekind module. In this article, we will generalize a concept of Dedekind module for noncommutative ring case and present a part of the above conjecture.

Keywords : dedekind domains; dedekind prime rings; dedekind modules; uniform modules

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 Incomplete split-plot designs constructed by _-resolvable designs

Kazuhiro Ozawa 1 and Shinji Kuriki 2

1 Department of Nursing, Gifu College of Nursing, Hashima, Gifu, 501-6295, Japan E-mail: [email protected] 2 Department of Mathematical Sciences, Graduate School of Engineering, Osaka Prefecture University, Naka-ku, Sakai, Osaka, 599-8531, Japan E-mail: [email protected]

ABSTRACT We consider a two-factor experiment of split-plot type. In a split-plot design, each of b blocks is divided into k1 whole- plots, and each whole-plot is divided into k2 subplots. The v1 levels of the _rst factor A are arranged on the whole-plots (called whole-plot treatments), and the v2 levels of the second factor B are arranged on the subplots (called subplot treatments). We consider an incomplete split-plot design (ISPD) such that k1 < v1 or k2 < v2. Mejza [3] and Mejza and Mejza [2] considered the constructions of ISPDs by the Kronecker product of the incidence matrices of two designs. Ozawa, et al. [5], Ozawa and Kuriki [4] and Kuriki and Nakajima [1] considered the constructions of ISPDs by a modi_ed Kronecker product (called the semi-Kronecker product) of the incidence matrices of two resolvable designs. In this talk, we construct an ISPD by the semi-Kronecker product using an _-resolvable design for the whole-plot treatments and an affine _-resolvable design for the subplot treat-ments. We give the stratum efficiency factors for such an ISPD, which has the general balance property.

Keywords: _-resolvable designs, Affine _-resolvable designs, General balance property,Incomplete split-plot designs, Stratum efficiency factors

References

[1] S. Kuriki and K. Nakajima, \Square lattice designs in incomplete split-plot designs," Journal of Statis tical Theory and Practice, 1(3-4), 417- 426 (2007). [2] I. Mejza and S. Mejza, \Incomplete split-plot designs generated by GDPBIBD(2)," Calcutta Statistical Association Bulletin, 46, 117-127 (1996). [3] S. Mejza, \Experiments in incomplete split-plot designs," In Pukkila, T. and Puntanen, S. (Eds.), Proceeding of Second International Tampere Conference in Statistics, University of Tampere, 575-584 (1987). [4] K. Ozawa and S. Kuriki, \Incomplete split-plot designs generated from _-resolvable designs," Statistics & Probability Letters, 76, 1245-1254 (2006). [5] K. Ozawa, S. Mejza, M. Jimbo, I. Mejza and S. Kuriki, \Incomplete split-plot designs generated by some resolvable balanced designs," Statistics & Probability Letters, 68, 9-15 (2004).

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 APPLICATION OF NEW MATHEMATICAL OPERATIONS ZERATION AND DELTATION IN ALGORITHMS OF IMAGES PROCESSING SYSTEM PANORAMIC

Konstantin Anatol’evich Rubcov 1, Igor Sergeevich Konstantinov 2 and Sergej Aleksandrovich Lazarev 3

1 Educational-Scientific laboratory IIiUKS, Belgorod State National Research University, Belgorod, Russia E-mail: [email protected] 2 Research and International Activities of the Institute of Engineering Technology and Science, Belgorod State National Research University, Belgorod, Russia E-mail: [email protected] 3 Research and International Activities of the Institute of Engineering Technology and Science, Belgorod State National Research University, Belgorod, Russia E-mail: lazarev [email protected]

ABSTRACT Modern systems of panoramic photos and video are characterized by a wide variety of ways of placing the light- sensitive sensors (cameras and object-glass). Insufficient performance microcontrollers led to the inability to use an array of light-sensitive sensors in compact devices. In paper we consider an array of 12 light-sensitive sensors with lenses arranged in the center of the facets of a dodecahedron [1]. Such disposition forms a camera in space(at the intersection of the scope of the camera) facets of the dodecahedron, containing unique to the selected camera image. Miniaturization of the system is complicated by the need to process a large number of real-time information, based on the calibration offset and rotation of each camera. This problem is solved by the use of PLD (programmable logic device) for pre-processing and multi-core microcontroller. At a preliminary stage of the image processing and calibration problem masking to use new mathematical operations is expedient: Zeration ( ) and inverse Deltation (∆) [2, 3]. These operations have a rank lower than ”addition” and ”subtraction”, and allow us to describe in a unified mathematical formalism as logical operations and systems of equations, and a number of special functions [3]: a b = c → c ∆ b = a → c∆a = b, where Zeration: a b = 1 + max{a, b} for a 6= b, a b = a + 2 = b + 2 for a = b, a, b Є R,

, . Using extended basis of mathematical operations implemented by hardware (e.g., via PLD), allows highly efficient computational algorithms preprocessing of images by compaction program part and produce a linear algorithm areas requiring the greatest timeconsuming. Research on this subject conducted as part of the a state contract No. 14.581.21.0003 Russian Ministry of Education. Keywords: Zeration, Deltation, Regular dodecahedron.

