abstract book

ABSTRACT BOOK OF ICRAPAM 2014

INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE and APPLIED MATHEMATICS 6-9 November 2014, ANTALYA, TURKEY www.icrapam.org

INTERNATIONAL CONFERENCE on RECENT ADVANCES in PURE and APPLIED MATHEMATICS (ICRAPAM 2014) 6-9 November 2014, ANTALYA, TURKEY BOOK OF ABSTRACT

BOOK OF ABSTRACT ISBN:

978-975-00211-1-4

ISBN: 978-975-00211-1-4

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INTERNATINAOL CONFERENCE on RECENT ADVANCES in PURE and APPLIED MATHEMATICS (ICRAPAM 2014) 6-9 November 2014, ANTALYA, TURKEY

ORGANIZING COMMITTEE Prof.Dr. Ekrem Savaş

Prof. Dr. Ants Aasma

Istanbul Ticaret University, Turkey

Tallinn University of Technology, Estonia

Prof.Dr. Feyzi Basar

Prof.Dr. Yılmaz Altun

Fatih University, Turkey

Artvin Çoruh University, Turkey

Prof.Dr. I. Naci Cangul

Prof.Dr. Mehmet Dik

Uludag University, Turkey

Rockford University, USA

Prof.Dr. M. Mursaleen

Prof.Dr. Fatih Nuray

Aligarh Muslim University, India

Afyon Kocatepe University, Turkey

Prof.Dr. Billy E. Rhoades

Assoc. Prof. Dr. Bunyamin Aydin

Indiana University, USA

Necmettin Erbakan University, Turkey

Prof.Dr. R. Patterson

Assoc. Prof. Dr. Necip Simsek

North Florida University, USA

Istanbul Ticaret University, Turkey

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INTERNATINAOL CONFERENCE on RECENT ADVANCES in PURE and APPLIED MATHEMATICS (ICRAPAM 2014) 6-9 November 2014, ANTALYA, TURKEY

SCIENTIFIC COMMITTEE Prof.Emine Mısırlı, Turkey

Prof.Claudio Cuevas, Brazil

Prof.Pratulananda Das, India

Prof.Allaberen Ashyralyev, Turkey

Prof.Huseyin Cakalli, Turkey

Prof.Reza Saadati, Iran

Prof.Mikail Et, Turkey

Prof.Ram Mohapatra, USA

Prof.Metin Basarir, Turkey

Prof.Charles Swartz, USA

Prof.Agron Tato, Albania

Prof.Mujahid Abbas, Pakistan

Prof.S. A. Mohiuddine, S. Arabia

Prof.Aref Jeribi, Tunisia

Prof.T. A. Chishti, India

Prof.Yusuf Yayli, Turkey

Prof.Billy E. Rhoades, USA

Prof.Husamettin Coskun, Turkey

Prof.Cihan Orhan, Turkey

Prof.Abdullah Aziz Ergin, Turkey

Prof.Ayhan Serbetci, Turkey

Prof.Cemil Tunc, Turkey

Prof.Bilal Altay, Turkey

Prof.Maria Zeltser, Estonia

Prof.Ljubisa Kocinac, Serbia

Prof.Salih Celebioglu, Turkey Prof.Kamalmani Baral, Nepal

Assoc.Prof.Ismail Ekincioglu, Turkey Prof.Ivana Djolovic, Serbia

Prof.Ants Aasma, Estonia

Prof.Leiki Loone, Estonia

Prof.Ismail N. Cangul, Turkey

Prof.Seyit Temir, Turkey

Dr.Lejla Miller Van-Wieren, Bosnia

Prof.Huseyin Aydin, Turkey

Prof.Yilmaz Simsek, Turkey

Assoc.Prof.Hamdullah Sevli, Turkey

Assoc. Prof.Bunyamin Aydin, Turkey

Assoc.Prof.Mehmet Gurdal, Turkey

Prof.Ali Fares, France

Prof.Seifedine Kadry, Kuwait

Assoc.Prof.M. Tamer Kosan, Turkey

Prof.A. Sinan Cevik, Turkey

Prof.G. Das, India

Prof.H. M. Srivastava, Canada

Prof.Naim Braha, Republic of Kosova

Prof.Halit Orhan, Turkey

Prof.Murat Tosun, Turkey

Prof.Vatan Karakaya, Turkey

Prof.Harry Miller, Bosnia

Prof.Hasan Akın, Turkey

Assoc.Prof.M. Kemal Karacan, Turkey

Prof.Amir Khosravi, Iran

Assoc.Prof.Ibrahim Canak, Turkey

Prof.Ali M. Akhmedov, Azerbaijan

Prof.Fariq M. Bhatti, Pakistan

Prof.Gangaram S. Ladde, USA

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Dear Colleaques May I offer you a warm welcome to the International Conference on Recent Advances in Pure and Applied Mathematics (ICRAPAM 2014) . Conferences generally provide the opportunities for professional and practitioners of common and related interest to exchange the ideas, knowledge and experience objective of expanding their horizons and raising their potentials in a highly competitive world. I am sure that many of you will meet old friends and also will make new ones. In the deliberations to follow, you will hear some familiar mathematics as well as some that are quite new. Mathematics develops faster and faster, many outstanding problems are solved and new areas demand new approaches. New applications make new demands, and surprising connections are discovered between apparently unrelated fields. In this exciting process the world of mathematics unites different parts of the globe making knowledge transfer easier and more pertinent One advantage of a congress like this one is bringing together mathematicians and scientists with different interests under one roof to share their ideas and exchange progress on problems of varied interest. Many times, we get to see how interconnected are our subjects, and how the most interesting results often occur between quite different areas. I hope this will allow us to see more clearly the unity of mathematics and will encourage us to meet new challenges with determination and skill. I would like to take this opportunity to thank those who are involved in making this conference possible, especially to the hardworking members of the international conference committee. The most important people of this conference are you, the delegates. It is your contribution in paper presentation that brings synergy and vitality. Thank you all for coming from far and near to participate in this conference, and may the conference be an enjoyable and beneficial one for each of us. Prof. Dr. Ekrem SAVAS Chair of the conference

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Contents Entanglement of Nanoresonator Interacting with Two Qubit Mahmoud Abdel-Aty Boundary Value Problems for Delay Differential Equations Ravi P Agarwal Determining Functionals for Damped Nonlinear Wave Equations Varga K. Kalantarov Calderon-Zygmund theory for Divergence Form Operators in Generalized Morrey Spaces Lubomira Softova On the Fine Spectra of n-th Band Triangular Matrices R. Birbonshi and P.D. Srivastava The Navier-Stokes Equations-A Never Ending Challenge? Werner Varnhorn The effect of the Terrorism on Tourism in Algeria Abdel Kader Boudi and Zouaoui Chikr el Mezouar An Estimate on Volumes of Trajectory -Balls for Kaehler Magnetic Fields Toshiaki Adachi Maximum Principle of Stochastic Switching Systems with Constraints Charkaz Aghayeva A Note on Delay Parabolic Equations Deniz Agirseven Analogies between Electromagnetism and Gravitation in General Relativity Zafar Ahsan Existence of Solutions for a Three -Point Second-Order Boundary Value Problems with Integral Boundary Conditions Ummahan Akcan and Nuket Aykut Hamal Necessary and Sufficient Conditions for the Solvability of Inverse Problem for a Class of Dirac Operators Ozge Akcay and Khanlar R. Mamedov Integral Inequalities for Log -Convex Functions via Riemann - Liouville Fractional Integrals Ahmet Ocak Akdemir, Erhan Set and M. Emin Ozdemir Generalization of Hausdorff Matrices F. Aydin Akgun and B.E. Rhoades New Indices on Special Graphs Nihat Akgunes, Ahmet Sinan Cevik and Ismail Naci Cangul The New Method of the Fine Spectrum of a Class of Operator Matrix in Some Sequences Spaces Ali M. Akhmedov On Compactness of the Hardy Operator in the Weighted Lp(.) (0, ¥) Space Lutfi Akin and Yusuf Zeren On the Behavior of a Class of p-Adic Dynamical Systems Hasan Akin, Farrukh Mukhamedov and Mutlay Dogan Sharp Markov -Type Inequalities for Rational Functions on Several Intervals Mehmet Ali Akturk and Alexey Lukashov Computing Fresnel Integrals via Modified Trapezium Rules M. Alazah, S.N. Chandler-Wilde and S. La Porte Animation and Graphics to Understand Mathematics Abir Alharbi and Fairouz Tchier On Certain Estimates for the Littlewood-Paley Operator Along Surfaces of Revolution Mohammed Ali Stabilized Mixed Finite Element Method Q1-Q0 for the Generalized Stokes Problem Chibani Alima and Nasserdine Kechkar Oscillation Theorem for One Spectral Problem Ziyatkhan S. Aliyev and Humay Sh. Rzayeva Taylor Series Solution of Ordinary Differential Equations Fathi M Allan Numerical Solution of an Integral Equation for Perpetual Bermudan Options Ghada Alobaidi Bounds for Oscillatory Singular Integrals on Rⁿ Hussain Al Qassem, Leslie Cheng, Ayako Fukui and Yibiao Pan

