5th INTERNATIONAL CONFERENCE ON RECENT ADVANCES IN PURE AND APPLIED MATHEMATICS, TRABZON, TURKEY 23-27 JULY 2018
Abstract Book
i
5th INTERNATIONAL CONFERENCE ON RECENT ADVANCES IN PURE AND APPLIED MATHEMATICS, TRABZON, TURKEY 23-27 JULY 2018
Abstract Book
List of Major Sponsors
• Karadeniz Technical University • The Turkish Academy of Sciences (Türkiye Bilimler Akademisi – TÜBA)
ii 5th INTERNATIONAL CONFERENCE ON RECENT ADVANCES IN PURE AND APPLIED MATHEMATICS, TRABZON, TURKEY, 23-27 JULY 2018
Honorary Chairs of Scientific Committee
Prof. Dr. B. E. Rhoades, USA Prof. Dr. H. M. Srivastava, Canada Prof. Dr. Ljubisa Kocinac, Serbia Prof. Dr. Mubariz Tapdigoglu Garayev, Saudi Arabia Prof. Dr. Sadek Bouroubi, Algeria Prof. Dr. Ali M. Akhmedov, Azerbaijan Prof. Dr. Werner Varnhorn, Germany Prof. Dr. Emine Mısırlı, Turkey Prof. Dr. Huseyin Cakalli, Turkey Prof. Dr. G. Das, India Prof. Dr. M. Perestyuk, Ukraine Prof. Dr. O. Boichuk, Ukraine Prof. Dr. I. Shevchuk, Ukraine Prof. Dr. Anatoliy M. Samoilenko, Ukraine Prof. Dr. V. Guliyev, Turkey Prof. Dr. M. Abbas, S.Africa Prof. Dr. M. Mursaleen, India Prof. Dr. W. Sintunavarat, Thailand Prof. Dr. V. Kalantarov, Turkey Prof. Dr. Cihan Orhan, Turkey Prof. Dr. Metin Basarir, Turkey
Organizing Committee
Prof. Dr. Ekrem Savas, Uşak Commerce University Prof. Dr. Hamdhllah Şevli, Istanbul Commerce University Prof. Dr. Necip Şimşek, Istanbul Commerce University Prof. Dr. Ömer Pekşen, Karadeniz Technical University Prof. Dr. Richard Patterson, North Florida University Prof. Dr. Mehmet Gürdal, Suleyman Demirel University Prof. Dr. Martin Bohner, Missouri S&T Prof. Dr. Ram Mohapatra, Uni. of Central Florida Prof. Dr. Fairouz Tchier, King Saud University Prof. Dr. Mehmet Dik, Rockford University Prof. Dr. Lubomira Softova, Second University of Naples Prof. Dr. Agron Tato, Polytechnic Uni. of Tirana Prof. Dr. Debasis Giri, Haldia Institute of Technology Prof. Dr. Naim Braha, Uni. of Prishtina Assoc. Prof. Dr. Rahmet Savas, Istanbul Medeniyet University Assoc. Prof. Dr. Erhan Deniz, Kafkas University Assoc. Prof. Dr. Mahpeyker Ozturk, Sakarya University Assoc. Prof. Dr. Bahadır Özgür Güler, Karadeniz Technical University Assoc. Prof. Dr. İdris Ören, Karadeniz Technical University ASsists. Prof. Dr. Ali Hikmet Değer, Karadeniz Technical University Assist. Prof. Dr. Gokhan Cuvalcioglu, Mersin University Assist. Prof. Dr. Emel Asici, Karadeniz Technical University Assist. Prof. Dr. Arzu Akgul, Kocaeli University Assist. Prof. Dr. Hafize Gumus, Necmettin Erbakan University Assist Prof. Dr. Veli Capali, Usak University Dr. Lakhdar Ragoub, Alyammah University
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5th INTERNATIONAL CONFERENCE ON RECENT ADVANCES IN PURE AND APPLIED MATHEMATICS, TRABZON, TURKEY, 23-27 JULY 2018
Local Organizing Committee
Abdurrahman Buyukkaya, Karadeniz Technical University Melek Eriş Büyükkaya, Karadeniz Technical University Ümmü Gülsüm AKBABA, Karadeniz Technical University Fatih Yilmaz, Karadeniz Technical University Rabia Savas, Sakarya University Sefa Anil Sezer, Istanbul Medeniyet University Tuğba Yıldırım, Istanbul Technical University Ekber Girgin, Sakarya University Neslihan Kaplan Kuru, Sakarya University Madiha Rashid, Pakistan Bouchra Ben AMMA, Morocco
Scientific Committee
Prof. Dr. Huseyin Cakalli, Turkey Prof. Dr. Charles Swartz, USA Prof. Dr. Jeff Connor, USA Prof. Dr. Yagub A. Sharifov, Azerbaijan Prof. Dr. Lubomira Softova, Italy Prof. Dr. Niyazi A. Ilyasov, Azerbaijan Prof. Dr. Reza Langari, USA Prof. Dr. Aref Jeribi, Tunisia Prof. Dr. Mikail Et, Turkey Prof. Dr. Husamettin Coskun, Turkey Prof. Dr. S. A. Mohiuddine, S. Arabia Prof. Dr. Maria Zeltser, Estonia Prof. Dr. Narendra Kumar Govil, USA Prof. Dr. Kamalmani Baral, Nepal Prof. Dr. T. A. Chishti, India Prof. Dr. Ants Aasma, Estonia Prof. Dr. Ayhan Serbetci, Turkey Prof. Dr. Ismail N. Cangul, Turkey Prof. Dr. Bilal Altay, Turkey Prof. Dr. Murat Tosun, Turkey Prof. Dr. Ismail Ekincioglu, Turkey Prof. Dr. Yilmaz Simsek, Turkey Prof. Dr. A. Sinan Cevik, Turkey Prof. Dr. Harry Miller, Bosnia Prof. Dr. Leiki Loone, Estonia Prof. Dr. Ali Fares, France Prof. Dr. Akbar B. Aliyev, Azerbaijan Prof. Dr. Ibrahim Canak, Turkey Prof. Dr. Vali M. Gurbanov, Azerbaijan Prof. Dr. Naim Braha, Kosova Prof. Dr. Faqir M. Bhatti, Pakistan Prof. Dr. Mustapha Cheggag, Algeria Prof. Dr. Said Melliani, Morocco Prof. Dr. Fahrettin Abdullayev, Kırgizistan Prof. Dr. Abdalah Rababah, Jordan Prof. Dr. Praveen Agarwal, India Prof. Dr. Radouane Yafia, Morocco Prof. Dr. P. D. Srivastava, India Prof. Dr. Sudarsan Nanda, India Prof. Dr. Mehmet Akbaş Prof. Dr. Seyit Temir, Turkey Prof. Dr. Erhan Coşkun Prof. Dr. Halit Orhan, Turkey Prof. Dr. Funda Karaçal Prof. Dr. Vatan Karakaya, Turkey Prof. Dr. Vasile Berinde Prof. Dr. Amir Khosravi, Iran Prof. Dr. Haskız Coşkun Prof. Dr. Seifedine Kadry, Kuwait Prof. Dr. Erdal Karapınar Prof. Dr. Ali M. Akhmedov, Azerbaijan Prof. Dr. Sultan Yamak Prof. Dr. Ziyatkan Aliyev, Azerbaijan Prof. Dr. Selçuk Han Aydın Prof. Dr. Poom Kumam, Thailand Assoc. Prof. Ayhan Aydın Prof. Dr. Agacik Zafer, Kuwait Assoc. Prof. Dr. Yasemin Sağıroğlu Prof. Dr. Tunay Bilgin, Turkey Assoc. Prof. Dr. Tülay Kesemen Prof. Dr. Gangaram S. Ladde, USA Assoc. Prof. Dr. Azhar Hussain Prof. Dr. Claudio Cuevas, Brazil Assoc. Prof. Dr. Bayram Ali Ersoy, Turkey Prof. Dr. Abdelmejid Bayad Assist. Prof. Vishnu Narayan Mishra, India Prof. Dr. Amiran Gogatishvili Assist. Prof. Dr. Hafize Gök Prof. Dr. Oktay Duman Assist. Prof. Dr. Sukran Konca Prof. Dr. Abdelmejid Bayad Dr. Dr.K.V.L.N. Acharyulu
iv Prof. Dr. Naila Rozi, Pakistan Dr. Lejla Miller Van-Wieren, Bosnia Prof. Dr. Emine Can, Turkey Dr. Mayssa Alqurashi, S. Arabia Prof. Dr. Hemen Dutta, India Dr. Fardous Taoufic, S. Arabia Prof. Dr. Reza Saadati, Iran Dr. Ammar Edress Mohamed, Iraq Prof. Dr. Salih Aytar, Turkey
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Dear Collogues; First of all I wish to offer you a warm welcome to the fifth International Conference on Recent Advances in Pure and Applied Mathematics (ICRAPAM 2018). The last conference of this series was organized in Kusadası, Turkey, during 11-15 May 2017 and it was attended by 350 scientists from 48 different countries, contributing 300 oral presentations and 50 posters. As the past conference, the aim of this conference is to provide a platform for mathematicians to present their recent Works, exchange ideas and new methods in several important areas of Mathematics and to provide an opportunity to improve collaboration between local and international participants in the wonderful historic city of Istanbul. Further we believe that, the development in various fields of Mathematics lead to new research areas in Mathematics and the richness of the new results can also provide basis for interdisciplinary collaborations. That is why; we have planned to provide a common forum for scientists to communicate their original results in various fields of analysis and applied mathematics. We would like to thank all the invited speakers who have kindly accepted our invitation and have come to spend their precious time by sharing their ideas during the conference. Finally, we would also like to thank all of the members of the Scientific Advisory Committee and the Organizing Committee of this conference. Again we would like to convey our heartiest welcome to each of you who have come to attend this conference and we wish for an enjoyable high scientific level conference and hope to meet you again in the future. With our best wishes and warm regards,
Prof. Dr. Ekrem SAVAS Chair of the Conference
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5th INTERNATIONAL CONFERENCE ON RECENT ADVANCES IN PURE AND APPLIED MATHEMATICS, TRABZON, TURKEY, 23-27 JULY 2018
INVITED TALKS
The Distance Between Two Sets and its1 Amazing Applications in Science and Technology 1 Prof. Dr. Vasile Berinde
Totally boundedness and uniform continuity via quasi Cauchy sequences 3 Prof. Dr. Huseyin Cakalli
Weighted norm inequalities for positive operators restricted on the cone of ρ-quasiconcave 4 functions Prof. Dr. Amiran Gogatishvilili
Cofactor Matrix Theory 5 Prof. Dr. Robin Harte
Indispensable remarks on some recent results in metric fixed point theory 6 Prof. Dr. Erdal Karapınar
Symmetry Methods and Conservation Laws for Differential Equations 8 Prof. Dr. Chaudry Masood Khalique
Best Uniform Approximation with 2n+1 Equioscillations 9 Prof. Dr. Abedallah Rababah
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5th INTERNATIONAL CONFERENCE ON RECENT ADVANCES IN PURE AND APPLIED MATHEMATICS, TRABZON, TURKEY, 23-27 JULY 2018
LIST OF TALKS
Multi-layer perceptrons with Levenberg-Marquardt training algorithm for predicting of heavy metals 10 concentrations in marine sediment Abdelaziz Abdallaoui, Kaoutar Elazhari, Hicham El Badaoui
Quarterly prediction of water consumption using some statistical methods. A comparative study 12 Qais Mustafa Abdulqader
Extremal polynomials and their approximation properties in complex plane 13 Fahreddin Abdullayev, Gülnara Abdullayev
On Modular Happy Numbers 15 Raghib Abusaris
Distances from Unbounded Trajectories to their Limit-Strings on a Hadamard Kȁhler Manifold 16 Toshiaki Adachi
The Generating Functions of Recurrence Relation of the Path of Minimal Length on Suborbital Graphs 17 Ümmügülsün Akbaba, Ali Hikmet Değer, Tuğba Tuylu
Portfolio Selection by Fuzzy Linear Programming 19 Serkan Akbaş, Türkan Erbay Dalkılıç
Performance Comparison of Fuzzy Clustering Approaches on Burn Region Detection 20 Yeşim Akbaş, Tolga Berber
Fekete-Szego Functional Problem For A New Class Of M-Fold Symmetric Analytic Functions 21 Arzu Akgül
Continued Fractions and Exact Hermite matrices 22 Tülay Ayyıldız Akoğlu
The Arrowhead-Pell Sequences in Finite Groups 23 Yeşim Aküzüm, Taha Doğan, Ömür Deveci
Boundedness of potential operators in modified Morrey spaces defined on Carleson curves 24 Canay Aykol
Robust PCA-Algorithms for Detection of Metagenomic Biomarkers 26 Mustafa Alshawaqfeh, Ahmad Bashaireh, Jan Suchodolski, Erchin Serpedin, Khalid Qaraqe
Estimates of Faber polynomial coefficients for an unified class of bi-univalent functions defined through 28 the Jackson (p,q)-derivative operator Şahsene Altınkaya, Sibel Yalçın
Total Lighting Level in the e-Studio and Polynomial Interpolation 29 Hamit Armağan, Tuncay Yiğit, Mevlüt Ersoy
Spherical fuzzy sets and its representation of spherical fuzzy ť-norms and ť-conorms 31 Shahzaib Ashraf, Saleem Abdullah
viii On some spectral problems of boundary value problem with boundary condition containing spectral 32 parameter Nigar Aslanova, Mamed Bayramoglu, Khalig Aslanov
Generalizing the order obtained from nullnorms 34 Emel Aşıcı
Numerical Treatment of Second Order Fuzzy Two-Point Boundary Value Problems 35 Basem S. Attili
On Fuzzy Metric Space of Continuous Function 37 Ebru Aydoğdu, Abdülkadir Aygünoğlu, Halis Aygün
Flip Bifurcation Analysis in a Discrete Bacteria Population Model 38 Ercan Balcı, Senol Kartal
Analysis of a Pneumonia Transmission Model with Random Components 39 Zafer Bekiryazici, Tulay Kesemen, Mehmet Merdan
Using Two-Layer Models for Flexible Pavement Sizing 41 Mouloud Belachia, Nadjette Bouacha
A Solution Approach for Multiobjective Probability Maximization Problems 43 Fatima Bellahcene
A Nonsmooth Newton Method for Solving a State Constrained Optimal Control Problem Governed by 44 Convection-Diffusion Equation Boubakeur Benahmed, Kheira Mostepha Hanchour
Properties of The Bianchi Groups and Digraphs 46 Murat Beşenk, Serkan Kader, Bahadır Özgür Güler
A New Solution of the Einstein-Maxwell Equations with Linear Equation of State 47 Rashida Bibi, Azad A. Siddiqui
Characterizations of extremal graphs for some bounds on k-domination number 48 Ahmed Bouchou, Mohmed Zemir, Mostafa Blidia
Global dynamics of a Fractional model for viral infection with adaptive immunity 49 Adnane Boukhouima, Khalid Hattaf, Noura Yousfi
On BCB protocol 51 Sadek Bouroubi
Some properties of modified new Szasz-Mirakyan operators in polynomial weight spaces via power 52 summability method Naim L. Braha
The Cardinal and Idempotent Number of Order-preserving and A-increasing Finite Transformations 54 Semigroup Leyla Bugay
Best Proximity Point Theorems for Generalized Contractions 55 Abdurrahman Büyükkaya, Mahpeyker Öztürk
On The Estimator of Semi-Markovian Inventory Model with Subexponential Component 56 Melek Eriş Büyükkaya, Aslı Bektaş Kamışlık, Tülay Kesemen, Tahir Khaniyev
Projective covariant α-completely positive linear maps 58 Tania Luminita Costache
ix Determination of a coefficient in a second-order hyperbolic problem 60 Arzu Erdem Coşkun
On the Existence and Uniqueness of Solutions for a First And Second-Order Discrete Boundary Value 62 Problem Arzu Erdem Coşkun, Ali Demir
Instability Intervals for Hill’s Equation with Symmetric Double Well Potential 64 Haskız Coşkun, Elif Başkaya
Analysis of Neutron Capture Cross Section Using Systematics of Different Level Density Model 65 Veli Çapalı
On the extensions of triangular norms and triangular conorms 66 Gül Deniz Çaylı
On Suborbital Graphs and Related Sequences 68 Ali Hikmet Değer, Ümmügülsün Akbaba, Tuğba Tuylu
Characterizations of Lipschitz spaces via commutators of fractional maximal operator in Orlicz spaces 69 Fatih Deringöz
Convergence Theorems on Measure Space of Exhaustive 70 Doris Doda
A New view of L-ideals on Semigroups 71 Emine Funda Ekinci, Sultan Yamak
Design and Application of Fractional Order Predictor for Unglazed Transpired Solar Collector 72 Köksal Erentürk, Saliha Erentürk
Determination of the Effective moisture Diffusivities in Convective Drying Systems of Banana using 74 Fractional Order Estimator Saliha Erentürk, Köksal Erentürk
On Nullnorms On Bounded Lattices 76 Ümit Ertuğrul
About the Grundy coloring critical graphs 77 Noureddine Ikhlef-Eschouf f - Statistical Boundedness of Order α 78 Mikail Et, Hüseyin Sönmez
The influence of fluid pressure on the displacement of the basilar membrane 79 Aboulkhouatem Fatima-Ezzahra
Change of the Cochlear Michromechanics model due to fluid presure 80 Kouilily Fatiha
Optimal scientific production over the life cycle 81 Gustav Feichtinger, Dieter Grass, Peter M. Kort
The Extended b-Metric Space and Related Fixed Point Results 82 Andreea Fulga
Suborbital Graphs For a Special Subgroup of the Normalizer 83 Nazlı Yazıcı Gözütok, Bahadır Özgür Güler
퐺퐿(푛, ℝ) Invariants For a Curve Family 85 Uğur Gözütok, Yasemin Sağıroğlu
x Conditions for Ruled Surfaces Obtained by Bending to be Developable 86 Uğur Gözütok, Hüsnü Anıl Çoban, Yasemin Sağıroğlu
Some Generalizations of Ricci Solitons Admitting Standard Static Spacetime Metric 87 Sinem Güler
Rough I - Statistical Convergence of Weight g 88 Hafize Gümüş
The concept of I-Asymptotically Lacunary Statistical Equivalence of Interval Numbers and A 89 Generalization With A Positive 푝 Sequence Hafize Gümüş, Nihal Demir
Exact Solution of Some Nonlinear Partial Differential Equation 90 Hami Gündoğdu, Ömer Faruk Gözükızıl
On Invariance of Hyperstoneanness under Lattice Isomorphisms 91 Banu Güntürk, Bahaettin Cengiz
Nanofluid flow due to rotating disk with variable thickness andhomogeneous-heterogeneous reactions 92 Tasawar Hayat, Madiha Rashid, Maria Imtiaz, Ahmed Alsaedi
Spectral Theory of q,ω -Dirac System 93 Fatma Hıra
Self-Organizing Map of Artificial Neural Networks for superficial sediments classification of the Sidi 94 Chahed dam (NE of Meknes, Morocco) Abdellah El Hmaidi, Mohamed Berrada, Abdelaziz Abdallaoui, Ali Essahlaoui, Abdelhadi El Ouali
Zero Operator Products on Hardy and Bergman spaces 95 Mualla Birgül Huban, Mübariz Garayev, Mehmet Gürdal
Compactness and Engliś Algebra 96 Mualla Birgül Huban, Mübariz Garayev, Mehmet Gürdal
Solvability of Infinite Systems of Differential Equations in Some BK Spaces 97 Merve İlkhan, Emrah Evren Kara
Dissipative Canonical Type Quasi-Differential Operators for First Order 98 Zameddin I. Ismailov, Pembe Ipek Al
Some Spectral Problems of Direct Sums of Operators 99 Zameddin I. Ismailov, Elif Otkun Çevik
New Exact Travelling Wave Solution of the Generalized Ito Integro-Differential Equation 100 Anwar Jaafar Mohamad Jawad
A Radon-Nikodym type theorem for completely positive multilinear ϕ-maps on Hilbert C*-modules 101 Maria Joita
Approximating Fixed Points of Certain Nonlinear mappings in CAT(0) Spaces 103 Amna Kalsoom, Hafiz Fukhar ud Din
A Parallel Multiobjective Evolutionary Algorithm with an application to the Knapsack Problem 105 Nedjmeddine Kantour, Sadek Bouroubi, Djamel Chaabane
Some Properties of t-closure Operators 106 Funda Karaçal, Mehmet Akif İnce
The Kinematic Model of Nonuniform Rotation of Liquid Medium 108 Zurab Kereselidze, Marina Chkhitunidze, Irine Khvedelidze, Nino Zhonzholadze
xi Generalized Jensen-Mercer Inequality for Functions with Nondecreasing Increments 109 Asif R. Khan, Sumayyah Saadi
Approximating Min Graphic k-Path TSP with no Prespecified Path Endpoints 111 Rezika Kheffache k- Generalized Pell Numbers and Its Properties 112 Havva Kırgız, Kemal Uslu
Exact and Nonstandard Finite Difference Schemes for the Generalized KdV-Burgers Equation 113 Canan Köroğlu, Ayhan Aydın
Some Studies on Congruence Equations using Suborbital Graphs 114 Tuncay Köroğlu, Zeynep Şanlı, Bahadır Özgür Güler, Murat Beşenk
On L1 - Convergence of Certain Cosine and Sine modified sums 115 Xhevat Krasniqi
Fixed Point Theorems for α-F-Suzuki Contraction Mapping with Rational Expressions in Branciari b- 116 Metric Spaces Neslihan Kaplan Kuru, Mahpeyker Öztürk
About the packing chromatic number in graphs 117 Rachid Lemdani
Some characterizations of the homogeneous ruled real hypersurface in a complex hyperbolic space 118 Sadahiro Maeda
Precise long-term prediction of behavior in a 3-D chaotic map 119 M. Mammeri
Constructing 3-D maps with complex chaotic phenomena 120 M. Mammeri
Sequential structures of statistical manifolds on deformed exponential families 122 Hiroshi Matsuzoe
Approximate solutions of the inverse problem without a priori information on the exact solution 123 Yuri Menshikov
Modelling Asymmetric Magnetic Recording Heads With a Soft Underlayer Using Multiple Images Method 124 Ammar Edress Mohamed
Coefficient bound estimates for beta-starlike functions of order alpha 126 Nizami Mustafa, Veysel Nezir
On the coefficient bounds of gamma and beta starlike functions 128 Nizami Mustafa, Veysel Nezir, Mustafa Ateş
Application of the Chebyshev polynomials to coefficient estimates of analytic functions 129 Nizami Mustafa, Veysel Nezir, Erdi Akbulut
On the coefficient bounds of certain subclasses of analytic functions of complex order 130 Nizami Mustafa, Veysel Nezir, Tarkan Öztürk
Some Results on Classical 2-Absorbing Submodules 131 Osama A. Naji
Fixed point properties for a degenerate Lorentz-Marcinkiewicz space 132 Veysel Nezir, Nizami Mustafa
xii Renorming c0 and affine fixed point property 134 Veysel Nezir, Nizami Mustafa, Tahsin Ateş,
Infinite dimensional subspaces of a degenerate Lorentz-Marcinkiewicz space with the fixed point property 135 Veysel Nezir, Nizami Mustafa, Merve Delibaş
Applying Fourier Analysis to Computing New variables for Determining SNR 136 Sajedeh Norozpour, Cem Ergün
On Nordenian Properties of the Riemannian extension 138 Filiz Ocak
Numerical Solution of Nonlinear Singular Ordinary Differential Equations Arising in Biology via 139 Operational Matrix of Bernstein Polynomials Sunday Adeyemi Olagunju, Peter Vanenchii Ayoo
On Ciric Type Contractions in Modular Spaces 141 Mahpeyker Öztürk
Some fixed point results concerning F-contractions in complete metric space 142 Alexandrina Maria Proca
Fixed point theorem for F-contraction type and applications to polynomial approximations 144 Abdalah Rababah, Hichem Ramoul, Nora Mahloul
Metric Properties of Fuzzy Curves and Fuzzy Invariants 145 Yasemin Sağıroğlu, Djavvat Khadjiev, Uğur Gözütok
Hamiltonicity and pancyclicity of superclasses of claw-free graphs 146 Abdelkader Sahraoui
On some evolution problems of degenerate type 147 Moulay Mohamed Said
Average approximate Sentinel for an Identification problem 148 S. Sandel, A.Berhail, A. Ayadi
λ – Double Statistical Convergence and Strongly Double Summable Functions of Weight g 150 Rabia Savaş, Mahpeyker Öztürk
On Infinite Matrices and Sequence Spaces 151 Rahmet Savaş
Numerical methods for certain classes of Markovian BSDEs and quasi-linear parabolic PDEs 152 Driss Seghir
Integral Type Darbo's Fixed Point Theorem via Sequences of Functions 153 Derya Sekman, Vatan Karakaya
Normal Differential Operators for Degenerate First-Order 154 Meltem Sertbaş, Fatih Yılmaz
Converse Theorems for the Discrete Power Series Methods of Summability 155 Sefa Anıl Sezer, İbrahim Çanak
α – Fuzzified Rough Set Model in Multigranulation Space 156 Tanzeela Shaheen
A Note on Generalized Bernstein-type Cheney-Sharma Operators 157 Dilek Söylemez, Fatma Taşdelen Yeşildal, Gülen Başcanbaz Tunca
xiii Evaluating Gaussian Fuzzy System Reliability 158 Halil İbrahim Şahin, Melek Eriş Büyükkaya
Smoothed Auxiliary Function With Multiple Extrema In Global Optimization 159 Ahmed Şahiner, Shehab A. Ibrahem
Application of Modern Optimization Techniques in Determination of the Academic Achievement 160 Ahmet Şahiner, Sumeyya Koman, Raziye Akbay Uçar
Radiation Shielding Properties of Borided Fe-Ni Binary Alloys by Fuzzy Logic Modelling 161 Ahmet Şahiner , Nazım Uçar , Adnan Çalık, Gülden Kapusuz
Temperature and pressure based estimation of daily global solar radiation over Turkey using fuzzy logic 162 modeling Ahmet Şahiner, Idris A. Masoud Abdulhamid, Murat Ozturk
Normalizer of Some Congruence Subgroups 164 Zeynep Şanlı, Tuncay Köroğlu, Bahadır Özgür Güler
̂2 Boundary Component of the Group Γ0 (N) 165 Hatice Şengül, Mehmet Akbaş
GUI-EFG: Guided Element Free Galerkin Method 166 Süleyman Şengül, Erhan Coşkun
On the Matrix Nearness Problem of the Generalized Sylvester Quaternion Matrix Equations 167 Sinem Şimşek
Korovkin Type Theorems in Modular Spaces via Summability Methods 168 Emre Taş, Tuğba Yurdakadim
Pollution Detection for the Singular Linear Parabolic Equation 169 Laıb Teldja, Ayadi Abdelhamid
Relation of Some Special Vertices of Suborbital Graphs and Continued Fractions 170 Tuğba Tuylu, Ali Hikmet Değer, Ümmügülsün Akbaba
Bounds for Atom-bond Connectivity Index 171 Ahmet Uğur, Ayşe Dilek Maden
Travelling waves in diffusion, aggregation and diffusion-aggregation-diffusion in a single population 172 Judith Pérez Velázquez, Faustino Sanchez-Garduno
On a Integral-Transform to Differential Equations 173 Ervenila Xhaferraj
Aczél Type Inequalities for Hilbert Space Operators 174 Ulaş Yamancı, Mehmet Gürdal
On the Artinianness of Top Local Cohomology Modules 175 Tuğba Yıldırım q-Quasinormal Operators and Its Extended Eginvalues 176 Fatih Yılmaz, Meltem Sertbaş
A New Algorithm Based on Penalty Function Approach for Inequality Constrained Global Optimization 177 Problems Nurullah Yılmaz, Ahmet Şahiner
On Fuzzy Prime Hyperideals(Hyperfilters) in ∧ - Hyperlattices 178 Şerife Yılmaz, Dilek Bayrak
xiv Korovkin Theory for Extraordinary Test Functions via Power Series Method 179 Tuğba Yurdakadim, Emre Taş
Criticality indices of 2-independence of some graphs 180 Mohamed Zemir, Ahmed Bouchou
xv
INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
The Distance Between Two Sets and its Amazing Applications in Science and Technology
Vasile Berinde Department of Mathematics and Computer Science, Technical University of Cluj-Napoca Baia Mare, Romania
Abstract: The distance between two sets has been introduced at the beginning of the XXth century by the successive contribution of D. Pompeiu (1873-1954), M. Frechet (1878-1973) and F. Hausdorff (1878-1942). The importance of this fundamental concept came rather late in mathematics (about 1940) and even later in applied sciences and technology but nowadays it is widely used in almost all research areas. The list of applications of what is generally known as Hausdorff metric and less often as Pompeiu-Hausdorff metric is really impressive as it is nowadays an indispensable mathematical tool in almost all fields of research, not only in mathematics and computer science, as shown for example by a search in Web of Science, where we find about 2800 articles covering more than 100 different research fields in which Pompeiu-Hausdorff metric is used. Amongst the research fields with the most research articles found in WoS database we mention: mathematics; mathematics applied; computer science artificial intelligence; engineering electrical electronic; computer science theory methods; computer science software engineering; imaging science photographic technology; computer science information systems; radiology nuclear medicine medical imaging; computer science interdisciplinary applications; engineering biomedical; statistics probability; automation control systems; telecommunications; operations research management science; mathematics interdisciplinary applications; remote sensing; mathematical computational biology; computer science cybernetics; multidisciplinary sciences etc. Amongst other research fields covered, we also mention: neurosciences; psychology mathematical; engineering civil; peripheral vascular disease; acoustics; nanoscience nanotechnology; biochemical research methods; metallurgy metallurgical engineering; engineering manufacturing; evolutionary biology; geography physical; education scientific disciplines; clinical neurology;
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org transportation science technology; transportation; biology; physics particles fields; management; microscopy; engineering biomedical; economics; dentistry oral surgery medicine; medical laboratory technology; water resources; green sustainable science technology; physics fluids plasmas; engineering marine; neuroimaging; electrochemistry; geochemistry geophysics; education educational research; engineering aerospace; chemistry analytical; biotechnology applied microbiology; astronomy astrophysics; social sciences mathematical methods; ergonomics; health care sciences services; environmental studies; environmental sciences; engineering petroleum; biochemistry molecular biology; engineering ocean; energy fuels; engineering chemical; computer science hardware architecture; construction building technology; endocrinology metabolism; ecology; dermatology; oceanography; crystallography; information science library science; cell biology; geography; business; oncology; genetics heredity; architecture etc. The main aim of this paper is to present some essential facts about Pompeiu- Hausdorff metric and to illustrate its importance and use in various fields of research by means of some relevant examples.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Totally boundedness and uniform continuity via quasi Cauchy sequences Huseyin Cakalli Maltepe University, Department of Mathematics, Graduate School of Science and Engineering, Istanbul, Turkey Abstract: A subset E of a metric space X is totally bounded if and only if any sequence of points in E has a quasi Cauchy subsequence, where a sequence (xn) is quasi-Cauchy if the sequence (d(xn+1, xn)) is a null se- quence. A function f from a totally bounded subset of a metric space X into a metric space Y preserves quasi Cauchy sequences if and only if it is uniformly continuous, i.e. (f (xn)) is a quasi Cauchy sequence whenever (xn) is a quasi Cauchy sequence of points of E. Keywords: quasi cauchy sequence, totally boundedness. References: [1] D. Burton, and J. Coleman, Quasi-Cauchy Sequences, Amer. Math. Monthly 117, 4, 328-333, (2010). [2] H.C¸ akallı, Sequential definitions of compactness, Appl. Math. Lett. 21 6, 594-598, (2008) [3] H. C¸ akallı, Forward continuity, J. Comput. Anal. Appl. 13, 2, 225- 230, (2011). [4] H. C¸ akallı, Statistical quasi-Cauchy sequences, Math. Comput. Modelling, 54, no. 5-6, 1620-1624, (2011). [5] H. C¸ akallı, Statistical ward continuity, Appl. Math. Lett. 24, 10, 1724-1728, (2011). [6] H. C¸ akallı, On G-continuity, Comput. Math. Appl. 61, 2, 313-318, (2011). [7] H.C¸ akallı, Sequential definitions of connectedness, Appl. Math. Lett. 25 3, 461-465(2012) [8] O. Mucuk, T. S¸ahan On G-Sequential Continuity, Filomat, 28, 6, 1181-1189, (2014). [9] R.W. Vallin, Creating slowly oscillating sequences and slowly oscillating continuous functions, With an appendix by Vallin and H. Cakalli, Acta Math. Univ. Comenianae, 25, 1, 71-78, (2011). ______3
INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Weighted norm inequalities for positive operators restricted on the cone of ρ-quasiconcave functions
Professor Amiran Gogatishvilili Institute of Mathematics Czech Academy of Sciences [email protected]
Abstract: In the talk I present a reduction theorems for weighted inequalities restricted on the cone of quasiconcave functions to slightly different inequalities, consider for all non-negative measurable functions. By using these reduction theorems will present the characterization of the weighted Hardy-type inequality restricted on the cone of quasiconcave functions.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Cofactor Matrix Theory
Robin Harte Trinity College, School of Mathematics Dublin 2, Ireland
Abstract: The "cofactor" of a matrix is defined inductively, in the first instance for block triangles. "Cofactor matrix theory" is not so much the theory of the cofactor, but rather a version of matrix theory developed through the medium of the cofactor.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Indispensable remarks on some recent results in metric fixed point theory
Erdal Karapınar Department of Mathematics, Faculty of Art and Science University of Atılım, Ankara, Turkey erdalKarapı[email protected]
Abstract: The main goal of this talk is to indicate some indispensable notes on the recent results in the frame of the metric fixed point theory. Starting with a brief history of metric fixed point theory, we shall emphasize some basic approaches on it. After then, we shall show the equivalence of the metric. Fixed point results that were proved in the setting of different abstract spaces. The talk will be largely expository. References: [1] H. Alsulami, S. Almezel, E. Karapınar, F. Khojasteh, “A note on fixed point results in complex valued metric spaces”, Journal of Inequalities and Applications, (2015), 2015:33 Doi:10.1186/s13660-015-0550-6. [2] R.P. Agarwal, E. Karapınar, D. O'Regan, A.F. Roldan-Lopez-de-Hierro, “Fixed Point Theory in Metric Type Spaces”, Springer International Publishing (2015). [3] R. P. Agarwal, H. Alsulami, E.Karapınar and F.Khojasteh, “Remarks on some recent fixed point results in quaternion-valued metric spaces”, Abstract and Applied Analysis, (2014) Article Id: 171624. [4] S. Banach , “Sur les operations dans les ensembles abstraits et leur applications aux equations integrales”, Fund. Math., 3, 133-181, (1922). [5] R.H. Haghi, Sh. Rezapour, N. Shahzad, “Some fixed point generalizations are not real generalizations”, Nonlinear Analysis: Theory, Methods &Applications, Volume 74, Issue 5, 1 March 2011, 1799-1803. [6] R.H. Haghi, Sh. Rezapour, N. Shahzad, “Be careful on partial metric fixed point results”, Topology and its Applications, Volume 160, Issue 3, 15 February 2013, 450-454.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
[7] J. Jachymski, “Equivalent conditions for generalized contractions on (ordered) metric spaces “, Nonlinear Analysis: Theory, Methods and Applications, Volume 74, Issue 3, 1 February 2011, 768-774. [8] E. Karapınar, W.-S. Du, “A note on b-cone metric and its related results: Generalizations or equivalence?” , Fixed Point Theory and Applications, (2013), 2013:210. [9] A. Roldan, J. Martinez Moreno, C. Roldan, and E. Karapınar, “Some remarks on multidimensional fixed point theorems”, Fixed Point Theory, FixedPoint Theory, 15(2014), No. 2, 545-558. [10] B. Samet, E. Karapınar, H. Aydi, V. Rajic, “Discussion on some coupled fixed point theorems”, Fixed Point Theory and Applications, 2013, 2013:50 (10 March 2013).