Keywords: Zeration, Deltation, Regular dodecahedron.

References [1] Weisstein, Eric W., “Dodecahedron,” MathWorld, Wolfram Web Resource. http://mathworld.wolfram.com/Dodecahedron.html. [2] K.A. Rubtsov, G.F. Romerio, “Homomorphism, Isomorphism, Tetration and Zeration applications in Numerical Methods: Mathematics in Science and Technology,” International Congress of Mathematicians, ICM-2014, 703-704 (2014). [3] K.A. Rubtsov, G.F. Romerio, “Hyperoperations, for science and technology: New algorithmic tools for computer science,” Lambert Academic Publishing, 185 p., (2011).

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 The stress of undergraduate students, faculty of science King Mongkut’s Institute of Technology Ladkrabang.

Pornchai Laipasu

Department of Statistics Faculty of Science KMITL,Thailand E-mail : [email protected]

Abstract The objective of this study is to explore the relationship between the stress of Undergraduate students, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang and gender, college year, department, age, GPA, congenital disease, financial status and family relationship. Stratified sampling and Systematic sampling were used and 481 Undergraduate students were participated. The survey data was obtained by the Suanprung Stress Test Questionnaire. The Chi-square test for Independence and Cramer’s V coefficient were applied for the data analysis.At the significance of 0.05, the stress levels were no significant relationship with gender, college year, department, age, GPA, congenital disease and family relationship but were significant relationship with financial status and Cramer’s V coefficient show that there is a weak relationship. keywords: stress , undergraduate students , test for independence

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 APPLICATION OF MAMDANI FIS METHOD FOR CLASSIFICATION OF MELINJO MATURITY ACCORDING TO ITS COLOUR

Hizir Sofyana , Marzuki Abubakara* , Asep Rusyanaa* , Dian Rahmata*

aDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, Syiah Kuala University , Indonesia E-mail: [email protected]

Abstract Fuzzy logic is a method of reasoning used as a dispute resolution containing the doubt. Fuzzy Inference System (FIS) is a method with fuzzy logic rules were developed in various fields such as control system, classification and various other systems. This research applied FIS as the determination of the level of melinjo maturity (Gnetum gnemon L.) by classification melinjo seed color. This study aimed to apply FIS in classification of melinjo seed color maturity. This application look at misclassification and the range level of melinjo seed maturity. Establishment FIS system used Mamdani method with the image data of melinjo seed. Processed using addictive primary colors of Red, Green, Blue (RGB). Variables used as many as 4 pieces, consisting of three input variables and one output variable. Input variables in the form of a Red, Green, and Blue variable in which each variable has three parameters; Rendah, Normal and Tinggi parameter variable input. Output variable is the percentage of Red with three levels of maturity that is Mentah, Mengkal dan Masak. The result showed that misclassification occurred only at Mengkal level maturity with a percentage error 5%. keywords: fuzzy inference system , mamdani , melinjo

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 The Number of Labelled Trees with r1,r2 End-Vertices in Kn,n

Thipapat Portawina, Wannaporn Sanprasertb and Decha Samanac

a,b,c Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok, Thailand

Abstract Let L(n,r1,r2) be the number of labelled trees with r1,r2 end-vertices in Kn,n. In this paper, we use the exponential generating function to find the formula of L(n,r1,r2).

Keywords: Complete bipartite graph; Labelled; Trees; End-vertices; Counting

References [1] Chartrand G, Lesniak L. Graphs & Digraphs. 4th ed. California: Chapmman and Hall; 2004. [2] Gross JL, Yellen J. Handbook of Graph Theory. Florida: CRC Press; 2000. [3] Longani V. A formula for the number of labelled trees. Comp. Math. Appl. 2008; 56: 2786-2788. [4] Abu-Sbeih MZ, On the number of spanning trees of K n and K m,n . Discrete Math. 1990; 84: 205-207. [5] Jin Y, Liu C. The enumeration of labelled spanning trees of K m,n . Aust. J. Combin. 2003; 28: 73-79. [6] Lewis RP. The number of spanning trees of a complete multipartite graph. Discrete Mathematics 1999; 197/198: 537-541. [7] Baron G, Prodinger H, Tichy RF, Boesch FT, Wang JF. The number of spanning trees in the square of a cycle. The Fibonacci Quart. 1985; 23: 258-264.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 SOME PROPERTIES OF ROTATIONAL RANDERS TWO- SPHERE OF REVOLUTION

Rattanasak Hama 1

1 Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok, Thailand E-mail: [email protected] Abstract

We study the behavior of geodesics on a rotational Randers surface of revolution homeomorphic to R2 [3] . The main tool is the extension of Clairaut relation from Riemannian case [2] to the Randers case [1]. In this research, we interested in the surface of revolution homeomorphic to S2, namely “two-sphere of revolution” [4].