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

On Lacunary Difference Sequence of Fuzzy Numbers Hifsi Altinok, Mikail Et and Rifat Colak Some Sequence Spaces Defined by the Weighted Mean Method and Modulus Function Selma Altundag and Bayram Sozbir Weighted Statistical Convergence of Double Sequences Selma Altundag and Bayram Sozbir On the Fine Spectrum of the Operator B ( r , s, t ) over the Class of Convergent Series Selma Altundağ and Merve Abay Exponential Extinction for Discrete Nicholson’s Blow Flies Model with Nonlinear Mortality and Patch Structure Terms Jehad Alzabut Numerical Approach for Solving Fractional Pantograph Equation Ayse Anapali, Yalcin Ozturk and Mustafa Gulsu Discovering Knowledge in Mathematics and Dynamic Modeling Halil Ardahan Fejer type inequalities for Logarithmically Convex Functions Merve Avcı Ardıc, M. Emin Özdemir and Alper Ekinci Stability in nonlinear neutral differential equations with infinite delay Abdelouaheb Ardjouni and Ahcene Djoudi On a Canonical Form for Maxwell Equations by Geometric Calculus and Convergence of Finite Element Schemes for a Vlasov-Maxwell System Mohammed Asadzadeh A Survey of Results in the Investigation of the Structure of Fractional Spaces Generated by Positive Operators in Banach Spaces Allaberen Ashyralyev Fractional Spaces Generated by the Positive Difference Operator in the Half-Line ℝ+ and Their Applications Allaberen Ashyralyev and Sema Akturk A Second Order of Accuracy Difference Scheme for a Fractional Schrödinger Differential Equation Allaberen Ashyralyev and Betul Hicdurmaz Application of Summability Process on Baskakov-Type Korovkin Theory Ismail Aslan and Oktay Duman On a Kirk–Type New Iteration Process Yunus Atalan, Vatan Karakaya, Kadri Dogan and Nour El Houda Bouzara 2-Quadratic Modules of Algebras Hasan Atik Generalized Plane Deformation Solutions of the Shallow Located Cavity at the Anisotropic Rock Massif under the Actions of Elastic SH-Waves Lyazzat Atymtayeva and Bagdat Yagaliyeva Peiffer Ideals, Precrossed Modules and Crossed Modules of R-Algebroids Osman Avcioglu and Ilker Akca Two-Interval Sturm-Liouville Differential Operators in Direct Sum Spaces Kadriye Aydemir and Oktay Mukhtarov The Variational Principle and Complexity of 𝑍𝑍 𝑛𝑛 Actions Bunyamin Aydin On The Rough Statistically Cauchy Sequences Salih Aytar Coincidence of Crisp and Fuzzy Functions Maliha Rashid, Akbar Azam and Nayyar Mehmood An Iterative Method for Solving a Combined Inverse Problem of Reservoir Parameters Identification Aliya Azhibekova Numerical Solution of System of Nonlinear Fredholm and Volterra Integral Equations Using Haar Wavelet Imran Aziz A Study on Involute-Evolute Curves in Euclidean 3–Space Vildan Bacak and Nihat Ayyildiz Bipas Flow with Dominant Poloidal Component A. A. Bachtiar and R. Kosasih Large Sample Variance of Simulation Using Refined Descriptive Sampling

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Leila Baiche and Megdouda Ourbih-tari Best Proximity Points for a New Proximal Amitabh Banerjee

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On the Domain of Riesz Mean in the Space 𝓛𝓛𝒔𝒔 Feyzi Basar Theorems on Generalized Bose-Einstein and Fermi-Dirac Functions Abdelmejid Bayad Non-Linear Characterization of Some Banach Spaces Maatougui Belaala Numerical Solutions of Boundary Integral Equation by Using the Galerkin Method Menad Bendehiba Weak Solution and Exact Controllability of the Caputo’s Fractional Cauchy Problem of Order α with 1 < α< 2 R. Boukhamla and S. Mazouzi A Delay Second Order Set-Valued Differential Equation with Hukuhara Derivative Wafiya Boukrouk Maximum Norm Analysis of a Nonmatching Grid Method for Semilinear Elliptic Variational Inequalities Messaoud Boulbrachene and Abida Harbi Existence of Fixed Points for Continuous Operators in Banach Spaces Using Measure of Noncompactness and Under an Integral Condition N.H. Bouzara, V. Karakaya, Y. Atalan and K. Dogan Some Geometric Properties Related to the Second Order Cesàro Operators Naim L. Braha and Valdete Loku Lacunary Statistically Upward Continuity Huseyin Cakalli Topological Indices of Subdivision Graphs Ismail Naci Cangul, Aysun Yurttas, Muge Togan, Ahmet Sinan Cevik Existence of Solutions for Nonlinear Fractional Differential Equations with m-Point Integral Boundary Conditions Tugba Senlik Cerdik, Nuket Aykut Hamal andFulya Yoruk Deren On Reciprocity Law of the Y(h,k) Sums Associated with the Two and Three-Term Polynomial Relations Elif Cetin, Yilmaz Simsek and Ismail Naci Cangul On the Solvability and Maximal Regularity of Complete Abstract Differential Equations of Elliptic Type with General Robin Boundary Conditions in Holder Spaces Mustapha Cheggag, Angelo Favini, Rabah Labbas, Stéphane Maingot and Ahmed Medeghri A Generalization of Gershgorin Circles Mao-Ting Chien Implementation of Public-Key Cryptosystems on Embedded Devices Noureddine Chikouche and Walid Tayoub Convergence Analaysis of Strang Splitting Method for Burgers-Huxley Equation Yesim Cicek and Gamze Tanoglu Computing Homology Groups of Complexes of Matchings İsmet Cinar and Ismet Karaca Deferred Statistical Convergence of Order α Muhammed Cinar, Mikail Et, Fatih Temizsu and Murat Karakas Some Fixed Point Theorems for a Hybrid Type of Bogin-Popescu Mappings in Complete Metric Spaces L. Ciric, P. Promsilpchai and N. Petrot On the Integral of Products of Higher-Order Bernoulli and Euler Polynomials M. Cihat Dagli and Mumin Can Algebraic Invariant and Stability of Differential System Dahira Dali Approximation by Chlodowsky Type q-Jakimovski-Leviatan Operators Ozge Dalmanoglu and Sevilay Kirci Serenbay Some Large Sets in Countable Integral Domains Dibyendu De Matrix Transformation of Statistically Convergent Sequences of Interval Numbers Shyamal Debnath and Subrata Saha