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Symmetry Methods and Conservation Laws for Differential Equations
Chaudry Masood Khalique Department of Mathematics, North-West University, Mmabatho, South Africa
Abstract: Symmetry methods were introduced in the latter part of the nineteenth century by the Norwegian mathematician Sophus Lie (1842-1899). Lie was inspired by the works of Galois and Abel. Lie’s work systematically unites the well-known ad hoc methods to construct exact solutions for differential equations. Conservation laws have numerous significant applications in the study of differential equations, particularly for determining conserved quantities and constants of motion. In this talk we present briefly the applications of Lie’s theory and conservation laws to differential equations.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Best Uniform Approximation with 2n+1 Equioscillations Abedallah Rababah Department of Mathematics, Jordan University of Science and Technology, Irbid, Jordan [email protected]
Abstract: For a given continuous function f, the following classical best uniform approximation problem is considered in the literature. Find a polynomial p of degree n s.t. the uniform norm of the resulting error is minimized. The existence is proved by Borel, and the uniqueness is proved by Chebyshev. The solution is characterized by Chebyshev by showing that there exist Chebyshev alternant of n+2 points. I.e. the error equioscillates n+2 times. However, there does not exist a method to find these solutions so far. We consider a smooth curve C rather than only a continuous function f. We ask the following question: Is it possible to find a polynomial p of degree n s.t. the uniform norm of the resulting error is minimized and the error function equioscillates m times, where m>n+2, rather than n+2 times? I.e does there exist an alternant m points s.t. the error equioscillates m times.
In this talk the following conjecture is shown to be valid for a class of curves of measure not equal zero:
Conjecture: For every smooth curve C, there exists a polynomial p of degree n s.t. the uniform norm of the resulting error is minimized and the error function equioscillates 2n+1 times rather than n+2 times. We further show that there exist alternant of 2n points. Keywords: Best uniform approximation, Chebyshev alternant.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Multi-layer perceptrons with Levenberg-Marquardt training algorithm for predicting of heavy metals concentrations in marine sediments
Abdelaziz ABDALLAOUI, Kaoutar ELAZHARI, Hicham EL BADAOUI Department of Chemistry, Analytical Chemistry and Environment Team Moulay Ismail University, Faculty of Science Meknes, Morocco. [email protected]
Abstract: With the ability for classification and generalization, artificial neural networks (ANN) are typically used of treating mathematical problems, in particular in the statistical problems where the variables are non-linear. Today, these neural networks, which are methods of calculation whose design, are inspired schematically the operation of biological neurons, found many applications in several areas, such as image processing, signal processing, optimization and also in the areas of forecasts and predictions. In the present work, we will develop a network model of artificial neurons (ANN) Multilayer Perceptron (MLP) type for the prediction of heavy metals (Fe, Mn and Zn) concentrations in red sea sediments. To determine the architecture of the network to use, we varied the number of hidden layers, the number of neurons in the hidden layer, the transfer functions and learning algorithms. Several statistical criteria such as mean square error (MSE) and the correlation coefficient (R) were evaluated to test the effectiveness of the developed models. The purpose of the study of these statistical criteria is to choose the most relevant neural model and most successful in predicting the heavy metals concentrations from the physicochemical parameters. The originality of this work lies in the application of ANN method for predicting the concentrations of heavy metals, in slices of sediment cores of the Red Sea from the physicochemical parameters. These cores were taken at the axial zone of the Red Sea between 19 ° and 23 ° N. This study showed that predictive models established by the recent method, which is based on the principle of artificial neural network multilayer perceptron ______10
INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org type (PMC) with learning algorithm of Levenberg-Marquardt, perform much better compared to those established by the method based on the multiple linear regression. This performance demonstrates the existence of a nonlinear relationship between physicochemical characteristics (independent variables) and the concentrations of heavy metals (dependent variables) of the Red Sea sediment.
Keywords: Prediction, ANN, MLP, Levenberg-Marquardt algorithm, Heavy metals, Red Sea.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Quarterly prediction of water consumption using some statistical methods. A comparative study
Qais Mustafa Abdulqader Department of Geology of Petroleum and Sediments, Duhok Polytechnic University, Duhok, Zakho, Iraq [email protected]
Abstract: Time-series analyses of water consumption data are important for investigating the amount of water variation and predicting consumption change. Many applications have been done for estimating and predicting water consumption. In this paper, some statistical analysis methods such as Box – Jenkins methodology, wavelet analysis, and artificial neural network have been used for obtaining a suitable model for making quarterly prediction of water consumption in Erbil city, Kurdistan Region of Iraq. The comparison procedure was depending on some statistical criteria. The results of the analysis have been discussed and mentioned.
Keywords: Time Series, Box-Jenkins, Wavelets, Artificial Neural Networks. References: [1] A. H. Nury, K. Hasan, and J. B. Alan " Comparative study of wavelet- ARIMA and wavelet-ANN models for temperature time series data in northeastern Bangladesh", Journal of King Saud University. 29(2017), 47–61. [2] A. Altunkaynak, M. Ozger, and M. Cakmakci " Water Consumption Prediction of Istanbul City by Using Fuzzy Logic Approach ", Water Resources Management 19(2005), 641–654. [3] J. Adamowski, H. F. Chan, S. O. Prasher, B. O. Zielinski, and A. Sluisarieva"Comparison of multiple linear and nonlinear regression, autoregressive integrated moving average, artificial neural network, and wavelet artificial neural network methods for urban water demand forecasting in Montreal, Canada", Water Resources Research, 48(2012), 1-14.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Extremal polynomials and their approximation properties in complex plane
Fahreddin Abdullayev1,2, Gülnara Abdullayev2 ¹Kyrgyz-Turkish Manas University, Bishkek, Kyrgyzstan ²Mersin University , Mersin, Turkey, [email protected] [email protected],
Abstract: Let G C be a finite Jordan region, 0G ; LG:= , 1 =:C\ G . For p 0 let AGp () denote the set of analytic in G functions fz() normalized by f (0)0,= f (0)1= and such that pp ffzd1 :(),= AGp () G where is a two dimensional Lebesgue measure. Let wz= () be the conformal mapping of G onto the disk Bww(0,):{:}00= normalized by (0)0= , (0)1= . Let us consider the following extremal problem for p 0:
−PPnnn 1 →,inf . AGp () In this work, we investigated some approximation properties of the extremal polynomials in different regions of the complex plane. Analogous questions was investigated in [1]-[6] and others. Keywords: Complex approximation, Coformal mapping, Quasiconformal curve References: [1] F.G.Abdullayev, Uniform convergence of the generalized Bieberbach polynomials in regions with non zero angles. Acta Math. Hung. Vol.77, No:3, (1997), pp. 223-246. ______13
INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
[2] F.G.Abdullayev, N.P.Özkartepe, Uniform convergence of the p-Bieberbach polynomials in domains with zero angles, Science China Math, 58 (5), (2015), 1063-1078. [3] V.V. Andrievskii, D. Uniform convergence of Bieberbach polynomials in domains with piecewise quasiconformal boundary (Russian). In: Theory of Mappings and Approximation of Functions. Kiev, Naukova Dumka (1983), pp.3- 18. [4] D.M.Israfilov, Uniform Convergence of the Bieberbach Polynomials in closed smooth domains of bounded boundary rotation, Journal of Approximation Theory, 125, (2003), 116-130. [5] D.Gaier, On the convergence of the Bieberbach polynomials in regions with corners. Constructive Approximation, 4 (1988), pp.289-305. [6] M.V.Keldych, Sur l'approximation en moyenne quadratique des fonctions analytiques. Math.Sb., 5(47), (1939), pp.391-401.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
On Modular Happy Numbers
Raghib Abusaris Department of Epidemiology and Biostatistics, College of Public Health and Health Informatics, King Saud bin Abdelaziz University for Health Science, Riyadh, Saudi Arabia. [email protected]
Abstract: In this paper, we investigate the asymptotic behavior of the sequences generated by iterating the process of summing the modular powers of the decimal digits of a number. In particular, we identify all modular happy numbers. A number is called modular happy if the sequence obtained by iterating the process of summing the modular powers of the decimal digits of the number ends with 1. Keywords: happy numbers, sequences, recurrence relations, difference equations, modular arithmetic.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Distances from Unbounded Trajectories to their Limit-Strings on a Hadamard Kȁhler Manifold
Toshiaki Adachi Department of Mathematics, Nagoya Institute of Technology, Nagoya, Japan [email protected]
Abstract: A smooth curve γ parameterized by its arclength on a Kȁhler manifold
M is said to be a trajectory for a Kȁhler magnetic field Bk = kBJ if it satisfies ′ ∇훾′훾 = 푘퐽훾′. Since it is a geodesic when k = 0, we may regard trajectories as generalizations of geodesics which are deeply concerned with complex structure. By using trajectories, we can define magnetic exponential maps by just the same way as we defined exponential maps by using geodesics. In [1] by studying trajectory-harps which consist of trajectories and variations of geodesics, we showed that they are diffeomorphisms when M is a Hadamard Kȁhler manifold of sectional curvature not greater than a negative constant c and the strength of Kȁhler magnetic field satisfies k2 ≤ |c|. For a Hadamard manifold, it has a geometric compactification with the ideal boundary ∂M which consists of all asymptotic classes of geodesic half-lines. In [2], it was shown that each magnetic exponential map extends to a homeomorphism of a unit tangent sphere to the ideal boundary. Thus, for each trajectory-half line γ, we have a unique geodesic σγ satisfying γ(0)= σ(0) and γ(∞)= σ(∞) in ∂M . In this paper, we study 2 the distance from each point γ(t) on γ to σγ and show that when k < |c| it is 2 bounded and when k = |c| it grows at most linear order. Keywords: Hadamard Kȁhler manifold, ideal boundary, trajectory-harps, limit- strings. References: [1] T. Adachi, “A theorem of Hadamard-Cartan type for Kähler magnetic fields”, J. Math. Soc. Japan, 64(2012), 969-984. [2] Q. Shi & T. Adachi, “Trajectory-harps and horns applied to the study of the ideal boundary of a Hadamard Kähler manifold”, Tokyo J. Math., 40(2017), 223- 236.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
The Generating Functions of Recurrence Relation of the Path of Minimal Length on Suborbital Graphs
Ümmügülsün AKBABA, Ali Hikmet DEĞER and Tuğba TUYLU Karadeniz Technical University Faculty of Science, Department of Mathematics,61080, Trabzon, Turkey. [email protected] [email protected] [email protected]
Abstract: Jones, Singerman and Wicks [1] used the idea of suborbital graphs for finite permutation groups, described by Sims [2], for the congruence subgroup
훤0(푢, 푁) of the modular group 훤. They studied the action of 훤 on the rational projective line by using suborbital graphs. These are 훤 invariant directed graphs with vertex set ℚ̂ and their edge-sets being the orbits of 훤 on the cartesian square ℚ̂ 2 . For each integer which is bigger than 1 and for each of the ф(푁) units (푁) , there is one suborbital graph 퐺푢,푁 with edge-set which is the orbit containing the pair (∞, 푢/푁). Then they extend the properties for 퐺1,1. Farey graphs to suborbital graphs of 퐹푢,푁, where 푢 and 푁 are relatively prime and 푁 is bigger than 1. Relation between continued fractions and vertices of the paths of minimal length on the subgraphs were established and valued of the farthest vertex which a vertex can be found on this path of the suborbital graph 퐹푢,푁 . In this work we study the generating function of the recurrence relation of continued fractions. In previous works we showed that every vertex on the path of minimal length of suborbital graph 퐹푢,푁 has a continued fraction. So this continued fraction generate a recurrence relation. Koshy [5] studied relation between Fibonacci numbers and generating functions. By this motivation we investigate relation between Fibonacci numbers and special vertices. Keywords: Minimal Length, Suborbital Graphs, Generating Functions References: [1] G.A. Jones, D. Singerman and K. Wicks,” The Modular Group and Generalized Farey Graphs”, London Mathematical Society Lecture Note Series 160 (1991), 316-338. ______17
INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
[2] C.C. Sims, “Graphs and Finite Permutation Group”, Mathematische Zeitschrift 95 (1967), 76-86. [3] A.H. Deger, “Vertices of Paths of Minimal Lengths on Suborbital Graphs”, Filomat 31:4(2017), 913-923 [4] A.H. Deger and Ü. Akbaba,”Some Special Values of Vertices of Trees on the Suborbital Graphs”, American Institute of Physics 1926(2018), 020013. [5] T. Koshy, Fibonacci and Lucas Numbers with Applications, A Wiley- İnterscience Publication, Canada, 2001.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Portfolio Selection by Fuzzy Linear Programming
Serkan AKBAŞ Türkan ERBAY DALKILIÇ [email protected] [email protected] Department of Statistics and Computer Science, Karadeniz Technical University, Trabzon, Turkey
Abstract: In this study, a new portfolio selection model based on the analytic hierarchy process was proposed, which would help investors who plans to make the most accurate investment in the face of uncertainties in financial markets. In this context, the weights of the criteria in the study were obtained by the Constrained Fuzzy AHP method proposed by Enea and Piazza. A fuzzy linear programming model is proposed in which the cost variables in the objective function is fuzzy. A portfolio selection problem existing in the literature is discussed to examine the effectiveness of the proposed model. The results obtained from the existing methods and the results obtained from the proposed model were compared.
Keywords: Fuzzy linear programming, Fuzzy AHP, Portfolio selection References: [1] Y.J. Lai and C.L. Hwang, “A new approach to some possibilistic linear programming problems”, Fuzzy Sets Syst., 49, 2, (1992), 121-133. [2] M. Enea and T. Piazza, “Project selection by constrained fuzzy AHP”, Fuzzy Optim. Decis. Mak. 3, 1, (2004), 39-62. [3] F. Tiryaki and B. Ahlatcioglu “Fuzzy portfolio selection using fuzzy analytic hierarchy process”, Inf. Sci. (Ny)., 179, 1-2, (2009), 53-69. [4] J. Krejčí, O. Pavlačka and J. Talašová, “A fuzzy extension of Analytic Hieararchy Process based on the constrained fuzzy arithmetic”, Fuzzy Optim. Decis. Mak. 16, 1, (2017), 89-110.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Performance Comparison of Fuzzy Clustering Approaches on Burn Region Detection
Yeşim AKBAŞ Tolga BERBER [email protected] [email protected] Department of Statistics and Computer Science, Karadeniz Technical University, Trabzon, Turkey Abstract: The World Health Organization reported that the annual number of deaths caused by burn wounds was 180.000 in 2017. Hence, it is important to develop utilities to help diagnosis of burn wounds. There are many parameters needed to be determined in the planning phase of burn treatment. Percentage of burn wound is the one of the most important parameters. In this study, performance of fuzzy clustering methods was assessed to identify burnt and normal skin lesions in burn images, which is required to determine the actual burn percentage. We selected 19 sample images from the burn wound image dataset, which is being developed using images of the patients who applied to the burn unit of the Karadeniz Technical University Faculty of Medicine Farabi Hospital. Fuzzy C-Means (FCM) and Gustafson Kessel (G-K) algorithms were applied to sample images for this task. We performed exhaustive series of experiments to find the optimal number of clusters for the selected sample images, with the help of fuzzy cluster validity indices for all clusters within C = [3, 9]. In addition, we conducted experiments to measure effects of Gauss filter with different levels of sigma on burn region identification task. Finally, results of our experiments are presented and discussed in detail. Keywords: Burn images, Fuzzy Clustering Methods References: [1] Shankar, A. S., Asokan, A. ve Sivakumar, D., Brain Tumor Classification Using Gustafson-Kessel (G-K) Fuzzy Clustering Algorithm Int. J. Latest Eng. Res. Appl., 1, 5 (2016) 68–72. [2] Dunn, J. C., A Fuzzy Relative of the ISODATA Process and Its Use in Detecting Compact Well-Separated Clusters J. Cybern., 3, 3 (1974) 32–57. [3] Bezdek, J. C., A Convergence Theorem for the Fuzzy ISODATA Clustering Algorithms IEEE Trans. Pattern Anal. Mach. Intell., PAMI-2, 1 (1980) 1–8. [4] Moertini, V. S., Introduction to Five Data Clustering Algorithms Integral, 7, 2 (2002) 87–96. ______20
INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Fekete-Szego Functional Problem For A New Class Of M-Fold Symmetric Analytic Functions
Arzu Akgül Department of Mathematics, Kocaeli University, Kocaeli, Turkey [email protected]
Abstract: In this paper, we investigate a new subclass consisting of analytic and m-fold symmetric bi-univalent functions satisfying subordination in the open unit disk U. We consider the Fekete-Szegö inequalities for this class. Also, we establish estimates for the coefficients for this subclas and several related classes are also considered and connections to earlier known results are made. Keywords: Analytic functions, m-fold symmetric bi-univalent functions, Coefficient bounds. References: [1] A. Akgül, On the coefficient estimates of analytic and bi-univalent m-fold symmetric functions, Mathematica Aeterna, 7 (3), 2017, 253 – 260 [2] S. Altınkaya and S. Yalçın, Coefficient Bounds for Certain Subclasses of m- Fold Symmetric Biunivalent Functions, Journal of Mathematics , Volume 2015, (2015) , 5 pages. [3] D. A. Brannan and J. Clunie, Aspects of contemporary complex analysis, Proceedings of the NATO Advanced Study Instute Held at University of Durham, New York: Academic Press, (1979). [4] D. A. Brannan and T. S. Taha, On some classes of bi-univalent functions, in Mathematical Analysis and Its Applications (S. M. Mazhar, A. Hamoui and N. S. Faour, Editors) (Kuwait; February 18.21, 1985), KFAS Proceedings Series, Vol. 3, Pergamon Press (Elsevier Science Limited), Oxford, 1988, pp. 53.60; see also Studia Univ. Babes¸-Bolyai Math. 31 (2) (1986), 70.77. [5] J.H.Choi, Y. C. Kim, and T. Sugawa, .Ageneral approach to the Fekete- Szegö problem, Journal of the Mathematical Society of Japan, vol. 59,no. 3, pp. 707.727, 2007.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Continued Fractions and Exact Hermite matrices
Tülay Ayyıldız Akoğlu Department of Mathematics, Karadeniz Technical University, Trabzon, Turkey [email protected]
Abstract: The aim of this study is to present a symbolic-numeric method to construct exact rational Hermite matrices using continued fractions. Efficient numerical methods can solve polynomial systems if the given system is well- posed. However, in most applications, only the knowledge of the location of the real roots are desired. The signature of Hermite matrices is defined by Hermite in 1856 [1], and this signature can provide important information on the location of the real roots [2]. In this study, we use approximate solutions and continued fractions to construct the exact Hermite matrix of the given polynomial system. This construction is used for root certification purposes [3,4], and it works even if the given system is not well-posed. This is joint work with Agnes Szanto (North Carolina State University). Keywords: Symbolic Computation, Continued Fractions, Polynomial Systems. References: [1] C. Hermite, "Extrait d'une lettre de Mr. Ch. Hermite de Paris à Mr. Borchardt de Berlin sur le nombre des racines d'une équation algébrique comprises entre des limites données." Journal für die reine und angewandte Mathematik 52 (1856): 39-51 [2] S. Basu, R. Pollack and M. Roy, “Algorithms in real algebraic geometry”, Springer (2007). [3] T. Ayyildiz Akoglu, J. D. Hauenstein, A. Szanto, “Certifying solutions to overdetermined and singular polynomial systems over Q”, Journal of Symbolic Computation (2018), 147--171. [4] J.D. Hauenstein and F. Sottile, “Algorithm 921: alphaCertified: certifying solutions to polynomial systems”, ACM Trans. Math. Software 38 (2012), 28:1--28:20
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
The Arrowhead-Pell Sequences in Finite Groups
¹ Yeşim Aküzüm, 2 Taha Doğan and 3Ömür Deveci 1,2,3 Department of Mathematics, Faculty of Science and letters, Kafkas University, Kars-Turkey [email protected], [email protected], [email protected]
Abstract: In [1], Akuzum and Deveci defined the arrowhead-Pell sequences and obtain miscellaneous properties of these sequences. In this work, we redefine the arrowhead-Pell sequences by means of the elements of groups which is called arrowhead-Pell-orbit. Then we examine the arrowhead-Pell-orbit of the finite groups in detail. Finally, we obtain the periods of the arrowhead-Pell orbit of the semidihedral group SD as applications of the results obtained. 2m Keywords: Sequence, Orbit, Group. Acknowledgement:This Project was supported by the Commission for the Scientific Research Projects of Kafkas University. The Project number. 2017- FM-21 References: [1] Y. Akuzum and O. Deveci, “The arrowhead-Pell sequences”, is submitted.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Boundedness of potential operators in modified Morrey spaces defined on Carleson curves
Canay Aykol Department of Mathematics, Ankara University, Ankara, Turkey
Abstract: In this talk we study the potential operator I , 0 1 in the ~ modified Morrey space L p, () and the spaces BMO() defined on 1− Carleson curves . We prove that for 1 p the potential operator ~ is bounded from the modified Morrey space to L q, () if and in 1 1 the case of infinite curve only if − , and from the spaces p q 1−
~ ~ L1, () to WL q, () if and in the case of infinite curve only if 1 1− 1 1− . Furthermore, for the limiting case p we q 1− show that if is an infinite Carleson curve, then the modified potential operator
~ I is bounded from to , and if is a finite Carleson curve, then the operator is bounded from to , Keywords: Carleson curves, modified Morrey spaces, BMO spaces, potential operators, Sobolev-Morrey inequality. References: [1] V.S. Guliyev, M.N. Omarova, M.A. Ragusa, A. Scapellato, ‘’Commutators and generalized local Morrey spaces,’’ Journal of Mathematical Analysis and Applications, 457 n.2, doi: 10.1016/j.jmaa.2016.09.070, (2018), 1388-1402. ______24
INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
[2] V. Kokilashvili, ‘’Fractional integrals on curves’’, (Russian) Trudy Tbliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. SSR, 95 (1990), 56-70. [3] V. Kokilashvili, S. Samko, ‘’Sobolev theorem for potentials on Carleson curves in variable Lebesgue spaces,’’ Mem. Differential Equations Math. Phys. 33 (2004), 157-158. [4] N. Samko, ‘’Weighted Hardy and singular operators in Morrey spaces’’, J. Math. Anal. Appl., 350 (2009), no. 1, 56-72.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Robust PCA-Algorithms for Detection of Metagenomic Biomarkers
Mustafa Alshawaqfeh, Ahmad Bashaireh, Jan Suchodolski, Erchin Serpedin and Khalid Qaraqe ECEN Department, Texas A&M University, College Station, USA [email protected]
Abstract: Recent progress in sequencing technologies have enabled the characterization of the microbial communities inhabiting the human body. In the same time, many metagenomic studies have suggested using microbial taxa as potential biomarkers for certain diseases. There are two major challenges associated with the design and the performance assessment of biomarker detection algorithms. The first challenge is to assess the reproducibility performance of an algorithm and to design algorithms that exhibit consistent results. The second challenge is due to the fact that microbial communities exhibit complex interactions among their constituent members. This renders the univariate algorithms that treat these features individually ineffective in capturing such complex dependencies. In this work, we propose a new metric to determine the reproducibility performance of the biomarker detection algorithms. Such a metric is referred to as the normalized common-feature consistency. To capture the reproducibility performance probabilistically, we propose also a framework to estimate its distribution based on random resampling. We also propose a robust principal component analysis (RPCA) based algorithm for biomarker detection. This is achieved by modeling the metagenomic data matrix as a superposition of a low-rank matrix depicting the abundance levels of the irrelevant bacteria and a sparse matrix capturing the abundance levels of the bacteria that are differentially abundant between different phenotypes. Comprehensive comparisons of RPCA with the state-of-the-art algorithms on two realistic datasets are conducted. Our preliminary results in [1]-[2] show that RPCA consistently outperforms the other algorithms in terms of classification accuracy and reproducibility performance. Keywords: bioinformatics, PCA, biomarker, detection
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
References: [1] M. Alshawaqfeh, A. Bashaireh, E. Serpedin and J. Suchodolski, “Consistent metagenomic biomarker detection via robust PCA”, Biology Direct, 12.4(2017). [2] M. Alshawaqfeh, A. Bashaireh, E. Serpedin and J. Suchodolski, “Reliable biomarker discovery from metagenomics data via RegLRSD algorithm,” BMC Bioinformatics, 18:328(2017).
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Estimates of Faber polynomial coefficients for an unified class of bi-univalent functions defined through the Jackson (p,q)- derivative operator
Şahsene Altınkaya1 and Sibel Yalçın2 1Department of Mathematics, Uludag University, [email protected] 1Department of Mathematics, Uludag University, [email protected]
Abstract: In this work, we introduce and investigate an unified class of bi- univalent functions defined through the Jackson (p,q)-derivative operator. Furthermore, by using the Faber polynomial expansions, we obtain upper bounds for the coefficients of functions belonging to this analytic and bi-univalent function class. Keywords: Bi-univalent functions, subordination, Faber polynomials, Jackson (p,q)-derivative operator. References: [1] H. Airault, “Remarks on Faber polynomials”, Int. Math. Forum, 3 (2008), 449-456. [2] H. Airault and H. Bouali, “Differential calculus on the Faber polynomials”, Bulletin des Sciences Mathematiques, (2006), 179-222. [3] R. Chakrabarti and R. Jagannathan, A (p,q)-oscillator realization of two- parameter quantum algebras, J. Phys. A: Math. Gen, 24 (1991) L711–L718. [4] P.L. Duren, “Univalent Functions”, New York: Grundlehren der Mathematischen Wissenschaften, Springer, 1983. [5] Ş. Altınkaya and S. Yalçın, “Faber polynomial coefficient estimates for Bi- univalent functions of complex order based on subordinate conditions involving of the Jackson (p,q)-derivative, Miskolc Mathematical Notes, 18 (2017), 555- 572.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Total Lighting Level in the e-Studio and Polynomial Interpolation
Hamit ARMAĞAN, Tuncay YİĞİT, Mevlüt ERSOY 1 Suleyman Demirel University, Dept. of Informatics, Isparta, Türkiye, [email protected] 2 Süleyman Demirel Üniversitesi, Engineering Faculty, Dept. of Computer Engineering, Isparta, Türkiye 3 Süleyman Demirel Üniversitesi, Engineering Faculty, Dept. of Computer Engineering, Isparta, Türkiye
Abstract: e-Studio is a platform that provides active participation of students who take lessons from universities/institutions that provide online (synchronous) training for distance education. This is a model designed and developed to increase the success of distance education by using and adapting educational technology at the highest potential in this environment (Turkish Patent Institute, Design Registration Number: 201100256). In this study, the lighting level generated by the lighting sources in the e-studio was calculated with a software developed and an interpolation polynomial model was created. The lighting level in the e-studio is optimized and modeled with the interpolation function. Keywords: e-Studio, Lighting Level, polynomial interpolation. References: [1] İşman, A., Uzaktan Eğitim. Geliştirilmiş 4.Baskı. Ankara: Pegem Akademi, 2011. [2] Bittinger, M.L., Basic College Mathematics. 11th Edition, International Edition. Boston: Pearson/Addison Wesley, 2010. [3] https://www.mathworks.com/help/curvefit/polynomial.html#d119e6504 (30.03.2018) [4] https://www.mathworks.com/help/curvefit/fit-comparison-in-curve-fitting- app.html (30.03.2018) [5] Carnicer, J. M. (2008). Interpolation and reconstruction of curves and surfaces. Rev. Real Academia de Ciencias. Zaragoza, 63, 7-40.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
[6] Chapra, S. C., Canale, R. P., Heperkan, H., & Kesgin, U. (2008). Yazılım ve programlama uygulamalarıyla: mühendisler için sayısal yöntemler. Literatür. [7] MathWorks Inc, 2018. Erişim Tarihi: 24.04.2018. https://www.mathworks.com/help/curvefit/evaluating-goodness-of- fit.html#bq_5kwr-3
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Spherical fuzzy sets and its representation of spherical fuzzy ť- norms and ť-conorms
푆ℎ푎ℎ푧푎𝑖푏 퐴푠ℎ푟푎푓1 and 푆푎푙푒푒푚 퐴푏푑푢푙푙푎ℎ1 퐷푒푝푎푟푡푚푒푛푡 표푓 푀푎푡ℎ푒푚푎푡𝑖푐푠, 퐴푏푑푢푙 푊푎푙𝑖 퐾ℎ푎푛 푈푛𝑖푣푒푟푠𝑖푡푦,1 Mardan, Pakistan [email protected] and [email protected]
Abstract: In this paper, we introduce spherical fuzzy sets (SFSs) which is an advanced tool of the fuzzy sets, intuitionistic fuzzy sets and picture fuzzy sets. We investigate the basic properties of SFSs and compare the idea SFSs with picture fuzzy sets. The spaces of spherical membership grades and picture membership grades are examined by graphically. Some useful operation such as spherical fuzzy ť-norms and spherical fuzzy ť-conorms are introduced. Also introduced spherical fuzzy negator and some classifications of spherical fuzzy ť- norms and spherical fuzzy ť-conorms which are useful for development the aggregation operator to aggregate the spherical fuzzy information. Keywords: Spherical fuzzy set, Spherical fuzzy ť-norm, Spherical fuzzy ť- conorm. References: [1] L. A. Zadeh, “Fuzzy sets”, Information and Control. 8(3) (1965) 338- 356. [2] K. Atanassov, “Intuitionistic fuzzy sets”, Fuzzy Sets and Systems, 20 (1986) 87-96. [3] B. C. Cuong, “Picture Fuzzy Sets- a new concept for computational intelligence problems”, In Proceedings of The World Congress on Information and Communication Technologies WIICT 2013, 1-6, December (2013) [4] B. C. Cuong, V. Kreinovitch, R. T. Ngan, “A classification of representable t- norm operators for picture fuzzy sets”, Eighth international conference on knowledge and systems engineering, (2016).
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
On some spectral problems of boundary value problem with boundary condition containing spectral parameter
Nigar Aslanova Department of Higher Mathematics, Azerbaijan University of Architecture and Construction, Baku,Azerbaijan [email protected], Mamed Bayramoglu, Department of differential Equations, Institute of Mthematics and Mechanics of NAS of Azerbaijan Baku, Azerbaijan [email protected] Khalig Aslanov Department of Mathematics, Azerbaijan State Economics University (UNEC) , [email protected]
Abstract: In present work our aim is to define self-adjoint operator associated with boundary value problem for second order differential operator equation with boundary condition depending rationally on spectral parameter. First we introduce the direct sum of Hilbert spaces and show self-adjointness of operator defined there. Further prove its discreteness and find asymptotics of spectrum. Finally, formula for regularized trace of the studied operator is driven. Results obtained for studied abstract problem might be applied to boundary value problems for partial differential equations.