Keywords: Randers, Surface of revolution, Clairaut relation

2010 Mathematics Subject Classification: 53B21, 53C60

References

[1] C. Robles, “Geodesics in Randers spaces of constant curvature,” Trans. AMS 359 (2007), no. 4, 1633-1651. [2] K. Shiohama, T. Shioya, and M. Tanaka, “The Geometry of Total Curvature on Complete Open Surfaces,” Cambridge tracts in mathematics, 159, Cambridge University Press, Cambridge, (2003). [3] P. Chitsakul , R. Hama and S. V. Sabau, “The Geometry of a Randers rotational surface,” (2015), arXiv:1502.00349v2. [4] R. Sinclair and M. Tanaka, “The cut locus of a two-sphere of revolution and toponogov’s comparison theorem,” Tohoku Math. J. 59 (2007), 379-399.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 Composition Operator on the generalize Segal-Bargmann space

Tapanee Kittinatgumtorn and Areerak Chaiworn

Department of Mathematics, Faculty of Science Burapha University, Chonburi 20131 Thailand [email protected] and [email protected] Abstract In this paper, we de_ne and study some property of the composition operator on the generalize Segal-Bargmann space.We also prove a necessary and sufficient condition for the bounded composition operator on the generalize Segal-Bargmann space.

Keywords: composition operator; Generalize Segal-Bargmann space

References

[1] Benchawan, S., 2000. Certain of the domains of multiplication and di_erentiation operators on a generalized Segal- Bargmann space. Bangkok: Chulalongkorn University. [2] Brian, C. 1998. Basic of Holomorphic function space. In: Holomorphic Methods in Analysis and Mathematical Physics., pp. 1-10. [3] Brown, J.w.,& Churchill, R.V. 2004. Analytic functions.In: Complex variables and applications., pp. 33-35. [4] Carswell, B.,& MacCluer, B.D.,& Schuster, A. 2003. Composition Operators on the Fock Space. Acta Sci.Math.(Szeged)., 69(3-4), 871-887. [5] Ueki, S. 2006. Weighted Composition Operator on the Fock Space. Amer.Math.Soc., 135(5), 1405-1410. [6] Wicharn, L. Notes on Functional Analysis. Bangkok: Chulalongkorn University.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 Skew Polynomials and Some Generalizations of Circulant Matrices

Prarinya Morrakutjinda and Somphong Jitmana,*

aDepartment of Mathematics, Faculty of Science, Silpakorn University, Nakhon Pathom 73000, Thailand

Abstract Two generalizations of classical circulant matrices over the field of complex numbers are introduced, namely, conjugatecirculant and conjugate-negacirculant matrices. An n ×n matrix A over is said to be conjugate-circulant (resp., conjugatenegacirculant) if

z0 z 1... znn 2 z 1 (z )  ( z ) ...  ( z )  ( z ) n1 0 n  3 n  2

A ( zn2 )  ( z n  1 ) ...  ( z n  4 )  ( z n  3 )   n1 n  1 n  1 n  1 (z1 )  ( z 2 ) ...  ( zn 1 )  ( z 0 )

z0 z 1... znn 2 z 1 (z )  ( z ) ...  ( z )  ( z ) n1 0 n  3 n  2

(resp., A(  zn2 )  (  z n  1 ) ...  ( z n  4 )  ( z n  3 ) )   n1 n  1 n  1 n  1 (z1 )  (  z 2 ) ...  (  zn 1 )  ( z 0 ) where zi  and (a) a denotes the complex conjugate. Such matrices become the classical circulant and negacirculant(skew circulant) matrices if ξ is replaced by the identity map. Some properties of skew polynomials over are proved. The characterization of the set of all n ×n conjugate-circulant matrices over (resp., the set of all n ×n conjugatenegacirculant matrices over ) is determined in terms of skew polynomials over .

Keywords: skew polynomials; circulant matrices; negacirculant matrices

References [1] M. T. Chu, Q. Guo. On the inverse eigenvalue problem for real circulant matrices, preprint, 1992. [2] P. M. Cohn, Skew Fields: Theory of General Division Rings, Cambridge University Press; 1995. [3] P. J. Davis., Circulant Matrices, Chelesa publishing, New York, second edition; 1994. [4] L. Fuyong. The inverse of circulant matrix. Applied Mathematics and Computation 2011;217:8495-8503. [5] J. Li, Z. Jiang, F. Lu. Determinants, Norms, and the Spread of Circulant Matrices with Tribonacci and Generalized Lucas Numbers. Hindawi Publishing Corporation 2014;2014:Article ID 381829(9 pages). [6] G. Sburlati. On prime factors of determinants of circulant matrices. Applied Mathematics and Computation 2010;432:100-106.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 Some inequalities via power series approach

Presarin Tangsiridamronga and Kanit Mukdasaib,*

aDepartment of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand E-mail: [email protected] bDepartment of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand E-mail: [email protected]

Abstract This research proposes the power series technique, weighted arithmetic mean-geometric mean (AM-GM) inequality, rearrangement inequality and Bernoulli’s inequality for proving and discovering new inequalities.