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57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81

A Study on Solvability of Functional Equations Arising in Dynamic Programming Deepmala and Arup Kumar Das On the Fixed Points for Pointwise Lipschitzian Semigroups in Modular Function Spaces Buthinah A. Bin Dehaish Monotone Iterative Technique and Existence Results for Fractional Functional Differential Equations Fulya Yoruk Deren, Nuket Aykut Hamal and Tugba Senlik Cerdik Best Proximity Point Theorem for F-Contraction in a Complete Metric Space Lakshmi Kanta Dey Relative and Tate Homology with Respect to Semidualizing Modules Zhenxing Di A Differential Equation Model for the Dynamics of Youth Gambling Tae Sug Do and Young S Lee On The Existence of Positive Solutions for the One-Dimensional 𝒑𝒑-Laplacian Boundary Value Problems on Time Scales Abdulkadir Dogan On a Kirk-MP Iteration Process Kadri Dogan and Vatan Karakaya On n - normed Cesàro Sequence Space Cesn ,f Cenap Duyar and Oguzhan Kanber Some Families of Generating Functions for Laguerre and Charlier Types d-Orthogonal Polynomials Duriye Korkmaz Duzgun and Esra Erkus Duman Traveling Wave Solutions for Some Nonlinear Evolution Equations Serife Muge Ege and Emine Misirli New Integral Inequalities of Ostrowski Type for Quasi-Convex Functions with Applications A.Ekinci, M. E. Ozdemir and E. Set On Boundedness of Multilinear Singular Integral Operators in Lorentz Spaces İsmail Ekincioglu, Cansu Keskin and Ozgun Gurmen Alansal Abstract Harmonic Analysis on Spacetime Poincare Group Kahar El-Hussein On the Fine Spectra of a New Matrix Operator Over the Sequence Spaces c0 and c Sumeyra Elmaci and Vatan Karakaya Eigenvalue Asymptotics and a Trace Formula for the Linear Damped Wave Equation Ahu Ercan and Etibar Panakhov On Some Topological Properties of Generalized Sequence Spaces of Non-Absolute Type Sinan Ercan and Cigdem A. Bektas A One-Sided Theorem for the Product of Abel and Cesàro Summability Methods Yilmaz Erdem and Ibrahim Canak On the Spectrum of the Product Operator 𝑾𝑾 on the Sequence Space 𝒃𝒃𝒃𝒃 Ezgi Erdogan and Vatan Karakaya Infinite Matrices and Invariant Means Rahmet Savas Eren Groups and Irreducible Character Degrees Temha Erkoc Energy Conservation for the 3-Coupled Nonlinear Schrödinger Equation by Using the Average Vector Field Method Sevim Ertug and Ayhan Aydin On Lacunary Statistical Convergence of Order α of Difference Sequences Mikail Et Colorings of Cycle Graph with Topological Approach Seher Fisekci and İsmet Karaca Estimation of the Presicion Matrix of an Elliptically Symmetric Distribution Dominique Fourdrinier, Fatiha Mezoued and Martin T. Wells Description of Bloch Spaces and Their Invariant Subspaces, and Related Questions Mubariz T. Garayev, Mehmet Gurdal and Ulas Yamancı Common Fixed Points of Almost Generalized Contraction on Modular Spaces Ekber Girgin and Mahpeyker Ozturk Functions Represented into a Newton Interpolating Series and Applications Ghiocel Groza Numerical Approach for Magneto-Hydrodynamic Flow Passed Through a Wedge

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Murat Gubes and Galip Oturanc An Algorithm for Some Small Dimensional Representations Kubra Gul, Nurullah Ankaralioglu and Abdullah Cagman Distribution of First Passage Times for Lumped States in Markov Chains Murat Gul and Salih Celebioglu On the Generalized Bernoulli, Euler and Genocchi Polynomials Esra Guldogan and Esra Erkus Duman On Boundedness of Singular Integral Operators Generated by Bessel Generalized Shift Operator in Weighted Beppo-Levi Spaces Serap Guner and Ismail Ekincioglu Continuity of Superposition Operators on the Double Sequence Spaces of Maddox L( p ) Nihan Gungor and Birsen Sagir Weyl Type Theorems for Unbounded Hyponormal Operators Anuradha Gupta and Karuna Mamtani Composition Operators on Lorentz-Karamata-Bochner Spaces Anuradha Gupta and Neha Bhatia A Note on Integral Inequalities for n-Time Differentiable Mappings Mustafa Gurbuz, Abdullah Yaradılmıs and M. Emin Ozdemir Statistical Convergence and Some Questions of Operator theory Mehmet Gurdal and Ulas Yamanci * Statistical Convergence and C -Operator Algebras Mehmet Gurdal and Mualla Birgul Huban New Runge-Kutta Methods for Numerical Solutions of Multiplicative Initial Value Problems Yusuf Gurefe and Emine Misirli On the Stability of Picard-Kirk-S Iterative Method Faik Gursoy and Vatan Karakaya Time series modeling a temperature data in Bechar South West of Algeria Lahmar Habib and Zouaoui Chikr el Mezouar On the Solutions of Some System of Difference Equation Nabila Haddad and Nouressadat Touafek On the Exact Values of Wavelet Functions Mohamed Ali Hajji Nonlinear Boundary Value Problems of p- Laplacian Fractional Differential Systems Nuket Aykut Hamal, Fulya Yoruk Deren and Tugba Senlik Cerdik The Study of Existence and Uniqueness of Certain Fractional Differential Equations Boulares Hamid Some Applications of Clifford Algebras and Octonions to Differential Geometry Hideya Hashimoto A Bayesian Estimation of Traffic Intensity in M/M/∞ Queue Under Different Loss Functions Braham Hayette Ideally Slowly Oscillating Continuity Bipan Hazarika Equivalent Cauchy Sequences on Generalized Metric Spaces Elida Hoxha and Sidite Duraj Generalization of Fixed Point Theorems in Quasi Cone Metric Space Relating to the Diameter of Orbits by Using a Comparison Function Elida Hoxha and Eriola Sila *

Riesz Idempotent and Generalized Weyl’s Theorem for k-Quasi Class An Operators Ilmi Hoxha and Naim L. Braha A Morgan-Voyce Collacation Method for Numerical Solution of Generalized Pantograph Equations Ozgul Ilhan Numerical Solution of Burger Equation by Using General Frechet Derivatives Combined with Differential Quadrature N. Imamoglu, G.Guraslan and G. Tanoglu Lacunary Statistical Convergence of Order α in Probabilistic Normed Spaces Mahmut Isik Evolution Modeling of NPZ and SIR Models with and without Diffusion Siraj-ul-Islam and Saeedullah Jan

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111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137