Consider in 퐿2(퐻, (0,1)), where H is abstract separable Hilbert space,the following problem −푦′′(푥) + 퐴푦(푥) + 푞(푥)푦(푥) = 휆푦(푥) = 0, ′ 푦(0) = 0, 푦 (1) = (푎휆 − 푏1 ) . 푦(1) 휆−푐 Here coefficients of differential operator equation 퐴 and 푞(푥) are operators. 퐴 is discrete bounded from below operator, while 푞(푥) is bounded operator valued function for each 푥 acting in space 퐻.Boundary condition constants 푎, 푏, 푐 are nonnegative.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Some spectral properties of second differential equation in scalar case and with more general boundary conditions are studied by Binding, Browne and Watson [1,2]. 2 Our results relate operator 퐿 defined in 퐿2(퐻, (0,1)),⨁퐻 by 푏 퐿푌 = (−푦′′(푥) + 퐴푦(푥) + 푞(푥)푦(푥), 푐푦 − 푏 푦(1), 푦′(1) + 1 푦(1) 1 1 휆 − 푐 with domain 퐷(푌) = (푌: 푌 = (푦(푥), 푦 , 푦 ) = (푦(푥), −푦(1) 푏1 , 푎푦(1)). 1 2 휆−푐 Keywords: differential operator equation, spectrum, regularized trace. References: [1] P.Binding, P.Browne, B.Watson, “Sturm Liouville problems with boundary conditions rational;ly dependent on eigenparameter.” Proceedings of Edinburgh Math. Soc.45(2002), , 631-645. [2] P.Binding, P.Browne, B.Watson, “Sturm Liouville problems with boundary conditions rational;ly dependent on eigenparameter.” Journal of Computational and Appl. Analysis,148(2002), 147-168.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Generalizing the order obtained from nullnorms Emel Aşıcı Faculty of Technology, Department of Software Engineering, Karadeniz Technical University, Trabzon, Turkey [email protected] Abstract: Nullnorms and t-operators were introduced by Calvo, De Baets, Fodor [2] and Mas, Mayor, Torrens by [5] to generalize the concepts of t-norms and t- conorms. Mas, Mayor and Torrens [6] have shown that nullnorms and t- operators are equivalent since they have the same block structures in [0,1]². Nullnorms and t-operators were generalized and semi t-operators were introduced by eliminating commutativity from the axiom of t-operators by Dryga푠́ [3]. These operators are interesting not only from a theoretical point of view, but also for their applications, since they have proved to be useful in several fields like fuzzy logic framework and fuzzy quantifiers [4], expert system and neural networks [7]. In this paper, we survey some properties of an order induced by nullnorms, called the 퐹-partial order. We show that an order induced by nullnorms and an order induced by uninorms do not coincide. We also obtain some important and critical results for 퐹-partial order. Keywords: Nullnorm, Partial Order. References: [1] E. Aşıcı, “An order induced by nullnorms and its properties”, Fuzzy Sets Syst. 325(2017), 35-46. [2] T. Calvo, B. De Baets and J. Fodor, “The functional equations of Frank and Alsina for uninorms and nullnorms”, Fuzzy Sets Syst. 120(2001), 385-394. [3] P. Drygas, “Distributivity between semi t-operators and semi nullnorms ”, Fuzzy Sets Syst. 264(2015), 100-109. [4] G. J. Klir and B. Yuan “Fuzzy Sets and Fuzzy Logic, Theory and Application ”, Prentice-Hall PTR, Upper Saddle River, New Jersey 1995. [5] M. Mas, G. Mayor and J. Torrens “t-operators”, Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 7(1999), 31-50. [6] M. Mas, G. Mayor and J. Torrens “The distributivity condition for uninorms and t-operators”, Fuzzy Sets Syst. 128(2002), 209-225. [7] M. Mas, G. Mayor and J. Torrens “The modularity condition for uninorms and t-operators”, Fuzzy Sets Syst. 126(2002), 207-218. ______34
INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Numerical Treatment of Second Order Fuzzy Two-Point Boundary Value Problems
Basem S. Attili Department of Mathematics, University of Sharjah, Sharjah, United Arab Emirates [email protected]
Abstract: Many problems in applied sciences and engineering require the solution of fuzzy differential equations that are subject to fuzzy initial or boundary conditions, see O’Regana and Lakshmikantham[4]. This gives rise to fuzzy initial value problems and two-point boundary value problems. It is too complicated to obtain a closed form solution for such problems. This leads to numerical approximations. We consider the fuzzy two-point boundary value problem of the form, see Guo, et al.[2] and. Li, et al.[3]. 풚′′(풙) = 풇(풙, 풚(풙), 풚′(풙)), 풂 ≤ 풙 ≤ 풃 subject to the fuzzy boundary conditions 풚(풂) = 휶, 풚(풃) = 휷, where 풚: [풂, 풃] × 푹푭 × 푹푭 → 푹푭 is continuous fuzzy valued function and 휶, 휷 are fuzzy numbers. Numerically, we start by transforming the two-point boundary value problem into a system of fuzzy initial value problems. The missing initial conditions at 풙 = 풂 will then be assumed and we solve the initial value problem along the interval. The assumed initial values will then be corrected using the shooting method, Attili[1], so that the numerical solution at 풙 = 풃 match the given boundary condition at the point 풙 = 풃 up to a certain tolerance. Some numerical results will be presented to give the numerical details and to show efficiency of the shooting method. Keywords: Two-point BVP’s, Fuzzy Differential Equations, Shooting Method. References: [1] B. S. Attili, "On the Numerical Implementation of the Shooting Methods to the one-dimensional Singular Boundary Value Problems", Intern. J. Computer Math., 47 (1993), 65-75. ______35
INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
[2] Guo, X., Shang, D. and Lu, X., “Fuzzy Approximate Solutions of Second Order Fuzzy Linear Boundary Value Problems”, Boundary Value Problems (2013), 212. http://dx.doi.org/10.1186/1687-2770-2013-212. [3] Li, D., Chen, M., Xue, X., “Two Point Boundary Value Problems of Uncertain Dynamical Systems”, Fuzzy Sets and Systems, 179(2011), 50-61. [4] O’Regana, D. and Lakshmikantham, V., “Initial and Boundary Value Problems for Fuzzy Differential Equations”, Nonlinear Analysis, 54(2003), 405- 415.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
On Fuzzy Metric Space of Continuous Function
Ebru Aydoğdu, Abdülkadir Aygünoğlu, Halis Aygün Department of Mathematics, Kocaeli University, Kocaeli, Turkey [email protected], [email protected], [email protected]
Abstract: In this study, a fuzzy metric on continuous function was obtained. Then several properties of this function spaces were investigated such as completeness and principal. Keywords: Continuous Function Spaces, Fuzzy Metric Space. References: [1] A. George and P. Veeramani, "Some theorems in fuzzy metric spaces." Journal of Fuzzy Mathematics 3 (1995), 933-940. [2] A. George and P. Veeramani, “On some results in fuzzy metric spaces”, Fuzzy Sets and Systems, 64 (1994), 395-399. [3] A. George and P. Veeramani, "On some results of analysis for fuzzy metric spaces", Fuzzy Sets and Systems 90.3 (1997), 365-368. [4] V. Gregori, A. L opez-Crevill en, S. Morillas and A. Sapena, “On convergence in fuzzy metric spaces”, Topology and its Applications, 156 (2009), 3002-3006. [5] V. Gregori and S. Romaguera, "Some properties of fuzzy metric spaces", Fuzzy sets and systems 115.3 (2000), 485-489. [6] D. Mihet, “On fuzzy contractive mappings in fuzzy metric spaces”, Fuzzy Sets and Systems,158 (2007), 915-921. [7] V. Gregori, S. Morillas, A. López-Crevillén, "On continuity and uniform continuity in fuzzy metric spaces." Proc. Work. App. Topology WIAT'09, 85-91.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Flip Bifurcation Analysis in a Discrete Bacteria Population Model
Ercan Balcı1 and Senol Kartal2 1Department of Mathematics, Erciyes University, Kayseri, Turkey [email protected] 2Department of Mathematics, Nevsehir Hacı Bektas Veli University Nevsehir, Turkey [email protected]
Abstract: In discrete time systems, it is very important to study bifurcation analysis for a better understanding mechanism of the biological models. Many interesting research works on bifurcation theory can be found in [1-4]. In this paper, we shall study Flip bifurcation in a discrete bacteria population model by using the center manifold theorem and bifurcation theory. We also obtain bifurcation diagrams, phase portraits and Lyapunov exponents by the numerical simulations. Keywords: piecewise constant arguments, difference equation, stability, bifurcation. References: [1] B. Xin, J. Ma, Q. Gao, “The complexity of an investment competition dynamical model with imperfect information in a security market”, Chaos. Soliton. Fract, 42(2009), 2425-2438. [2] M. Peng, “Multiple bifurcations and periodic “bubbling” in a delay population model”, Chaos. Soliton. Fract, 25(2005), 1123-1130. [3] S. M. Sohel Rana, “Bifurcation and complex dynamics of a discrete-time predator-prey system”, Comput. Ecol. Softw, 5(2015), 187-200. [4] Z. He, X. Lai, “Bifurcation and chaotic behavior of a discrete-time predator- prey system”, Nonlinear Anal. Real, 12(2011), 403-417.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Analysis of a Pneumonia Transmission Model with Random Components
Zafer Bekiryazici Department of Mathematics, Recep Tayyip Erdogan University, Rize, Turkey [email protected] Tulay Kesemen Department of Mathematics, Karadeniz Technical University, Trabzon, Turkey [email protected] Mehmet Merdan Department of Mathematical Engineering, Gumushane University, Gumushane, Turkey [email protected]
Abstract: Recently, a SCIR-type compartmental model has been given by Kizito and Tumwiine to model Pneumonia infection dynamics with treatment and vaccination [1]. In our study, this model is used to investigate the random behavior of Pneumania transmission. Random approximation methods are used to obtain random numerical characteristics of the model such as the expected value and variance. The results are compared with the simulation results to comment on the randomness of the model components.
Keywords: Random Differential Equation, Pneumonia, Mean Square Calculus, Expected Value, Simulation. References: [1] M. Kizito and J. Tumwiine, "A Mathematical Model of Treatment and Vaccination Interventions of Pneumococcal Pneumonia Infection Dynamics." Journal of Applied Mathematics 2018(2018), Article ID 2539465. [2] C. J. Carlos, L. Jódar, and L. Villafuerte, "Numerical solution of random differential equations: a mean square approach." Mathematical and Computer Modelling 45.7-8(2007): 757-765. [3] M. Mehmet, Z. Bekiryazici, T. Kesemen and T. Khaniyev, "Comparison of stochastic and random models for bacterial resistance." Advances in Difference Equations 2017.1(2017), 133. ______39
INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
[4] T. T. Soong, Random differential equations in science and engineering. Elsevier, 1973. [5] World Health Organization, Pneumonia Fact Sheet, September 2016. [6] L. Villafuerte, C. A. Braumann, J. C. Cortés and L. Jódar, "Random differential operational calculus: theory and applications." Computers & mathematics with applications 59.1 (2010): 115-125. [7] M. A. El-Tawil and A. H. TOLBA, "On the application of mean square calculus for solving random differential equations." Electronic Journal of Mathematical Analysis and Applications 1.2 (2013): 202-211.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Using Two-Layer Models for Flexible Pavement Sizing
Mouloud BELACHIA, Nadjette BOUACHA Laboratory of Materials, Geotechnics, Habitat and Urban Department of Civil engineering, University of 20 Aout 1955 - Skikda ALGERIA [email protected]
Abstract: The construction of roads and highways has long been based on experience and empiricism and it is only since the Second World War that pavement structures are calculated so that they can meet certain traffic constraints. Taking into account the carrying capacity of infrastructure soils [1]. Two schools of thought, empiricism and mechanism have developed in parallel to meet the ever-increasing needs of pavements until their relatively recent merger [2], [3]. In general, all these methods follow the following thread:
• Determine the soil-bearing index • Appreciate the expected composite traffic and reduce it to a fictitious number of repetitions of a reference load. • Use graphs, based on the number of repetitions of the reference load, either the total thickness of the pavement "old methods" or a structural index that takes into account the qualities of the different layers of the roadway. In general, the rules for pavement sizing are based on geotechnical knowledge at break and the characteristics of deformability of materials determined by laboratory tests and findings on the behavior of structures and, on the other hand [4], Mathematical methods: rational approaches through a suitable mathematical model and finally, confrontation, between technological knowledge and theoretical results [5]. The examination of a set of analytical models which succeeded one another in time from the simplest model such as that of Boussinesq to the most complicated model like that of Burmister, led us to conclude that the main fault is to introduce a lot Simplifying hypotheses, it is necessary to introduce the finite element method because the development of the latter makes it possible to envisage the use of more realistic models which have the possibility to study the problems of ______41
INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org loading on board and the possibility of To consider materials not exhibiting elastic behavior [6]. Keywords: Mathematical model, analytical model, pavement design, finite element methodspace. References: [1] P. Autret, A. Boissoudy, J. Baucheron Marchand and P. Alize iii practice. Proc. 5th Int. Conf. Structural Design of Asphalt Pavements, 1982. [2] J. Boussinesq Potential application to the study of equilibrium and motion of elastic cops. Gauthier Villars, Paris, 1985. [3] N. Bouacha. Dimensioningand Choiceofthe Bodyof Flexible Pavements. PhD Thesis, University of Skikda, Algeria, 2010. [4] C. Peyronie, G. Caroff and C. Gilbert, Route - Design of pavements, edited by G. Jeuffroy and R. Sauterey, Presses de l'EcoleNationale des Pontset Chaussées, 1991. [5] LCPC. Design and measurements of pavement structures. Technical Guide, LCPC-SETRA, 1994. [6] S. Salasc, Contact phenomena in concrete pavements: theoretical modeling and experimental validation. Thesis: Ecole Centrale de Nantes, 1998.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
A Solution Approach for Multiobjective Probability Maximization Problems
Fatima Bellahcene Department of Mathematics, Faculty of Sciences, Mouloud Mammeri University, Tizi-Ouzou, Algeria [email protected]
Abstract: We suggest a method which enables the decision maker to freely search for a compromise solution to stochastic multiobjective problems where the objective functions depend on parameters which are continuous random variables with normal multivariate distributions. The developed algorithm is based on the combined use of the bisection method and the probabilities of achieving goals. The main advantage of this approach is to allow the decision- maker to act, at any moment, on the results and to revise, if necessary, the proposed choices made by the mathematical model in order to insure that they reflect his preferences in the best possible way. Keywords: Multiobjective programming; Stochastic programming; Nonlinear programming; Minimum-risk criterion. References: [1] F. Bellahcene, M. Abbas, Cutting plane method for multiple objective stochastic integer linear programming problem. Eur. J. of oper. Res. 168 (3), (2006), 967-984. [2] R. Caballero, E.Cerda, M. Del Mar, L. Rey, “Efficient Solution Concepts and their Relations in Stochastic Multiobjective programming”. J. of Opt. Theo. and Appl. 110 (1) (2001), 53-74. [3] K.M. Miettinen,”Nonlinear Multiobjective Optimization”. Kluw. Inter Series (1999).
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
A Nonsmooth Newton Method for Solving a State Constrained Optimal Control Problem Governed by Convection-Diffusion Equation
Boubakeur Benahmed Department of Mathematics and Computer Sciences, National Polytechnic School of Oran-Maurice Audin, Oran, Algeria [email protected] Kheira Mostepha Hanchour Ecole Supérieure d'Economie d'Oran, Oran, Algeria [email protected]
Abstract: We are interesting in solving numerically the optimal control problem governed by convection-diffusion equation with state inequality constraint [1]. First the infinite dimensional problem is discretized by application of the Upwind Symmetric Interior Penalty Galerkin (SIPG) method [2]. Then, we write the optimality conditions for the discretised problem. We reformulate these conditions into an equivalent system of nonlinear and nonsmooth equations by use of the Fischer-Burmeister function. A nonsmooth Newton’s method ([4],[5]) is applied to solve this system of non linear and nonsmooth equations, the resulting matrix system for each Newton iteration will be of saddle point structure [3]. We give sufficient conditions to ensure the nonsingularity of such matrix. Keywords: PDE-Constrained Optimisation, Convection-Diffusion Equation, Fisher- Burmeister Function,Smoothing Method, Newton Iteration, Saddle Point System. References: [1] A. Quarteroni, G. Rozza, and A. Quaini. Reduced basis methods for optimal control of advection-diffusion problems. In Advances in Numerical Mathematics. pages 193-216, Moscow, Russia and Houston, USA, 2007. [2] H. Yucel, P. Benner. Adaptive discontinuous Galerkin methods for state constrained optimal control problems governed by convection diffusion equations. Comput Optim. Appl (2015). ______44
INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
[3] M. Benzi, Gene H. Golub, and J¨org Liesen. Numerical solution of saddle point problems. Acta Numer., 14, pp. 1-137, 2005. [4] M. Gerdts. A Nonsmooth Newton’s Method for discretized Optimal Control problems with State and Control Constraints. Journal of industrial and management optimization, volume 4, Number 2, pp. 247- 270, May 2008. [5] L. Qi and J. Sun, A nonsmooth version of Newton's method, Mathematical Programming, 58 (1993) 353-367.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Properties of The Bianchi Groups and Digraphs
Murat Beşenk1, Serkan Kader2, Bahadır Özgür Güler3 1Department of Mathematics, Pamukkale University, Denizli, Turkey, 2Department of Mathematics, Ömer Halisdemir University, Niğde, Turkey, 2Department of Mathematics, Karadeniz Technical University, Trabzon, Turkey, [email protected], [email protected], [email protected]
Abstract: The group PSL(2, ℂ) has a natural action on 3-dimensional hyperbolic space ℍ3 which may be described in geometric terms. Any element of PSL(2, ℂ) induces a biholomorphic map of the Riemann sphere ℂ∞. Jules Henri Poincare (1854-1912) observed that PSL(2, ℂ) can be identified with the group of orientation preserving isometries of ℍ3. As in the study of the hyperbolic plane, the importance of finding discrete groups of hyperbolic isometries of ℍ3 was emphasized. Starting with an example by Emile Picard (1856-1941) and pursued by Luigi Bianchi (1856-1928) one particularly interesting class of discrete subgroups of PSL(2, ℂ) was considered. Denote by 푂푑 the ring of integers of an imaginary quadratic number field ℚ(√푑) with 푑 < 0 and square free. Then 푂푑 gives rise to a discrete group which is known Bianchi group Γ푑 ≔ 푃푆퐿(2, 푂푑) < 푃푆퐿(2, ℂ) consisting of fractional linear transformations with coefficients in 푂푑. In this study we discuss properties of the Bianchi groups and give an extension of suborbital digraphs on 3-dimensional upper half space ℍ3. Keywords: Bianchi groups, Quadratic number field, Suborbital digraphs, Circuits. References: [1] Grunewald F., Schwermer J., “Subgroups of Bianchi groups and arithmetic quotients of hyperbolic 3-space”, American Mathematical Society, Vol:335, 47-78, 1993. [2] Sims C.C., “Graphs and finite permutation groups”, Math. Zeitschrift, Vol:95, 76-86, 1967. [3] Maclachlan C., Reid A.W., “The arithmetic of hyperbolic 3-manifolds”, Springer, 2003.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
A New Solution of the Einstein-Maxwell Equations with Linear Equation of State
Rashida Bibi, and Azad A. Siddiqui National University of Science and Technology, Islamabad, Pakistan [email protected] Abstract: In the literature, different equations of state have been assumed to obtain solutions for charged static spherically symmetric spacetimes [1,9]. Theses equations are highly non-linear partial differential equations. Here we obtain a new solution of the Einstein-Maxwell equations with linear equation of state, p = αρ + β. The solution fulfils all the requirements to be a physically valid solution and can be considered as a model of a compact star. Keywords: Non-linear PDEs, Einstein-Maxwell equation, Equation of state, and Physically valid solution. References: [1] S. Thirukkanesh and S. D. Maharaj, Charged Anisotropic Matter with Linear Equation of State, Class. Quant. Grav., 25 (2008) [2] T. Feroze, Exact Solutions of the Einstein-Maxwell Equations with Linear Equation of State, Can. J. Phys., 90 (2012). [3] M. K. Mak and T. Harko, Quark Stars Admitting a One Parameter Group of Conformal Motions, Int. J. Mod. Phys. D, 13 (2004). [4] J. M. Sunzu, S. D. Maharaj and S. Ray, Quark Star Model with Charged Anisotropic Matter, Astrophys. Space Sci., 354 (2014). [5] M. Malaver, Strange Quark Star Model with Quadratic Equation of State, Frontiers of Mathematics and its Applications, 1 (2014). [6] T. Feroze and A. A. Siddiqui, Some Exact Solutions of the Einstein-Maxwell Equations with a Quadratic Equation of State, J. Korean Phys. Soc., 65 (2014). [7] T. Feroze and Azad A. Siddiqui, Charged Anisoptropic Matter with Quadratic Equation of State, Gen. Rel. Grav., 43 (2011). [8] S. D. Maharaj and P. M. Takisa, Regular Models with Quadratic Equation of State, Gen. Rel. Grav., 44 (2012). [9] P. M. Takisa, S. D. Maharaj and S. Ray, Stellar Objects in the Quadratic Regime, Astrophys. Space Sci., 354 (2014). ______47
INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Characterizations of extremal graphs for some bounds on k-domination number
Ahmed Bouchou 1, Mohmed Zemir1 and Mostafa Blidia 2, 1Dept. of Mathematics and Computer Science University of Médéa, Algeria 2Dept. of Maths, University of Blida, B.P. 270, Blida, Algeria E-mail: [email protected], [email protected], m_blidia @yahoo.fr,
Abstract: Let k 1 be an integer and let G be a graph with vertex set V(G). A subset SV(G) is called a k-dominating set if every vertex not in S has at least k neighbors in S. The k-domination number k(G) of G is the minimum cardinality of a k-dominating set in G. We know that for any graph G of order n, k(G) ≤ n. Obviously the upper bound n is sharp for a graph with maximum degree at most k-1. In this work, we give 푘푛 2푚−(푘−)푛 characterizations of graphs satisfying k(G) = and k(G) = with 푘+∆ 2−푘 maximum degree k. Also, we give characterizations of graphs with k(G) = n-1 and k(G) = n-2. Finally, we give a new upper bound for k(G). And, we characterize graphs achieving this bound, which generalize the result of Cockayne, Gamble and Shepherd [1]. Keywords: k-domination number. References [1] E. J. Cockayne, B. Gamble and B. Shepherd. An upper bound for the k- domination number of a graph. J . Graph Theory 9 (1985) 533-534. [2] O. Favaron, A. Hansberg and L. Volkmann, On k-dominationt and minimum degree in graphs, J. Graph Theory 57 (2008) 33-40. [3] J. F. Fink and M. S. Jacobson, n-domination in graphs, in : Graph Theory with Applications to Algorithms and Computer. John Wiley and Sons, New York (1985) 283-300.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Global dynamics of a Fractional model for viral infection with adaptive immunity
Adnane Boukhouima1, Khalid Hattaf1,2 and Noura Yousfi1 1Laboratory of Analysis, Modeling and Simulation (LAMS), Hassan II University, Casablanca, Morroco 2Centre Régional des Métiers de l’Education et de la Formation (CRMEF), Casablanca, Morroco [email protected]
Abstract: Fractional order differential equations (FDEs) are a generalization of ordinary differential equations (ODEs) and recently, they become an interesting tool to model real process in various fields of sciences and engineering due to the long-range memory property whish exist in most biological systems. In this work, we propose a fractional mathematical model in order to describe the role of the adaptive immunity in viral infections and take into account the memory effect. In the proposed model, the infection transmission is modeled by a general functional response which covers various types existing in the literature. We first show that the model is mathematically and biologically well-posed. By using the fractional Lyapunov method, the global stability of the equilibria is established and characterized by five treshold parameters. Some applications are presented to prove our theoretical results. Keywords: Viral infection, adaptive immunity, Caputo fractional derivative, global stability. References: [1] A. Boukhouima, K. Hattaf and N. Yousfi: "Dynamics of a Fractional Order HIV Infection Model with Specific Functional Response and Cure Rate." International Journal of Differential Equations 2017 (2017): 1-8. [2] K. Hattaf and N. Yousfi: "A class of delayed viral infection models with general incidence rate and adaptive immune response." International Journal of Dynamics and Control 4.3 (2016): 254-265. [3] K. Hattaf, M. Khabouz and N. Yousfi: "Dynamics of a generalized viral infection with adaptive immune response." International Journal of Dynamics and Control 3.3 (2015): 253-261 ______49
INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
[4] M. Maziane, E.M. Lotfi, K. Hattaf and N. Yousfi: "Dynamics of a class of HIV Infection Models with Cure of Infected Cells in Eclipse Stage." Acta Biotheor 63 (2015): 363-380.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
On BCB protocol
Sadek BOUROUBI USTHB University, Faculty of Mathematics, L’IFORCE Laboratory Algiers, Algeria [email protected]
Abstract: Vernam cipher, also known the One Time Pad Cipher, provides perfect security, despite its simplicity. The certificate that Vernam cipher is unconditionally secure, has transformed the problem to ensure the confidentiality of information to a problem of the secret key distribution used in the encryption process between two parties. Until the eighties, one way to distribute the secret key, apart from hand to hand, was to use algorithms whose security is based on the computational complexity. Keys generated by such algorithms are reasonably secret but not unconditionally secret. In this presentation, we developed a new cryptographic protocol, called BCB (Bouroubi-Charchali-Benyahia), which will be used to provide random fresh secret keys shared via a classical channel, using the set partitions. Keywords: Cryptography, Vernam Cipher, BCB protocol, Set Partitions. References: 1. C.E. Shannon. Communication Theory of Secrecy Systems. Bell System Technical Journal, Volume: 28 , Page: 657-715, 1949. 2. G. Brassard. A Bibliography of Quantum Cryptography. Département IRO, Université de Montréal, Canada, 3 December 1993. 3. G. S. Vernam. Cipher Printing Systems for Secret Wire and Radio Telegraphic Communications. J. AIEE 45, Pages: 109-115, 1926.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Some properties of modified new Szasz-Mirakyan operators in polynomial weight spaces via power summability method
Naim L. Braha Department of Mathematics and Computer Sciences, University of Prishtina Avenue Mother Teresa, No-5, Prishtine, 10000,Kosova [email protected]
Abstract: In this paper we will prove the Korovkin type theorem for new modified Szasz-Mirakyan operators via A-statistical convergence and power summability method. Also we give the rate of the convergence related to the above summability methods and in the last chapter we give a kind of Voronoi type theorem for A-statistical convergence. Keywords: A- statistical convergence, new modified Szasz-Mirakyan operators, power summability method, Korovkin type theorem, Voronoi type theorem, rate of convergence. References: Atlihan, Ozlem Girgin; Unver, Mehmet; Duman, Oktay, Korovkin theorems on weighted spaces: revisited. Period. Math. Hungar. 75 (2017), no. 2, 201-209. F.Basar, Summability theory and its applications, Istanbul, 2011. J.Boos, Classical and Modern Methods in Summability. OxfordUniversity Press, Oxford (2000). N.L.Braha, Some weighted Equi-Statistical convergence and Korovkin type- theorem, Results Math. 70 (2016), no. 3-4, 433-446. N.L. Braha, Valdete Loku, H.M. Srivastava, Lambda^2-Weighted statistical convergence and Korovkin and Voronovskaya type theorems, Appl. Math. Comput. 266 (2015), 675-686. Naim L. Braha, H. M. Srivastava and S. A. Mohiuddine, A Korovkin Type Approximation Theorem for Periodic Functions via the Summability of the Modified de la Vallee Poussin Mean, Appl. Math. Comput. 228 (2014), 162-169. N. L. Braha, Some properties of Baskakov-Schurer-Szasz operators via power summability method,(submitted for publication). Campiti, Michele; Metafune, Giorgio. L^p-convergence of Bernstein- Kantorovich-type operators. Ann. Polon. Math. 63 (1996), no. 3, 273-280. ______52
INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
O.Duman, M.K.Khan, C.Orhan, A-Statistical convergence of approximating operators. Math. Inequal. Appl. 6, 689-699 (2003) H.Fast, Sur la convergence statistique, Colloq. Math. 2 (1951) 241-244. J.A.Fridy, H.I.Miller, A matrix characterization of statistical convergence. Analysis 11, 59-66 (1991) Ugur Kadak, Naim L. Braha and H. M. Srivastava, Statistical Weighted B- Summability and Its Applications to Approximation Theorems, Appl. Math. Comput. 302 (2017), 80-96. Kirisci, Murat; Karaisa, Ali. Fibonacci statistical convergence and Korovkin type approximation theorems. J. Inequal. Appl. 2017, Paper No. 229, 15 pp. W.Kratz, U.Stadtmuller,Tauberian theorems for J_p-summability. J.Math.Anal. Appl. 139, 362-371 (1989) Loku, Valdete; Braha, N. L. Some weighted statistical convergence and Korovkin type-theorem. J. Inequal. Spec. Funct. 8 (2017), no. 3, 139-150. Soylemez, Dilek; Unver, Mehmet. Korovkin Type Theorems for Cheney-Sharma Operators via Summability Methods. Results Math. 72 (2017), no. 3, 1601-1612. U.Stadtmuller, A.Tali, On certain families of generalized N\"orlund methods and power series methods. J. Math. Anal. Appl. 238, 44-66 (1999) E.Tas, T.Yurdakadim, Approximation by positive linear operators in modular spaces by power series method. Positivity 21 (2017), no. 4, 1293-1306. E.Tas, Some results concerning Mastroianni operators by power series method. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 63(1), 187-195 (2016) M.Unver, Abel transforms of positive linear operators. In: ICNAAM 2013. AIP Conference Proceedings, vol. 1558, pp. 1148-1151 (2013) Walczak, Zbigniew. Error estimates and the Voronovskaja theorem for modified Szász-Mirakyan operators. Math. Slovaca 55 (2005), no. 4, 465-476.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
The Cardinal and Idempotent Number of Order-preserving and A-increasing Finite Transformations Semigroup
Leyla Bugay Department of Mathematics, Çukurova University, Adana, Turkey [email protected]
Abstract: Let Tn be the (full) transformation semigroup on Xn={1,...,n}, under its natural order. A transformation f is called order-preserving if
xyxfyfx yXn (for each ,) Moreover, for any non-empty subset A of Xn, a transformation f is called A- increasing if
xxfxA(for each ). Then the subsemigroup of all order-preserving and A-increasing transformations in Tn is denoted by On(A+). In this talk we give the cardinal and idempotent (the element whose square is itself) number of On(A+) connection with Fibonacci numbers. Keywords: Order-preserving/Increasing transformation, Idempotent, Fibonacci numbers. References: [1] V.H. Fernandes, G.M.S. Gomes, M.M. Jesus, “The cardinal and the idempotent number of various monoids of transformations on a finite chain” Bull. Malays. Math. Sci. Soc. 34(2011), 79-85. [2] P.M. Higgins, “Combinatorial results for semigroups of order-preserving mappings”, Math. Proc. Cambridge Phil. Soc. 113(1993), 281-296. [3] J.M. Howie, “Products of idempotents in certain semigroups of transformations”, Proc. Edinburgh Math. Soc. 17(1970/71), 223-236. [4] A. Laradji, A. Umar, “Combinatorial results for semigroups of order- preserving full transformations”, Semigroup Forum 72(2006), 51-62. [5] P. Zhao, “On the semigroups of order-preserving and A-decreasing finite transformations”, Algebra Colloq. 21(2014), 653-662.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Best Proximity Point Theorems for Generalized A− Contractions
Abdurrahman Büyükkaya1 , Mahpeyker Öztürk2 1Department of Mathematics, Karadeniz Technical University, Trabzon, Turkey 2Department of Mathematics, Sakarya University, Sakarya, Turkey [email protected] , [email protected]
Abstract: In this paper, we investigate the existence of best proximity points of of generalized A-contraction mappings in the frame of complete metric spaces endowed with a partial order. We obtain some consequences which extend and generalize existing literature. Keywords: Fixed Point, Best Proximity Point, Generalized A-Conrtaction, Metric Spaces References: [1] M. Akram, A. A. Zafar, A. A. Siddiqui, A general class of contractions: A- contractions, Novi Sad J. Math., 38(1), 25-33, 2002. [2] K. Fan, Extensions of two fixed point theorems of F. E. Browder. Math. Z. 112, 234–240, 1969. [3] Kirk, WA, Reich, S, Veeramani, P: Proximinal retracts and best proximity pair theorems. Numer. Funct. Anal. Optim. 24,851-862, 2003. [4] Sadiq Basha, S., Veeramani, P., Best proximity pair theorems for multifunctions with open _bres J. Approx Theory, 103, 119-129, 2000. [5] A. Amini-Harandi, Best proximity points for proximal generalized contractions in metric spaces, Optim Lett, (7), 913-921, 2013. [6] S Sadiq Basha, N. Shahzad, Best proximity point theorems for generalized proximal contractions, Fixed Point Theory and Applications, 42, 1-9, 2012. [7] H.K. Nashine, P. Kumam, C. Vetro, Best proximity point theorems for rational proximal contractions, Fixed Point Theory and Applications, 95, 1-11, 2013.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
On The Estimator of Semi-Markovian Inventory Model with Subexponential Component
Melek Eriş Büyükkaya Department of Statistics and Computer Sciences, Karadeniz Technical University, [email protected] Aslı Bektaş Kamışlık Department of Mathematics, RecepTayyipErdoğan University, [email protected] Tülay Kesemen Department of Mathematics, Karadeniz Technical University, [email protected] Tahir Khaniyev Department of Industrial Engineering, TOBB University of Economics and Technology, [email protected]
Abstract:In this study, a semi Markovian inventory model with subexponential demands has been investigated. New statistical estimators for ergodic distribution and moments for ergodic distribution of the process which define the model have been obtained, using renewal process. A statistical estimation problem for some characteristics of a semi Markovian inventory model of type (s,S) has been studied comprehensively in the literature [2],[3],[4],[5]. In all of the current studies in the literature, it is assumed that random variables representing demands are light tailed.Unlike other studies in the literature, in this study a semi Markovian inventory model will be considered with the assumption that the random variables expressing the demands have heavy tail distribution and the statistical estimators for the characteristics of the process will be investigated under this assumption.Semi Markovian inventory model of type (s,S) with subexponentialWeibull distributed demand quantities has been studied by Kesemen et. al. [6] and two term asymptotic expansions have been obtained for some probabilistic characteristics of this model. It is well known that heavy tailed distributions tend to produce extreme values and using heavy-tailed distributions when modeling datas related to unusual events gives more realistic results.The main purpose of this study is proposing statistical estimators for some characteristics of the stochastic process expressing the model based on the main results of the study by Kesemen et. al. [6] and using statistical estimators ______56
INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org presented by Frees [1]. Thus, the effect of the heavy tailed demands, which tend to produce extreme values on the semi-Markovian inventory models, will be examined statistically. Keywords: Statistical estimation, Semi Markovian inventory model with heavy tailed component, Subexponential distributions. References: E. W. Frees, “Nonparametric renewal function estimation, Annals of Statistics”, 14.4(1986), 1366-1378. E. Gökpınar, T. Khanıyev, H. Gamgam, F. Gökpınar, “Estimators of the moments for the inventory model of type (s,S), Iranian Journal of Science and Technology”, 42(2018), 5-12. E. Gökpınar, T. Khanıyev, H. Gamgam, F. Gökpınar, “A new estimators for stationary distribution of the inventory model of type (s,S)”, Gazi University Journal of Science, 28.1(2015), 87-101. [4]E. Gökpınar, T. Khanıyev, H. Gamgam, “Asymptotic properties of the straight line estimator for a renewal function, SainsMalaysiana”, (2015), 1041-1051. [5]E. Gökpınar, T. Khanıyev, H. Gamgam, F. Gökpınar, “Estimators of the moments for the inventory model of type (s,S) with a discrete interference of chance, Journal of the Turkish Statistical Association”, 9.1(2016), 17-28. [6] T. Kesemen, A. B. Kamışlık, Z. Küçük, E. Şenol, “On the asymptotic expansion for the moments of an inventory model of type (s,S) with subexponentialWeibull distributed demand” Journal of the Tuekish Statistical Association, 3(2016), 81-92.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Projective covariant α-completely positive linear maps