Keywords: power series approach, weighted arithmetic mean-geometric mean inequality, rearrangement inequality, Bernoulli’s inequality

References [1] Cirtoaje V. Problem 2983. Crux Mathematicorum, 7; 2004, p.430 [2] Cloud M J, Drachman B C. Inequalities with Applications to Engineering. New York: Springer; 1998. [3] Ghorpade S R, Limaye B V. A Course in Calculus and Real Analysis. New York: Springer; 2006. [4] Mortici C. A power series approach to some inequalities. Amer Math Monthly, 119(2); 2012, p.147-15

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 Numerical Study of Turbulent Convection in Oblique-Ribbed Tube Somchai Sripattanapipata and Pongjet Promvongeb

aDepartment of Mechanical Engineering, Faculty of Engineering, Mahanakorn University of Technology, Bangkok 10530, Thailand bDepartment of Mechanical Engineering, Faculty of Engineering, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand

Abstract This paper presents a numerical study on heat transfer and flow characteristics in a heat exchanger tube with two oblique-rib pairs (RP) placed on opposite tube walls. Water as the working fluid flows into the ribbed tube having a constant wall temperature condition with Reynolds numbers between 3000 and 18,000. The computations are based on the finite volume method with the SIMPLE algorithm for handling the pressure and velocity coupling. The computation reveals that the appearance of two pairs of counter-rotating vortices caused by the RPs can induce impingement/attachment flows on rib and tube wall region resulting in greater increase in the heat transfer rate. In addition, an effect of rib parameters such as relative rib height (e/D) and relative rib pitch (PR) on flow and thermal characteristics is numerically examined. The use of RP provides considerably higher thermal performance than the circular tube alone.

Keywords: Numerical simulation; Heat transfer; Oblique ribs; Turbulent flow References [1] Webb R.L., Kim N.H., Principles of Enhanced Heat Transfer, 2nd ed. New York: Taylor Francis; 2005. [2] Webb R., Narayanamurthy R., Thors P., Heat transfer and friction characteristics of internal helical-rib roughness, J. Heat Transf. 2000;122:134-142. [3] Pal S., Saha S.K., Laminar fluid flow and heat transfer through a circular tube having spiral ribs and twisted tapes, Exp. Therm Fluid Sci. 2015; 60:173-181. [4] Wang L., Sunden B., An experimental investigation of heat transfer and fluid flow in a rectangular duct with broken V-shaped ribs, Exp.Heat. Transf. 2004; 17:243-259. [5] Meng J.A., Liang X.G., Li Z.X., Field synergy optimization and enhanced heat transfer by multi-longitudinal vortexes flow in tube, Int. J Heat Mass Transf. 2005; 48:3331-3337. [6] Li X.W., Yan H., Meng J.A., Li Z.X., Visualization of longitudinal vortex flow in an enhanced heat transfer tube, Exp. Therm. Fluid Sci.2007; 31:601-608. [7] Tang X.Y., Zhu D.S., Flow structure and heat transfer in a narrow rectangular channel with different discrete rib arrays, Chem. Eng.Process. 2013; 69:1-14. [8] Kathait P.S., Patil A.K., Thermo-hydraulic performance of a heat exchanger tube with discrete corrugations, Appl. Therm. Eng. 2014;66:162-170. [9] Moon M.A., Park M.J., Kim K.Y., Evaluation of heat transfer performances of various rib shapes, Int. J. Heat Mass Transf. 2014; 71:275-284. [10] Xie G., Liu J., Ligrani P.M., Sunden B., Flow structure and heat transfer in a square passage with offset mid-truncated ribs, Int. J. Heat Mass Transf. 2014; 71:44-56. [11] Wang H., Lee W., Chan J., To S., Numerical and experimental analysis of heat transfer in turbulent flow channels with two- dimensional ribs, Appl. Therm. Eng. 2015; 75:623-634. [12] Versteeg H.K., Malalasekera W., An Introduction to Computational Fluid Dynamics: The Finite Volume Method, Longman Scientific & Technical, Longman Group Limited; 1995. [13] Promvonge P., Changcharoen W, Kwankaomeng S. and Thianpong C., Numerical heat transfer study of turbulent square-duct flow through inline V-shaped discrete ribs, Int. Commun. Heat Mass Transf., 2011; 38:1392–1399

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 FURTHER RESULTS ON PATH-(SUPER)MAGIC TREES

T.K. Maryati and O. Suhyanto

Mathematics Education Department, Faculty of Tarbiyah and Teachers Training, Syarif Hidayatullah State Islamic University (UIN) Jakarta, Jl. Ir. H. Djuanda 95, Ciputat 15412, Indonesia E-mail: [email protected]; [email protected].