Inverse Problem of Finding Diffusion Coefficient in Heat Equation with Nonlocal Boundary Conditions Mansur I. Ismailov and Bulent Ogur Improved R-order of convergence for solving nonlinear equations Jai Prakash Jaiswal On the Basis Number of the Wreath Product of Paths with Wheels and Some Related Problems M.M. M. Jaradat, M.S. Bataineh and M.K. Al-Qeyyam Soft Completely Simple Semigroups Mehmet Kalkan and Haci Aktas Determination of a Time Dependent Diffusion Coefficient of a Quasilinear Parabolic Equation in the Case of Nonlocal Conditions Fatma Kanca On the Metric Dimension of Uniform Fuzzy Graphs Vasantha Kandasamy W.B and Regin Thangaraj Some Common Coupled Fixed Point Theorems for Rational Expressions in Complex Valued 𝑮𝑮𝒃𝒃 -Metric Spaces Neslihan Kaplan and Mahpeyker Ozturk Stability and Accuracy of Time-Stepping Schemes for a Second-Order Wave Equation Samir Karaa On H(θ)-Open Sets and Modifications on Hereditary Generalized Topological Spaces Umit Karabiyik On Positive Solutions for Fourth-Order Four-Point Boundary Value Problems with Alternating Coefficient on Time Scales Ilkay Yaslan Karaca A New Difference Sequence Set of Order a and Its Geometrical Properties Vatan Karakaya, Yunus Atalan and Mikail Et Numerical Solution of Non-Linear Equations via Multiplicative Calculus Tolgay Karanfiller Notes on Banach Contraction Principle Erdal Karapinar Gröbner-Shirshov Bases of Some Exceptional Braid Groups Eylem G. Karpuz, Nurten Urlu and A. Sinan Cevik Scalarization Methods in Multiobjective Optimization Refail Kasimbeyli Some Convergence Theorems of Nonlinear Integral Functionals Jun Kawabe Numerical and Exact Solutions for Time Fractional a Nonlinear Equation Dogan Kaya and Asıf Yokus Common Fixed Point Results for (Ϝ,ψ)-Contractions in Ordered Partial Metric Spaces Meltem Kaya, Mahpeyker Ozturk and Hasan Furkan Inverse Nodal Problem for p-Laplacian Sturm Liouville Equation H. Kemaloglu(Koyunbakan) and E. Yilmaz On the Uniform Convergence of the Fourier Series for One Spectral Problem with a Spectral Parameter in a Boundary Condition Nazim B. Kerimov and Emir Ali Maris Benjamin-Bona-Mahony Equation with Variable Coefficients: Conservation Laws Chaudry Masood Khalique Excess of Retro Banach Frames G.Khattar and L.K. Vashisht On Binomial Transformations of a Product of Rising and Falling Factorials Emrah Kilic and Halit Ozturk An examinationtion on the positions of Frenet ruled surfaces along the evolute-involute curves, according to their normal vector fields in Euclidean 3-space Seyda Kilicoglu Iterative Schemes and Common Fixed Point Problems on a Complete Geodesic Space Yasunori Kimura Weighted Lacunary Statistical Convergence in a Locally Convex Topological Vector Space Sukran Konca and Metin Basarir Numerical Solution for a Telegraph Equation via Bernestein Polynomials A. Kouadri and D. Belakroum

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138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164

Probability Theory on a Topological Monoid of Strings and Its Application to Statistical Machine Learning Hitoshi Koyano and Morihiro Hayashida On generalized absolute Cesàro summability of orthogonal series Xhevat Z. Krasniqi q-Barnes Multiple Bernoulli Polynomials Veli Kurt Multi-Spectral Image Classification by Nonparametric Regression Splines Semih Kuter, Zuhal Akyurek and Gerhard-Wilhelm Weber Controlling of Period-2 Unstable Orbits in a Bouncer System Using Patterns of H-Ranks Mantas Landauskas and Minvydas Ragulskis Approximation by q-Balazs-Szabados Operators Nazim Mahmudov Existence of Solutions of Fractional Boundary Value Problems with p-Laplacian Operator Nazım I.Mahmudov, Sinem Unul Some Paranormed Difference Sequence Spaces of Order m-Derived by Generalized Means and Compact Operators Amit Maji and P. D. Srivastava Fuzzy and Set-Valued Stochastic Differential Equations Marek T. Malinowski A New Curvaturelike Tensor Field in an Almost Contact Riemannian Manifold Koji Matsumoto Probability-Theoretic Foundations of International Trade Models Andrei Matveenko and Taras Hrendash Asymptotic Behaviour of Solutions to Initial Boundary Value Problems for Marine Riser Equations Muge Meyvaci Co­integration Analysis between Oil price and Algeria Inflation Zouaoui Chikr el Mezouar New Shift-Compactness Results Harry I. Miller Some Statistical Cluster Point Theorems Leila Miller, Van Wieren and Harry I. Miller Homogenization of the Membrane Model of Perforated Shell Ait Yahia Mohamed and Mourad Lhannafi A New Approach to Differential Evolution Algorithm for Solving Stochastic Programming Problems Ali Wagdy Mohamed On the Travelling Wave Solutions of a Generalized Zakharov-Kuznetsov Equation Dimpho Millicent Mothibi and Chaudry Masood Khalique Mixed d Semi Prefuzzy Topological Spaces and Some Results of Separation Axioms in Mixed d Semi Prefuzzy Topological Spaces Anjan Mukherjee Second-Order Operator-Differential Equations with Transmission Conditions Oktay Sh. Mukhtarov, Kadriye Aydemir and Hayati Olgar General Stability in Memory-Type Thermoelasticity with Second Sound Muhammad I. Mustafa Time Series Forecasting Using Box-Jenkins Methodology Application on Census Data in Iraq Qais Mustafa Fixed Point Theorems for Weakly T-Chatterjea and Weakly T-Kannan Contractions in b-Metric Spaces Zead Mustafa, Jamal Rezaei Roshan, Vahid Parvaneh and Zoran Kadelburg Nonlinear three point boundary value problem Farid Nouioua A Note on the Solutions of the Nonlinear Fractional Differential Equations Meryem Odabasi and Emine Misirli Charge or Dipole Simulation Method for Approximations of Complex Analytic Functions Hidenori Ogata On New Cesàro-Orlicz Double Difference Sequence Space Oguz Ogur and Cenap Duyar Positive Solutions for a Singular Semipositone Dynamic System on Time Scales Arzu Denk Oguz and S. Gulsan Topal

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165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192

G2-Congruence Classes of Curves in Purely Imaginary Octonions Misa Ohashi On the Riesz Basis Property of Eigenfunctions of One Boundary-Value Problem with Transmission Condition Hayati Olgar and Oktay Sh. Mukhtarov Cauchy Type Problem for Nonlinear Fractional Integro-Differential Equations with Multivariate Mittag-Leffler Function in the Kernel Mehmet Ali Ozarslan On a Double Integral Equation Including a Set of Two Variables Polynomials Suggested by Laguerre Polynomials Mehmet Ali Ozarslan and Cemaliye Kurt On Some Fixed Point Results for Hybrid Rational a-Type Contractive Mappings Mahpeyker Ozturk New Integral Operator for Solution of Differential Equations Ali Ozyapici The Differential Geometry of Regular Curves on Regular Time-Like Surface Emin Ozyilmaz and Yusuf Yayli Lacunary Invariant Statistical Convergence of Sequences of Sets with Respect to a Modulus Function Nimet Pancaroglu and Fatih Nuray Stochastic Modelling and Inference of Model Parameters in Complex Biochemical Systems Vilda Purutcuoglu Nash Equilibrium for Binary Convexities Taras Radul Approximate Solutions to a Problem of Two Moving Boundaries Governed with Fractional Time Derivative in Drug Release Devices Rajeev and M.S. Kushwaha Carleman Estimate for a One-Dimensional System of m-Coupled Parabolic PDEs with BV Diffusion Coefficients Hichem Ramoul Waterloo Numbers and Their Relation to Pascal Triangle and Polygons Wajdi Mohamed Ratemi and Otman Basir A Note on Derivations in Rings and Banach Algebras Mohd Arif Raza On Global Solutions of Fractional Evolution System Samira Rihani and Amor Kessab Risk Modeling Insurance IARD by Decision Trees and V-TEST Khadidja Sadi, Nora Lounnici and Hanya Kherchi Boundedness of Superposition Operators on the Double Sequence Spaces of Maddox L( p ) Birsen Sagir and Nihan Gungor Some Convergence Results for Nonexpansive Mappings in Uniformly Convex Hyperbolic Spaces Aynur Sahin and Metin Basarir A Multi-Criteria Neutrosophic Group Decision Making Metod Based TOPSIS for Supplier Selection Ridvan Sahin and Muhammed Yigider Existence and stability of a damped wave equation with two delayed terms in boundary Zitouni Salah and Amiar Rachida Lp Boundedness for Marcinkiewicz Integrals and Extrapolation Salti Samareh Approximation Properties of Max-Product Operators Engin Sari Some Inequalities Associated with the Hermite-Hadamard-Fejér Type for Convex Function Mehmet Zeki Sarikaya, Hatice Yaldiz and Samet Erden Equivalent Norms in Nikol’skij-Triebel-Morrey Spaces and Lizorkin-Triebel-Morrey Spaces Merey Sautbekova Ideal Statistical Quasi Cauchy Sequences Ekrem Savas and Huseyin Cakalli SBT - Hausdorff Space Guzide Senel and Naim Cagman Rate of Convergence of Generalized Favard-Szàsz Type Operators