Tania Luminita Costache Department of Mathematical Methods and Models, Faculty of Applied Sciences, University Politehnica of Bucharest, Bucharest, Romania [email protected]
Abstract: In this paper we construct a Krein space, a J-representation and a projective J-representation associated with a unital projective J-covariant completely positive linear map. We also find a Krein space representation for a unital projective (θ,u)-covariant α-completely positive map. For a given projective unital (θ,u)-covariant α-completely positive map ρ and a projective (Ƭ,σ,u)-covariant ρ-map we construct a projective covariant J-representation of a C*-dynamical system. We form projective J-unitary representations associated to a projective (u,u’)-covariant completely positive ρ-map. Also, we prove that there is a projective covariant representation associated with a projective covariant α-completely positive map on an S-module. Keywords: Hilbert space, Krein space, completely positive map, projective representation, C*-dynamical system Acknowledgment : This work has been financed by University Politehnica of Bucharest, through the “Excellence Research Grants” Program, UPB – GEX 2017, “Aplicatii complet pozitive”, Id 5, No. SA 54-17-08. References: [1] B.V. Rajarama Bhat, G. Ramesh, K. Sumesh, Stinespring's theorem for maps on Hilbert C*-modules, J. Operator Theory 68, No. 1 (2012), 173-178. [2] T.-L. Costache, Projective version of Stinespring type theorems, Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie, Vol. 53, No.2 (2010), 109-124. [3] T.-L. Costache, KSGNS type representations on Krein C*-modules associated with projective J-covariant - completely positive maps, UPB Sci. Bull., Series A, Vol. 77, Iss.2 (2015), 67-78. [4] J. Heo, Hilbert C*-modules and projective representations associated with multipliers, J. Math. Anal. Appl. 331 (2007), 499-505. ______58
INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
[5] J. Heo, J. P. Hong, U. C. Ji, On KSGNS Representations on Krein C*- modules, J. Math. Phys. (5), 51 (2010), 1-17. [6] J. Heo, U. C. Ji, Y. Y. Kim, Projective covariant representations of locally C*-dynamical systems, Taiwanese J. Of Math., vol.17, No.2 (2013), 529-544. [7] J. Heo, Un Cig Ji, Y. Y. Kim, -completely positive maps on locally C*- algebras, Krein modules an Radon-Nicodym theorems, J. Korean Math. Soc. (50), No.1 (2013), 61-80. [8] J. Heo, Covariant representations on Krein C*-modules associated to pairs of two maps, J of Math. Anal. and Appl. 398 (2013), 35-45. [9] J. Heo, -completely positive maps of groups systems and Krein module representations, J. of Math. Anal. and Appl., vol. 409, Issue 1 (2014), 544-555. [10] U. C. Ji, M. Joita, M. Sal Moslehian, KSGNS type construction for - completely positive maps on Krein C*-modules, Complex Analysis and Operator Theory, 10 (2016), 3, 617-638. [11] M. Joita, Covariant version of the Stinespring type theorem for Hilbert C*-modules, Cent. Eur. J. Math. 9 (2011), 4, 803-813. [12] H. Trivedi, A covariant Stinespring type theorem for -maps, Surveys in Mathematics and its Applications, Vol. 9 (2014), 149-166.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Determination of a coefficient in a second-order hyperbolic problem
Arzu Erdem Coşkun Department of Mathematics, Kocaeli University, Kocaeli,Turkey [email protected]
Abstract: We consider an inverse problem of determination of the coefficient
푘(푥), 푥 ∈ Ω in the second-order hyperbolic equation 푢푡푡 = ∇(푘(푥)∇푢) in ΩT = Ω × (0, T) from the initial and boundary information 푢(푥, 0), 푢푡(푥, 0) and n 푘(푥)∇푢풏|휕Ω×(0,T). Here Ω ⊂ ℝ is a rectangularly-shaped bounded domain and 풏 is the outward unit normal to the boundary of Ω at the point 푥 ∈ 휕Ω. This problem is playing an important role in ground-water hydrology and contaminant transport in porous media, vibrations of a membrane, acoustic vibrations of a gas, and electromagnetic processes in non-conducting media by (1) The inverse problem of identifying unknown coefficients has already been investigated by some authors (2; 3; 4). We prove an existence and uniqueness theorem for the associated inverse coefficient hyperbolic problem. Our approach consists of monotonicity method (5; 6) based on integral relationships between the input and output data. Finally, we present various numerical results that show feasibility of our approach. Keywords: Inverse coefficient problem, the second order hyperbolic PDEs, the adjoint problem, monotonicity, existence, uniqueness. References: 1. Petrovsky, I.G. Lectures on Partial Differential Equations. New York : Interscience, 1966. 2. Determination of a coefficient in an acoustic equation with a s ingle m easurement. Imanuvilov, O.Y. and Yamamoto, M. s.l. : Inverse Problems, 2003, Vol. 19, pp. 157-171. 3. A posteriori error estimates in a globally convergent FEM for a hyperbolic coefficient inverse problem. Asadzadeh, M. and Beilina, L. s.l. : Inverse Problems, 2010, Vol. 26, p. 34.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
4. Uniqueness for a hyperbolic inverse problem with angular control on the coefficients. Rakesh and Sacks, P. s.l. : J. Inv. Ill-Posed Problems, 2011, Vol. 19, pp. 107 - 126. 5. Monotonicity and invertibility of coefficient-to-data mappings for parabolic inverse problems. DuChateau, P. 6, s.l. : SIAM J. Math. Anal., 1005, Vol. 26, pp. 1473-1487. 6. Monotonicity of input-output mappings in inverse coefficient and source problems for parabolic equations. Hasanov, A., Demir, A. and Erdem, A. 2, s.l. : Journal of Mathematical Analysis and Applications, 2007, Vol. 35, pp. 1434- 1451.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
On the Existence and Uniqueness of Solutions for a First And Second-Order Discrete Boundary Value Problem
Arzu Erdem Coşkun, Ali Demir Department of Mathematics, Kocaeli University, Kocaeli,Turkey [email protected], [email protected]
Abstract: In recent years, we witness that the discrete boundary value problems serve as mathematical models in diverse fields, such as economy, biology, physics, mechanics, computer science, finance. Several approaches such as fixed point theorem, critical point theory and global bifurcation techniques have been proposed for solving for the discrete boundary value problems, (1; 2; 3; 4; 5). In this paper.there are two parts In the first part, subjected to two-point boundary condition, we consider the nonlinear first order discrete boundary value problem. A new sufficient condition for the existence and uniqueness of the nonlinear first order difference evolution equation are established . We define an iteration procedure by means of Banach contraction principle and apply our results to show that iterated solutions converge to the solutions of the discrete problem. When the residual is acceptably small we prove the iteration procedure is terminated. To illustrate the existence of a unique solution of the contraction mapping theorem some examples are included. In the second part of the study, we consider the following second-order difference boundary value problem 훥2푥 𝑖 = 푓(푡 , 푥 ), 𝑖 = 0,1,2, … , 푛 − 1, 휏2 𝑖 𝑖 푢푥0 + 푣푥푛 = 0, 훥푥 훥푥 푢̅ 0 + 푣̅ 푛 = 0, { 휏 휏 where f: [0, T] × ℝ → ℝ, and the difference operator is defined as follows 푥 − 2푥 + 푥 , 푓표푟 𝑖 = 1,2, … , 푛 − 2, 훥²푥 = { 𝑖+1 𝑖 𝑖−1 . 𝑖 0, 푓표푟 𝑖 = 0 표푟 𝑖 = 푛 − 1, By using Banach fixed point theorem we establish some sufficient conditions for the existence and uniqueness of the above second-order difference boundary value problem. ______62
INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Keywords: Existence of solutions; First-order Discrete Boundary Value Problems; Second-order Discrete Boundary Value Problems; Banach contraction; Fixed Point Iteration. References: 1. On first-order discrete boundary value problems. Tisdell, C.C. 12, s.l. : Journal of Difference Equations and Applications, 2006, Vol. 12, pp. 1213-1223. 2. A note on improved contraction methods for discrete boundary value problems. Tisdell, C.C. 10, s.l. : Journal of Difference Equations and Applications, 2012, Vol. 18, pp. 1773-1777. 3. Discrete First-Order Three-Point Boundary Value Problem. Mohamed, M. 2, s.l. : Journal of Mathematics Research, 2009, Vol. 1, pp. 207-215. 4. Initial-boundary-value problems for discrete linear evolution equations. Biondini, G. and Wang, D. s.l. : IMA Journal of Applied Mathematics, 2010, Vol. 75, pp. 968-997. 5. On positive periodic solutions of second-order difference equations with attractive-repulsive singularities. Lu, Yanqiong and Ma, Ruyun. s.l. : Advances in Difference Equations, 2012, Vol. 2012, p. 186.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Instability Intervals for Hill’s Equation with Symmetric Double Well Potential
Haskız Coşkun and Elif Başkaya Department of Mathematics, Karadeniz Technical University, Trabzon, Turkey [email protected], [email protected]
Abstract: In this paper, we derive some estimates explicitly for the periodic and the semi-periodic eigenvalues and the length of the instability intervals of Hill’s equation with symmetric double well potential by using an auxiliary eigenvalue problem. We also give bounds for the gaps of Dirichlet and Neumann eigenvalues. Keywords: Hill’s equation, symmetric double well potential, instability intervals. References: [1] H. Coşkun and B. J. Harris, Estimates for the periodic and semi-periodic eigenvalues of Hill’s equations, Proc. Roy. Soc. Edinburgh Sec. A 130 (2000), 991-998. [2] H. Coşkun, Some inverse results for Hill’s Equation, J. Math. Anal. Appl. 276 (2002), 833-844. [3] H. Coşkun, On the spectrum of a second order periodic differential equation, Rocky Mountain J. Math. 33 (2003), 1261-1277. [4] M. S. P. Eastham, The spectral theory of periodic differential equations, Scottish Academic Press, Edinburgh and London, 1973. [5] M. J. Huang, The first instability interval for Hill equations with symmetric single well potentials, Proc. Amer. Math. Soc. 125 (1997), 775-778. [6] M. J. Huang and T. M. Tsai, The eigenvalue gap for one-dimensional Schrodinger operators with symmetric potentials, Proc. Roy. Soc. Edinburgh Sec. A 139 (2009), 359-366.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Analysis of Neutron Capture Cross Section Using Systematics of Different Level Density Model
Veli Çapalı Usak University, [email protected]
Abstract: The neutron capture cross–section reactions for some isotopes have been calculated with different level density models by using TALYS 1.6 and EMPIRE 3.2 codes for incident neutron energies up to 300 keV. The obtained results have been analyzed with each level density model parameters exists in Reference Input Parameter Library (RIPL–3) and available experimental data. As an outcome, to obtain more precise and coherent calculations with the experimental values, level density model and its parameters have been determined.
Keywords: Cross section; Reactor materials; Level density models; Hadronic interactions
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
On the extensions of triangular norms and triangular conorms
Gül Deniz Çaylı Department of Mathematics, Faculty of Sciences, Karadeniz Technical University, 61080, Trabzon, Turkey [email protected]
Abstract: Triangular norms (t-norms) and the corresponding triangular conorms (t-conorms), introduced by Schweizer and Sklar in [8], are used in several branches of mathematics in different manners such as in probabilistic metric spaces, many-valued logic, fuzzy logic, fuzzy sets, decomposable measures and their applications. A t-norm (t-conorm) on a lattice 퐿 is a function 푇 ∶ 퐿2 → 퐿 (푆 ∶ 퐿2 → 퐿) which is commutative, associative, nondecreasing in both variables and fulfills, for all 푥 ∈ 퐿, the boundary condition 푇(1, 푥) = 푥 (푆(0, 푥) = 푥). In this contribution, we consider the extensions of t-norms and t-conorms on lattices and investigate their characteristics. Moreover, some examples are provided to illustrate the feasibility of the proposed extensions. Keywords: Fuzzy logic, Triangular norm, Triangular conorm, Lattice. References: [1] D. Butnariu, E.P. Klement, “Triangular Norm-Based Measures and Games with Fuzzy Coalitions”, Kluwer, Dordrecht, 1993. [2] G.D. Çaylı, “On a new class of t-norms and t-conorms on bounded lattices”, Fuzzy Sets Syst. 332(2018), 129-143. [3] G.D. Çaylı, “Characterizing ordinal sum for t-norms and t-conorms on bounded lattices”, In Advances in Fuzzy Logic and Technology 2017. IWIFSGN 2017, EUSFLAT 2017. Advances in Intelligent Systems and Computing; Kacprzyk, J. et al. (eds), vol.641 Springer, Cham, 2018. [4] Ü. Ertuğrul, F. Karaçal, R. Mesiar, “Modified ordinal sums of triangular norms and triangular conorms on bounded lattices”, Int. J. Intell. Syst. 30(2015), 807-817. [5] E.P. Klement, “Construction of fuzzy a-algebras using triangular norms”, J. Math. Anal. Appl. 85(1982), 543-565 [6] J. Medina, “Characterizing when an ordinal sum of t-norms is a t-norm on bounded lattices”, Fuzzy Sets Syst. 182(2012), 75-88. ______66
INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
[7] S. Saminger “On ordinal sums of triangular norms on bounded lattices” Fuzzy Sets Syst. 157.10(2006), 1403-1416. [8] B. Schweizer, A. Sklar, “Probabilistic Metric Spaces”, In North-Holland, New York, 1983. [9] H.J. Zimmermann, “Fuzzy Set Theory and Its Applications”, Kluwer, Dordrecht, 1991.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
On Suborbital Graphs and Related Sequences
Ali Hikmet DEĞER1, Ümmügülsün AKBABA1, Tuğba TUYLU1 1Department of Mathematics, Karadeniz Technical University, Ortahisar, Trabzon, Turkey [email protected], [email protected], [email protected] Abstract: The two number sequences Fibonacci and Lucas, which have a very popular place in the literature and are important applications in various fields. On the other hand, the action of a group on a set is also used in different areas. In particular, the Möbius transformation is an important transformation of the Complex Analysis field of theory of Analysis and Functions. The modular group Γ and its congruence subgroups, which are a group of linear fractional transformations obtained from these Möbius transformations, also yield results in different fields. The suborbital graphs were studied based on the action of the congruence subgroup Γ0(N) < Γ on ℚ̂ ≔ ℚ ∪ {∞} and the results related to the vertex which can be joined with the farthest vertex on these suborbital graphs were obtained. Taking these results into account, significant and different results were obtained in relation to the Fibonacci and Lucas numbers from the minimal length problem of the respective vertices. It is expected that different results will be reached by taking all the features of the Fibonacci and Lucas number sequences by going out from these results obtained in this work. Generally, on the minimal-length paths in the suborbital graphs, the relevant vertices will be related to these number sequences. Keywords: Suborbital graphs, Continued fraction, Fibonacci and Lucas sequences References: [1] A.H. Değer, M. Beşenk and B.Ö. Güler, “On suborbital graphs and related continued fractions”, Applied Mathematics and Computation, 218 (2011), 746- 750. [2] G. A. Jones, D. Singerman and K. Wicks, “The modular group and generalized Farey Graphs”, London Math. Soc. Lecture Notes, CUP, Cambridge, 160 (1991), 316-318. [3] A.H. Değer, “Vertices of Paths of Minimal Lengths on Suborbital Graphs”, Filomat, 31:4 (2017), 913-923.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Characterizations of Lipschitz spaces via commutators of fractional maximal operator in Orlicz spaces
Fatih Deringöz Department of Mathematics, Ahi Evran University, Kırşehir, Turkey [email protected]
Abstract: In this talk, we give necessary and sufficient conditions for the boundedness of fractional maximal operator M on Orlicz spaces. As an application of this result we consider the boundedness of fractional maximal commutator M b, and nonlinear commutator of fractional maximal operator
[bM , ] on Orlicz spaces, when b belongs to the Lipschitz space, by which some new characterizations of the Lipschitz spaces are given.
This work is supported by Ahi Evran University Scientific Research Projects Coordination Unit (Project Number : FEF.A4.17.009).
This contribution is based on recent joint work with V.S Guliyev and S.H. Hasanov.
Keywords: Orlicz spaces, Lipschitz spaces, fractional maximal operator, commutator. References: [1] V.S. Guliyev, F. Deringoz, S. H. Hasanov, “Fractional maximal function and its commutators on Orlicz spaces”, Anal. Math. Phys., DOI 10.1007/s13324- 017-0189-1.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Convergence Theorems on Measure Space of Exhaustive
Doris Doda Wisdom University Economics Faculty Business Management [email protected]
Abstract:In this paper we propose some propositions in reference to notion of exhaustivness which applies both for families and sequences of functions. This new notion given for the first time from Gregoriades and Papanastassiou in 2008 and has a good progress and in mathematical community is followed by many papers. We are concerned in study these families in framework of measure theory and Henstok-Kurzweil integration.We investigate the properties of new convergence which we named -convergence and compare it with other known convergencies. Keywords: Exhaustivness, alfa-convergenece, exhaustiv sequence, equicontinuity, -convergence, Henstok-Kurzweil integral.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
A New view of L-ideals on Semigroups
Emine Funda Ekinci, Sultan Yamak Department of Mathematics, Karadeniz Technical University, Trabzon, Turkey [email protected], [email protected]
Abstract: In this paper, we first introduce the notion of L-left (resp. L-right) ideals of a TL-subsemigroup in a semigroup, and develop some properties of them. We also build the relation between L-ideals of a semigroups and L-ideals of a TL-subsemigroups. Furthermore, the lattice structure of L-left (resp. L-right) ideals of a TL-subsemigroups are studied.
Keywords: t-norm, semigroups, TL-subsemigroups, L-ideals. References: [1] Chon, I., On fuzzy bi-ideals in semigroups, Korean J. Math, 19, (2011), 321- 330. [2] J.A. Goguen, L-fuzzy sets, J. Math. Anal. Appl. 18 (1967) 145–174. [3] N. Kuroki, Fuzzy bi-ideals in semigroups, Comment. Math. Univ. St. Paul. 28 (1979), 17-21. [4] N. Kuroki, On fuzzy ideals and fuzzy bi-ideals in semigroups, Fuzzy Sets Syst. 5 (1981), 203-215. [5] N. Kuroki, Fuzzy semiprime ideals in semigroups, Fuzzy Sets Syst. 871-80 (1982). [6] N. Kuroki, On fuzzy semigroups, Inform. Sci. 53:203-236 (1991). [7] Mordeson, J.N., Malik, D.S., Kuroki, N., Fuzzy semigroups. Springer-Verlag, 2003.
[8] N. Thillaigovindan, V. Chinnadurai, S. Coumaressane, T-fuzzy subsemigroups and T-fuzzy ideals of regularΓ-semigroups, Ann. of Fuzzy Math. And Inf., 11. 4 (2016), 669–680. [9] Yandong Yu, Zhudeng Wan, TL-subrings and TL-ideals. Part 1. Basic concepts, Fuzzy Sets and Systems, 68-1, 28(1994), 93-103. [10] L. A. Zadeh, Fuzzy sets, Information and Control 8 (1965) 338–353.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Design and Application of Fractional Order Predictor for Unglazed Transpired Solar Collector
Köksal ERENTÜRK, Saliha ERENTÜRK Department of Computer Engineering, Ataturk University, Erzurum, Turkey [email protected]
Abstract: In order to evaluate different modeling techniques for Unglazed Transpired Collectors (UTC), not only mathematical modeling method for UTC based on heat transfer expressions to estimate the various heat transfer coefficients for the UTC components and empirical relationship, but also fractional order predicting approach have been designed and introduced, in this study. Thermal performance experiments of UTC have been carried out on an optimized experimental setup. Firstly, obtained experimental results have been compared with the mathematical model. To constitute a common point, output temperature of the UTC has been selected as the output variable. Then, a fractional order predictor has been used to forecast the output temperature with higher accuracy with the aid of simple mathematical equations. Finally, obtained results have been compared and comparison results have been illustrated in both graphical and tabular form. Fractional order predictor is the simplest method to forecast the output temperature with high accuracy.
Keywords: Solar heating, fractional order modeling, fractional order predictor, unglazed transpired collectors. References: [1] Sozer H. Improving energy efficiency through the design of the building envelope. Building and Environment 2010; 45 (12): 2581–93. [2] SOLARWALL, 2016. The SOLARWALL Solar Heating System. Conserval Engineering Inc., Canada. Available from:
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
[4] Feng J, Xin W, Yinping Z. A new method to estimate optimal phase change material characteristics in a passive solar room. Energy Conversion&Management 2011; 52(6): 2437–41. [5] Wei S, Jie J, Chenglong L, Wei H. Performance of PV-trombe wall in winter correlated with south facade design. Applied Energy 2011; 88(1): 224–31. [6] Yanfeng L, Dengjia W, Chao M, Jiaping L. A numerical and experimental analysis of the air vent management and heat storage characteristics of a trombe wall. Solar Energy 2013; 91: 1–10. [7] KUDAKA Technical Report, 2016. Available from:
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Determination of the Effective moisture Diffusivities in Convective Drying Systems of Banana using Fractional Order Estimator
Saliha ERENTÜRK, Köksal ERENTÜRK Department of Chemical Engineering, Ataturk University, Erzurum, Turkey [email protected]
Abstract: Drying techniques have been used for the food preservation for centuries as it caused the minimize biochemical, chemical and microbiological deterioration. Despite high energy consumption and decreasing of quality, obtained product gains longer life by drying. The moisture diffusivity of a foodstuff is a material property and it changes with many factors including moisture content, process variables, water holding capacity and physiochemical attributes of food. Effective moisture diffusivity describes all possible mechanisms of moisture movement within food, which is combination of liquid diffusion, vapor diffusion, surface diffusion, capillary flow and hydrodynamic flow. In this work, the effective moisture diffusivity of banana was determined in air convective drying system. In the system three different air velocities, air temperatures and solid thickness were investigated. Effective moisture diffusivities varied between 4.75-6.48 10-10m2/s for temperature investigated, 3.66-9.53 10-10m2/s for air velocities investigated and 6.48-3.12 10-10m2/s for solid thickness investigated. In this study, amount of effective moisture diffusivity of banana has been determined using Fractional Order Estimator. Based on obtained results, an effective approach has been developed and better results have been observed compared with classical mathematical modeling approaches and methods. Keywords: Fractional order estimator, drying, banana, effective moisture diffusivity. References: S.Erenturk, M. S. Gulaboglu, S. Gultekin. “Experimental determination of effective moisture diffusivities of whole- and cut-rosehips in convective drying” Food and Biop. Processing, 88(2010), 99–104. ______74
INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
G.P. Sharma, S. Prasad,”Effective moisture diffusivity of garlic cloves undergoing microwave-convective drying” Journal of Food Engineering, 65, (2004), 609–617. M. Vasic, Z. Grbavcic, Z. Radojevic, “Determination of the moisture diffusivity coefficient andmathematical modeling of drying”, Chem. Eng. and Processing, 76, (2014), 33– 44. A. Fabbri, C. Cevoli, R. Troncoso,”Moisture diffusivity coefficient estimation in solid food by inversion of a numerical model”, Food Research International, 56, (2014),63-67. B. D.A. Porciuncula, M. F. Zotarelli, B. A.M. Carciofi, J. B. Laurindo,“Determining the effective diffusion coefficient of water in banana (Prata variety) during osmotic dehydration and its use in predictive models”,Journal of Food Engineering, 119, 3, (2013),490-496.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
On Nullnorms On Bounded Lattices
Ümit Ertuğrul Department of Mathematics, Karadeniz Technical University, Trabzon, Turkey [email protected]
Abstract: Special aggregation functions nullnorms are generalization of t-norms and t-conorms ([6]). Because of this feature, they are being studied extensively by researchers ([2],[4]). Nullnorms are useful not only in theory but also in many applications. Nullnorms are first defined on the unit real interval [0,1]. Subsequently, the work has been detailed, taking into account the bounded lattice case ([3],[4],[6]). In this study, some properties of nullnorms on bounded lattices have been investigated. Keywords: Nullnorm, T-norm, T-conorm, Bounded Lattices. References: [1] G. Birkhoff, “Lattice Theory”, American Mathematical Society Colloquium Publishers, Providence, RI, 1967. [2] P. Drygás, “A characterization of idempotent nullnorms”, Fuzzy Sets Syst. 145 (2004), 455-461. [3] M. Grabish, J.-L. Marichal, R. Mesiar, E. Pap, “Aggregation Functions”, Cambridge University Press, 2009. [4] F. Karaçal, M.A.İnce, R. Mesiar, “Nullnorms on bounded lattices”, Inf. Sci. 325 (2015), 227-236. [4] F. Karaçal, M.N. Kesicioğlu, “A T-partial order obtained from t-norms”, Kybernetika 47 (2011), 300-314. [5] E.P. Klement, R. Mesiar, E. Pap, “Triangular norms”, Kluwer Academic Publishers, Dordrecht, 2000. [6] M. Mas, G. Mayor, J. Torens, “t-Operators”, Int. J. Uncertain. Fuzziness Knowl.-Based Syst. (1999) 31-50.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
About the Grundy coloring critical graphs
Noureddine Ikhlef-Eschouf Department of Mathematics and Computer Sciences, University of Yahia Farès Médéa, Algeria [email protected]
Abstract:Let G be a graph with a vertex-set V. A proper coloring of a graph G with k colors is a partition {V1,V2,…,Vk} of V into k independent sets (color classes). A vertex v Vi is a Grundy vertex if it is adjacent to at least one vertex in each color class Vj for every j < i. A Grundy coloring is a proper coloring such that every vertex is a Grundy vertex, and the Grundy number (G) of a graph G is the maximum number of colors in a Grundy coloring. A graph G is called g- edge critical if the removal of any edge of G decreases its Grundy number. In this paper, we explain some properties in g-edge critical graphs, and as consequence, we characterize trees, P4-sparse graphs and d-regular graphs that are g-edge critical. Keywords:Coloring, Grundy coloring, Grundy number, edge-critical graphs References: [1] C.A. Christen and S. M. Selkow, Some Perfect coloring properties of graphs, H. Combin. Theory Ser. B27 (1979) 49-59. [2] Results on the Grundy chromatic number of graphs, Discrete Appl. V. 306, 23(2006), 3166-3173.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
f - Statistical Boundedness of Order α
Mikail Et and Hüseyin Sönmez Department of Mathematics, Firat University, Elazığ, Turkey [email protected] [email protected]
Abstract: In this paper, using an unbounded modulus function, we introduce the notion of f-statistical boundedness of order α for scalar sequences and give some relations about this concept. Keywords: Statistical Convergence, Statistical boundedness, Modulus function. References: [1] Bhardwaj V. K. and Gupta, S. On some generalizations of statistical boundedness, J. Inequal. Appl. 2014, 2014:12 [2] Çolak R. Statistical Convergence of Order α. Modern Methods in Analysis and Its Applications, NewDelhi, India: Anamaya Pub., 2010: 121-129. [3] H. Fast, “Sur la convergence statistique”, Colloq. Math. 2(1951), 241-244. [4] J. A. Fridy, “On statistical convergence”, Analysis, 5(1985), 301-313. [5] I. J. Schoenberg, “The integrability methods”, Amer. Math. Monthly, 66(1959), 361-375. [6] E. Savaş, “Asymptotically J-lacunary statistical equivalent of order $\alpha$ for sequence of sets” J. Nonlinear Sci. Appl. 10(6) (2017), 2860-- 2867 [7] T. Salat, “On statistically convergent sequences of real numbers”, Math Slovaca, 30.2(1980), 139-150.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
The influence of fluid pressure on the displacement of the basilar membrane
Aboulkhouatem Fatima-Ezzahra Department of Mathematics and Computer Science, Faculty of Sciences Ben M'sik, Hassan II University, Casablanca, Morocco [email protected]
Abstract: An increase of pressure on the structure of cochlea causes hearing loss. In this paper, we established the relationship between the pressure and the amplitude of displacement of Basilar membrane. Therefore, our goal is to clarify the mechanisms of hearing loss caused by increasing of pressure. So, a mathematical cochlear model was formulated using finite difference method in order to explain and demonstrate this malfunction in passive model. Numerical simulations are helpful tools which may extend and complete the understanding of the cochlea physiology. Keywords: Mathematical model, hearing loss, Basilar membrane, Finite difference method, Fluid pressure. References: [1] K. Kamieniecki, J. Piechna & P. Borkowski, “Basilar Membrane Vibration in Time Domain Predicted by Fluid–Structure Interaction Model in Pre-and Post- stapedotomy State”, Procedia IUTAM, 24(2017), 48-63. [2] M. Jimenez-Hernandez, “Power analysis of the basilar membrane in the cochlea by mechanical resonance”, Rev. Mex. Ing. Bioméd , 38(2017), 1. [3] S.T. Neely , “Mathematical modeling of cochlear mechanics”, J. Acoust. Soc. Am., 78(1985), 345-352. [4] L.C. Peterson, B.P. Bogert, “A dynamical theory of the Cochlea”. J. Acoust. Soc. Am. 22(1952), 175-84.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Change of the Cochlear Michromechanics model due to fluid presure
Kouilily Fatiha Department of Mathematics and Computer Science, Faculty of Sciences Ben M'sik, Hassan II University, Casablanca, Morocco [email protected]
Abstract: Abnormality in the disposition of the structure of the inner ear leads to hearing loss. In this paper, we studied the effect of fluid pressure on the displacement of Basilar Membrane (BM) model included the amplification mechanism of Outer hair cell (OHC) using finite difference method. As result the distribution of the characteristic frenquency was observed and the displacement of the BM was decreased by applying a fluid pressure to BM. These changes are considered to be the reasons for hearing loss caused by fluid pressure. Keywords: Basilar membrane, Outer hair cell, hearing loss, Fluid pressure. References: [1] Lee, S., & Koike, T. (2017). Simulation of the Basilar Membrane Vibration of Endolymphatic hydrops. Procedia IUTAM, 24, 64-71. [2] Kouilily, F., Aboulkhouatem, F. E., Yousfi, N., & Achtaich, N. Predicting the Effect of Physical Parameters on the Amplitude of the Passive Cochlear Model. [3] S.T. Neely, “Mathematical modeling of cochlear mechanics”, J. Acoust. Soc. Am., 78(1985), 345-352.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Optimal scientific production over the life cycle
Gustav Feichtinger ORCOS, Institute of Statistics and Mathematical Methods in Economics, Vienna University of Technology, Vienna, Austria. [email protected] Dieter Grass ORCOS, Institute of Statistics and Mathematical Methods in Economics, Vienna University of Technology, Vienna, Austria. Peter M. Kort Econometrics and Operations Research, Tilburg School of Economics and Management Tilburg, Netherlands
Abstract: The paper develops an optimization model of the career of a scientist. Recognizing that research efforts and networking get more efficient if the scientist is more knowledgeable, history dependent solutions are developed. We give a theoretical underpinning of the four different research patterns detected in [1]. If the scientist does not bother about his reputation at the end of his career, we show that a sufficient education level is needed for the scientist to develop a typical research pattern where productivity increases in the beginning of his career, while it declines towards retirement. If the education level is not sufficient, a fading research pattern will result where productivity declines over time. On the other hand, when the scientist appreciates to have a good reputation at the end of his career, sufficient education will result in increasing productivity over the career lifetime, preventing a midlife slump. Keywords: Optimal control, research patterns, Skiba, age-dependent scientific production, networking: initial knowledge References: [1] Way, S. F., Morgan, A. C., Clauset, A., Larremore, D. B., 2017. The misleading narrative of the, canonical faculty productivity trajectory. Proceedings of the National Academy of Sciences 114 (44), E9216–E9223
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
The Extended b-Metric Space and Related Fixed Point Results
Andreea Fulga Department of Mathematics and Computer Science, Transilvania University of Brasov, Romania [email protected]
Abstract. Very recently, Kamran et al. [7] replaced the modified triangle inequality 푑(푥, 푧) ≤ 푠(푑(푥, 푦) + 푑(푦, 푧)) by 푑(푥, 푧) ≤ 휃(푥, 푧)(푑(푥, 푦) + 푑(푦, 푧)) where 휃: 푋 × 푋 → [1, ∞) and they proved a Banach type fixed point theorem. In this paper, continuing in this direction, we investigate the existence of fixed points of certain mapping in the frame of extended b-metric space. We state some examples to illustrate our results. References [1] H. Afshari, H. Aydi, E. Karapinar, “Existence of Fixed Points of Set-Valued Mappings in b-Metric Spaces”, East Asian mathematical journal, volume 32, issue 3, 2016, Pages 319 332 [2] U. Aksoy, E. Karapınar and Y. M. Erhan, “Fixed points of generalized alpha- admissible contractions on b-metric spaces with an application to boundary value problems”, Journal of Nonlinear and Convex Analysis, (2016), Volume 17, Number 6, 1095-1108 [3] M. Bota, C. Chifu, E. Karapinar, “Fixed point theorems for generalized (alpha-psi)-Ciric-type contractive multivalued operators in b-metric spaces” J. Nonlinear Sci. Appl. 9 (2016), Issue: 3 pages 1165-1177 [4] L.B. Ciric, “On some maps with a nonunique fixed point.”, Publ. Inst. Math., 17, 52–58 (1974). [5] M. Geraghty, “On contractive mappings”, Proc. Amer. Math. Soc. 40(1973), 604-608. [6] E. Karapinar, A New Non-Unique Fixed Point Theorem, J. Appl. Funct. Anal. 7 (2012), no:1-2, 92-97 [7] T. Kamran, M. Samreen, O. U. Ain, “A Generalization of b−Metric Space and Some Fixed Point Theorems”
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Suborbital Graphs For a Special Subgroup of the Normalizer
Nazlı Yazıcı Gözütok and Bahadır Özgür Güler Department of Mathematics, Karadeniz Technical University, Trabzon, Turkey [email protected], [email protected]
Abstract: Let 푃푆퐿(2, ℝ) denote the group of all linear fractional transformation 푎푧 + 푏 푇: 푧 → , 푤ℎ푒푟푒 푎, 푏, 푐 푎푛푑 푑 푎푟푒 𝑖푛 ℝ 푎푛푑 푎푑 − 푏푐 = 1. 푐푧 + 푑 In terms of matrix representation, the elements of 푃푆퐿(2, ℝ) correspond to the matrices 푎 푏 ± ( ) ; 푎, 푏, 푐 푎푛푑 푑 푎푟푒 𝑖푛 ℝ 푎푛푑 푎푑 − 푏푐 = 1. 푐 푑 This is the automorphism group of the upper half plane ℍ ≔ {푧 ∈ ℂ: 퐼푚(푧) > 0}. The modular group Γ is the subgroup of 푃푆퐿(2, ℝ) such that 푎, 푏, 푐, 푑 are integers. Γ0(푁) = {푔 ∈ 훤: 푐 ≡ 0(푚표푑 푁)} is a well known congruence subgroup of the classical modular group Γ for a positive integer 푁. The normalizer of
Γ0(푁) in 푃푆퐿(2, ℝ) turns to be a very important group in the study of moonshine and for this reason has been studied by many authors. It consists exactly of the matrices 푎푒 푏/ℎ ( ) 푐푁/ℎ 푑푒 where all parameters are integers, 푒|| 푁 and ℎ is the largest divisor of 24 for ℎ2 which ℎ2|푁 with understandings that the eterminant 푒 of the matrix is positive, and that 푟||푠 means that 푟|푠 and (푟, 푠) = 1 (푟 is called an exact divisor of s). We 푟 denote the normalizer by Γ퐵(푁). Jones, Singerman and Wicks examined suborbital graphs o the modular group Γ [1]. After this, similar studies were done for related finitely generated groups. Since the group structure of 훤퐵(푁) is much more complex than the modular group, its suborbital graphs have been studied under various restriction in many studies [2,3]. Two important subgroups of
Γ퐵(푁) are Γ푊(푁) and Γ퐶(푁). Suborbital graphs of the Atkin-Lehner group
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Γ푊(푁) is also studied in [4]. The aim of this paper fills the gap in literature examining suborbital graphs of Γ퐶(푁). Keywords: Normalizer, Congruence subgroup, Suborbital graphs. References: [1] G. A. Jones, D. Singerman, K. Wicks, “The modular group and generalized Farey graphs”, London Math. Soc. Lecture Note Series, 160(1991), 316-338. [2] B.Ö. Güler, M. Beşenk, A.H. Değer, “Elliptic Elements and Circuits In Suborbital Graphs”, Hacettepe Journal of Mathematics and Statistics, 40(2011), 203-210.