Abstract A simple graph G = (V,E ) admits a path-covering if every edge in E belongs at least to one subgraphs of G isomorphic to a given path Ph . Then the graph G is called to be Ph -magic if there exists a total labeling ’ ’ ’ f: V E  {1,2,..., V  E } such that for each subgraph P h = (V ,E ) of G isomorphic to Ph , f(v) f ( e ) v V e E is constant. When f( V ) {1,2,..., V } , then G is said to be Ph - supermagic . In this paper, we study the path-(super )magic behavior of several classes of trees and consider another path-(super )magic tree conjecture.

Keywords: path-covering , path-(super )magic, total labeling.

REFERENCES [1] K. Carlson, “Generalized books and -snakes are prime graphs”, Ars Combinatoria, 80, 215-221 (2006). [2] H. Enomoto, A. Llado, T. Nakamigawa, and G. Ringel, “Super edge magic graphs”, SUT Journal of Mathematics, 34, 105-109 (1998). [3] J.A. Gallian, “A dynamic survey of graph labeling”, Electronic Journal of Combinatorics 17 #DS6 (2014) [4] A. Gutierrez and A. Llado, “Magic coverings”, Journal of Combinatorial Mathematics and Combinatorial Computing, 55, 43-56 (2005). [5] P. Jeyanthi and P. Selvagopal, “Some C4-supermagic graphs”, Ars Combinatoria, Vol.111, 129-136 (2013). [6] A. Kotzig and A. Rosa, “Magic valuations of finite graphs”, Canadian Mathematical Bulettin, 13 (4), 451-461 (1970). [7] S.M. Lee and Q. X. Shan, “All trees with at most 17 vertices are super edge-magic”, 16th MCCCC Conf., Carbondale, University Southern Illinois, Nov. (2002). [8] A. Lladó and J. Moragas, “Cycle-magic graphs”, Discrete Mathematics, 307 (23), 2925-2933 (2007). [9] T.K. Maryati, E.T. Baskoro, and A.N.M. Salman, “Ph-(super)magic labelings of some trees”, Journal of Combinatorial Mathematics and Combinatorial Computing, 65, 197-204 (2008). [10] T.K. Maryati, E.T. Baskoro, A.N.M. Salman, and Irawati, “On the path-(super)magicness of a cycle with some pendants”, Utilitas Mathematica 96, 319-330 (2015). [11] T.K. Maryati, A.N.M. Salman, and E.T. Baskoro, “Supermagic coverings of the disjoint union of graphs and amalgamations”, Discrete Mathematics, 313, 397- 405 (2013). [12] T.K. Maryati, A.N.M. Salman, E.T. Baskoro, and Irawati, “On Ph-supermagic labelings of cPn”, The Proceedings of The 14th National Conference of Mathematics, 281-285 (2009). [13] T.K. Maryati, A.N.M. Salman, E.T. Baskoro, J. Ryan, and M. Miller, “On H-supermagic labelings for certain shackles and amalgamations of a connected graph”, Utilitas Mathematics, 83, 333-342 (2010). [14] A.A.G. Ngurah, A.N.M. Salman, and L. Susilowati, “H-supermagic graphs”, Discrete Mathematics, 310, No. 8, 1293-1300 (2010). [15] A.A.G. Ngurah, A.N.M. Salman, and I.W. Sudarsana, “On supermagic coverings of fans and ladders”, SUT Journal of Mathematics, 46, No. 1, 67-78 (2010). [16] G. Ringel, and A. Llado, “Another tree conjecture”, Bull. Inst. Combin. App., 18, 83-85 (1996). [17] A. Rosa, “On certain valuations of the vertices of a graph”, Theory of graphs (Internat. Symposium, Rome, July 1966). Gordon and breach, N.Y. and Dunod Paris 349-355 (1967). [18] M. Roswitha, and E.T. Baskoro, “H-magic covering of some classes of graphs”, AIP Conf. Proc. On ICREM5, ITB Bandung, 1450, 135-138 (2012). [19] M. Roswitha, E.T. Baskoro, T.K. Maryati, N.A. Kurdhi, and I. Susanti, “Further Result on Cycle-Supermagic Labeling”, AKCE International Journal of Graphs and Combinatorics, 10, No. 2, 1-10 (2013).