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Sevilay Kirci Serenbay Sufficient Tauberian Conditions for the Weighted Mean Summability of Sequences of Fuzzy Numbers Sefa Anil Sezer, Ibrahim Canak and Zerrin Onder On Fine Spectra and Subspectrum (Approximate Point, Defect and Compression) of Operator with Periodic Coefficients Necip Simsek and Vatan Karakaya Pretopologies for Structuring the Digital Plane Josef Slapal Linear Parabolic Boundary-Value Problems in Generalized Morrey Spaces Lubomira Softova Main Chaos-Based Image Encryption Algorithms Ibtissem Talbi The Way-Below Soft Set Relation Bekir Tanay and Gozde Yaylali A New Operator Splitting Method for Non-Linear Systems and Its Abstract Analysis Gamze Tanoglu and Sila Ovgu Korkut A New Three Step Iteration and Convergence of Pseudocontractive Mappings Balwant Singh Thakur Contrastings on Textual Entailmentness and Algorithms of Syllogistic Logics Selcuk Topal and Tahsin Oner Some Tauberian Conditions for the Weighted Mean Method of Summability Umit Totur and Ibrahim Canak A Tauberian Theorem for the Power Series Method of Summability Umit Totur and Ibrahim Canak Some Tauberian Theorems for the Logarithmic Integrability Method Umit Totur and Muhammet Ali Okur Eigenvalues for Kaehler Graphs of Connected Product Type Yaermaimaiti Tuerxunmaimaiti Generalized Weighted Norlund Mean and Ideal Convergence Orhan Tug and Feyzi Basar On Convergence Methods of Functions Defined on Time Scales Ceylan Turan and Oktay Duman Classification of Integral Curves of a Linear Vector Field on (2n+1) Dimensional Semi-Euclidean Space Tunahan Turhan and Nihat Ayyildiz More Results on the Upper Solution Bounds of the Continuous Algebraic Riccati Matrix Equation Zubeyde Ulukok Global Attractors for Quasilinear Parabolic-Hyperbolic Equations Governing Longitudinal Motions of Nonlinearly Viscoelastic Rods Suleyman Ulusoy (�)-boundedness of localization operators involving watson transform associated to regular representations and wavelet multipliers S.K.Upadhyay A Maximum Modulus Estimate for the Steady Stokes Equations Werner Varnhorn Approximation Properties of Chlodowsky-Durrmeyer Type q-Bernstein-Schurer-Stancu Operators Tuba Vedi and Mehmet Ali Ozarslan On Relative Homology Groups of Khalimsky Spaces Tane Vergili and İsmet Karaca Stabilization in a n-Species Chemotaxis System with a Logistic Source Wang Wenjia Hermite-Hadamard-Fejer Type Inequalities Hatice Yaldiz A Note on a Functional Identity on Lie Ideals Nihan Baydar Yarbil On the Higher Order Gaussian Curvatures in Lorentz Space Ayse Yasar Yavuz and F. Nejat Ekmekci On Soft Dual Space of Soft Normed Spaces Murat Ibrahim Yazar, Yilmaz Altun and Tunay Bilgin On Some Properties of the B-Convex Functions

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220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247

İlknur Yesilce and Gabil Adilov Statistical Convergence of Multiple Sequences on a Product Time Scale Emrah Yilmaz, Yavuz Altin and Hikmet Koyunbakan Optimality Conditions for Non-Lipschitz Optimization Nurullah Yılmaz and Ahmet Sahiner Groups and Graphs Utku Yilmazturk Center Coloring and the Other Colorings Zeynep Ors Yorgancioglu and Pinar Dundar Dual Transformations and One-Paremeter Motions Gulsum Yuca and Yusuf Yayli p (.)

On Boundedness of Fractional Maximal Operator in the Weighted L (0,1) Space Yusuf Zeren and Lutfi Akin Global Existence and Asymptotic Properties of the Solution to a Two-Species Chemotaxis System Qingshan Zhang One Dimensional Model of Biodegradable Elastic Curved Rods Bojan Zugec Convergence Analysis and Numerical Solution of Benjamin-Bona-Mahony Equation by Lie-Trotter Splitting Fatma Zurnaci, Nurcan Gucuyenen andMuaz Seydaoglu and Gamze Tanoglu

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248 249 250 251 252 253 254 255 256

Entanglement of Nanoresonator Interacting with Two Qubit Mahmoud Abdel-Aty Vice President African Academy of Science University of Science and Technology at Zewail City Egypt [email protected]

Abstract: In this communication we discuss different aspects of multi-qubit system interacting with nanoemchanical resonators. Information dynamics of charge qubits coupled to a nanomechanical resonator under influence of both a phonon bath in contact with the resonator and irreversible decay of the qubits is considered. The focus of our analysis is devoted to multi-particle entanglement and the effects arising from the coupling to the reservoir. Even in the presence of the reservoirs, the inherent entanglement is found to be rather robust. Due to this fact, together with control of system parameters, the system may therefore be especially suited for quantum information processing. Our findings also shed light on the evolution of open quantum many-body systems. For instance, due to intrinsic qubitqubit couplings our model is related to a driven XY spin model.

1

Boundary Value Problems for Delay Differential Equations Ravi P Agarwal Texas A&M–Kingsville [email protected]

Abstract: We develop an upper and lower solution method for second order boundary value problems for nonlinear delay differen-tial equations on an infinite interval. Sufficient conditions are imposed on the nonlinear term which guarantees the existence of a solution between a pair of lower and upper solutions, and triple solutions between two pairs of upper and lower solu-tions. An extra feature of our existence theory is that the obtained solutions may be unbounded. Two examples which show how easily our existence theory can be applied in prac-tice are also illustrated.

2

Determining Functionals for Damped Nonlinear Wave Equations Varga K. Kalantarov Koc University, Istanbul [email protected]

Abstract: The problem of determining by finitely many functionals of asymptotic behavior of solutions as t → ∞ to initial boundary value problems for strongly damped semi-linear wave equations and wave equations with nonlinear damping terms will be discussed.

3

Calderon-Zygmund theory for divergence form operators in Generalized Morrey spaces Lubomira Softova Department of Civil Engineering, Design, Construction and Environment, Second University of Naples, Italy [email protected]

Abstract: We study the regularity properties of the solutions of the Cauchy-Dirichlet problem for divergence form parabolic equations with measurable data in non-smooth domains. Problems like these arise in the modeling of composite materials and in the mechanics of membranes and films of simple non-homogeneous materials which form a linear laminated medium. Assuming partial BMO smallness of the coefficients and Reifenberg flatness of the boundary of the underlying domain, we develop a Calderon-Zygmund type theory for such parabolic operators in the settings of the generalized Morrey under various conditions on the weight. As consequence of the main result, we get regularity in parabolic Morrey scales for the spatial gradient of the weak solutions to the considered problem. Key words: Calderon – Zygmund estimates, generalized Morrey spaces, weak solutions, Cauchy-Dirichlet problem References: [1] S. Byun, L. Softova, Gradient estimates in generalized Morrey spaces for parabolic operators, submitted

[2] V. Guliyev, L. Softova, Generalized Morrey estimates for the gradient of divergence form parabolic operators with discontinuous coefficients, submitted

.