[3] R. Keskin, “Suborbital graphs for the normalizer of 횪ퟎ(풎)”, European J Combin, 27(2)(2006), 193-206. [4]T. Köroğlu, B.Ö. Güler, Z. Şanlı, “Suborbital graphs for the Atkin-Lehner group”, Turk J Math., 41(2017), 235-243.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
푮푳(풏, ℝ) Invariants For a Curve Family
Uğur Gözütok, Yasemin Sağıroğlu Department of Mathematics, Karadeniz Technical University, Trabzon, Turkey [email protected] , [email protected]
Abstract: Differential geometry of curves has been studied in many aspects in the groups 푆퐿(푛, ℝ), 퐸퐴(푛, ℝ), 퐺퐿(푛, ℝ) which are the subgroups of the affine group. In some of these studies, invariants such as arc-length, curvature have been examined. In [1] centro-affine invariants, arc length and curvature functions, of a curve in affine 푛 −space are obtained. In addition, several authors studied the affine curves and their invariants in several works [2,3]. Invariants of 푛 curves and equivalence of 푛 curves in 푆퐿(푛, ℝ) are investigated in [4]. In 푆퐴푓푓(푛, ℝ), the equivalence problem of two curves is studied in [5]. In this study, the system of differential invariants for three curves in 퐺퐿(푛, ℝ) is studied and by using this system, equivalence of two curve families which consist of three curves is obtained. Also, it is shown that the system of differential invariants of this curve family is minimal. It should be noted that we study the problem under a fixed parametrization of the curves. Keywords: Differential invariants, equivalence problem, curves References: [1] H. Liu, “Curves in affine and semi Euclidean spaces”, Results. Math., 65(2014), 235-249. [2] P.J. Giblin, T. Sano, “Generic equi-centro-affine differential geometry of plane curves”, Topology Appl., 159(2012), 476-483. [3] D. Khadjiev, Ö. Pekşen, “The complete system of global differential and integral invariants for equi-affine curves”, Dif. Geom. Appl., 20(2004), 167-175. [4] Y. Sağıroğlu, “Centro-equiaffine differential invariants of curve families”, IEJG, 9(2016), 23-29. [5] Y. Sağıroğlu, “Equi-affine differential invariants of a pair of curves”, TWMS J. Pure Appl. Math., 6(2015), 238-245.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Conditions for Ruled Surfaces Obtained by Bending to be Developable Uğur Gözütok1, Hüsnü Anıl Çoban2, Yasemin Sağıroğlu3 Department of Mathematics, Karadeniz TechnicalUniversity, Trabzon, Turkey [email protected] [email protected] sagı[email protected]
Abstract: Ruled surfaces, being a special type of surface, have an important place in the study of surfaces, because ruled surfaces are the easiest of all to parametrize. In the papers [1,2], authors study some properties of ruled surfaces. The ruled surfaces with vanishing Gaussian curvature, which can be transformed into the plane without any deformation and distortion, are called developable surfaces. These surfaces are related to various applications from contemporary architacture to manufacturing of clothing, since they are suitable to the modeling of surfaces which can be made out of leather, paper, fiber, and sheet metal [3,4]. In this study, we consider the infinitesimal bending of a curve to obtain a ruled surface. We reveal the relation between them and give conditions to get a developable surface from a ruled surface obtained by bending. Keywords: Ruled Surfaces, Bending of Curves, Developable Surfaces. References: [1] Izumiya, S., Takeuchi, N., “Special curves and ruled surfaces”, Contributions to Algebra and Geometry 44(1), 203-212, 2003. [2] Ali, A.T., Aziz, H.S.A., Sorour, A.H., “Ruled surfaces generated by some special curves in Euclidean 3-space”, Journal of the Egyptian Mathematical Society 21(3), 285-294, 2013. [3] Glaeser, G., Gruber, F., “Developable surfaces in contemporary architecture”, Journal of Mathematics and the Arts 1(1), 59-71, 2007. [4] Liu, Y., Pottmann, H., Wallner, J., Yang, Y.L., Wang, W., “Geometric modeling with conical meshes and developable surfaces”, ACM Transactions on Graphics 25(3), 681-689, 2006.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Some Generalizations of Ricci Solitons Admitting Standard Static Spacetime Metric
Sinem Güler Department of Mathematics, Istanbul Technical University, Istambul, Turkey [email protected]
Abstract: In this talk, we focus on certain generalizations of Ricci solitons endowed with the standard static spacetime metric and we give some characterizations of such spacetimes via their potential functions. Also, some necessary and sufficient conditions have been obtained regarding the questions of the existence of certain vector fields on such standard static spacetimes. In the final part of this presentation, by taking into account the Walker metric, we construct some explicit examples of the spacetimes we are working on. Keywords: Standard Static Spacetime, Ricci Soliton, Walker metric. References: [1] F. Dobarro, B. Ünal, “Special standard static spacetimes”, Nonlinear Analysis: Theory, Methods and Applications. 59(2004), 759-770. [2] G. Catino, “Generalized quasi Einstein manifols with harmonic Weyl tensor”, Math. Z., 271(2012), 751-756. [3] F. Dobarro, B. Ünal, “Characterizing killing vector fields on standard static spacetimes”, J. Geo. Phys., 62(2012), 1070-1087. [4] B. O’Neill, “Semi-Riemannian geometry with applications to Relativity”, Academic Press, NewYork, (1983), 336-341.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Rough I - Statistical Convergence of Weight g
Hafize Gümüş Department of Mathematics Education, Necmettin Erbakan University, Konya, Turkey [email protected]
Abstract: We know from previous studies, it has been shown that we can extend the concept of natural or asymptotic density by considering natural density of weight g. The function 푔: 푁 → [0, ∞) mentioned here satisfies lim 푔(푛) = ∞ 푛→∞ and lim 푛 ≠ 0 properties. By using this extension, we define rough I- 푛→∞ 𝑔(푛) statistical convergence of weight g which is a natural combination of rough convergence and I-statistical convergence of weight g. We also investigate some observations about these new classes. Keywords: Rough Convergence, I- convergence, I- statistical convergence. References: [1] Aytar, S., 2008, Rough statistical convergence, Numerical Functional Analysis and Optimization, 29, Issue 3-4, 291-303. [2] Dündar, E. and Çakan, C., 2014, Rough I-convergence, Demonstratio Mathematica, Vol. XLVII, No.3. [3] Pal, S. K., Chandra, D. and Dutta, S., 2013, Rough ideal convergence, Hacettepe Jour. of Math.and stat., Vol. 42(6), 633-640. [4] Phu, H. X., 2002, Rough convergence in normed linear spaces, Numer. Funct. Anal. Optmiz. 22:201-224. [5] Savaş, E., 2017, On I-lacunary statistical convergence of weight g of sequences of sets, Filomat 31:16, 5315-5322.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
The concept of I-Asymptotically Lacunary Statistical Equivalence of Interval Numbers and A Generalization With A Positive 푝 Sequence
Hafize Gümüş* and Nihal Demir** *Department of Mathematics Education, Necmettin Erbakan University, Konya, Turkey [email protected] **İkizli Middle School, Emirgazi, Konya, Turkey [email protected]
Abstract: Previous studies for statistical convergence and I-convergence have recently begun to study for interval numbers. One of these studies is asymptotically lacunary statistical equivalence concept defined by Esi [4]. In our study, we define the concept of I-asymptotically lacunary statistical equivalence of interval numbers and we extend it for any sequence of positive numbers
푝 = (푝푘). We will examine our studies separately according to whether 푝 is constant or not. Keywords: I-statistical convergence, lacunary I-statistical convergence, asymptotic equivalence, interval numbers References: [1] P. Kostyrko, T. Salát and W. Wilezyński, “I-Convergence”, Real Analysis Exchange Vol. 26(2), (2000), 669-686. [2] M. S. Marouf, “Asymptotic Equivalence And Summability”. Internat. Jour. Math & Math. Sci. Vol. 16 No.4 (1993), 755-162. [3] E. Savas and R. F. Patterson, “An Extension Asymptotically Lacunary Statistical Equivalent Sequences”, Aligarh Bull. Math. 27(2),(2008), 109-113. [4] A. Esi and A. Esi, “Asymptotically Lacunary Statistically Equivalent Sequences of Interval Numbers”, Int. Jour. of Math. and its Appl.1 (1),(2013), 43-48.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Exact Solution of Some Nonlinear Partial Differential Equation
Hami Gündoğdu, Ömer Faruk Gözükızıl Department of Mathematics, Sakarya University, Sakarya, Turkey [email protected], [email protected]
Abstract: In this paper, we are interested in obtaining the approximate analytical solutions of nonlinear partial differential equations. In this regard, the Laplace decomposition method is utilized. Nonlinear Gardner equation and Benjamin- Bona-Mahony-Peregrine-Burgers equation are studied. The method is applied to these equations with their initial values. Then, the solutions satisfying the given initial condition are gained. Keywords: Laplace decomposition method, Gardner equation, Benjamin-Bona- Mahony-Peregrine-Burgers equation . References:
[1] Damil N., Potier-Ferry M., Najah A., Chari R., Lahmam H., An iterative method based upon Pade approximamants, Communications In Numerical Methods In Engineering, 15, (1999), 701-708.
[2] He J.-H., A coupling method of homotopy technique and perturbation technique for nonlinear problems, International Journal Of Non-Linear Mechanics, 35, (2000), 37-43
[3] He J.-H., An approximate solution technique depending upon artificial parameter, Communications in Nonlinear Science and Numerical Simulaton, 3, (1998), 92-97.
[4] T.B. Benjamin, J.L. Bona, J.J. Mahony, Model equations for long waves in nonlinear dispersive systems, Philos TransR Soc London, Ser A, 272 (1972) 47-78.
[5] Peregrine D. H., Calculations of the development of an undular bore, J. Fluid Mech., 25, (1996), 321-330.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
On Invariance of Hyperstoneanness under Lattice Isomorphisms
Banu Güntürk 1,Bahaettin Cengiz 2 1Faculty of Engineering, Baskent University, Ankara, Turkey [email protected] 2Faculty of Engineering, Baskent University, Ankara, Turkey [email protected]
Abstract: Let 푋 and 푌 be compact Hausdorff spaces with 푌 hyperstonean. In this paper we prove that if 퐶(푋, ℝ) and 퐶(푌, ℝ) are lattice isomorphic then these Banach spaces are linearly isometric and, consequently, 푋 and 푌 are homeomorphic, which in turn implies that 푋 is also hyperstonean. Actually we prove more than what is announced in the headline above. This result, in some ways, is a generalization of the well-known Banach-Stone theorem.
Keywords: Hyperstonean space, Banach-Stone theorem, lattice isomorphism.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Nanofluid flow due to rotating disk with variable thickness and homogeneous-heterogeneous reactions
Tasawar Hayat, Madiha Rashid, Maria Imtiaz and Ahmed Alsaedi, Department of Mathematics, Department of Mathematics, Quaid-I-Azam University 45320,Islamabad 44000, Pakistan Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia [email protected] Abstract: An analysis has been carried out to examine the water based nanofluid flow with silver nanoparticles. Flow due to a rotating disk with variable thickness is considered. Heat and mass transfer subject to volume fraction of nanoparticles and homogeneous-heterogeneous reactions are examined. Homotopy concept is utilized for the development of solutions. Special emphasis is given to the non-dimensional velocity, temperature, concentration, skin friction coefficient and Nusselt numbers. It is observed that with an increase in disk thickness the radial, axial and azimuthal velocities are enhanced. Here surface shear stress rates increase for larger thickness coefficient of disk and volume fraction of silver based nanoparticles while magnitude of heat transfer rate decreases for higher thickness coefficient of disk. Keywords: Variable thickness; Rotating disk; Nanofluid; Homogeneous- heterogeneous reaction. References: [1] S. U. S. Choi and J. A. Eastman, Enhancing thermal conductivity of fluids with nanoparticles ASME Int. Mech. Eng. Cong. Expo. 66 (1995) 99-105. [2] T. Fang, J. Zhang and Y. Zhong, Boundary layer flow over a stretching sheet with variable thickness, Appl. Math. Comp. 218 (2012) 7241-7252. [3] M. Turkyilmazoglu, Nanofluid flow and heat transfer due to a rotating disk, Comp. Fluids 94 (2014) 139-146. [4] T. Hayat, M. Imtiaz, A. Alsaedi and F. Alzahrani, Effects of homogeneous- heterogeneous reactions in flow of magnetite-Fe₃O₄ nanoparticles by a rotating disk, J. Mol. Liq. 216 (2016) 845-855. [5] S.AS. Liao, On the homotopy analysis method for nonlinear problems, App. Math. & Comput. 147 (2004) 499-513.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Spectral Theory of 풒, 흎 -Dirac System
Fatma Hıra Department of Mathematics, Hitit University, Çorum, Turkey [email protected]
Abstract: Hahn [1] introduced the difference operator f( qt+−) f( t) D f( t) = , where 01q and 0 are fixed real q, (qt+−) t number. This operator extends the classical difference operator ftft( +−) ( ) =ft( ) as well as Jackson [2] q - difference operator fqtft( ) − ( ) Dft ( ) = . In this paper, we introduce q, -analogue of q (qt−1) Dirac system and obtain some spectral properties of this q, -Dirac system similar to -Sturm-Liouville problems in [3]. Keywords: q,w-Dirac system, Hahn difference operator. References: [1] W. Hahn,“Über orthogonalpolynome, die q-differenzenlgleichungen genügen”, Math. Nachr. 2(1949), 4-34. [2] F.H. Jackson, “Basic integration”, Quart. J. Math. 2(1951), 1-16. [3] M. H. Annaby, A. E. Hamza, and S. D. Makharesh, “A Sturm–Liouville Theory for Hahn Difference Operator”, Frontiers in Orthogonal Polynomials and q-Series: (2018) pp. 35-83.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Self-Organizing Map of Artificial Neural Networks for superficial sediments classification of the Sidi Chahed dam (NE of Meknes, Morocco)
Abdellah El HMAIDI1, Mohamed BERRADA2, Abdelaziz ABDALLAOUI3, Ali ESSAHLAOUI1 and Abdelhadi El OUALI1 1 University of Moulay Ismail, Faculty of Science, Department of Geology, Research Team "Water Sciences and Environmental Engineering", BP 11201, Zitoune, Meknes, Morocco. Email: [email protected] 2University of Moulay Ismail, ENSAM, Laboratory of Mathematical and Computational Modeling, Marjane II, BP 15290, Al Mansour, 50000, Meknes, Morocco. 3University of Moulay Ismail, Faculty of Science, Department of Chemistry, Research Team "Analytical Chemistry and Environment", BP 11201, Zitoune, Meknes, Morocco.
Abstract: The dam of Sidi Chahed is located downstream of the Mikkes and Lmaleh rivers. It is located about 30 km NE of Meknes city in north of Morocco. The classification approach proposed in this work is based on a network of artificial neurons type of self-organizing map (SOM). It has been applied on the physico-chemical parameters of surface sediments of the dam Sidi Chahed. The use of ArcGIS software enabled the realization of thematic maps related to the distribution in time with the seasons, and space from upstream to downstream of the dam. The principal component analysis (PCA) and hierarchical classification by SOM (SOM-HC) validated classification and detected seasonal variations in physical and chemical parameters of the sediment dam Sidi Chahed. Dependencies between different parameters have been identified and their spatial and temporal distribution. The classes obtained were represented by season. The studied sediments generally have slight physicochemical changes that are related to the importance of the geological formations, anthropogenic activity and particularly strong surrounding farming. Keywords: Dam Sidi Chahed, Self-organizing map (SOM), Artificial Neural Networks, Physico-chemical parameters, Superficial sediments, ACP, AHC, GIS.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Zero Operator Products on Hardy and Bergman spaces
Mualla Birgül Huban, Mübariz Garayev and Mehmet Gürdal Department of Mathematics, Süleyman Demirel University, Isparta,Turkey [email protected]
Abstract:In this paper, we study zero operator products, in particular, zero Toeplitz products. It is proved that if 1,...,n L (T) are n functions and
F 2 H1,...,Hn are operators from the Engliš algebra H such that (T + H )...(T + H )= 0, then ... = 0. This generalizes the known 1 1 n n 1 2 n Douglas' lemma. In particular, we obtain a new proof of Brown-Halmos theorem. The similar results are proved for zero Toeplitz products on the 2 Bergman space La . In particular, we partially solve a conjecture due to Čučkovič [5] (see Corollary 4.7).
Keywords:Reproducing kernel, Berezin symbol, Toeplitz operator, Hardy space, Bergman space. References: [1] A. Aleman and D. Vukotic, "Zero products of Toeplitz operators", Duke Math. J. 148(3)(2009),373-403. [2]S. Axler, S.-Y. A. Chang and D. Sarason, "Products of Toeplitz operators”, Integral Equations Operator Theory, 1(1978), 285-309. [3] Ž, Čućković, "Berezin Versus Mellin", J. Math. Anal. Appl. 287 (2003), 234- 243. [4]K. Zhu, “Operator Theory in Function Spaces”, Marcel Dekker, New York, 1990.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Compactness and Engliś Algebra
Mualla Birgül Huban, Mübariz Garayev and Mehmet Gürdal Department of Mathematics, SüleymanDemirelUniversity, Isparta,Turkey [email protected]
Abstract:In this paper, we mainly interested with the following question: if 0 A, B,C belong to Engliš algebra A H , then under which conditions AB −C is a compact operator on a reproducing kernel Hilbert space (RKHS) H = H()?Here we characterize in terms of Berezin symbols compactness of the operator AB −C. Keywords: Reproducing kernel, Berezin symbol, Compact operator, Engliś algebra. References: [1] S. Axler and D. Zheng, “Compact operators via the Berezin transform”, Indiana Uni. Math. 47(1998), 387-400. [2] M. Engliś, “Toeplitz operators and the Berezin transform on H2”, Linear Algebra Appl., 223/224 (1995), 171-204. [3] K. Zhu, “Operator Theory in Function Spaces”, Marcel Dekker, New York, 1990.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Solvability of Infinite Systems of Differential Equations in Some BK Spaces
Merve İlkhan and Emrah Evren Kara Department of Mathematics, Düzce University, Düzce, Turkey [email protected] [email protected]
Abstract: Infinite systems of ordinary differential equations define numerous real world problems which can be seen in the theory of branching processes, neural nets, mechanics etc. The theory of measure of noncompactness has been used in determining the classes of compact operators on some sequence spaces (cf. [1,2]). In [3,4], the authors have studied the solvability of infinite systems of differential equations in classical Banach sequence spaces by using the measure of noncompactness. In this presentation, we investigate solvability of infinite sysytems of differential equations in some BK spaces by applying the technique of measure of noncompactness. Keywords: Sequence spaces, BK spaces, Measure of noncompactness, Infinite system of differential equations. References: [1] M. Mursaleen and A.K. Noman, Applications of the Hausdorff measure of noncompactness in some sequence spaces of weighted means. Comput. Math. Appl., 60 (2010) 1245-1258. [2] M. Başarır, E.E. Kara, On the B-difference sequence space derived by generalized weighted mean and compact operators, J. Math. Anal. Appl., 391 (2012) 67-81. [3] J. Banas, M. Lecko, Solvability of infinite systems of di erential equations in Banach sequence spaces, J. Comput. Appl. Math., 137(2) (2001) 363-375. [4] M. Mursaleen, S.A. Mohiuddine, Applications of measure of noncompactness to the infinite system of differential equations in l_p spaces. Nonlinear Anal., 75 (2012) 2111-2115.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Dissipative Canonical Type Quasi-Differential Operators for First Order
Zameddin I. Ismailov and Pembe Ipek Al Department of Mathematics, Karadeniz Technical University, Trabzon, Turkey [email protected] Institute of Naturel Sciences, Karadeniz Technical University, Trabzon, Turkey [email protected]
Abstract: In this work, based on Calkin-Gorbachuk method a description of all maximally dissipative extensions of the minimal operator generated by first order linear symmetric singular canonical type quasi-differential expression in the weighted Hilbert space of vector-functions is given. Finally, the spectrum set of such extensions is studied. Keywords: Dissipative operator, quasi-differential operator, spectrum. References: [1] V. I. Gorbachuk and M. I. Gorbachuk, “Boundary Value Problems for Operator Differential Equations”,Kluwer, Dordrecht, (1999). [2] J. von Neumann, “Allgemeine eigenwerttheorie hermitescher funktionaloperatoren”, Math. Ann., 102(1929), 49-131. [3] C. Fischbacher, “On the Theory of Dissipative Extensions”, PhD Thesis, University of Kent School of Mathematics, Statistic and Actuarial Science, Canterbury, 2017. [4] B. Sz.-Nagy and C. Foias, “Analyse harmonique des operateurs de L’ espace de Hilbert”, Masson, Paris and Akad Kiodo, Budapest, (1997) (English transl, North-Holland, Amsterdam and Akad Kiado, Budapest: 1970). [5] F. S. Rofe-Beketov and A. M. Kholkin, “Spectral analysis of differential operators.”, World Scientific Monograph Series in Mathematics, 7(2005).
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Some Spectral Problems of Direct Sums of Operators
Zameddin I. ISMAILOV 1, Elif OTKUN ÇEVIK 2 1 Department of Mathematics, Karadeniz Technical University, Trabzon/TURKEY [email protected]
2Department of International Finance and Banking, Avrasya University, Trabzon/TURKEY [email protected]
Abstract: The connection between some spectral properties (as power and polynomial boundedness, nilpotentity, quasinilpotentity) of direct sum of operators in the direct sum of Hilbert spaces and its coordinate operators has been investigated. Keywords: Power bounded operator, polynomial bounded operator, nilpotent operator, quasinilpotent operator. References: [1] N. Dunford, “A Spectral Theory for Certain Operators on a Direct Sum of Hilbert Spaces”, Math. Ann., 162(1966), 294-330. [2] L.A. Fialkow, “A Note of Direct Sums of Quasinilpotent Operators”, Proc. Amer. Math. Soc., 48(1975), 125-131. [3] E.J. Ionascu, “On Power Bounded Operators”, Proc. Amer. Math. Soc., 125(1997), 1435-1441. [4] M.A. Naimark and S.V.Fomin, “Continuous Direct Sums of Hilbert Spaces and Some of Their Applications”,Uspehi Mat.Nauk.64 (1955), 111-142 (In Russian).
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
New Exact Travelling Wave Solution of the Generalized Ito Integro-Differential Equation
Anwar Jaafar Mohamad Jawad Al -Rafidain University College, Computer Engineering Department Baghdad,10014 Iraq.
Abstract: Three different methods are applied to construct new types of solutions of nonlinear evolution equations. First, the Csch method is used to carry out the solutions then the Extended Tanh-Coth method and the modified simple equation method are used to obtain the soliton solutions. The effectiveness of these methods is demonstrated by applications to the generalized Ito integro-differential equation. The solitary waves from the Csch and Tanh- Coth methods illustrate a significant similarity in behavior. The modified simple equation method does not produce the soliton solution in general case. The obtained solutions are very useful in the nonlinear evolution equations.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
A Radon-Nikodym type theorem for completely positive multilinear ϕ-maps on Hilbert C*-modules
Maria Joita Department of Mathematics Methods and Models, University Politehnica of Bucharest Bucharest Romania [email protected]
Abstract: In theory of quantum information, quantum operations are modeled by completely positive linear maps between C*-algebras. Stinespring [7] showed that an operator valued completely positive linear map on a C*-algebra A is of the forma V*π(⋅)V, where π is a ∗-representation of A and V is a bounded linear operator. A Stinespring type construction for a pair of completely positive linear maps on Hilbert C*-modules and C*-algebras was obtained by Bhat, Ramesh and Sumesh [1]. Christensen and Sinclair [5], were the first to formulate the notion of completely bounded (respectively, completely positive) multilinear maps from a C*-algebra into L(H). Using Wittstock's matricial Hahn-Banach theorem, they gave representations for completely bounded symmetric multilinear maps in terms of ∗-representations of the algebra and suitable bridging operators between the Hilbert spaces. As a generalization of invariant sesquilinear forms, Heo [2] introduced the notion of invariant multilinear maps and construct a family of commuting representations associated with a completely bounded and completely positive invariant multilinear map which extend the Stinespring's construction. This representation is different from the multilinear representation of Christensen and Sinclair, it does not depend on the concept of the matricial sublinearity as developed by Wittstock. In [4] it is proved a Stinespring type construction for a pair of symmetric invariant completely positive and completely bounded multilinear maps on Hilbert C*-modules and C*-algebras. Heo [3] introduced a partial order relation on the set of all operator valued symmetric invariant completely positive and completely bounded multilinear maps on C*-algebras. In this talk we will discuss about a Radon Nikodym type theorem for symmetric invariant completely positive and completely bounded multilinear maps on Hilbert C*-modules and C*-algebras [6]. ______101
INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Acknowledgement. The research was supported by "Excellence Research Grants" Program, UPB -- GEX 2017, No. SA 54-17-08 /2017. Keywords: completely positive multilinear map; invariant multilinear map; Hilbert C*-module; ϕ-map References: [1] B.V.R. Bhat, G. Ramesh, K. Sumesh, "Stinespring's theorem for maps on Hilbert C*-modules," J. Operator Theory, 68(2012), 173--178. [2] J. Heo, "Representations of invariant multilinear maps and Hilbert C*- modules", Israel J. Math. 118(2000), 125--146. [3] J. Heo, "A Radon-Nikodym theorem for completely positive invariant multilinear maps and its applications", Math. Proc. Camb. Phil. Soc. 132(2002), 181--192. [4] J. Heo, M. Joiţa, "A Stinespring type theorem for completely positive multilinear maps on Hilbert C*-modules", To appear in Linear and Multilinear Algebra. [5] E. Christensen, A. Sinclair, "Representations of completely bounded multilinear operators", J. Funct. Anal. 72(1987), 151--181. [6] J. Heo, M. Joiţa, "A Radon-Nikodym type theorem for symmetric invariant completely positive and completely bounded maps on Hilbert C*-modules", preprint. [7] W. Stinespring, "Positive functions on C*-algebras", Proc. Amer. Math. Soc.,6(1955),211-216.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Approximating Fixed Points of Certain Nonlinear mappings in CAT(0) Spaces
Amna Kalsoom and Hafiz Fukhar ud Din Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan [email protected]
Abstract: CAT(0) space was firstly introduced by Alexandrov in 1950's [1]. Fixed point theory in CAT(0) spaces was firstly studied by Kirk [2]. He also assured the existence of fixed point in nonexpansive mapping defined on a bounded closed and convex subset of a complete CAT(0) space. Nonexpansive mappings are continuous on their domain. In 2016 Rajendra Pant & Rahul Shukla introduce a new type of nonexpansive mappings, α-nonexpansive mapping, Suzuki type generalized nonexpansive mapping , generalized α- nonexpansive mapping which don’t need to be continuous. They also presented some existence and convergence theorem for generalized nonexpansive mapping in Banach space. In 1976, Lim [4] presented the concept of Δ-convergence in general metric spaces and in Kirk and Panyank [5] specialized this concept to CAT(0) space. They show that many weak convergence theorems in a Banach space setting can be extended to a CAT(0) space. In this paper we extend the above mappings on CAT(0) space. Some convergence results including Δ- convergence and strong convergence for generalized α-nonexpansive mapping on CAT(0) space using some iterative schemes faster than Mann and Ishikawa are also discussed. Some useful examples are given to illustrate the importance of generalized α-nonexpansive mapping. Keywords: generalized α-nonexpansive mapping, CAT(0) Space, Δ- convergence, References: 1 W. A. Kirk, Geodesic geometry and fixed point theory, In Seminar of Mathematical Analysis 64(2003)195-225. 2 W. A. Kirk, A fixed point theorem for mappings which do not increase distances, Am. Math. Monthly. 72(1965)1004-1006.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
3 R. Pant, R. Shukla, Approximating fixed points of generalized α-nonexpansive mappings in Banach spaces, Numerical Functional Analysis and Optimization. 38(2017)248-266 4 T. C. Lim, Remarks on some fixed point theorems, Proc. Amer. Math. Soc. 60(1976)179-182. 5 W. A. Kirk, B. Panyanak, A concept of convergence in geodesic spaces, Nonlinear Anal. 68(2008)3689-3696
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
A Parallel Multiobjective Evolutionary Algorithm with an application to the Knapsack Problem
Nedjmeddine Kantour 1, Sadek Bouroubi 2, Djamel Chaabane 3. Faculty of Mathematics, University of Sciences and Technology Houari Boumedien, Algiers, Algeria [email protected], [email protected], [email protected]
Abstract: In this presentation, we propose a parallel multiobjective evolutionary algorithm, with an application to the Mutliobjective Knapsack Problem. The suggested search strategy is based on a periodic decomposition of potentially efficient solutions, while combining both criterion-based and dominance-based approaches. It addresses two main sub-objectives: (1) minimizing the distance between the current non-dominated solutions and the ideal point, (2) ensuring the spread of potentially efficient solutions. Experimental results are included, where we compare the suggested algorithm against some of well-known multiobjective Metaheuristics. Keywords: Multiobjective optimization, Evolutionary Algorithms, Knapsack Problem. References: [1] Srinivas, N. and Deb, K. (1995) Multi-Objective function optimization using non-dominated sorting genetic algorithms, Evolutionary Computation, 2(3): 221- 248. [2] K Deb, A Pratap, S Agarwal, T Meyarivan. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE transactions on evolutionary computation, 2002. [3] E. Zitzler and L. Thiele. Multiobjective Evolutionary Algorithms: A Comparative Case Study and the Strength Pareto Approach. IEEE Transactions on Evolutionary Computation, 3(4): 257-271, November 1999. [4] E. Zitzler, M. Laumanns, and L. Thiele. SPEA2: Improving the Strength Pareto Evolutionary Algorithm. EUROGEN 2001. Evolutionary Methods for Design, Optimization and Control with Applications to Industrial Problems, pages 95-100, Athens, Greece, 2001. ______105
INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Some Properties of t-closure Operators
Funda Karaçal 1 and Mehmet Akif İnce 2 1 Department of Mathematics, Karadeniz Technical University, Trabzon, Turkey [email protected] 2 Department of Mathematics, Recep Tayyip Erdoğan University, Rize, Turkey [email protected]
Abstract: Closure operators have influenced many areas of mathematics and have been studied on a variety of structures (on lattices, on topological spaces, on fuzzy sets, on graphs, in categories, etc.). In this regard, closure operators are not only an abstract concept that works in the theoretical sense but also important maps which have many applications on various areas ( [3,4,7]). Schweizer and Sklar ([8]) introduced triangular norms (or just t-norm) in the framework of probabilistic metric spaces and their definition is based on a notion used by Menger in order to extend the triangle inequality in the definition of metric spaces towards probabilistic metric spaces. In this study, based on the knowledge of the existence of t-norms on an arbitrary given bounded lattice, we introduce t-closure operators with the help of a t-norm on the lattice and a subset of the lattice including the top element. We define two equivalence relations by using t-closure operators. The first one is on the set of all t-norms on a bounded lattice. An important class is obtained according to this relation. We define a partially order on the set of all equivalent relations given as secondly. Lastly, we define a set, denoted by 퐿∗, and by using this set, we investigate under which conditions 퐿 can be embedded into 퐿 . 퐶퐴,푇 Keywords: Closure operator, triangular norm, bounded lattice. References: [1] G. Birkhoff, Lattice Theory, 3 rd edition, Providence, 1967. [2] S. Burris, H. P. Sankappanavar, A Course in Universal Algebra, Springer- Verlag, 1981. [3] K. Denecke, J. Koppitz, Closure Operators and Lattices, in: M-Solid Varieties of Algebras. Advances in Mathematics, vol 10. Springer, Boston, MA.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
[4] V. Even, M. Gran, Closure operators in the category of quandles, Topology and its Applications, 200 (2016), 237-250. [5] M.A. İnce, F. Karaçal, R. Mesiar, Medians and nullnorms on bounded lattices, Fuzzy Sets and Systems, 289 (2016), 74-81. [6] E.P. Klement, R. Mesiar, E. Pap, Triangular Norms, Kluwer Academic Publishers, Dordrecht, 2000. [7] B. Pang, Y. Zhao, Z. Xiu, A new definition of order relation for the introduction of algebraic fuzzy closure operators, International Journal of Approximate Reasoning, 92 (2018), 87-96. [8] B. Schweizer, A. Sklar, Probabilistic Metric Spaces, Elsevier, Amsterdam, 1983.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
The Kinematic Model of Nonuniform Rotation of Liquid Medium
Zurab Kereselidze1, Marina Chkhitunidze1, Irine Khvedelidze1, Nino Zhonzholadze2 1M.Nodia institute of Geophysics, Ivane Javakhishvili Tbilisi State University, Tbilisi, Georgia, [email protected], [email protected], [email protected] 2Telavi Iakob Gogebashvili State University, Telavi, Georgia, [email protected]
Abstract: Development of perturbances in a liquid medium may be formally considered as a failure of uniform rotation, the result of which in most cases is initiation and development of nonuniform motion . Perfect modeling of such process, regarding the solution of motion equation, may appear either very difficult or completely impossible due to specific mathematical problems. In this case the matter is the approximation of the rotation velocity field, which must be sufficiently adequate for the real motion. In some cases such goal is reached by means of some kinematic model of velocities. By strict standards it must satisfy certain criteria, so called conditions of motion dynamics. We consider the above criteria are fulfilled by following plane kinematic model [1] 1 푟 푟 푉푟 = 푢0 ( ) (푐표푠휑 + 푠𝑖푛휑), 푉휑 = 푢0 ( ) (푐표푠휑 − 푠𝑖푛휑), 2 푅0 푅0 where 푅0- the characteristic radius, 0< 푟 ≤ 푅0, 0 < 휑 < 2휋, 푢0 - the characteristic velocity of rotational noncompressible liquid. It is obvious that the restrictions imposed by the probable dynamics reduce the class of the flows, which may be modeled in kinematic approximation. However, at the same time the restrictions raise the value of the kinematic models, which are sufficiently adequate for some types of motions realized in some cases. Keywords: Kinematic model, velocity. References: [1] V.Kirtskalia, Z. Kereselidze, N. Dzonzoladze and M. Chkhitunidze. An Analytical Model of an Asymmetrical Temperature Field in the Polar and Auroral Ionosphere. Georgian International Journal Of Science and Technology, Volume3,Issue4,pp.381-390.2012 https://www.novapublishers.com/catalog/product_info.php?products_id=32804 ______108
INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Generalized Jensen-Mercer Inequality for Functions with Nondecreasing Increments
ASIF R. KHAN AND SUMAYYAH SAADI Department of Mathematics, University of Karachi, Karachi, Pakistan [email protected]
Abstract: In year 2003, A. McD. Mercer established an interesting variation of Jensens Inequality and later in 2009 Mercer's result was generalized to higher dimensions by M. Niezgoda. Recently, Asif et al. has stated an integral version of Niezgoda's result for convex functions. We further generalize Niezgoda's integral result for functions with nondecreasing increments, and give some refinements with applications. In the way we generalize an important result, Jensen-Boas inequality, using functions with nondecreasing increments. These results would constitute a valuable addition to Jensen-type inequalities in the literature. Keywords: Convex Functions, Functions with non-decreasring increments, Jensen’s Ineqaulity, Niezgoda’s Inequaltiy, Majorization and refinements. References: [1] H. D. Brunk, Integral inequalities for functions with nondecreasing increments, Pacific J. Math. 14(1964), 783-793. [2] W. S. Cheung, A. Matkovic, and J. Pecaric, A variant of Jessen's inequality and generalized means, J. Ineq. Pure Appl. Math., 7 (1), Article 10, 2006. [3] Jan Haluska and Ondrej Hutnik, Some Inequalities involving Integral Means, Tatra Mountains Mathematical Publications, 35,131-146 [4] G. H. Hardy, J. E. Littlewood and G. Polya, Inequalities, Cambridge University Press, Cambridge 1978. [5] Milica Klaricic Bakula, ANita Matkovic, and J. Pecaric, On a Variant of Jensen's Inequality for functions with nondecreasing increments, J. Korean Math. Soc.,45 (2008), pp.821{834 [6] M. Adil Khan, Asif R. Khan and J. Pecaric, On the refinements of Jensen- Mercer's Inequality, Rev. Anal. Number. Theor. Approx., 41 (2012), 62-81. ______109
INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
[7] Asif R. Khan, J. Pecaric, Marjan Praljak, A note on generalized Mercer's Inequality, Bulletin of Malaysian Maths Science Society (2015). [8] A. McD. Mercer, An “error term” for the Ky Fan inequality, J. Math. Anal. Appl., 220, no. 2 (1998) 774-777. [9] Malika Klari_ci_c, Anita Matkovic, J. Pecaric, On A Variant Of Jensen's Inequality For Functions with Nondecreasing Increments,J'Korean Maths.Soc., 45 (2008), 821{834. [10] A. McD. Mercer, A variant on Jensen's Inequality, J. Ineq. Pure and Appl. Maths4(2003), Article 73 [11] J. Pecaric, On some inequalities for functions with nondecreasing increments, J. Math. Anal. Appl., 98 (1984) 188-197.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Approximating Min Graphic k-Path TSP with no Prespecified Path Endpoints
Rezika Kheffache Department of Mathematics, Mouloud Mammeri University, AMCD & RO,USTHB, Algeria [email protected]
Abstract: We consider a generalized Path Traveling Salesman Problem where the distances are defined by a 2-edge-connected graph metric and a number of salesmen have to cover all the destinations by traveling along paths without prespecified endpoints, of minimum total length. We show that for this problem there is an algorithm with asymptotic approximation ratio of 3/2 that runs in polynomial time whenever the number of paths is bounded by a fixed constant. Keywords: T-joins, Graphic Path TSP, Multiple Path TSP , Approximation Algorithms , 2-edge connected graph. References: [1] H.C. An, R. Kleinberg, D.B. Shmoys, “ Improving Christofides' algorithm for the s-t path TSP”, In Proc. of the 44th ACM STOC,(2012), 875-886. [2] J. Bae, S. Rathinam, “Approximation algorithms for multiple terminal, Hamiltonian path problems”, Optimization Letters 6 (p) (2012): 69-85. [3] A. Sebo, “ Eight-Fifth Approximation for the Path TSP”, In Proc. IPCO (2013), LNCS 7801: 362-374. [4] N. Christofides, “Worst-case analysis of a new heuristic for the traveling salesman problem”, Report 388 (1976), Graduate School of industrial Administration. Carnegie-Mellon University, Pittsburgh .