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[20] A.N.M. Salman and A.D. Purnomo, “Some cycle-(super)magic labelings of some complete bipartite graphs”,East-West Journal of Mathematics, 283-291 (2010). [21] W.D. Wallis, Magic Graphs, (2001) Birkhäuser and Boston

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015 COMPARISON BETWEEN NATURAL NEIGHBOR INTERPOLATION METHOD AND SPLINE INTERPOLATION METHOD OF ARCGIS IN SALINE LEVELS IN BANDA ACEH AFTER ONE DECADE OF TSUNAMI DISASTER

Muslima , Richa Yusima Maulizab

aDepartment of Mathematics, Faculty of Math & Natural Sciences, Syiah Kuala University E-mail: [email protected] bDepartment of Informatics, Faculty of Math & Natural Sciences, Syiah Kuala University E-mail: [email protected]

ABSTRACT Banda Aceh lies between 05016'15 "- 05036'15" North Latitude and 96016'15"-95022'35" East Longitude with an average height above sea level of 0.80 meter. This city is located in coastal areas. An earthquake measuring 8.9 magnitude by the devastating tsunami have caused considerable damage including an increase in the salinity of the sea water and its intrusion into inland and the river. The area is initially ground water turns into salty water. This study aims to map the salinity of the brine in Banda Aceh 10 years after the disaster, using Natural Neighbor Interpolation Method and Interpolation Spline Method available in ArcGIS. Calculation of both methods is compared to some point samples taken in the field.The result is Natural Neighbor interpolation method more accurate than the results of Interpolation Spline method. Classification of the good water is: freshwater 0.01% -0.05%, semi salty water 0.05% - 1.8% and salty water 1.8% -2.97%. Based on Natural Neighbor interpolation method, the fresh water that is still fit for consumption are in districts of Baiturrahman, Lueng Bata, Ulee Kareng and Kuta Alam.Whereas with Spline Interpolation method, pure water is located in the District of Banda Raya, Kuta Alam, Kuta Raja and Syiah Kuala. On the other hand, salty water is located in the district of Kuta Raja, Meuraxa and Jaya Baru resulted by Natural Neighbor Interpolation method. Main while, Spline Interpolation method results the majority of salty water is in the district of Kuta Raja.

Keywords: Salinity, Interpolation, Natural Neighbor, Spline, ArcGis.

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015

THE EFFECT OF WOLBACHIA INFECTION IN DENGUE TRANSMISSION MODEL WITH AGE- DEPENDENT SURVIVAL RATES

Asep K. Supriatna

Department of Mathematics, Padjadjaran University, Sumedang 45363, Indonesia E-mail: [email protected]

Abstract

In this paper a mathematical model in the form of a system of integral equations, describing the transmission of dengue disease between human and mosquitoes, are proposed and analyzed. Age-dependent functions are used to describe the survival of individuals in human and mosquitoes populations. In this case, decreasing of mosquito’s life expectancy and biting rate are assumed to reﬂect a wolbachia bacterial infection into the mosquito population. The dengue basic reproduction number is derived and analyzed. The results showed that there is a threshold determining the existence of the non-trivial endemic equilib- rium, which is also the same threshold for its stability. We also re-establish the well known rule of thumb of the minimum vaccination coverage to control a disease in the context of vector-borne disease with age-dependent survival rates. Further we discuss the eﬀect of the presence of wolbachia infection in the basic reproduction number and its consequence in the transmission of the disease. The presence of wolbachia is potential as a biological control agent to eliminate the dengue in human population. We compare the strategy of wolbachia introduction with the existing strategy such as vaccination.

Keywords: system of integral equations, dengue disease, wolbachia infection, biological control

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015

EVALUATION OF PROCESSES GOVERNING GROUNDWATER SALINIZATION IN AN EPHEMERAL COASTAL FLOOD PLAIN: GULF OF KHAMBHAT, INDIA

Pankaj Kumar1*, Srikantha Herath1, Ram Avtar1

1United Nations University, Institute for the Advanced Study of Sustainability (UNU-IAS) 5-53-70, Shibuya-ku, Tokyo 150-8925, Japan

E-mail address - [email protected]*

ABSTRACT

Intense agricultural and industrial activities along with indiscriminate exploitation of groundwater, are likely to make it vulnerable with respect to its quality especially in coastal areas. This work strives to evaluate the sources of groundwater salinization/mineralization in the Gulf of Khambhat, Western India with the help of integrated approach for analysis of major ions and stable isotopes. This work is vital considering Gulf of Khambhat as one of the major harbor for business trading and groundwater is the only source for domestic consumption. Integration of various ion plots and graphs, saturation index values (obtained from PHREEQC Code), GIS and different statistical operation (factor analysis and principle component analysis) was useful to deduce spatial variation in respective water quality parameters. Stable isotopes are useful tools to help us understand recharge processes and to differentiate between salinity origins. Result suggests that leaching of wastes disposed from anthropogenic activities and intensive agriculture with indiscriminate use of fertilizers leads to salt enrichment in groundwater from central part of the plain, while unplanned extraction and other groundwater development influences migration of saltwater into freshwater aquifers of the coastal part of the plain. From stable isotopic results, it was found that most of sample points plotted near the local meteoric water line (LMWL) i.e. origin of ground water is meteoric in principle; however point away from the LMWL might favors exchange with rock minerals. The results could constitute an important background for decision makers to take the suitable countermeasures for sustainable water resources management.