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On the Fine Spectra of n-th Band Triangular Matrices R. Birbonshi and P.D. Srivastava Department of Mathematics, Indian Institute of Technology Khargapur, India [email protected], [email protected]

Abstract: Bilgic and Furkan [4] have studied the fine spectra of the operator B(r,s) over the sequence spaces 𝑙𝑙𝑝𝑝 and 𝑏𝑏𝑏𝑏𝑝𝑝 ; (1 < 𝑝𝑝 < ∞) which are generalized by Furkan, Bilgic and Basar [7] to B(r,s,t). The fine spectra of the operator B(r,s) are studied by Altay and Basar [1] and Furkan, Bilgic and Kayaduman [5] over the sequence spaces 𝑐𝑐0 , 𝑐𝑐, 𝑙𝑙1 & 𝑏𝑏𝑏𝑏 respectively. Furkan, Bilgic and Altay [6], Bilgic and Furkan [3] generalized these result to B(r,s,t) over the sequence space 𝑐𝑐0 , 𝑐𝑐, 𝑙𝑙1 & 𝑏𝑏𝑏𝑏 respectively. The fine spectra of the upper triangular double band matrices over the sequence spaces 𝑐𝑐0 , 𝑐𝑐 have been studied by Karakaya and Altun [8]. Later on, Altun [2] has examined the fine spectra of triangular Toeplitz operator over the sequence spaces 𝑐𝑐0 & 𝑐𝑐. Here we have derived some general results for finding the spectrum and fine spectrum of n th band lower and upper triangular matrix. Our results include the corresponding results of [1, 3, 4, 5, 6, 7, 8] as well as the results of [2]. References: [1] B. Altay, F. Basar, “On the fine spectrum of the generalized difference operator B(r,s) over the sequence spaces 𝑐𝑐0 and 𝑐𝑐” , Int. J. Math. Sci. 18 (2005) 3005-3013. [2] M. Altun, “On the fine spectra of tranglar Toeplitz operator”, App. Math. Comput. 217 (2011) 8044-8051. [3] H. Bilgic, H. Furkan, “On the fine spectrum of the operator B(r,s,t) over the sequence spaces 𝑙𝑙1 and 𝑏𝑏𝑏𝑏”, Math. Comput. Model. 45 (7-8) (2007) 883-891. [4] H. Bilgic, H. Furkan, “On the fine spectrum of the generalized difference operator B(r,s) over the sequence spaces 𝑙𝑙𝑝𝑝 and 𝑏𝑏𝑏𝑏𝑝𝑝 , 1 < 𝑝𝑝 < ∞”, Nonlinear Anal. 68 (3) (2008) 499-506. [5] H. Furkan, H. Bilgic, K. Kayaduman, “On the fine spectrum of the generalized difference operator B(r,s) over the sequence spaces 𝑙𝑙1 and 𝑏𝑏𝑏𝑏”, Hokkaido Math. J. 35 (2006) 897-908. [6] H. Furkan, H. Bilgic, B. Altay, “On the fine spectrum of the operator B(r,s,t) over 𝑐𝑐0 and 𝑐𝑐”, Comput. Math. Appl. 53 (2007) 989-998. [7] H. Furkan, H. Bilgic, F. Basar, “On the fine spectrum of the operator B(r,s,t) over the sequence spaces 𝑙𝑙𝑝𝑝 and 𝑏𝑏𝑏𝑏𝑝𝑝 ; 1 < 𝑝𝑝 < ∞”, Comput. Math. Appl. 60 (2010) 2141-2152. [8] V. Karakaya, M. Altun, “Fine spectra of upper triangular double-band matrices”, J. Comput. Appl. Math. 234 (2010), 1387-1394.

5

The Navier-Stokes Equations – A Never Ending Challenge? Werner Varnhorn Institute of Mathematics, Kassel University, Germany [email protected]

Abstract: We consider the nonstationary nonlinear three-dimensional Navier-Stokes equations 𝑣𝑣𝑡𝑡 − 𝜈𝜈 ∆𝑣𝑣 + 𝑣𝑣 • 𝛻𝛻𝛻𝛻 + 𝛻𝛻𝛻𝛻 = 𝑓𝑓, ∇ • v = 0, (N) v|∂Ω = 0, 𝑣𝑣|𝑡𝑡 = 0 = 𝑣𝑣0 . These equations describe the motion of a viscous incompressible fluid flow: The vector function v = v(t, x) = (v1 (t, x), v2 (t, x), v3 (t, x)) denotes the velocity and the scalar function p = p(t, x) the pressure of the fluid at time t > 0 in x = (x1 , x2 , x3 ) ∈ Ω. Here the constant ν > 0 represents the kinematic viscosity, the vector function f = (f1 (t, x), f2 (t, x), f3 (t, x)) is the given external force density, and the steady vector function v0 = (v01 (x), v02 (x), v03 (x)) denotes the prescribed initial velocity at time t = 0. In the following we consider the fluid flow always in a bounded domain Ω ⊂ R3 with smooth boundary ∂Ω of class C 2,µ (0 < µ ≤ 1).

The system (N) occupies a central position in the study of nonlinear partial differential equations, dynamical systems, scientific computation, and classical fluid dynamics. Because of the complexity and variety of fluid dynamical phenomena on the one hand, and the simplicity and exactitude of the equations’ shape on the other hand, a strong depth and beauty is expected in the mathematical theory. It is a source of pleasure and fascination that many of the most important questions in the theory remain yet to be answered. So the famous American Clay Mathematics Institute created the Navier-Stokes Millennium Price Problem and offered one Million Dollar for its solution, stating: Although the Navier-Stokes equations were written down in the 19th Century, our understanding of them remains minimal. The challenge is to make substantial progress toward a mathematical theory, which will unlock the secrets hidden in the Navier-Stokes equations. The modern mathematical theory of the Navier-Stokes equations (N) started with the pioneer- ing work of Jean Leray in 1933 - 34. Leray was the first to use methods of functional analysis for the treatment of partial differential equations. He developed the concept of weak solutions for the Navier-Stokes Cauchy problem and proved their existence globally in time long before the theory of distributions was established by Schwartz and even before Sobolev systematically introduced the spaces which bear his name. Leray has laid the basis of the mathematical theory for (N) as we know it today, and he has introduced many tools and ideas used constantly since then. The lecture introduces the Navier-Stokes equations from a historical and physical point of view, touches some fundamental mathematical problems of viscous incompressible fluid flow and ends up with recent regularity results on strong solutions.

6

The effect of the Terrorism on Tourism in Algeria Abdel Kader Boudi and Zouaoui Chikr el Mezouar Laboratory of Study Economics and Local Development in South West of Algeria University of Bechar E-mail : [email protected] and [email protected]

Abstract: The objective of this research is to show the effect of terrorism on tourism in Algeria and to show also how terrorism event has damaged the tourism sector in Algeria and how it has deeply affected the number of foreign arrival tourists to Algeria using mathematical model. References: [1] Boudi Abdel Kader (2006) “The importance of marketing tourism in the development of tourism in Algeria” PhD theses, University of Algeria. [2] Chatfield, C. (2004) “The Analysis of Time Series: An Introduction”. 6th Edn., New Jersey:Chapman & Hall. [3] Neter, J. , Wasserman, W. and Kutner, M.H. (1989) “ Applied Regression Models ” 2nd Edn,IRWIN. [4] Wei, W.W.S. (1990) “Time series analysis: Univariate and multivariate methods”. Addison-Wesley Publishing Company, Inc.