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
k − Generalized Pell Numbers and Its Properties
Havva Kırgız Kemal Uslu Department of Mathematics, Selcuk University, Konya, Turkey [email protected]
Abstract: The aim of this study is to introduce generalized new family of k-Pell numbers. The recurrence relations and the relation between new k-Pell numbers and generalized numbers are also considered. Keywords: Pell numbers, Pell-Lucas numbers, generalized numbers. References: [1] M. El-Mikkawy, T. Sogabe, A New Family of k-Fibonacci Numbers, Applied Mathematics and Computation, 215(2010), 4456-4461. [2] P. Catarino, “On some identities and generating functions for k-Pell numbers”, Int. Journal of Math. Analysis, 7(2013), 1877-1884. [3] Y. Taşyurdu, N. Çobanoğlu, Z. Dilmen, “On the a new family of k-Fibonacci numbers”, Erzincan Üniversitesi Fen Bİlimleri Enstitüsü Dergisi, 9.1 (2016), 95- 101. [4] N. Yılmaz, Y. Yazlık, N. Taşkara, “On the k-Generalized Fibonacci Numbers”, Selcuk Journal of Applied Mathematics, 13.1(2012), 83-88. [5] A. F. Horadam and Bro. J. M. Mahon, “Pell and Pell-Lucas Polynomials”, Fibonacci Quarterly, 23.1(1985), 17-20. [6] E. Özkan, A. Aydoğdu, İ. Altun, “Some identities for a family of Fibonacci and Lucas numbers”, Journal of Mathematics and Statistical Science, 3.10 (2017), 295-303.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Exact and Nonstandard Finite Difference Schemes for the Generalized KdV-Burgers Equation
Canan Köroğlu1 and Ayhan Aydın2 1 Department of Mathematics, Hacettepe University, Ankara, Turkey 2 Department of Mathematics, Atilim University, Ankara, Turkey [email protected] [email protected]
Abstract: In this study, we propose a nonstandard finite difference scheme (NSFD) for the numerical solutions of the generalized KdV-Burgers equation. Moreover, exact finite difference schemes are constructed for KdV-Burgers equation. Some numerical examples are given to demonstrate the accuracy of the schemes. Keywords: Nonstandard finite difference scheme, exact finite difference scheme, generalized KdV-Burgers equation. References: [1] R. Mickens, “Nonstandard Finite difference models of differential equations”, World Scientific, 1994 [2] R. Mickens, “Advances in applications of Nonstandard Finite Difference Schemes”, Wiley-Interscience, Singapore, 2005. [3] L. Zhang, L. Wang and X. Ding, “Exact Finite Difference Scheme and Nonstandard Finite Difference Scheme for Burgers and Burgers-Fisher Equations”, Journal of Applied Mathematics, 2014(2014), 1-12. [4] S. Zibaei, M. Zeinadini and M. Namjoo, “Numerical solutions of Burgers- Huxley equation by exact finite difference and NSFD schemes ”, Journal of Difference Equations and Applications, 22.8(2016), 1098-1113.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Some Studies on Congruence Equations using Suborbital Graphs
Tuncay Köroğlu1, Zeynep Şanlı2, Bahadır Özgür Güler3, Murat Beşenk4, 1,2,3Department of Mathematics, Karadeniz Technical University, Trabzon, Turkey, 4Department of Mathematics, Pamukkale University, Denizli, Turkey, [email protected], [email protected], [email protected], [email protected]
Abstract: It was shown that suborbital graph is useful tool in the study of the modular group which is a finitely generated Fuchsian group, some other finitely generated groups have been studied by suborbital graphs [1, 2]. Interesting number theoretic results arise from suborbital graphs are as follows: • A shortest path in subgraphs can be expressed as a continued fraction; • A shortest path in trees of suborbital graphs is a special case of Pringsheim continued fraction;
• The subgraph F1,2 can be defined as a new kind of continued fraction
and any irrational numbers has a unique F1,2 expansion; • The set of vertices of some suborbital graphs is strongly connected to the Fibonacci sequence. The aim of this paper is to examine the action of the normalizer of which produce some congruence equations with solutions. Keywords: Bianchi groups, Quadratic number field, Suborbital digraphs, Circuits. References: [1] Jones G.A., Singerman D., Wicks K., “The modular group and generalized Farey graphs”, Lond Math Soc Lect Note Ser 160(1991), 316–338. [2] Sims C.C., “Graphs and finite permutation groups”, Math. Zeitschrift, Vol:95, 76-86, 1967.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
On 푳ퟏ - Convergence of Certain Cosine and Sine modified sums
Xhevat Krasniqi Faculty of Education, University of Prishtina “Hasan Prishtina” 10000 Prishtina, Republic of Kosovo [email protected]
Abstract: In this paper we have introduced some new modified cosine and sine sums. We have studied their pointwise convergence as well as their 푳ퟏ – convergence whose coefficients belong to the well-known Sidon’s class 푺. As a consequence of these results is that a cosine or sine series converges in 푳ퟏ-norm to the its sum-function. Keywords: L1 - convergence, modified sums, Sidon’s class, trigonometric series. References: [1] S. Y. Sheng, Extension of the theorems of Č. V. Stanojević and B. V. Stanojević. Chinese Sci. Bull. 35 (1990), no. 23, 2014 - 2016. [2] S. A Teljakovskiĭ, A certain sufficient condition of Sidon for the integrability of trigonometric series. (Russian) Mat. Zametki 14 (1973), 317 - 328. [3] J. Kaur; S. S. Bhatia, Convergence of new modified trigonometric sums in the metric space L. J. Nonlinear Sci. Appl. 1 (2008), no. 3, 179 - 188. [4] A. N. Kolmogorov, Sur l’ordere de grandeur des coefficients de la series de Fourier-Lebesgue. Bull. Acad. Pol. Sci. Ser. Sci. Math. Astronom. Phys., (1923), 83-86. [5] B. Ram; S. Kumari, On L1-convergence of certain trigonometric sums. Indian J. Pure Appl. Math. 20 (1989), no. 9, 908 - 914. [6] B. Ram, Convergence of certain cosine sums in the metric spaces L. Proc. Amer. Math. Soc. 66 (1977), no. 2, 258–260.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Fixed Point Theorems for α-F-Suzuki Contraction Mapping with Rational Expressions in Branciari b-Metric Spaces
Neslihan Kaplan Kuru, Mahpeyker Öztürk Department of Mathematics, Sakarya University, Sakarya, Turkey [email protected] Department of Mathematics, Sakarya University, Sakarya, Turkey [email protected]
Abstract: Recently, Piri and Kumam [Fixed Point Theory and Applications, 2014: 2014:210] improved concept of F-contraction and proved some Wardowski and Suzuki type fixed point results in metric space. The aim of this work is to establish some new fixed point theorems for α-F-Suzuki contraction mappings satisfying rational expressions in Branciari b-metric space. Keywords: Fixed point, α-admissible, F-Suzuki contraction, Branciari b-metric space References: [1] P. Hossein, P. Kumam, “Fixed point theorems for generalized F-Suzuki- contraction mappings in complete b-metric spaces” , Fixed Point Theory and Applications, 2016:90(2016), 13 pages. [2] S. Gülyaz Özyurt, “On some α-admissible contraction mappings on Branciari b-metric spaces”, Advances in the Theory of Nonlinear Analysis and its Applications, 1.1(2017), 13 pages. [3] A. Latif, V.Parvaneh, P.Salimi, A.E. Al-Mazrooei,”Various Suzuki type theorems in b-metric spaces”, Journal of Nonlinear Science and Applications, 8(2015), 363-377.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
About the packing chromatic number in graphs
Rachid Lemdani Department of MI, Faculty of sciences, Medea University,Algeria [email protected] Moncef Abbas USTHB, Algiers, Algeria [email protected]
Abstract: Let 퐺 = (푉, 퐸) be a simple graph with no isolated vertices. A packing coloring of order 푘 in 퐺 is a function 휋: 푉 → {1, … , 푘} that is if 휋(푢) = 휋(푣) implies that 푑(푢, 푣) ≻ 휋(푢). The minimum order of a packing coloring is called the packing chromatic number of 퐺 and is denoted by 휒푝(퐺). It was introduced by Goddard et al. in [2] under the name Broadcast chromatic number of graphs and study its properties. They showed that it is NP-hard to determine if 휒푝(퐺) ≤ 4 and they also determined the packing chromatic number of all trees of diameter at most 4. In this paper we will use the following results on 휒푝(퐺) in [2] and others to determine the packing chromatic number of the finite super subdivision of the classes of graphs: tree, cycle, neighborhood corona of cycle with path. Keywords: Graph theory, Finite super subdivision of graph, Neighborhood corona of graph. References: [1] B. Brear, S. Klavsar, D. F. Rall, On the packing chromatic number of cartesian products, Hexagonal lattice, and trees, May 24, 2007. [2] W. Goddard, S.M. Hedetniemi, J. M. Harris, D.F. Rall, Broadcast chromatic numbers of graphs, Ars Combin., 86:33-49, 2008. [3] G. Indulal, The spectrum of neighborhood corona of graphs, Kragujevac J. Math., 35(3)(2011),493-500. [4] A. William and S. Roy. Packing chromatic number of certain trees and cycle related graphs. International Conference on Mathematical Computer Engineering (ICMCE), 2013.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Some characterizations of the homogeneous ruled real hypersurface in a complex hyperbolic space
Sadahiro Maeda Department of Mathematics, Saga University, Saga, Japan [email protected]
Abstract: Motivated by the notion of ruled surfaces in Euclidean 3-space, we consider ruled real hypersurfaces isometrically immersed into an n-dimensional complex hyperbolic space of constant holomorphic sectional curvature c(<0). The purpose of this expository paper is to give some geometric characterizations of the homogeneous ruled real hypersurface, that is, this ruled real hypersurface is an orbit of some subgroup of the full isometry group of the ambient space (see [1, 2, 3, 4]). Keywords: ruled real hypersurfaces, the homogeneous ruled real hypersurface, complex hyperbolic space, characteristic vector filed, integral curves, circles, the first curvature. References: [1] T. Adachi, Y.H. Kim and S. Maeda, “A characterization of the homogeneous minimal uled real hypersurface in a complex hyperbolic space”, J. Math. Soc. Japan 61(2009), 315-325. [2] M. Kimura, S. Maeda and H. Tanabe, “Integral curves of the characteristic vector field of minimal ruled real hypersurfaces in non-flat complex space forms’’, to appear in Hokkaido Math. J.. [3] M. Kimura, S. Maeda and H. Tanabe, “The homogeneous ruled real hypersurface in a complex hyperbolic space”, to appear in J. Geometry. [4] S. Maeda and H. Tanabe, “A characterization of the homogeneous ruled real hypersurface in a complex hyperbolic space in terms of the first curvature of some integral curves”, Arch. Math. (Basel) 105(2015), 593-599.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Precise long-term prediction of behavior in a 3-D chaotic map
M. Mammeri Department of Mathematics, University of Kasdi Merbah, Ouargla, Algeria E-mail: [email protected] E-mail: [email protected] Abstract: In this paper, the prediction accuracy on long-term of future behavior in a 3-D chaotic map is possible. This paper introduces and justifies by numerical simulation a new phenomenon, shown by the 3-D map which is the behavior in the 3-D map is always regular and periodic and bounded on large time, i.e., that the behavior repeats itself regularly after cycles on large time intervals. The new 3-D map produces new several chaotic attractors obtained via quasi-periodic route to chaos. Keywords: Precise prediction, 3-D map, future behavior, symmetric intervals, regular behavior. References: [1] Lorenz EN. Deterministic non-periodic flow., J Atmos Sci, 1963, 20, 130-41
[2] K. Mandal, S. Banerjee, C. Chakraborty., "Symmetry-Breaking Bifurcation in Series-Parallel Load Resonant DC-DC Converters.," IEEE Trans. Circuits Syst. I., vol.60, no.3, 2013, 778-787.
[3] S. V. Gonchenko, J. D. Meiss, I. I. Ovsyannikov., Chaotic Dynamics of Three-Dimensional Hénon Maps that Originate from a Homoclinic Bifurcation., Regular and Chaotic Dynamics, 11 (2), 2006, 191-212.
[4] S. V. Gonchenko, I. I. Ovsyannikov, C. Simó, D. Turaev., Three- Dimensional Hénon-like Maps and Wild Lorenz-like Attractors., International Journal of Bifurcation and Chaos, 15 (11), 2005, 3493-3508.
[5] S. V. Gonchenko, I. I. Ovsyannikov, C. Simó, D. Turaev., Three- Dimensional Hénon-like Maps and Wild Lorenz-like Attractors., International Journal of Bifurcation and Chaos, 15 (11), 2005, 3493-3508.
[6] Arrow, K. J.et al., The promise of prediction markets. Science, 320, 2008, 877-878. ______119
INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Constructing 3-D maps with complex chaotic phenomena
M. Mammeri Department of Mathematics, University of Kasdi Merbah, Ouargla, Algeria E-mail: [email protected] E-mail: [email protected]
Abstract: Any dynamical phenomena has higher unpredictability and more randomness than simple chaotic phenomena is called complex chaotic phenomena. The essential motivation of this letter is to proposed 3D maps with the necessaries conditions for the existence of the chaotic phenomena, and is to detecting the complex chaotic phenomena of the maps. The direct method of analysis used here is the analytic calculation of the biggest Lyapunov exponents (BLEs).
Keywords: 3-D map, complex chaotic phenomena, biggest Lyapunov exponents (BLEs).
References: [7] Chen, G & Lai, D, Making a discrete dynamical system chaotic: feedback control of lyapunouv exponents for discrete-time dynamical system, IEEE Trans. Circ. Syst.-I, 44, 1997, 250-253.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
[8] Wang, X. F., Chen, G, On feedback anticontrol of discrete chaos. Int.J. Bifur. Chaos, 9, 1999, 1435-1441.
[9] S. V. Gonchenko, J. D. Meiss, I. I. Ovsyannikov., Chaotic Dynamics of Three- Dimensional Hénon Maps that Originate from a Homoclinic Bifurcation., Regular and Chaotic Dynamics, 11 (2), 2006, 191-212.
[10] G. Baier, M. Klein, Maximum hyperchaos in generalized Hénon maps, Phys. Lett. A, 151, (6-7), 1990, 281--284.
[11] S. V. Gonchenko, I. I. Ovsyannikov, C. Simó, D. Turaev., Three-Dimensional Hénon-like Maps and Wild Lorenz-like Attractors., International Journal of Bifurcation and Chaos, 15 (11), 2005, 3493-3508.
[12] Marotto, F. R, Snap-back repellers imply chaos in ℝⁿ. J. Math. Anal. Appl.,3, 1978, 199-223.
[13] M. Mammeri., A Large Chaotic Region in a 3-D Sinusoid Discrete Map. International Journal of Applied Mathematics and Statistics. Vol. 55, no. 3, 133- 144, 2016.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Sequential structures of statistical manifolds on deformed exponential families
Hiroshi Matsuzoe Department of Computer Science and Engineering, Nagoya Institute of Technology, Nagoya, Japan [email protected]
Abstract: Information geometry is one of differential geometrical methods of statistical sciences. In information geometry, a statistical model which is a set of probability density distributions is regarded as a Riemannian manifold with dual affine connections (cf. [1]), In the case of exponential family, a statistical manifold structure is reduced to a Hessian structure, and such a manifold structure is applied various fields of statistical sciences. A deformed exponential family is a generalization of an ordinary exponential family, and it naturally admits at least three kinds of statistical manifold structures [2]. In this talk, we show that such statistical manifold structures are obtained as a sequence (cf. [3]). The alpha-divergence and the beta-divergence are closely related to the sequence of statistical manifolds. Keywords: information geometry, statistical manifold, anomalous statistics. References: [1] S. Amari, “Information Geometry and Its Applications”, Springer, Tokyo, 2016. [2] H. Matsuzoe and M. Henmi, “Hessian Structures and Divergence Functions on Deformed Exponential Families”, Geometric Theory of Information, Signals and Communication Technology, Springer, (2014), 57-80. [3] H. Matsuzoe, “A sequence of escort distributions and generalizations of expectations on q-exponential family”, Entropy, 19(2017), no. 1, 7.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Approximate solutions of the inverse problem without a priori information on the exact solution
Yuri Menshikov Department of Mechanics & Mathematics, Dnepro University, Dnepro, Ukraine [email protected]
Abstract: One of the main assumptions in the theory of inverse problems is the hypothesis that the exact solution of the inverse problem belongs to the set of possible solutions Q which is determined by the inaccuracy of the original data [1]. This hypothesis makes it possible to construct approximate solutions that converge to the exactness of the solution with a decrease in the error of the initinal data. However, in the practice of solving inverse problems, problems have recently appeared in which the indicated property of convergence does not make sense [2]. These are the problems of constructing (synthesis) an adequate mathematical description of physical processes and they play an important role in the use of methods of mathematical simulation [3]. In this paper it is proposed to abandon the hypothesis of an exact solution. This will allow us to proceed to a more reliable formulation of certain types of inverse problems. The examples were given [2]. Keywords: Inverse problems, exact solutions, adeguate mathematical descriptions. References: [1] A.N. Tikhonov, V.Y. Arsenin,”Methods of incorrect problems solution”, Science, Moscow (1979), 288p. [2] Yu. L. Menshikov,“Synthesis of Adequate Mathematical Description as Solution of Special Inverse Problems“, European Journal of Mathematical Sciences, 2, n.3,(2013), 256-271.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Modelling Asymmetric Magnetic Recording Heads With a Soft Underlayer Using Multiple Images Method
Ammar Edress Mohamed Dohuk Polytechnic University, Technical College of Petroleum and Minerals / Zakho, Iraq [email protected]
Abstract: For magnetic recording heads, the case when the SUL is present, the head fields are calculated using two methods; Firstly, Green functions are employed along with evaluating the integration numerically. The results follow closely the corners, while the gap region shows linear behaviour for d/g < 0.5 compared with the calculated fields from finite-element the reason of the disagreement caused by using the potential for head without underlayer case. The second method is superposition technique, which utilising the principle of the single image method for d=g. It was found that for the head with the underlayer present, the superposition (single image method) results follow closely the shape of the calculated fields from finite-element modelling. The results shows that y field components based on the superposition (single image method) are in very good agreement with finite-element calculations for angles up to 45 for y/g≤0.1. Keywords: Magnetic Recording Heads, Multiple Images Method, Magnetic field. References: [1] G. Fan, “A study of the playback process of a magnetic ring head,” IBM J. Res. Dev., vol. 5, pp. 321–325, 1961. [2] 0. Karlqvist, “Calculation of the magnetic field in the ferromagnetic layer of a magnetic drum,” Trans. Roy. Inst. Technol. Stock. Sweden, vol. 86, no. 1, pp. 1–27, 1954. [3] N. Curland and J. Judy, “Calculation of exact ring head fields using conformal mapping,” Magnetics, IEEE Transactions on, vol. 22, no. 6. pp. 1901– 1903, 1986.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
[4] J. S. Yang and H. L. Huang, “Calculation of exact head and image fields of recording heads by conformal mapping,” IEEE Trans. Magn., vol. 25, no. 3, pp. 2761–2768, 1989. [5] T. J. Szczech, D. M. Perry, and K. E. Palmquist, “Improved Field Equations For Ring Heads,” IEEE Trans. Magn., vol. M, no. 5, pp. 5–9, 1983. [6] S. Iwasaki, “Perpendicular Magnetic Recording,” IEEE Trans. Magn., vol. 16, no. 1, pp. 71–76, 1980. [7] 0. Lopez, W. P. Wood, N. H. Yeh, and M. Jursich, “Interaction of a ring head and double layer media-field calculations,” IEEE Trans. Magn., vol. MAG- 18, no. 10, pp. 1179–1181, 1982. [8] D. Bloomberg, “Spectral response from perpendicular media with gapped head and underlayer,” IEEE Trans. Magn., vol. 19, no. 4, pp. 1493–1502, 1983. [9] S. I. Iwasaki and K. Ouchi, “On design of Co-Cr perpendicular recording media for usage of a ring-type head,” IEEE Trans. Magn., vol. 26, no. 1, pp. 97–99, 1990. [10] D. T. Wilton, H. A. Shute, and D. J. Mapps, “Accurate approximation of fields and spectral response functions for perpendicular recording heads,” IEEE Trans. Magn., vol. 35, no. 4, pp. 2172–2179, Jul. 1999.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Coefficient bound estimates for beta-starlike functions of order alpha
Nizami Mustafa1,a, Veysel Nezir1,b 1Department of Mathematics, Kafkas University, Kars, Turkey a [email protected] [email protected]
Abstract: It is well-known that the coefficient problems of analytic functions is one of the frequently studied mathematical problems. There are many studies on this subject (see for example [1-5] and references therein). In this paper, we investigate coefficients problems for the so-called beta starlike functions of order alpha fz( ) , which is analytic and univalent in the open unit disk Uzz= :1 in the complex plane, and normalized so that ff(0010) =−=( ) , and satisfying the condition
1− zfzzfz( ) ( ) Re1+ , 0,1) . We give upper bound fzfz ( ) ( ) estimates for the first three coefficients of the functions belonging to this class. Fekete-Szegö problem for this mentioned function class is also examined. The main results obtained here for the coefficients bounds estimates extend the results obtained by Thomas in [4]. Keywords: starlike function, convex function, beta-starlike function, coefficient bound References: [1] S. Prema, B. S. Keerthi, “Coefficients bounds for certain subclasses of analytic functions”, J. Math. Anal., 4.1(2013), 22-27. [2] N. Mustafa, “Fekete-Szegö problem for certain subclass of analytic and bi- univalent functions”, Journal of Scientific and Engineering Research, 4.8(2017), 390-400.
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[3] S. Topkaya and N. Mustafa, “The General Sublasses of the Analytic Functions and their Various Properties”, Asian Research Journal of Mathematics, 7.4(2017), 1-12. [4] H. Orhan and P. Zaprawa, “Third Hankel Determinants for Starlike and Convex Functions of Order Alpha”, Bull. Korean Math. Soc. 55.1(2018), 165- 173. [5] N. Mustafa, G. Murugusundaramoorthy, T. Janani, “Second Hankel determinant for a certain subclass of bi-univalent functions”, Mediterranean Journal of Mathematics (accepted). [6] Derek K. Thomas, “On the coefficients of gamma-starlike functions”, J. Korean Math. Soc., 55.1(2018), 175-184.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
On the coefficient bounds of gamma and beta starlike functions
Nizami Mustafa1,a, Veysel Nezir1,b, Mustafa Ateş1,c 1Department of Mathematics, Kafkas University, Kars, Turkey a [email protected] [email protected] c [email protected]
Abstract: In this paper, we introduce and investigate a new subclass of the analytic functions in the open unit disk. Here, we obtain upper bound estimates for the first three coefficients for the functions belonging to this class. Keywords: analytic function, coefficient bound estimate, gamma and beta starlike functions References: [1] O. Altıntaş, “On a subclass of certain starlike functions with negative coefficient”, Math. Japon., 36(1991), 489-495. [2] O. Altıntaş, H. Irmak and H. M. Srivastava, “Fractional calculus and certain starlike functions with negative coefficients”, Comput. Math. Appl., 30.2(1995), 9-16. [3] O. Altıntaş and S. Owa, “On subclasses of univalent functions with negative coefficients”, Pusan Kyongnam Mathematical Journal, 4(1988), 41-56. [4] O. Altıntaş, H. Irmak, S. Owa and H. M. Srivastava, “Coefficients bounds for some families of starlike and convex functions of complex order”, Applied Mahematics Letters, 20(2007), 1218-1222. [5] O. Altıntaş, Ö. Özkan and H. M. Srivastava, “Neighborhoods of a Certain Family of Multivalent Functions with Negative Coefficients”, Comput. Math. Appl., 47(2004), 1667-1672. [6] P. L. Duren, “Univalent Functions”, Grundlehrean der Mathematischen Wissenshaften, Bd. 259, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1983.
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JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Application of the Chebyshev polynomials to coefficient estimates of analytic functions
Nizami Mustafa1,a, Veysel Nezir1,b, Erdi Akbulut,1,c 1Department of Mathematics, Kafkas University, Kars, Turkey a [email protected] [email protected] c [email protected]
Abstract: In this paper, making use of the Chebyshev polynomials, we introduce and investigate new subclasses of the analytic functions in the open unit disk in the complex plane. Here, upper bound estimates for the initial second coefficients of the functions belonging to these classes are obtained. Keywords: analytic function, coefficient bound, Chebyshev polynomials References: [1] E. H. Doha, “The first and second kind Chebyshev coefficients of the moments of the general order derivative of an infinitely differentiable function”, Intern. J. Comput. Math., 51(1994), 21-35. [2] P. L. Duren, “Univalent Functions”, Grundlehren der Mathematischen Wissenschaften 259, Springer-Verlag, New York, 1983. [3] A. W. Goodman, “Univalent Functions”, Volume I, Polygonal, Wasington, 1983. [4] E. Netanyahu, “The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in |z|<1”, Arch. Rational Mech. Anal. 32(1969),100-112. [5] M. Lewin, “On a coefficient problem for bi-univalent functions”, Proc. Amer. Math. Soc. 18(1967), 63-68. [6] H. M. Srivastava and S. Owa, “Current Topics in Analytic Function Theory”, World Scientific, Singapore, 1992.
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JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
On the coefficient bounds of certain subclasses of analytic functions of complex order
Nizami Mustafa1,a, Veysel Nezir1,b, Tarkan Öztürk1,c 1Department of Mathematics, Kafkas University, Kars, Turkey a [email protected] [email protected] c [email protected]
Abstract: In this paper, we introduce and investigate a new subclass SC**(,,0,0 ) =− of analytic functions of complex order in the open unit disk. Here, we obtain upper bound estimates for the first three coefficients for the functions belonging to this class. Keywords: analytic function, coefficient bound, starlike function, convex function, analytic function of complex order References: [1] P. L. Duren, “Univalent Functions”, Grundlehren der Mathematischen Wissenschaften 259, Springer-Verlag, New York, 1983. [2] A. W. Goodman, “Univalent Functions”, Volume I, Polygonal, Wasington, 1983. [3] C. H. Pommarenke, “Univalent Functions”, Vandenhoeck and Rupercht, Göttingen, 1975. [4] H. M. Srivastava and S. Owa, “Editors, Current Topics in Analytic Function Theory”, World Scientific, Singapore, 1992.
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JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Some Results on Classical 2-Absorbing Submodules
Osama A. Naji Department of Mathematics, Sakarya University, Sakarya, Turkey [email protected]
Abstract: Let 푅 be a commutative ring with identity and 푀 be a unitary 푅 – module. In this paper, we investigate some properties of classical 2-absorbing submodules of M as a new generalization of 2-absorbing. We also give some characterizations of classical 2-absorbing submodules under some conditions. Keywords: 2-absorbing submodules, classical 2-absorbing submodules. References: [1] Ashour, A.E., Al-Ashker, M.M. and Naji, O.A., On Almost 2-Absorbing Primary Sub-modules. IUG Journal of Natural Studies. (2017). [2] Ashour, A.E., Al-Ashker, M.M. and Naji, O.A., Some results on almost 2- absorbing sub-modules. Journal of Al Azhar University-Gaza (Natural Sciences).Vol.18, pp.1-13, (2016). [3] Azizi, A. On prime and weakly prime submodules, Vietnam Journal of mathematics, Vol. 36, No. 3 pp. 315-325, (2008). [4] Darani, A.; Soheilnia, F. 2-Absorbing and Weakly 2-Absorbing Submodules, Thai Journal of Mathematics. Vol. 9, No. 3, pp. 577-584, (2011). [5] Dubey, M.; Aggarwal, P. On 2-absorbing primary Submodules of modules over commutative rings, Asian-European Journal of Mathematics. Vol. 8, No. 4, (2015). [6] Mostafanasab, H.; Tekir, U.; Oral, K. Classical 2-Absorbing Submodules of Modules over Commutative Rings ,European Journal of Pure Mathematics Vol.8,No. 3, pp. 417-430, (2015). [7] Payrovi, Sh.; Babaei, S. On 2-Absorbing Submodules, Algebra Colloquium 19 (Spec 1), pp 913-920, (2012).