Key words: Gulf of Khambhat, Coastal aquifer, Ground water, salinization

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The 11th IMT-GT International Conference on Mathematics, Statistics and Its Applications 2015

EXPONENTIAL STABILITY OF AN COUPLED SYSTEM FOR THE VIBRATIONS MODELED BY THE STANDARD LINEAR SOLID MODEL WITH A THERMAL EFFECTS

Octavio Vera Villagran

Department of Mathematics, Faculty of Science, Bio-Bio University, Concepcion, Chile E-mail: [email protected] , [email protected]

Abstract

We consider a coupled system of vibrations modeled by the standard linear solid model of viscoelasticity which are coupled to a heat equation modelling an expectedly dissipative e ect through heat conduction. We show that the exponential stability under the Fourier law of heat conduction holds. We establish the well-posedness and the exponential stability using multiplier techniques.

Keywords: C0-semigroup. Coupled system. Exponential stability.

References [1] M. S. Alves, C. Buriol, M. V. Ferreira, J. E. Mu~noz Rivera, M. Sep_ulveda, O. Vera, \Exponential stability for the vibrations modeled by the standard linear model of viscoelastic type," Journal Mathematics. Analysis and Applications, 399, 472-479(2013). [2] G. C. Gorain, \stabilization for the vibrations modeled by the standard linear model of viscoelasticity," Proc. Indian Acad. Sci., 120(4), 495-506 (2010).

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List of Invited Speakers and Participants

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NUMBER OF PARTICIPANTS BY UNIVERSITY

1 CHILE BIBO-BIO UNIVERSITY, Concepcion 1 2 CZECH REPUBLIC BRNO UNIVERSITY OF TECHNOLOGY, CZECH 2 REPUBLIC 3 INDONESIA 13 GADJAH MADA UNIVERSITY 1 INSTITUT TEKNOLOGI BANDUNG 4 PADJADJARAN UNIVERSITY 1 SILIWANGI UNIVERSITY 1 SYARIF HIDAYATULLAH ISLAMIC STATE 2 UNIVERSITY SYIAH KUALA UNIVERSITY 4 4 JAPAN 4 GIFU COLLEGE OF NURSING 1 TOKAI UNIVERSITY 1 UNIVERSITY OF ELECTRO-COMMUNICATIONS 1 UNITED NATIONS UNIVERSITY 1 5 MALAYSIA 7 INTERNATIONAL ISLAMIC UNIVERSITY MALAYSIA 1 UNIVERSITI KEBANGSAAN MALAYSIA 3 UNIVERSITI SAINS MALAYSIA 1 UNIVERSITI UTARA MALAYSIA 1 UNIVERSITY OF MALAYA 1 6 PAKISTAN QUAID-E-AWAM UNIVERSITY NAWABSHAH 1 7 POLAND POZNAN UNIVERSITY OF TECHNOLOGY 1 8 RUSSIAN FEDERATION BELGOROD STATE NATIONAL RESEARCH 1 UNIVERSITY (BELSU)

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9 THAILAND 79 BURAPHA UNIVERSITY 1 CHANDRAKASEM RAJABHAT UNIVERSITY 1 CHIANG MAI UNIVERSITY 1 CHULALONGKON UNIVERSITY 4 KASETSART UNIVERSITY 3 KHON KAEN UNIVERSITY 6 KING MONGKUT'S INSTITUTE OF TECHNOLOGY 43 LADKRABANG KING MONGKUT'S UNIVERSITY OF TECHNOLOGY 1 THONBURI NATIONAL INSTITUTE OF DEVELOPMENT 1 ADMINISTRATION PRINCE OF SONGKLA UNIVERSITY 2 SILPAKORN UNIVERSITY 5 SURANAREE UNIVERSITY OF TECHNOLOGY 1 THAMMASAT UNIVERSITY 9 UBON RATCHATHANI RAJABHAT UNIVERSITY 1 10 TURKEY YILDIZ TECHNICAL UNIVERSITY 2 11 UNITED ARAB EMIRATES 5 UNITED ARAB EMIRATES UNIVERSITY 3 AMERICAN UNIVERSITY OF SHARJAH 2 Total 116

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LIST OF INVITED SPEAKERS AND PARTICIPANTS ADILAN WIDYAWAN MAHDIYASA INSTITUT TEKNOLOGI BANDUNG, INDONESIA AHMED AL-RAWASHDEH UNITED ARAB EMIRATES UNIVERSITY, UNITED ARAB EMIRATES ALFI YUSROTIS ZAKIYYAH INSTITUT TEKNOLOGI BANDUNG, INDONESIA AMMAR ALSABERY UNIVERSITI KEBANGSAAN MALAYSIA, MALAYSIA ANTON ABDULBASAH KAMIL UNIVERSITI SAINS MALAYSIA, MALAYSIA APHINAT NINSRI THAMMASAT UNIVERSITY, THAILAND ARCHARA PACHEENBURAWANA THAMMASAT UNIVERSITY, THAILAND AREERAK CHAIWORN BURAPHA UNIVERSITY, THAILAND ARIYA UNCHAI KHON KAEN UNIVERSITY, THAILAND ASEP K. SUPRIATNA PADJADJARAN UNIVERSITY, INDONESIA BETY HAYAT SUSANTI INSTITUT TEKNOLOGI BANDUNG, INDONESIA BOONYARIT CHOOPRADIT PRINCE OF SONGKLA UNIVERSITY, THAILAND BUSAYAMAS PIMPUNCHART KING MONGKUT'S INSTITUTE OF TECHNOLOGY LADKRABANG, THAILAND CHANIN SRISUWANNAPA KING MONGKUT'S INSTITUTE OF TECHNOLOGY LADKRABANG, THAILAND CHIDCHANOK LURSINSAP CHULALONGKON UNIVERSITY, THAILAND CHIRANYA SURAWUT UBON RATCHATHANI RAJABHAT UNIVERSITY, THAILAND CHUCKAPHUN ARAMPHONGPHUN KASETSART UNIVERSITY, THAILAND