7

An Estimate on Volumes of Trajectory-Balls for Kaehler Magnetic Fields Toshiaki Adachi Department of Mathematics, Nagoya Institute of Technology, Nagoya, Japan [email protected]

Abstract: Let M be a Kaehler manifold with complex structure J. We call constant multiples of the Kaehler form BJ on M Kaehler magnetic fields. Under the action of a Kaehler magnetic field Bk = kBJ, the motion of an electric charged particle is expressed as a smooth curve γ which is parameterized by its arclength and satisfies the equation ∇𝛾𝛾′ 𝛾𝛾 ′ = 𝑘𝑘𝑘𝑘𝑘𝑘′. We say such curves to be trajectories for Bk. As trajectories for the trivial magnetic field B0 are geodesics, we can regard them as natural extended objects of geodesics. Since geodesics play quite an important role in the study of Riemannian manifolds (cf. [3]), we consider that trajectories give us some clues to study Kaehler manifolds from the Riemannian geometric point of view. In this paper, we study trajectory-harps which consist of trajectories and geodesics and compare those on a general Kaehler manifolds and those on a complex space form. By use of a result corresponding to the Toponogov’s comparison theorem on triangles, we give an estimate on volumes of trajectory-balls from below. Keywords: Kaehler magnetic fields; Trajectories; Kaehler manifolds; Comparison theorems; Trajectory-harps; Trajectory-balls. References: [1] T. Adachi, “A theorem of Hadamard-Cartan type for Kaehler magnetic fields”, J. Math. Soc. Japan 64(2012), 969-984. [2] P. Bai, “Volume densities of trajectory-balls and trajectory-spheres for Kaehler magnetic fields”, Prospects of Differential Geometry and Related Fields, World Scientific (2013), 115-128. [3] J. Cheeger, D. G. Evin, “Comparison Theorems in Riemannian Geometry”, 1975, North-Holland Pub. Co.

8

Maximum Principle of Stochastic Switching Systems with Constraints Charkaz Aghayeva Department of Industrial Engineering, Anadolu University, Eskisehir, Turkey [email protected]

Abstract: A lot of theoretical and numerical advances have recently been realized in the field of stochastic control. Necessary conditions satisfied by an optimal solution, play an important role for investigation of optimization and optimal control problems. This paper is devoted to stochastic optimal problem of switching control systems. Dynamics of these processes are governed by the collection of stochastic differential equations with control terms in the drift and diffusion coefficients. Necessary conditions of optimality for described systems with the restrictions in each interval are obtained. The constraints on the transitions are described by the set of functional inclusions. Ekeland's variational principle are applied to prove maximum principle in general form. The necessary conditions developed in this study can be viewed as a stochastic analogues of the problems that are formulated in [1,2,3]. And main result, the maximum principle for considered problem, is a natural evolution of the results given in [4,5,6]. Keywords: Stochastic Control Systems; Necessary Condition of Optimality; Optimal Switching Systems; Condition of Transversality. References: [1] S. Bengea, A. Raymond, “Optimal Control of Switching systems”,Autom., 41(2005),11-27. [2] D. Capuzzo, L. Evans, “Optimal Switching for ordinary differential equations”, SIAM,Journal on Con. and Optimization, 22(1984), 143-161. [3] T. Seidmann, “Optimal control for switching systems”, Proceedings of the 21st Ann. Con. in Formations Science and Systems ,(1987),485-489. [4] Ch. Aghayeva, Q.Abushov,“The maximum principle for the nonlinear stoch- astic optimal control problem of switching systems”, JOGO,56(2013), 341-352. [5] Q. Abushov, Ch. Aghayeva, “Stochastic maximum principle for the nonlinear optimal control problem of switching systems”, CAM, 259(2014),371-376. [6] Ch. Aghayeva, Q. Abushov, “Stochastic maximum principle for switching systems”,Proc. of the 4th Int.Conf: Prob. of Cyb.and Infor.,3(2012), 198-201.

9

A Note on Delay Parabolic Equations Deniz Agirseven Department of Mathematics, Trakya University, Edirne, Turkey [email protected]

Abstract: In this study, two main theorems on well-posedness of the initial value problem for delay differential equations with unbounded operators acting on delay terms.are established. The coercive stability estimates in Hölder norms for solutions of delay parabolic equations are obtained. Theorems on well-posedness of first and second order of accuracy of difference schemes for approximate solutions of the initial value problem for delay differential equations with unbounded operators acting on delay terms are established. The coercive stability estimates for the solution of difference schemes of delay parabolic equations are obtained. Finally the illustrative numerical experiment for numerical solution of delay parabolic equations is given. Keywords: Delay parabolic equations, fractional spaces, stability, well-posedness. References: [1] A. Ashyralyev, D. Agirseven, “On Convergence of Difference Schemes for Delay Parabolic Equations”, Computers and Mathematics with Applications, 66(7), 1232-1244, 2013. [2] A. Ashyralyev, D. Agirseven, “Well Posedness of Delay Parabolic Difference Equations”, Advances in Difference Equations, 2014:18, 2014. [3] A. Ashyralyev, D. Agirseven, “Well Posedness of Delay Parabolic Equations with Unbounded Operators Acting on Delay Terms”, Boundary Value Problems, 2014:126, 2014.

10

Analogies between Electromagnetism and Gravitation in General Relativity Zafar Ahsan Department of Mathematics, Aligarh Muslim University, Aligarh, India [email protected]

Abstract: The correspondence between electromagnetism and gravitation is very rich and detailed. Some of these correspondence are still uncovered while some of them are further developed. This correspondence is reflected in the Maxwell-like form of the gravitational field tensor (the Weyl tensor), the super-energy-momentum tensor (the BelRobinson tensor) and the dynamical equations (the Bianchi identities). In this talk, we shall discuss some of the analogies between electromagnetism and gravitation. It is known that electromagnetic field has two invariants and the vanishing of these invariants is the criterion for the existence of electromagnetic radiation. Since the gravitational field is truly characterized by the Riemann curvature tensor, based on the analogy with electromagnetism, we shall make a study of the invariants of Riemann curvature tensor. The Riemann curvature tensor has fourteen invariants. There are four invariants of the Weyl curvature tensor, three invariants of the Einstein curvature tensor, six invariants of the mixed Weyl and Einstein curvature tensors and there is a Ricci scalar. The study of these invariants is important in general theory of relativity since they allow a manifestation of coordinate invariant characterization of certain geometrical properties of the space-times. In empty space-time, Riemann tensor reduces to Weyl tensor and thus there are four invariants of the Riemann tensor. Here, we have obtained a criterion for the existence of gravitational radiation in terms of these invariants and it is found that the vanishing of these invariants provides the existence of gravitational radiation. This assertion is then verified for some well known metrics of general relativity. Also, it is known that a physical field is always produced by a source, which is termed as its charge. Manifestation of fields when charges are at rest is called electric and magnetic when the charges are in motion. This general feature is exemplified by the Maxwell's theory of electromagnetism from where the terms of electric and magnetic are derived. This decomposition can be adapted in general relativity and the Weyl tensor can be decomposed into electric and magnetic parts. Based on this decomposition, we have made a classification of the space-times and have established the conditions under which a given space-time is purely electric or purely magnetic. It is found that the Petrov types III and N space times are neither purely electric nor purely magnetic. This classification scheme is then applied to number of known space-time solutions of general relativity. Moreover, the decomposition of Riemann tensor involves certain irreducible tensors. In empty space-time, pure gravitational radiation field is described by the Weyl tensor. However, the Weyl tensor is still pertinent when the gravitational waves propagate through matter. It was thought by Lanczos, in 1962, that the Weyl tensor can also be derivable from a simpler tensor field. This tensor field is now known as Lanczos potential. Moreover, it is known that an electromagnetic field can be generated by a potential, the question then arises that whether or not it is possible to generate the gravitational field through a potential. The answer is in affirmative - this indeed can be done through Lanczos potential. Using the methods of general observers, we have made a study of Lanczos potential. The kinematical quantities such as expansion, shear, rotation, etc., have been translated into the language of the tetrad formalism given by Newman and Penrose (known as spin coefficient formalism); and the Lanczos potential for perfect fluid space-times have been obtained in terms of the spin coefficients. The gravitational potentials for the Godel cosmological solution and Kasner metric has also been obtained. Using another tetrad formalism, known as compacted spin coefficient formalism, a potential for a Petrov type D space-time has been obtained. These results are then applied to a Kerr black hole.