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JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Fixed point properties for a degenerate Lorentz-Marcinkiewicz space
Veysel Nezir1,a and Nizami Mustafa1,b 1Department of Mathematics, Kafkas University, Kars, Turkey a [email protected] b [email protected]
Abstract: We construct an equivalent renorming of ℓ1 which turns out to 1 produce a degenerate ℓ -analog Lorentz-Marcinkiewicz space ℓ훿,1, where the weight sequence 훿 = (훿푛)푛∈푁 = (2,1,1,1, ⋯ ) is a decreasing positive sequence ∞ 1 in ℓ \푐0, rather than in 푐0\ℓ (the usual Lorentz situation). Then, we obtain its 0 isometrically isomorphic predual ℓ훿,∞ and dual ℓ훿,∞, corresponding degenerate ∞ 푐0-analog and ℓ -analog Lorentz-Marcinkiewicz spaces, respectively. We prove 0 that both spaces ℓ훿,1 and ℓ훿,∞ enjoy the weak fixed point property (w-fpp) for nonexpansive mappings; besides, ℓ훿,1 has the weak* fixed point property (w*- 0 fpp) with respect to its predual ℓ훿,∞ yet they fail to have the fixed point property (fpp) for nonexpansive mappings since they contain an asymptotically isometric 1 copy of ℓ and 푐0, respectively. In fact, we prove for both spaces that there exist non-empty, closed, bounded and convex subsets with invariant fixed point-free affine, nonexpansive mappings on them and so they fail to have fpp for affine 0 nonexpansive mappings. Also, we show that any non-reflexive subspace of 푙훿,∞ contains an isomorphic copy of 푐0 and so fails fpp for strongly asymptotically nonexpansive maps. Finally, we get a Goebel and Kuczumow analogy by proving that there exists an infinite dimensional subspace of ℓ훿,1 with fpp for nonexpansive mappings. Keywords: nonexpansive mapping, non-reflexive Banach space, fixed point property, weak fixed point property, asymptotically isometric copy of c0, asymptotically isometric copy of l1, Lorentz-Marcinkiewicz spaces References: [1] D. E. Alspach, “A fixed point free nonexpansive map”, Proceedings of the American Mathematical Society, 82(1981), 423–424.
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JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
[2] N. L. Carothers, S. J. Dilworth and C. J. Lennard, “On a localization of the
UKK property and the fixed point property in L(w,1)”, Lecture notes in Pure and Applied Mathematics, (1996), 111–124. 1 [3] P. N. Dowling, C. J. Lennard and B. Turett, “Renormings of l and c0 and Fixed Point Properties”, in Handbook of Metric Fixed Point Theory, Springer Netherlands, (2001), 269–297. [4] K. Goebel and W. Kirk, “Topics in metric fixed point theory”, Cambridge University Press, 1990. [5] K. Goebel and T. Kuczumow, “Irregular convex sets with fixed-point property for nonexpansive mappings”, Colloq. Math., 40(1979), 259–264. [6] P. K. Lin, “There is an equivalent norm on l1 that has the fixed point property”, Nonlinear Analysis 68(2008), 2303–2308. [7] J. Lindenstrauss and L. Tzafriri, “Classical Banach spaces I: Sequence Spaces, Ergebnisse der Mathematik und ihrer Grenzgebiete”, 92(1977), Springer-Verlag. [8] G. G. Lorentz, “Some new functional spaces”, Annals of Mathematics, (1950), 37-55.
[9] V. Nezir, “Fixed Point Properties for c0-like Spaces”, Ph.D. thesis, University of Pittsburgh, 2012.
[10] V. Nezir and N. Mustafa, “c0 can be renormed to have the fixed point property for affine nonexpansive mappings”, Filomat, to appear.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Renorming c0 and affine fixed point property
Veysel Nezir1,a, Nizami Mustafa1,b, Tahsin Ateş,c 1Department of Mathematics, Kafkas University, Kars, Turkey a [email protected] b [email protected] c [email protected]
Abstract: Reflexivity is strongly related to the fixed point property for nonexpansive mappings [FPP(n.e)]. It was a long time open question as to whether or not non-reflexive spaces can be renormed to have FPP(n.e). Recently, Lin provided the first example of a non-reflexive Banach space with FPP(n.e) by verifying this fact for 푙1. It is natural to ask whether there is an analogue of Lin's theorem for another non-reflexive space that shares many common properties while it may not offer nice tools like Schur property. 푐0, another non-reflexive Banach space of great importance in Banach space theory, is one of the most well-known such these spaces. Recently, Nezir and Mustafa gave positive answer for the 푐0-analogue of P. K. Lin’s theorem under affinity condition. In this study, we prove that there is another renorming of 푐0 with the fixed point property and a family of equivalent norms on 푐0 that has FPP(n.e) if the mappings are affine.
Keywords: nonexpansive mapping, non-reflexive Banach space, fixed point property, renorming, affine mapping References: 1 [1] P. N. Dowling, C. J. Lennard and B. Turett, “Renormings of l and c0 and Fixed Point Properties”, in Handbook of Metric Fixed Point Theory, Springer Netherlands, (2001), 269–297. [2] K. Goebel and T. Kuczumow, “Irregular convex sets with fixed-point property for nonexpansive mappings”, Colloq. Math., 40(1979), 259–264. [3] P. K. Lin, “There is an equivalent norm on l1 that has the fixed point property”, Nonlinear Analysis 68(2008), 2303–2308.
[4] V. Nezir and N. Mustafa, “c0 can be renormed to have the fixed point property for affine nonexpansive mappings”, Filomat, to appear.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Infinite dimensional subspaces of a degenerate Lorentz- Marcinkiewicz space with the fixed point property
Veysel Nezir1,a, Nizami Mustafa1,b, Merve Delibaş1,c 1Department of Mathematics, Kafkas University, Kars, Turkey a [email protected], b [email protected],b c [email protected]
Abstract: We work on some infitine dimensional subpaces of a degenerate ℓ1- analog Lorentz-Marcinkiewicz space ℓ훿,1, where the weight sequence 훿 = ∞ (훿푛)푛∈푁 = (2,1,1,1, ⋯ ) is a decreasing positive sequence in ℓ \푐0, rather than 1 in 푐0\ℓ (the usual Lorentz situation). We show that a Goebel and Kuczumow analogy can be obtained by proving that there exist large classes of non-weak*, closed, bounded and convex subsets of ℓ훿,1 with the fixed point property for nonexpansive mappings. Keywords: nonexpansive mapping, non-reflexive Banach space, fixed point property, closed bounded convex subset, Lorentz-Marcinkiewicz spaces References: 1 [1] P. N. Dowling, C. J. Lennard and B. Turett, “Renormings of l and c0 and Fixed Point Properties”, in Handbook of Metric Fixed Point Theory, Springer Netherlands, (2001), 269–297. [2] K. Goebel and T. Kuczumow, “Irregular convex sets with fixed-point property for nonexpansive mappings”, Colloq. Math., 40(1979), 259–264. [3] J. Lindenstrauss and L. Tzafriri, “Classical Banach spaces I: Sequence Spaces, Ergebnisse der Mathematik und ihrer Grenzgebiete”, 92(1977), Springer-Verlag. [4] G. G. Lorentz, “Some new functional spaces”, Annals of Mathematics, (1950), 37-55.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Applying Fourier Analysis to Computing New variables for Determining SNR
Sajedeh Norozpour Department of Mathematics and computer science, Eastern Mediterranean University, Gazimagusa, Cyprus [email protected] Cem Ergün Department of computer Engineering, Eastern Mediterranean University, Gazimagusa, Cyprus [email protected]
Abstract: In this paper the quantitive description of signal to noise ratio through novel computational parameters will be debated and computed using Fourier analysis method. The significance of this study is when the geomagnetic observed field has high transient noise and high energy content and it is going to be more important to work on, if signal analysing action leans to the quasi- punctiform, low energy and kinetic magnetic source recognition. The following study demonstrates the consequences which are obtained by defining two new informative spectral parameters: the informative capability “C” and the enhanced informative capability “eC”. These variables are depending on the assessment of the signal target energy with total field energy. C and eC lead to compute the value of the “visibility” of the informative signals in high energy geomagnetic field or spectrum. The problem of the visibility becomes quite complex when the target signal is coming from a quasi-punctiform and low amplitude source, inside a high energy (noise) geomagnetic volume and also the low visibility problem becomes practically unsolvable when these classes of sources are in motion and their signals are recorded by a fixed sensor. In order to quantify the phenomena of visibility the parameter “C” and its derivate “eC” has been used. Keywords: Signal to noice ratio (SNR), Fourier transforms, computational parameter. References: [1]Cooley, J.W. and Tukey, J.W. (1965), An algorithm for the machine calculation of complex Fourier series, Mathematics of Computation, 19, 297.
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JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
[2]Faggioni, O., Soldani, M., Gabellone, A., Hollett, R.D., and Kessel, R.T. (2010) Undersea harbour defence: A new choice in magnetic networks. Journal of Applied Geophysics, 72, n. 1, 46-56. [3]De Vuyst, A., and De Meyer, F. (1973) Spectral analysis of geomagnetic data from one station (Dourbes 1960-1970). Institut Royal Meteorologique de Belgique, Publ., A, n° 80, 32.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
On Nordenian Properties of the Riemannian extension
Filiz OCAK Department of Mathematics, Karadeniz Technical University, Trabzon, Turkey [email protected]
Abstract: In this study, we investigate the Nordenian properties of the Riemannian extension by using compatible almost complex structure in the cotangent bundle. Then, we get the conditions under which the cotangent bundle endowed with the almost complex structure and the Riemannian extension is a Kähler-Norden manifold and anti-Kähler-Codazzi manifold.
Keywords: Riemann extension, cotangent bundle, almost complex structure, Norden metric. References: [1] S. Aslanci, S. Kazimova and A.A Salimov, “Some notes concerning Riemannian extensions”, Ukrainian Math. J., 62(2010), 661–675. [2] G. T. Ganchev and A. V. Borisov, “ Note on the almost complex manifolds with a Norden metric”, C. R. Acad. Bulg. Sci., 39 (1986), 31–34 . [3] E.M Patterson and A.G. Walker, “ Riemann Extensions”, Quart. J. Math. Oxford Ser., 3 (1952), 19-28. [4] A. Salimov, “ Tensor Operators and Their Applications”, Nova Science Publishers, New York, 2012. [5] A. Salimov, S. Turanli, “Curvature properties of anti-Kähler-Codazzi manifolds”, C. R. Math. Acad. Sci. Paris, 351(2013), 225-227. [6] K. Yano and S. Ishihara , “Tangent and Cotangent Bundles”, Pure and Applied Mathematics, Marcel Dekker, Inc., New York, 1973.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Numerical Solution of Nonlinear Singular Ordinary Differential Equations Arising in Biology via Operational Matrix of Bernstein Polynomials
Sunday Adeyemi Olagunju and Peter Vanenchii Ayoo Department of Mathematics, Federal University Lafia, PMB 146 Lafia, Nigeria [email protected], [email protected]
Abstract: Many authors including Akyuz-Dascioglu and Acar[1] and Ordokhani and Far[2] have studied Bernstein polynomials, their properties and applications to linear ordinary differential equations. The Bernstein method since its introduction, has undergone improvements including that by Olagunju[3]. Maleknejad and Hashemicadeh[4] and Singh et.al[5] studied singular boundary value problems (SBVPs) that arise in biology and physiology which are of linear or nonlinear functions. Some of these arise in the study of steady-state oxygen diffusion in a spherical cell with Michaelis-Menten uptake kinetics according to Lin[6] and in heat conduction model in human head according to Gray [7]. In this paper, we deploy Bernstein polynomials to find solution to nonlinear SBVPs that arise in biology and physiology. With the aid of operational matrix of derivatives, the entire nonlinear differential equation is written in algebraic equations that are handled by an algebraic solver- MATLAB. Keywords: Nonlinear Singular Boundary Value Problem, Bernstein Polynomials, Physiology, Biology. References: [1] A. Akyuz-Dascioglu and N. I. Acar, “Bernstein collocation method for solving linear differential equations”, GU J Sci. 26.4(2013), 527-534. [2] Y. Ordokhani and S. D. Far, “Approximate solutions of differential equations by using the bernstein polynomials”, ISRN Applied Mathematics, 2011(2011), 1- 15. [3] A. S. Olagunju, “Chebyshev series representation for product of chebyshev polynomials and some notable functions”, IOSR Journal of Mathematics, 2.2(2012), 9-13.
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JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
[4] K. Maleknejad and E. Hashemicadeh, “Numerical solution of nonlinear singular ordinary differential equations arising in biology via operational matrix of shifted Legendre polynomials”, AJCM, 1.1(2011), 15-19. [5] R. Singh, J. Kumar and G. Nelakanti, “Singular boundary value problems arising in physiology” The Scientific World Journal, 2014(2014), 1-10. [6] S. H. Lin, “Oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics” Journal of Theoretical Biology, 60.2(1976), 449-457. [7] B. F. Gray, “The distribution of heat sources in the human head theoretical consideration” Journal of Theoretical Biology, 82.3(1980), 473-476.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
On Ciric Type Contractions in Modular Spaces
Mahpeyker Öztürk Department of Mathematics, Sakarya University, Sakarya, Turkey [email protected]
Abstract: In this study, common fixed point theorems for some mappings satisfying Ciric type contractions in modular spaces are established. The theorems proved herein extend, generalize and improve some results of the existing literature. An illustrative example to support the given results is constructed.
Keywords: Ciric type contraction, common fixed point, modular space. References: [1] Ljubomir B. Ćirić, On some maps with a nonunique fixed point, Publications de l Institut Mathematique, 17 (31), (1974). [2] Memudu Olaposi Olatinwo, Some non-unique fixed point theorems of Ćirić type using rational-type contractive conditions, Georgian Math. J., (2016) [3] Erdal Karapınar, Ravi P Agarwal, A note on Ćirić type nonunique fixed point theorems, Fixed Point Theory and Applications, (2017) [4] J. Musielak, Orlicz Spaces and Modular Spaces, Lecture Notes in Mathematics, 1034, Springer, Berlin (1983) [5] J. Musielak, W. Orlicz, On modular spaces, Studia Mathematica, 18, (1959)
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JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Some fixed point results concerning F-contractions in complete metric space
Alexandrina Maria Proca Department of Mathematics and Computer Science, Transilvania University of Brasov, Brasov, Roumania [email protected]
Abstract: In this paper, we extend the results of Wardowski by applying some new conditions on the self map on a complete metric space, concerning the F- contractions defined by Wardowski. We present some fixed point results of Wardowski type. An example is given to demonstrate the novelty of our work. Keywords: Wardowski type contraction, fixed point, metric space References: [1] S.Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fundamenta Mathematicae 3(1922), 133-181. [2] V.Berinde, F.Vetro, Common fixed points of mappings satisfying implicit contractive conditions, Fixed Point Theory and Applications 2012:105 (2012). [3] M.Concertino, P.Vetro, Fixed point results for F-Contractive Map- pings of Hardy-Rogers type, Filomat 28:4(2014), 715-722; doi: 10.2298/FIL1404715C. [4] N.Van Dung, V.L.Hang, A fixed point theorem for generalised F- contractions on complete metric space, Vietnam J.Math, 43, 743-753(2015). [5] A.Fulga, A.M.Proca, A new Generalization of Wardowski Fixed Point Theorem in Complete Metric Spaces, Advances in the Theory of Nonlinear Analysis and its Applications 1 (2017) No. 1, 57–63 DOI:10.31197\atnaa.379119 [6] O.Popescu, Some new fixed point theorems for -Geraghty contraction type maps in metric spaces, Fixed Point Theory Appl.2013, Article ID 329(2013). [7] O.Popescu, A new type of contractive mappings in complete metric spaces, submitted. [8] H.Piri, P.Kumam, Some fixed point theorems concerning F-contraction in complete metric spaces, Fixed Point Theory Appl., 2014, 210(2014) doi:10.1186/1687-1812-2014-210. ______142
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JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
[9] N.A.Secelean, Iterated function sistems consisting of F-contractions, Fixed Point Theory Appl.2013, Article ID 277(2013).doi:10.1186/1687- 1812-2013- 277. [10] T.Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal 71, 5313-5317 (2009). [11] T.Suzuki, Generalized distance and existence theorems in complete metric spaces, J.Math.Appl.253, 440-458 (2001). [12] T.Suzuki, Several fixed point theorems concerning -distance, Fixed Point Theory Appl.2004, 195-209 (2004). [13] D.Wardowski, Fixed Points of a new type of contractive mappings in com- plete metric spaces, Fixed Point Theory and Applications 2012, 2012:94. [14] D.Wardowski, N. Van Dung, Fixed points of F-weak contractions on com- plete metric space, Demonstr.Math. 1, 146-155(2014).
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JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Fixed point theorem for F-contraction type and applications to polynomial approximations
Abdalah Rababah1, Hichem Ramoul2, Nora Mahloul3 1Department of Mathematics and Statistics, University of Science and Technology Irbid, Jordan [email protected] 2ICOSI laboratory, Abbes Laghrour University-Khenchela, Khenchela, Algeria [email protected] 3USTHB, Faculty of Mathematics Algebra and Number Theory Department [email protected]
Abstract: The purpose of this work is to prove a new result concerning a fixed point for F-contraction type in b-metric space. We establish existence and uniqueness without the continuity of the function F. As an application, we give some results about polynomial operators. Keywords: Orthogonals polynomials, fixed point. References: [1] Wardowski, D: Fixed point theory of a new type of contractive mappings in complete metric spaces. Fixed Point Theory Appl. 2012, 94 (2012) [2] S. Ostrovska, q-Bernstein polynomials and their iterates, Journal of Approximation Theory, 123 (2003) 232-255. [3] I. Altun, N. AL Arifi, M. Jleli, A. Lashin, B. Samet, A fixed point theorem for JS-contraction type with applications to polynomial approximation, Filomat 31 :15 (2017), 4969-4978.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Metric Properties of Fuzzy Curves and Fuzzy Invariants
Yasemin Sağıroğlua, Djavvat Khadjievb, Uğur Gözütoka aDepartment of Mathematics, Karadeniz Technical University, Trabzon, Turkey [email protected], [email protected] bInstitute of Mathematics, National University of Uzbekistan, Tashkent, Uzbekistan [email protected]
Abstract: Geometric properties of fuzzy sets and fuzzy geometric concepts are introduced in the papers [1,2,3]. Metric properties of fuzzy sets are considered in papers [4,5]. Our study is devoted to an investigation of metric properties of fuzzy paths and fuzzy curves in the 3-dimensional Euclidean space. In this paper, 퐸(3)-equivalence of fuzzy paths and 퐸(3)-equivalence of fuzzy curves are introduced. Definition of the fuzzy type of a fuzzy curve and an invariant parametrization of a fuzzy curve are given. We show that the fuzzy type of a fuzzy curve is an 퐸(3)-invariant. Also, the conditions of the global 퐸(3)- equivalence of fuzzy curves are given in terms of the fuzzy type and the three differential invariants (curvatures) of fuzzy curves. Finally, the description of the complete system of correlations between these invariants of a fuzzy curve is given. Keywords: Differential invariant, Fuzzy path, Fuzzy curve. References: [1] X. Yuan, Z. Shen, “Notes on fuzzy plane geometry i, ii”, Fuzzy Sets and Systems, 121(2001), 545-547. [2] J. J. Buckley, E. Eslami, “Fuzzy plane geometry i: Points and lines”, Fuzzy Sets and Systems, 86(1997), 179-187. [3] A. Rozenfeld, “Fuzzy geometry: An updated overview”, Information Sciences, 110(1998), 127-133. [4] A. Bogomolny, “On the perimeter and area of fuzzy sets”, Fuzzy Sets and Systems, 23(1987), 257-269. [5] L. Boxer, “On Housdorff-like metrics for fuzzy sets”, Pattern Recognition Letters, 18(1997), 115-118.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Hamiltonicity and pancyclicity of superclasses of claw-free graphs
Abdelkader Sahraoui Department of Mathematics, Medea University, Medea, Algeria [email protected]
Abstract : The class of claw-free graphs was a _eld of research interesting for many researchers. Many of the known results for claw-free graphs are extended to superclasses of claw-free graphs. The superclass of partly claw-free graphs, defined by Z. Benmeziane ([1]), contains the two superclass of quasi claw-free graphs, defined by A. Ainouche ([2]) , and almost claw-free graphs, defined by Z. Ryjàĉek ([3]). A graph G is parlay claw-free graph if for each vertex v of A, the set of centers of claw of G, there exists two vertices x and y of V (G) - A such that NG(v) subset of N[x] [ N[y]. Here, we will extend the fully extendable cycle graphs to the partly claw-free graphs. Keywords: Nearly Claw-Free Graphs, partly claw-free graphs, quasi claw-free graphs, et fully extendable cycle graphs. Ryjàĉek
References: [1] M. Abbas and Z. Benmeziane. Hamiltonicity in partly claw-free graphs. RAIRO Oper. Res., 43 1 (2009) 103-113. [2] A. Ainouche. Quasi claw-free graphs. Discrete Math. 179 (1998) 13-26. [3] Z. Ryjàĉek, Almost claw-free graphs. J. Graph Theory. 18(1994), 469-477. [4] M. Zhan, Full cycle extendability of triangulary connected almost claw-free graphs. ABS Combinatoria, vol. 96 (2010). [5] M. Zhan et Shuxin Zhan, Full cycle extendability of Nearly Claw-Free Graphs. April 6,2012.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
On some evolution problems of degenerate type
MOULAY Mohamed Said Faculty of Mathematics, USTHB, Algiers [email protected]
Abstract: We consider some nonlinear problems of degenerate type. Some class of them are of parabolic kind and arise in the modeling of oil in the porous medium, or in biological reaction diffusion systems. In this case we look especially for the regularity of solutions and for that purpose we use a generalized method of De Giorgi iterations type in some appropriate functional spaces to show the optimal regularity.
Other class of our interest arises in physical area and it is of anisotropic elliptic or parabolic type. For this purpose, we use the anisotropic singular perturbation method to study the existence of solutions. Keywords: degenerate problems, nonlocal term, porous media, anisotropic, singular perturbation, regularity, reaction diffusion system
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Average approximate Sentinel for an Identification problem
S. Sandel University of Abbse Laghrour, Algeria.. A.Berhail University 08 May 1945, Guelma, Algeria A. Ayadi University Larbi Ben M'hidi, Oum El Bouaghi, Algeria
.Abstract: In this paper, we intoduce the problem of identification of the Pollution term in a heat system when the dynamics of the state is gouverned by a parametrized operator. In this way, we introduce a new notion called average approximate sentinel. First, we prove the existence of such average approximate sentinels by solving a problem of approximate average controllability introduced by Zuazua. Secondly, we give information for the polution term by the average obsevation. Keywords: Average approximate sentinel, Average approximate controllability, pollution term References: [1] A. El JAI, E. ZERRIK, K. ZTOT, Systèmes dynamiques, Analyse et contrôle des systèmes localisés. Presses Universitaires de Perpignan, 2008. [2] J.P. KERNEVEZ, The sentinel method and its aplications to envirenmental pollution problems, CRC Methematical modeling series, CRC Press, Boca Raton, 1997. [3] J. L. LIONS, Contrôle optimal des systèmes gouvernés par des équations aux dérivées partielles, Dunod. Paris, 1968. [4] J. L. LIONS, Contrôlabilité exacte, stabilisation et perturbation des systèmes distribuès, Vol 1. Masson, 1988. [5] J. L. LIONS, Controllability, penalty and stiffness, Anal, Scie, Nor, Serie 4, Tome 25, N 3- [6] J .L. LIONS, Sentinelle pour les systèmes distribués à données incomplètes.Vol 21, Masson, RMA, Paris, 1992. [7] J. L. LIONS, Remarks on systems with incompletely given initial data and incompletely given part of boundary, pp. 239-250, 1990. [8] E. Zuazua, Averaged Control. Preprint submitted to Automatica, 2014. ______148
INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
[9] E. Zuazua,Q.Lu, Averaged controllability for parameter-dependent Evolution Partial Differential Equations. Preprint submitted to Automatica, 2014. [10] E. Zuazua, M. Lazar, Averaged control and observation of parameterdepending wave equations. C. R. Acad. Sci. Paris, Ser.JUNE 2014.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
λ – Double Statistical Convergence and Strongly Double Summable Functions of Weight g
Rabia Savaş and Mahpeyker Öztürk Department of Mathematics, Sakarya University, Sakarya, Turkey [email protected] and [email protected]
Abstract: In this paper, by using a nonnegative real valued measurable functions of two variables in the interval (1, ∞) × (1, ∞) we present the concepts of g g strongly W -summable and S -statistically convergence of weight g: p
[0, ∞) → [0, ∞) where g(푥푛) → ∞ for any sequences (푥푛) in [0, ∞) with 푥푛 → ∞. Moreover, using these definitions we examine a series of basic results, and inclusions of theorem, extensions as well as variations are proved. Keywords: Lebesgue measurable functions of two variables, weight g, statistically convergence, strong summability. References: [1] M. Balcerzak, P. Das, M. Filipczak, and J. Swaczyna, Generalized kinds of density and the associated ideald, Acta. Math. Hungar. 147 (2015), no:1, 97-115. [2] H. Fast, “Sur la convergence statistique”, Colloq. Math. 2(1951), 241-244. [3] M. Mursaleen and O. H. Edely, Statistical Convergence of Double Sequence, J. Math. Anal. Appl. 288 (2003), no:1, 223-231. [4] F. Nuray, \lambda-Strongly Summable and \lambda- Statistically Convergence Functions, İranian Jour. Science and Tech. Trans.A, Vol. 34, No:A4, (2010), 335-339.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
On Infinite Matrices and Sequence Spaces
Rahmet SAVAS Department of Mathematics, Istanbul Medeniyet University, Istanbul, Turkey [email protected]
Abstract: The purpose of this paper is to study the spaces Vp ()and Vp () 0 by using de la Val´ee poussin and generalized almost convergence. Furthermore we characterize certain matrices in ()V which will up a gap in the existing literature. Also we prove that Vp () and Vp () are complete linear 0 topological spaces. Keywords: Infinite matrices, Sequence Spaces, de la Val’ee Poussin References: [1] S. Banach, Theorie des Operations linearies, Warszawa,1932. [2] G. Das and S. K. Mishra, Banach limits and lacunary strong almost convergence, J. Orissa Math. Soc. 2(2)(1983), 61-70. [3] V. Karakaya, θσ-sumable sequences and some matrix transformations, Tamkang J. Math. 35(4)(2004), 313-320. [4] G. G. Lorentz, A contribution to the theory of divergent sequences, Acta. Math. 80(1948),167-190. [5] I. J. Maddox, Spaces of strongly summable sequences, Quart. J. Math. 18(1967), 345-355. [6] M. Mursaleen, A. M. Jarrah and S. A. Mohiuddine, Bounded linear operators for some new matrix transformations, Iran. J. Sci. Technol. Trans. A Sci. 33 (2009), no. 2, 169177.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Numerical methods for certain classes of Markovian BSDEs and quasi-linear parabolic PDEs
Driss Seghir Department of Mathematics, Faculty of sciences in Meknes, Moulay Ismail University, Meknes, Morocco. [email protected]
Joint work with : Aissa Sghir and Soukaina Hadiri
Abstract: In this paper, we use the Girsanov's theorem of change of probability measure to give an approximation result and numerical simulation for certain classes of Markovian coupled forward-backward stochastic differential equations. As application, by using the Feynman-Kac's formula, we give a time- space discretization scheme for certain classes of quasi-linear parabolic partial differential equations. Keywords: Backward stochastic differential equation, Girsanov's theorem, parabolic partial differential equation, discrete time approximation, Monte Carlo simulation. References: [1] B. Bouchard and N. Touzi (2004). Discrete-time approximation and Monte- Carlo simulation of backward stochastic differential equations. Stochastic Processes and their Applications, 111(2), p. 175- 206. [2] N. El Karoui, S. Peng and M.C. Quenez (1997). Backward stochastic differential equations in finance. Mathematical Finance, 7 (1), p. 1-71. [3] E. Pardoux and S. Peng (1992). Backward stochastic differential equations and quasilinear parabolic partial differential equations. Lecture Notes in CIS, 176, Springer Berlin, p. 200-217.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Integral Type Darbo's Fixed Point Theorem via Sequences of Functions
2 Derya Sekman 1 , Vatan Karakaya 1 ,2 Department of Mathematics, Kirsehir Ahi Evran University, Kirsehir, Turkey Department of Mathematical Engineering, Yildiz Technical University, Istanbul, Turkey [email protected], [email protected]
Abstract: In this paper, we will give a generalization of the integral type Darbo's fixed point theorem with the help of sequences of functions having shifting distance property and an application of integral equation.
This work was supported by the Ahi Evran University Scientific Research Projects Coordination Unit. Project Number: RKT.A3.17.001. Keywords: Fixed point, Integral type mapping, Measure of noncompactness, Sequences of functions, Shifting distance property. References: [1] A. Samadi and M. B. Ghaemi, “An extension of Darbo's theorem and its application”, Abstract and Applied Analysis 2014 (2014), Article ID 852324, 11 pages. [2] L. Cai, J. Liang, “New generalization of Darbo's fixed point theorem”, Fixed Point Theory and Applications, 2015:156 (2015), DOI: 10.1186/s13663-015- 0406-2. [3] M. Berzig, “Generalization of the Banach contraction principle” (2013), arXiv:1310.0995 [math.CA].