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DECHA SAMANA KING MONGKUT'S INSTITUTE OF TECHNOLOGY LADKRABANG, THAILAND DOUNGRAT CHITCHAREON CHANDRAKASEM RAJABHAT UNIVERSITY, THAILAND DUSADEE SUKAWAT KING MONGKUT'S UNIVERSITY OF TECHNOLOGY THONBURI, THAILAND ELVIRA KUSNIYANTI INSTITUT TEKNOLOGI BANDUNG, INDONESIA GUNTAPHON TASSANASOPHON THAMMASAT UNIVERSITY, THAILAND HABIBIS SALEH UNIVERSITI KEBANGSAAN MALAYSIA, MALAYSIA HIDENORI OGATA UNIVERSITY OF ELECTRO-COMMUNICATIONS, JAPAN HIZIR SOFYAN SYIAH KUALA UNIVERSITY, INDONESIA I-MING TANG KASETSART UNIVERSITY, THAILAND ISHAK HASHIM UNIVERSITI KEBANGSAAN MALAYSIA, MALAYSIA ISNAINI ROSYIDA GADJAH MADA UNIVERSITY, INDONESIA JAIPONG KASEMSUWAN KING MONGKUT’S INSTITUTE OF TECHNOLOGY LADKRABANG, THAILAND JOSEF DIBLIK BRNO UNIVERSITY OF TECHNOLOGY, CZECH REPUBLIC KAMONPAD MANSILP KING MONGKUT’S INSTITUTE OF TECHNOLOGY LADKRABANG, THAILAND KAMPANAT NAMNGAM KING MONGKUT’S INSTITUTE OF TECHNOLOGY LADKRABANG, THAILAND KANAWOOT SUBKLAY KINGMONGKUT'S INSTITUTE OF TECHNOLOGY LADKRABANG, THAILAND KANCHANA KUMNUNGKIT KING MONGKUT’S INSTITUTE OF TECHNOLOGY LADKRABANG, THAILAND KANIT MUKDASAI KHON KAEN UNIVERSITY, THAILAND

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KANNANUT CHAMSRI KING MONGKUT’S INSTITUTE OF TECHNOLOGY LADKRABANG, THAILAND KAZUHIRO OZAWA GIFU COLLEGE OF NURSING, JAPAN KRITTIDEJ CHANTHAWARA UBONRATCHATHANI RAJABAT UNIVERSITY, THAILAND KUMPONSAK BOONGOY KING MONGKUT’S INSTITUTE OF TECHNOLOGY LADKRABANG, THAILAND LAZHAR BOUGOFFA AL-IMAM IBN SAUD ISLAMIC UNIVERSITY, SAUDI ARABIA M MIFTAHUDDIN SYIAH KUALA UNIVERSITY, INDONESIA MAHAVEER GADIYA SAVITRIBAI PHULE PUNE UNIVERSITY, INDIA MANUNCHAYA NOOWATTANA THAMMASAT UNIVERSITY, THAILAND MARZUKI ABUBAKAR SYIAH KUALA UNIVERSITY, INDONESIA MİRSAT YEŎİLTEPE YILDIZ TECHNICAL UNIVERSITY, TURKEY MOHAMED ALI HAJJI UNITED ARAB EMIRATES UNIVERSITY, UNITED ARAB EMIRATES MOHAMMAD ALMAHAMEED IRBID NATIONAL UNIVERSITY, JORDAN MOHAMMED AL-REFAI UNITED ARAB EMIRATES UNIVERSITY, UNITED ARAB EMIRATES MUHAMMET KURULAY YILDIZ TECHNICAL UNIVERSITY, TURKEY MUSLIM MUSLIM SYIAH KUALA UNIVERSITY, INDONESIA NATHAPHON BOONNAM PRINCE OF SONGKLA UNIVERSITY, SURAT THANI CAMPUS NATITA WANGSOH KING MONGKUT'S UNIVERSITY OF TECHNOLOGY THONBURI NATTAWUT PONGNU KINGMONGKUT'S INSTITUTE OF TECHNOLOGY LADKRABANG, THAILAND

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