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Normal Differential Operators for Degenerate First-Order
Meltem Sertbaş & Fatih Yılmaz Department of Mathematics, Karadeniz Technical University, Trabzon, Turkey [email protected] [email protected]
Abstract: In this paper, in terms of boundary values all normal extensions of a class of formally normal minimal operators, generated by a linear differential- operator expression of degenerate first-order with smooth operator coefficients are described in Hilbert space of vector-functions in a finite interval. The structure of the spectrum of the normal extensions is examined. Keywords: Degenarete differential operator, Formally normal and normal operator, Minimal and maximal operators, Extension, Spectrum. References: [1] E. A. Coddington, ‘‘Extension theory of formally normal and symmetric Subspaces’’, Mem. Amer. Math. Soc., 134(1973), 1-80. [2] G. Biriuk and E. A. Coddington, ‘‘Normal extensions of unbounded formally normal operators’’, J. Math. and Mech., 13(1964), 617-638. [3] J. Stochel and F. H. Szafraniec, ‘‘On normal extensions of unbounded operators’’, I, Oper. Theory, 14(1985), 31-55. [4] N. Dunford and J.T. Schwartz, ‘‘Linear Operators’’, vol. II, Interscience, New York, 1963. [5] V. I. Gorbachuk and M. L. Gorbachuk, ‘‘Boundary value problems for operator differential equations’’, Kluwer Academic, Dordrecht, 1991. [6] Z. I. Ismailov, ‘‘Compact inverses of first-order normal differential operators’’, J. Math. Anal. Appl. 320(2006), 266-278.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Converse Theorems for the Discrete Power Series Methods of Summability
Sefa Anıl Sezer 1, İbrahim Çanak 2 1 Department of Mathematics, İstanbul Medeniyet University, İstanbul, Turkey [email protected] 2 Department of Mathematics, Ege University, İzmir, Turkey [email protected]
Abstract: The discrete type power series methods were introduced by Watson [4]. In this study, under certain conditions we recover convergence of an infinite series from its discrete power series summability. Our results both extend and generalize Ishiguro's [1] theorems. Keywords: Tauberian theorems, power series methods of summability. References: [1] K. Ishiguro, Two Tauberian theorems for (J, p) summability, Proc. Japan Acad. 41 (1965) 40-45. [2] S. A. Sezer, İ. Çanak, On converse theorems for the discrete Bürmann power series method of summability, Maejo Int. J. Sci.Technol. 10 (2016) 346-353. [3] S. A. Sezer, İ. Çanak, Conditions for the equivalence of power series and discrete power series methods of summability, Filomat 29 (2015) 2275-2280. [4] B.Watson, Discrete power series methods, Analysis (Munich) 18 (1998) 97- 102. [5] B.Watson, A Tauberian theorem for discrete power series methods, Analysis (Munich) 22 (2002) 361-365.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
α – Fuzzified Rough Set Model in Multigranulation Space
Tanzeela Shaheen Department of Mathematics, Air University, Islamabad, Pakistan [email protected]
Abstract: Multigranulation rough set structure has been developed in recent years [2] by extending the Pawlak’s rough set [1] (single granularity) approach. Multigranulation approach is getting attention of many researchers as it has widened the possible application areas of rough set technique. Recently, a new approach has been presented for defining the rough approximations of α- indiscernible objects (indiscernible up to a certain degree α) under fuzzy environment [3]. In this paper, we extend that approach under the framework of multigranulation over two different universes of discourse, that is, multigranulation α-fuzzified rough set model over two universes. Structural properties have been discussed and an algorithm has been presented to deal with multi criteria group decision making problems. The proposed model not only extends α-fuzzified rough set approach but also provides a new perspective for multiple criteria group decision making with uncertainty. Keywords: Rough sets, α-fuzzified rough sets, rough sets over two universes, multigranulation α-fuzzified rough sets, multiple criteria group decision making. References: [1] Z. Pawlak, “Rough Sets” International Journal of Computer and Information Sciences 11(5) (1982) 341-356. [2] Y. Qian, J. Liang, Y. Yao, C. Dang, “MGRS: A multi-granulation rough set”, Information Sciences, 180(6) (2010), 949-970. [3] M. Shabir, T. Shaheen, A new methodology for fuzzification of rough sets based on α-indiscernibility. Fuzzy Sets and Systems, 312, (2017)1-16.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
A Note on Generalized Bernstein-type Cheney-Sharma Operators
Dilek Söylemez, Department of Computer Programming of Elmadag Vocational School, Ankara University, Ankara, Turkey [email protected] Fatma Taşdelen Yeşildal Department of Mathematics, Ankara University, Ankara, Turkey [email protected] Gülen Başcanbaz Tunca Department of Mathematics, Ankara University, Ankara, Turkey [email protected] Abstract: In this paper, we deal with the Korovkin type approximation properties of Cheney-Sharma Chlodovsky operators by using A-statistical convergence . We also study rate of convergence. Furthermore, we show that these operators preserve properties of the modulus of continuity function when f is a modulus of continuity function and Lipschitz condition of a given Lipschitz continuous function f. Finally, we give a result for the new operators when f is a convex functions and we add a graphical example for these operators. Keywords: Chlodovsky operators, Lipschitz continuous function, modulus of continuity function. References: [1] F. Altomare, M. Campiti, Korovkin-type approximaton theory and its applications, Walter de Gruyter, Berlin-New York, 1994. [2] B.M. Brown, D. Elliott, D.F. Paget, Lipschitz constants for the Bernstein polynomials of a Lipschitz continuous function, J. Approx. Theory, 49(1987), no.2, 196-199. [3] E. W. Cheney, A. Sharma, On a generalization of Bernstein polynomials, Riv. Mat. Univ.Parma, 2(5)(1964), 77-84. [4] D. D. Stancu, C. Cisma¸siu,On an approximating linear positive operator of Cheney-Sharma, Rev. Anal. Numer. Theory Approx., 26(1997),no.1-2, 221-227. ______157
INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Evaluating Gaussian Fuzzy System Reliability
Halil İbrahim Şahin Department of Statistics and Computer Sciences, Karadeniz Technical University, [email protected] Melek Eriş Büyükkaya Department of Statistics and Computer Sciences, Karadeniz Technical University, [email protected]
Abstract: Gaussian fuzzy membership functions are quite popular in the fuzzy logic literature. Therefore, if we accept components fuzzy reliability as a Gaussian membership, it is important to calculate fuzzy system reliability. It is difficult to find Gaussian membership system reliability, because of erf function. Therefore, in this study, we approximate Gaussian membership to triangular membership function. As a results, we obtained fuzzy system reliability as a function of mean and standard deviation . Keywords: Fuzzy System Reliability, Gaussian Fuzzy Membership, Triangular Membership Function. References: [1]A., K., Shaw and T., K., Roy ,Generalized Trapezoidal Fuzzy Number with its Arithmetic Operations and its Application in Fuzzy System Reliability Analysis, International Journal of Pure and Applied Sciences and Technology ISSN 2229- 6107 Int. J. Pure Appl. Sci. Technol., 5(2), pp. 60-76, 2011. [2]E., A., Elsayed, Reliability Enginering, Addison Wesley Longman, Inc., USA, 1996. [3]I. M. Aliyev and Z. Kara, Fuzzy system reliability analysis using time dependent fuzzy set, Control and cybernetics vol.33, 2004. [4]J. Yao, J. Su and T. Shih , Fuzzy System Reliability Analysis Using Triangular Fuzzy Numbers Based on Statistical Data, Journal of information science and engineering 24, 1521- 1535 ,2008.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Smoothed Auxiliary Function with Multiple Extrema in Global Optimization
Ahmed SAHINER and Shehab A. IBRAHEM Department of Mathematics, Suleyman Demirel University, Isparta, Turkey [email protected], [email protected] Abstract: In this study, we present a new auxiliary function method to solve unconstrained global optimization. First, a new smoothing auxiliary function with multiple extrema is constructed by using local smoothing approximations and then the algorithm and its properties are demonstrated. Second, we apply the algorithm to the test problems in order to explain the efficiency and effectiveness of the method. Keywords: Global optimization, Smoothing technique, Auxiliary function. References: [1] Z. Y. Wu and A. M. Rubinov, “Global Optimality Conditions for Some Classes of Optimization Problems”, J. Optimiz. Theory App., 145(2010), 164- 185. [2] Y. Lin and Y. Yang, “A new filled function method for constrained nonlinear equations”, Appl. Math. Comput, 219(2012), 3100-3112. [3] N. Yilmaz and A. Sahiner, “A new smoothing approximation to piecewise smooth functions and applications”, International Conference on Analysis and Application, (2016), 226-226. [4] B. W. K. Ling, C. Z. Wu, K. L. Teo and V. Rehbock, “Global Optimal Design of IIR Filters via Constraint Transcription and Filled Function Methods”, Circ. Syst. Signal Pr., 32(2013) 1313-1334.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Application of Modern Optimization Techniques in Determination of the Academic Achievement
Ahmet Sahiner, Sumeyya Koman and Raziye Akbay Uçar Department of Mathematics, Süleyman Demirel University, Isparta, Turkey [email protected], [email protected]
Abstract: In the study, we develop an attitude scale with the aim of measuring students’ interest towards the lesson and the teacher. The prepared scales are applied to the students. The obtained data are tabulated. The data is modeled using fuzzy logic and neural networks techniques separately. Obtained results are compared with each other and the real data. Keywords: Fuzzy logic, Neural network, Attitude scale, Academic achievement. References: [1] R. Akbay, A. Şahiner, & N. Yılmaz, “Determining of The Achievement of Students by Using Classical and Modern Optimization Techniques” International Journal of Physics and Chemistry Education 8(1) (2016), 3–13. [2] S. Wagner, “Conservation of equation and function under transformations of variable”, Journal For Research in Mathematics Education, 12(2) (1981), 107- 118. [3] M. Saltan, S. Saltan S. & A. Sahiner , Fuzzy logic modelling of deflection behavior against dynamic loading in flexible pavements, Construction and Building Materials, 21(2007), 1406-1414.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Radiation Shielding Properties of Borided Fe-Ni Binary Alloys by Fuzzy Logic Modelling
Ahmet Şahiner1, Nazım Uçar2, Adnan Çalık3 and Gülden Kapusuz1 1 Department of Mathematics, Suleyman Demirel University, Isparta, Turkey 2Department of Physics, Suleyman Demirel University, Isparta, Turkey 3Department of Machine and Manufacturing, Suleyman Demirel University, Isparta,Turkey [email protected], [email protected], [email protected], [email protected]
Abstract: In this study, firstly the radiation shielding properties of borided Fe-Ni binary alloys (Ni-60 wt.% and Ni-80 wt.%) have been investigated. For this purpose, linear attenuation coffecients as a function of boronizing parameters (time and temperature) have been measured at photon energy levels of 662 keV, 1173 keV and 1332 keV. According to experimental results, the fuzzy logic model (FLM) is established. The results showed that the fuzzy logic model can be used to predict the radiation shielding properties of borided Fe-Ni alloys for untested conditions. Keywords: Fuzzy Logic Modelling, Boriding, Radiation Shielding, Binary Alloys. References: [1] A. Sahiner, F. Ucun, G. Kapusuz, N. Yilmaz, “Completed Optimized Structure of Threonine Moleculeby Fuzzy Logic Modeling”, Z. Naturforsch A, 71( 4),(2016), 381–386. [2] A. Sahiner, H. Gokkaya, N. Uçar, “Nonlinear Modelling of the Layer Microhardness of Fe-Mn Binary Alloys” , Journal of the Balkan Tribological Association, 19(4),(2013), 537-548. [3] A. Calik, S. Akbunar, N. Ucar, N. Yilmaz, M. S. Karakas and I. Akkurt, “A Comparison of Radiation Shielding of Stainless Steel with Different Magnetic Properties”, Nuclear Technology & Radiation Protection 29(2014), 186-189.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Temperature and pressure based estimation of daily global solar radiation over Turkey using fuzzy logic modeling
Ahmet Şahiner Department of Mathematics, Süleyman Demirel University, Isparta, Turkey [email protected] Idris A. Masoud Abdulhamid Department of Mathematics, Süleyman Demirel University, Isparta, Turkey [email protected] Murat Ozturk Department of Mechatronics Engineering, Süleyman Demirel University, Isparta, Turkey [email protected]
Abstract: In this paper, a fuzzy logic model (FLM) for predicting and modeling of the daily average solar radiation for Turkey is developed. The daily values of ambient temperature and relative pressure duration as meteorological data are utilized for FLM. These data for estimating solar radiation are generally obtained easily. Also, the calculated daily solar radiation values by using the FLM for selected twelve cities are compared with the actual data and the national database of selected cities. For similarity tests, the most common statistical procedures (MAE, RMSE, MSE, MAPE and R2) are utilized. The fuzzy logic based models show the stable processor different meteorological data introduced to the operation for modeling of daily average solar radiation. Keywords: Fuzzy system modeling, optimization modeling, artificial intelligence. References: [1] V. Gomez and A. Casanovas, “Fuzzy modeling of solar irradiance on inclined surfaces”, Solar Energy 75(4) (2003), 307–315. [2] O., “Modeling of solar radiation using remote sensing and artificial neural network in Turkey”, Energy 35(12) (2010), 4795–4801.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
[3] M. Ozturk, “An Evaluation of Global Solar Radiation Empirical Formulations in Isparta, Turkey”, Energy Sources, Part A: Recovery, Utilization, and Environmental Effects 37(22) (2015), 2474–2486. [4] M. Iqbal, “An introduction to solar radiation”, Elsevier, 2012. [5] Ö. Çelik, A. Teke and H.B. Y, “The optimized artificial neural network model with Levenberg-Marquardt algorithm for global solar radiation estimation in Eastern Mediterranean Region of Turkey”, Journal of cleaner production 116 (2016), 1–12.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Normalizer of Some Congruence Subgroups
Zeynep Şanlı, Tuncay Köroğlu, Bahadır Özgür Güler Department of Mathematics, Karadeniz Technical University, Trabzon, Turkey [email protected], [email protected], [email protected]
푘 Abstract: The purpose of the this paper is to obtain the normalizers of Γ0 (푛) in the groups Γ푘. The groups we consider in here are analogous to some congruence subgroups of Γ. Our method is based on Ivrissimtzis in [6]. The paper is organised as follows: In section 2, we give the definition of a H axes of X which defining an equivalence relation on X, and give some preliminary 2 3 results. In section 3, we obtained the normalizers of two groups Γ0 (푛) and Γ0 (푛) by using the H axes notion.
Keywords: Modular groups; congruence subgroup; group action References:
[1] M. Akbaş, D. Singerman, The normalizer of Γ0 (푛) in PSL(2,R), Glasgow Math. 32 (1990), 317–327.
[2] A. O. L. Atkin, J. Lehner, Hecke operators on Γ0 (푛), Math. Ann. 185 (1970), 134–160.
[3] F. Bars, The Group Structure of the Normalizer of Γ0 (푛) after Atkin-Lehner, Communications in Algebra 36(6) (2008) 2160–2170. [4] K. S. Chua, M. L. Lang, Congruence subgroups associated to the monster, Experimental Mathematics 13(3) (2004) 343–360. [5] C. Conway, S. Norton, Monstrous moonshine, Bull. London Math. Soc. 11 (1979), 308–339. [6] I. Ivrissimtzis, Congruence subgroups of Hecke groups and regular dessins,Ph.D. Thesis, University of Southampton, 1998.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
ퟐ Boundary Component of the Group 횪̂ퟎ (퐍)
Hatice Şengül*, Mehmet Akbaş Department of Mathematics, Karadeniz Technical University, Trabzon, Turkey [email protected], [email protected]
Abstract: In this paper, the number of boundary components in the signature of ̂2 the subgroup Γ0 (N) obtained by taking squares of the elements of the extended modular group Γ̂ and the numbers of cusps and finite link periods in each boundary components are obtained by using Hoare-Uzzel Theorem. Keywords: Signature, Period cycles, Boundary components. References: [1] M. Akbaş, The Normalizer of Modular Subgroups, PhD Thesis, University of Southampton, 1989. [2] D. Singerman, “On the Sturucture of non-Euclidean Crystallographic Groups”, Proc. Camb. Phil. Soc., 76(1974), 233-240. [3] B. Uzzell, Groups Acting on Hyperbolic 3-Space, PhD Thesis, University of Birmingham, 1981. [4] H. C. Wilkie, “On non-Euclidean Crystallographic Groups”, Math. Zeit., 91(1966), 87-102.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
GUI-EFG: Guided Element Free Galerkin Method
Süleyman ŞENGÜLa , Erhan COŞKUNb aDepartment of Mathematics, Recep Tayyip Erdoğan University, Rize, Turkey [email protected] bDepartment of Mathematics, Karadeniz Technical University, Trabzon, Turkey [email protected]
Abstract: An interactive tool, called GUI-EFG, using MATLAB GUI[1] feature is developed that allows for interactive solution of boundary value problems on finite intervals using Element Free(meshless) Galerkin(EFG) method[2]. GUI- EFG allows for using user defined coefficient functions including discontinuous ones, as well as various types of boundary conditions and values. The numerical results are displayed graphically and compared with analytical solution, if obtainable by analytical methods. Dependence of solutions on the use of weight functions are investigated using two types of weight functions. Furthermore, computational load of shape functions is reduced by using the so-called translation-invariance property of shape functions[3,4]. We observe that EFG whose shape functions are computed with translation invariant property becomes compatible with the Finite Element Method(FEM). GUI-EFG allows for numerical solution of various boundary value problems, including singular ones and also leads to a comparitive study of various approaches. Keywords: Element Free Galerkin method, MATLAB GUI, Shape functions. References: [1] MATLAB, www.mathworks.com, The MathWorks . [2] Y. Belytschko, Y.Y. Lu, and L. Gu, “Element Free Galerkin methods”, International Journal for Numerical Methods in Engineering, 37(1994), 229-256. [3] Şengül, S. ve Coşkun, E., Optimized EFG Method and its Applications on one and two dimensional Problems, 14th Mathematics Symposium, MATDER, Niğde, May 14-16, 2015. [4] Şengül, S., Optimization of Meshless Galerkin Method and it’s Applications with some New Adaptive Algorithms, Dissertation, The Graduate School of Nature and Applied Science, Karadeniz Technical University, 2016. ______166
INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
On the Matrix Nearness Problem of the Generalized Sylvester Quaternion Matrix Equations
Sinem ŞİMŞEK Department of Mathematics, Kırklareli University, Kırklareli, Turkey [email protected]
Abstract: The generalized Sylvester quaternion matrix equations have a great number of applications in control theory, signal and color image processing. So, investigating solutions of this matrix equations should be significant and interesting. In this work, it is established the precise solution for the matrix nearness problem of the generalized Sylvester quaternion matrix equations by Moore Penrose Inverse. Keywords: Quaterion Matrices, Matrix nearess problem, Moore Penrose Inverse. References: [1] S. F. Yuan, Q. W. Wang, “L-structured quaternion matrices and quaternion linear matrix equations”, Linear and Multilinear Algebra, 64.2(2016), 321-339. [2] S. F. Yuan, Q. W. Wang, “Two Special Kinds of Least Squares Solutions for the Quaternion Matrix Equation”, Electron J. Linear Algebra, 23(2012), 257-274. [3] Z. H. He, O. M. Agudelo, Q. W. Wang ad B. D. Moor, “Two-sided coupled generalized Sylvester matrix equations solving using a simultaneous decomposition for fifteen matrices”, Linear Algebra Appl., 496(2016), 549-593. [4] S. Şimşek, M. Sarduvan and H. Özdemir, “Centrohermitian and Skew- Centrohermitian Solutions to the Minimum Residual and Matrix Nearness Problems of the Quaternion Matrix Equation (AXB,DXE) = (C,F)”, Adv. Appl. Clifford Algebras, 27.3(2017), 2201-2214.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Korovkin Type Theorems in Modular Spaces via Summability Methods
Emre Taş, Tuğba Yurdakadim Department of Mathematics, Ahi Evran University, Kırşehir, Turkey Department of Mathematics, Hitit University, Çorum, Turkey [email protected], [email protected]
Abstract: In this talk , we examine the problem of approximation to a function by means of positive linear operators in modular spaces via summability methods. Indeed, in order to get stronger results than the classical cases, we use the power series method which also includes both Abel and Borel methods. An application that satisfies our theorem is also provided. Keywords: Power series method, Modular spaces, Positive linear operators References: [1] F. Altomare and S. Diomede, “Contractive Korovkin subsets in weighted spaces of continuous functions”, Rend. Circ. Mat. Palermo 50(2001), 547-568. [2] C. Bardaro and I. Mantellini, “Approximation properties in abstract modular spaces for a class of general sampling-type operators”, Appl. Anal. 85(2006), 383-413. [3] C. Bardaro and I. Mantellini, “Multivariate moment type operators: approximation properties in Orlicz spaces”, J. Math. Ineq. 2(2008), 247-259. [4] P. P. Korovkin, “Linear Operators and Approximation Theory”, Hindustan Publ. Co., Delhi, (1960) 37.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Pollution Detection for the Singular Linear Parabolic Equation
LAIB TELDJA AND AYADI ABDELHAMID Laboratory of Dynamical Systems and Control, Larbi Ben Mhidi University, OEB, Algéria, [email protected], [email protected]
Abstract: In this article we are concerned by the problem of identification of pollution terms which arise in singular problems as for remote sensing problems, and which are modeled by a linear singular parabolic equation. Some data are missing, then the sentinel method of J.-L. Lions (1992) is changed and a new sentinel is used; it is a particular least square method which permits to distinguish between the missing terms and the pollution terms. In particular, the new sentinel is given here in its more general and more realistic setting for singular parabolic problems: in this case, the observation and the control have their supports in different open sets. The problem of finding a new sentinel is equivalent to finding singular optimality system of the least square control for the parabolic equation that we solve. Keywords: Singular heat equation, controlability, optimal control, sentinels References: [1] Lions J. L., Control of distributed singular systems, Bordas, Paris, (1985). [2] Lions J. L., Contrˆolabilit´e exacte, stabilisation et perturbations des syst`emes distribués, Vol. 1. Controlabilité exacte, Masson, Paris (1988). [3] Lions J. L., Sentinelles pour les syst`emes distribu´es `a donn´ees incompl`etes, Masson, Paris (1992). [4] Mizohata .S, Mem.coll.Sc.Univ.Kyoto,A 31,(3),1958,p.219-239.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Relation of Some Special Vertices of Suborbital Graphs and Continued Fractions Tuğba TUYLU, Ali Hikmet DEĞER, Ümmügülsün AKBABA Department of Mathematics, Karadeniz Technical University, Trabzon, Turkey [email protected] [email protected] [email protected]
Abstract: In this work, suborbital graphs for congruence subgroups Γ0(푛) of the moduler group Γ and some properties have been studied. Some connections were made between the special vertex values on the paths in these graphs and the continued fractions. Moreover, this has been viewed as a special case of continued fractions from Pringsheim’s theorem. Keywords: Suborbital Graphs, Modular Group, Möbius Transformations. References: [1] G. A. Jones, D. Singerman, and K. Wicks, “The Modular Group and Generalized Farey Graphs”, London Math. Soc. Lecture Note Ser., 1991, pp. 316-338. [2] A. H. Değer, M. Beşenk, and B. Ö. Güler, “On Suborbital Graphs and Related Continued Fractions”, Applied Math. and Computation, 2011, 746-750. [3] C. C. Sims, “Graphs and Finite Permutation Groups”, Math. Zeitschr., 1967, pp. 76-86. [4] M. Akbaş, “On Suborbital Graphs for the Modular Group”, Bull. London Math. Soc., 2001, pp. 647-652. [5] P. M. Neumann, “Finite Permutation Groups, Edge-Coloured Graphs and Matrices”, Topics in Group Theory and Computation, Academic Press, New York, 1977. [6] T. Tsukuzu, “Finite Groups and Finite Geometries”, Cambridge University Press, 1982. [7] N. L. Biggs, and A. T. White, “Permutation Groups and Combinatorial Structures”, London Math. Soc. Lecture Note Ser., Cambridge, CUP, 33, 1982. [8] A. Cuty and V. B. Petersen and B. Verdonk and H. Waadeland and W. B. Jones, “Handbook of Continued Fractions for Special Functions”, Springer Science + Business Media B. V., 2008. ______170
INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Bounds for Atom-bond Connectivity Index
Ahmet Uğur, Ayşe Dilek Maden Department of Mathematics, Selcuk University, Konya, Turkey [email protected] [email protected]
Abstract: Atom-bond connectivity (ABC) index, introduced by Ernesto Estrada et al.[2], attracted a great deal of interest in mathematical chemistry. Kinkar Ch. Das[1] gave some lower and upper bounds on ABC index of graphs. In this work, we give new bounds for this summation index by using a different method. Since ABC index is a function of two variables, its terms have monotone behaviour on certain domains. Then, we can give possible upper and lower bounds with the help of Comparison Theorem for Integrals. Keywords: Molecular graph, Atom-bond connectivity index. References: [1] K. C. Das, “Atom-bond connectivity index of graphs”, Discrete Applied Mathematics, 158(2010),1181-1188. [2] E. Estrada, L. Torres, L. Rodriguez, I. Gutman, “An atom-bond connectivity index: modelling the entalpy of formation of alkanes”, Indian J. Chem., 37A (1998), 849-855. [3] L. Gan, H. Hou, B. Liu, “Some results on atom-bond connectivity index of graphs”, MATCH Commun.Math Comput. Chem., 66(2011), 669-680. [4] W. Rudin, “Principal of Mathematical Analysis”, McGraw-Hill,Newyork, 1976. [5] R. Xing, B. Zhou, Z. Du, “Further results on atom-bond connectivity index of trees”, Discrete Applied Mathematics, 158(2010), 1536-1545.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Travelling waves in diffusion, aggregation and diffusion- aggregation-diffusion in a single population Judith Pérez Velázquez Institute of Computational Biology, Helmholtz Zentrum München, Germany [email protected] Faustino Sanchez-Garduno Universidad Nacional Autonoma de Mexico Faculty of Science, Department of Mathematics
Abstract: Reaction-diffusion equation (RDE) are, under specific conditions, known to possess travelling wave solutions (TWS). These equations are sometimes employed to model dispersion of individuals of one specie. Certain species however, rather present aggregative behavior, which is also modeled through a density dependent equation but with a negative term, also proved to have TWS, see [1]. Furthermore, in diffusion-aggregation, one single population is capable to present both modes. Here we revise these concepts in the context of TWS and also present an example of a RDE where the diffusive part is a nonlinear density dependent function and the growth rate is given by Fisher-KPP type also call monostable reaction term. By using a biased random walks approach, the diffusive part was derived by Turchin (see [2] and revisited by us in [1])). By choosing the appropriate parameter values, the diffusive term is capable of describing different types of population movements including: strong diffusion, diffusion-aggregation-diffusion and strong aggregation. Because of this, the RDE would have up to two points of degeneracy which, combined with the negativity of the diffusion density-dependent coefficient, give rise to interesting problems from both, mathematical and interpretative, points of view. Keywords: travelling wave solutions, degeneracy, reaction/diffusion equations. References: [1] F Sanchez-Garduno, P.K. Maini and J. Perez-Velazquez. A nonlinear degenerate equation for direct aggregation and traveling wave dynamics. Disc. Cont. Dyn. Syst. Series B, Vol. 13, No. 2, pp. 455-487.2010. [2] P Turchin (1989): Population consequences of aggregative movement. J. An. Ecol., 58 , pp. 75-1
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
On a Integral-Transform to Differential Equations
Ervenila Xhaferraj Department of Mathematics, Faculty of Mathematics and Physics Engineering, Polytechnic University of Tirana , Albania, [email protected] Abstract: In this paper we presented a bilateral integral transform which results in the new Fourier-like integral transform of the function f(t) . In addition, some properties of the NITF are explored . We present the new application of the NITF integral transform to solve a steady heat transfer problem equation in this work. The fundamental solutions of this problem with the initial conditions were obtained with the use of the NITF integral transform . Keywords: NIFT integral transform, analytical solution, heat equation, References: [1] Beerends, R. J., et al., Fourier and Laplace Transforms, Cambridge University Press, Cambridge, UK, 2003 [2] Dyke, P., An Introduction to Laplace Transforms and Fourier Series. Springer, New York, USA, 2014 [3] John, W., Integral Transforms in Applied Mathematics, Cambridge University Press, Cambridge, UK, 1971 [4] I. J. Schoenberg, “The integrability methods”, Amer. Math. Monthly, 66(1959), 361-375. [5] A. Kashuri & A. Fundo & M. Kreku, “Mixture of a New Integral Transform and Homotopy Perturbation Method for Solving Nonlinear Partial Differential Equations”, Advances in Pure Mathematics, Vol. 3, No. 3 (2013), pp. 317 − 323.. [6] Yang, X. J., A New Integral Transform with an Application in Heat-Transfer Problem, Thermal Science, 20 (2016), Suppl. 3, pp. S677-S681 [7] Yang, X. J. A New Integral Transform Method for Solving Steady Heat- Transfer Problem, Thermal Science, 20 (2016), Suppl. 3, pp. S639-S642.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Aczél Type Inequalities for Hilbert Space Operators
Ulaş Yamancı and Mehmet Gürdal Department of Mathematics, Süleyman Demirel University, Isparta, Turkey [email protected]; [email protected]
Abstract: Some Aczél type inequalities for Hilbert space operators are established. Several particular cases of interest are given as well. Keywords: Berezin symbol, Reproducing kernel Hilbert space, Aczel-type inequalities. References: [1] J. Aczél, “Some general methods in the theory of functional equations in one variable”, New applications of functional equations, Uspehi. Mat. Nauk (N. S.), 11(3)(1956), 3-68 (in Russian). [2] J. Tian, “Reversed version of a generalized Aczél's inequality and its application”, J. Inequal. Appl., 2012, 2012: 202. [3] J. Tian and M.H HA, “Properties and refinemets of Aczél-type inequalities”, Journal of Mathematical Inequalities, 12(1) (2018), 175-189.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
On the Artinianness of Top Local Cohomology Modules
Tuğba Yıldırım Department of Mathematical Engineering, Istanbul Technical University, Istanbul, Turkey [email protected]
Abstract: Throughout, let R be a Noetherian ring, I an ideal of R, M an R- 𝑖 module and let 퐻퐼(푀) denote the i-th local cohomology module of M with support in I. Local cohomology theory is an active area of research in commutative algebra, algebraic geometry and related fields. One of the classical and long-standing problem in this theory is to determine whether a given local cohomology module is Artinian, or not [Third Problem, [1]]. It has been studied by several authors, see eg. [2, 3, 4]. In this talk, we collect some results related to this problem, 푐푑(퐼,푀) particularly for the top local cohomology modules, 퐻 퐼 (푀), where 𝑖 푐푑(퐼, 푀) = 푠푢푝{𝑖 ∈ ℕ|퐻퐼(푀) ≠ 0}. Keywords: Local cohomology, cohomological dimension, Artinian module. References: [1] C. Huneke, “Problems in local cohomology”, Free Resolutions in Commutative Algebra and Algebraic Geometry Sundance 90, Res. Notes in Math. Jones and Barlett 2 (1992) 93–108. [2] M. Aghapournahr and L. Melkersson, “Artinianness of local cohomology modules”, Ark. Mat. 52 (2014) 1–10. [3] M. T. Dibaei and A. Vahidi, “Artinian and Non-Artinian Local Cohomology Modules”, Canad. Math. Bull. 54 (2011) 619–629. [4] M. Hellus and J. Stückrad, “Artinianness of local cohomology”. J. Commut. Algebra, 1 (2009), no. 2, 269–274.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
q-Quasinormal Operators and Its Extended Eginvalues
Fatih YILMAZ, Meltem SERTBAŞ Department of Mathematics, Karadeniz Technical University, Trabzon, Turkey [email protected] , [email protected]
Abstract: In this paper, the relation between q-deformed quasinormal operators and q-quasinormal operator classes is investigated. Moreover, we proof that these are same. Also, we consider some extended eginvaule problems for q- quasinormal operators. Keywords: q-Quasinormal operator, q-Deformed operators, Extended eigenvalue. References: [1] S. Ota, “Some classes of q-deformed operators”, J. Operator Theory. 48(2002), 151-186. [2] S. Lohaj, “Quasi-normal operators”, Int. J. of Math. Analysis, 4(2010), no. 47, 2311-2320. [3] S. Ota, F. H. Szafraniec, “q-Positive definiteness and related operators”, J. Math. Anal. Appl., 329(2007), 987-997. [4] A. Biswas, A. Lambert, S. Petrovic “Extended eigenvalues and the Volterra operator”, Glasg. Math. J., 44.3(2002), 521-534. [5] M.T. Karaev, “On extended eigenvalues and extended eigenvectors of some operator classes”, Proc. Amer. Math. Soc., 134.8(2006), 2383-2392.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
A New Algorithm Based on Penalty Function Approach for Inequality Constrained Global Optimization Problems
Nurullah Yılmaz and Ahmet Şahiner
Department of Mathematics, Süleyman Demirel University Isparta, Turkey [email protected], [email protected]
Abstract: In this study, the nonlinear constrained global optimization ploblems are handled. A new smoothing for exact penalty functions in constrained optimization problems is invetigated. The new exact penalty function is combined with the auxiliary function and an adapted algorithm for solving nonlinear inequality constrained global optimization problems is presented. Finally, the efficiency of the algorithm on some numerical examples is illustrated. Keywords: Constrained optimization, penalty function, smoothing approach. References: [1] S. S. Rao, “Engineering Optimization 4th ed.” John Wiley & Sons, New Jersey (2009). [2] M. C. Pinar, & S. Zenios, “On smoothing exact penalty functions for convex constrained optimization”, SIAM Journal on Optimization, 4(1994), 468-511.
[3] S.J. Lian, “Smoothing approximation to l1 exact penalty for inequality constrained optimization”, Appl. Math. Comput., 219 (2012), 3113-3121. [4] A. Sahiner, G. Kapusuz, & N. Yilmaz, “A new smoothing approach to exact penalty functions for inequality constrained optimization problems”, Numerical Algebra Control and Optimimization, 6(2) (2016), 161-173.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
On Fuzzy Prime Hyperideals(Hyperfilters) in ∧ - Hyperlattices
Şerife YILMAZ1, Dilek BAYRAK2 1Department of Mathematics, Karadeniz Technical University, Trabzon, Turkey [email protected] 2Department of Mathematics, Tekirdağ Namık Kemal University, Tekirdağ, Turkey [email protected]
Abstract: The purpose of this paper is the study of fuzzy prime hyperideals and fuzzy prime hyperfilters in ∧-hyperlattices. Some properties of such hyperideals are investigated. The relationship between fuzzy prime hyperideals and fuzzy prime filters is discussed. Keywords: ∧ - hyperlattice; hyperideal; hyperfilter. References: [1] O. Kazancı, B. Davvaz, “On the structure of rough prime (primary) ideals and rough fuzzy prime (primary) ideals in commutative rings”, Information Sciences, 178(2008), 1343-1354. [2] R. Ameri, M. Amiri-Bideshki, A. B. Saeid, S. Hoskova-Mayerova, “Prime filters of hyperlattices”, An. Şt. Univ. Ovidius Constanta. 24(2)(2016), 15-26. [3] M. Amiri-Bideshki, R. Ameri, A. Borumand Saeid, “On Prime Hyperfilters (Hyperideals) in ∧ - Hyperlattices”, European Journal of Pure and Applied Mathematics, 11(1)(2018), 169-188.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Korovkin Theory for Extraordinary Test Functions via Power Series Method
Tuğba Yurdakadim, Emre Taş Department of Mathematics, Hitit University, Çorum, Turkey Department of Mathematics, Ahi Evran University, Kırşehir, Turkey [email protected] , [email protected]
Abstract: Korovkin subsets are the subsets of functions satisfying the same property as {1, 푥, 푥2} and have been studied by many authors. In this talk we introduce Korovkin subsets in the sense of power series method for T and present a characterization theorem that a subset of 퐶0(푋) is Korovkin subset in the sense of power series method for T. Keywords: Power series method, Korovkin subset. References: [1] F. Altomare and S. Diomede, “Contractive Korovkin subsets in weighted spaces of continuous functions”, Rend. Circ. Mat. Palermo 50(2001), 547-568. [2] J. Boos, “Classical and Modern Methods in Summability”, Oxford University Press (2000). [3] S. E. Takahasi, “Bohman-Korovkin-Wulbert operators on normed spaces”, J. Approx. Theory 72(1993), 174-184. [4] P. P. Korovkin, “Linear Operators and Approximation Theory”, Hindustan Publ. Co., Delhi, (1960) 37.
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INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE AND APPLIED MATHEMATICS (ICRAPAM2018)
JULY 23-27 2018, Karadeniz Technical University, Prof. Dr. Osman Turan Convention Center, Trabzon, TURKEY www.icrapam.org
Criticality indices of 2-independence of some graphs
Mohamed Zemir and Ahmed Bouchou Department of Mathematics and computer science Yahia Fares University of medea, Algeria [email protected] [email protected]
Abstract: Let 퐺 = (푉, 퐸) be a simple graph of order n, and of sise m with vertex set 푉(퐺) and edge set 퐸(퐺), A subset 푆 of 푉 is 2-independent set if ∆(푆) < 2 , and the 2-independence number 훽2(퐺) is the maximum cardinality of a 2- independent set . For a graphe 퐺, we define the criticality index of an edge 푒 ∈ 퐸(퐺) as 푐𝑖− (푒) = 훽2 훽 (퐺) − 훽 (퐺 − 푒), and the removal criticality index of a graph 퐺 as 푐𝑖− (퐺) = 2 2 훽2 (∑푚̅ 푐𝑖− (푒)) /푚(퐺) . 𝑖=1 훽2 Similarity we define the criticality index of an edge 풆 ∈ 푬(푮̅) as 풄풊+ (풆) = 휷ퟐ 휷 (푮) − 휷 (푮 + 풆), and the adding criticality index of a graph 푮 as 풄풊+ (푮) = ퟐ ퟐ 휷ퟐ ∑풎̅ 풄풊+ (풆) /풎(푮̅) and 푮̅ is the complementary of the graph 푮. ( 풊=ퟏ 휷ퟐ ) In this work, now we determine the removal and the adding criticality indices of 2-independence of cycles and paths.
Keywords: 2-independence number, Criticality index. References: [1] J. F. Fink and M.S. Jacobson, “n-domination, n-dependence and forbidden subgraphs in: Graph Theory with Applications to Algorithms and Computer (kalamazoo, Mich.1984)eds. Alavi, Chartrand, Lesniak, Lick and wall, Wiley, New-York (1985), 283–300. [2] J. F. Fink and M.S. Jacobson, “n-domination, n-dependence and forbidden subgraphs in: Graph Theory with Applications to Algorithms and Computer (kalamazoo, Mich.1984)eds. Alavi, Chartrand, Lesniak, Lick and wall, Wiley, New-York (1985), 301–311. [3] M. Chellali and N. J. Rad, “On k-independence critical graphs,” Australasian Journal of Combinatorics 53(2012), 289–298. ______180