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Existence of Solutions for a Three-Point Second-Order Boundary Value Problems with Integral Boundary Conditions Ummahan Akcan and Nuket Aykut Hamal Department of Mathematics, Faculty of Science, Anadolu University, Eskisehir, Turkey Department of Mathematics, Ege University, Bornova, Izmir, Turkey [email protected], [email protected]

Abstract: In this study, we make use of the monotone iterative technique to verify the existence of concave symmetric positive solutions of a second-order three-point boundary value problem with integral boundary conditions. The interesting point here is that the nonlinear term f depends on the first-order derivative explicitly. An example which supports our result is also indicated. Keywords: Boundary value problems; Symmetric positive solution; Integral bıundary condition; Monotone iterative technique. References: [1] V. A. Il'in, E.I. Moiseev, “Nonlocal boundary value problem of the second kind for a Sturm-Liouville operator”, Differ. Eqn. 23 (1987), 979-987. [2] F. Hao, “Existence of symmetric positive solutions for m-point boundary value problems for second-order dynamic equations on time scales”, Math. Theory Appl. (Changsha) 28 (2008), 65-68. [3] W. Feng, “On an m-point boundary value problem”, Nonlinear Anal. 30 (1997) , 5369-5374. [4] C.P. Gupta, “A generalized multi-point boundary value problem for second order ordinary differential equations”, Appl. Math. Comput. 89 (1998), 133-146. [5] Y. Sun, X. Zhang, “Existence of symmetric positive solutions for an m- point boundary value problem”, Bound. Value Probl. Art. ID 79090 (2007) 14 pp. [6] H. Pang, Y. Tong, “Symmetric positive solutions to a second-order boundary value problem with integral boundary conditions”, Boundary Value Problem. (2013):150 doi:10.1186/1687-2770-2013-150.

12

Necessary and Sufficient Conditions for the Solvability of Inverse Problem for a Class of Dirac Operators Ozge Akcay and Khanlar R. Mamedov Mathematics Department, Mersin University, Mersin, Turkey [email protected] and [email protected]

Abstract: In this work, the boundary value problem generated by one dimensional Dirac differential equations system By '+ W( x) y = lr ( x) y, 0< x

0 . A complete solution of the inverse spectral problem for a class of Dirac operators is given by spectral data. The main theorem on the necessary and sufficient conditions for the solvability of this inverse problem is proved and a solution algorithm of the inverse problem is given. Keywords: Dirac operator; inverse problem; necessary and sufficient condition References: [1] M. G. Gasymov and B. M. Levitan, “The inverse problem for the Dirac system”, Dokl. Akad. Nauk SSSR 167(1966), 967-970. [2] H. M. Huseynov and A. R. Latifova “On eigenvalues and eigenfunctions of one class of Dirac operators with discontinuous coefficients”, Trans. Natl. Acad. Sci. Azerb. 24(2004), 103-112.

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Integral Inequalities for Log-Convex Functions via Riemann-Liouville Fractional Integrals Ahmet Ocak Akdemir, Erhan Set and M. Emin Ozdemir Department of Mathematics, Agrı İbrahim Cecen University, Agrı, Turkey Department of Mathematics, Ordu University, Ordu, Turkey Department of Mathematics Education, Atatürk University, Erzurum, Turkey [email protected], [email protected], [email protected]

Abstract: In this paper, we established some new Hadamard-type integral inequalities for functions whose derivatives of absolute values are log-convex functions via Riemann-Liouville fractional integrals. Acknowledgement: This study was supported by Ağrı İbrahim Çeçen University BAP with the project number FEF.14.011. Keywords: Log-convex functions; Riemann-Liouville fractional integral. References: [1] S. S. Dragomir, “Refinements of the Hermite-Hadamard integral inequality for log-convex functions”, Aust. Math. Soc. Gaz., 28 (3), 129-134 (2001). [2] J. Pečarić, F. Proschan, Y. L. Tong, “Convex Functions, Partial Orderings and Statistical Applications”, Academic Press, Inc., 1992.

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Generalization of Hausdorff Matrices F. Aydin Akgun and B.E. Rhoades Department of Mathematical Engineering, Yildiz Technical University, Istanbul, Turkey Department of Mathematics, Indiana University, Bloomington, USA [email protected], [email protected]

Abstract: In 1926 W.A. Hurwitz showed that a row finite matrix is totally regular if and only if it has at most a finite number of diagonals with negative entries. He also proved that a regular Hausdorff matrix is totally regular if and only if it has all nonnegative entries. In 1921 Hausdorff proved that the Hölder and Cesaro Matrices are equivalent for each 𝛼𝛼 > −1. Basu, in 1949, compared the matrices totally. In this paper we investigate these theorems of Hurtwitz, Hausdorff, and Basu for the E-J and H-J generalized matrices. Keywords: Generalized Hausdorff matrices; Totally regular; Totally equivalence. References: [1] S. K. Basu, “On the total relative strength of the Hölder and Cesaro methods”, J. London Math. Soc. 50, 51- 59, (1948- 49). [2] F. Hausdorff, “Summationsmethoden und Momentfolgen”, I, Math. Z. 9, 74-109, (1921). [3] W. A. Hurwitz, “Some properties of methods of evaluation of divergent sequences”, Proc. London Math. Soc. 26, 231- 248, (1926).

15

New Indices on Special Graphs Nihat Akgunes, Ahmet Sinan Cevik and Ismail Naci Cangul Department of Mathematics-Computer Sciences, Faculty of Science, Necmettin Erbakan University,, Konya-Turkey Department of Mathematics, Faculty of Science, Selcuk University, Campus, Konya-Turkey Department of Mathematics, Faculty of Arts and Science, Uludag University, GorukleCampus, Bursa, Turkey [email protected] , [email protected], [email protected]

Abstract: In this talk, for a simple graph G with n vertices and m edges, we will introduce two new indices, namely Harmonic Mean Index and Average Harmonic Mean Index. By considering some special type of graphs, we will compare these indices with Harmonic Index (cf. [2, 3, 4]). Keywords: Topological indices; Harmonic index; Graph parameters. References: [1] N. Akgunes, K.Ch. Das, A.S. Cevik, “Topological indices on a graph of monogenic semigroups”, In: Ivan Gutman (Ed.), Topics in Chemical Graph Theory, Mathematical Chemistry Monographs, University of Kragujevac and Faculty of Science Kragujevac, Kragujevac (2014). ISBN 978-86-6009-027-2. [2] R. Chang, Z. Yan, “On the harmonic index and the minimum degree of a graph”, Romanian Journal of Information Science and Technology, 15(4) (2012), 335-343. [3] R. Wu, Z. Tang, H. Deng, H, “A lower bound for the harmonic index of a graph with minimum degree at least two”, Filomat, 27(1) (2013) , 51-55. [4] L. Zhong, “The harmonic index for graphs”, Applied Mathematics Letters, 25(3) (2012), 561-566.

16

The New Method of the Fine Spectrum of a Class of Operator-Matrix in Some Sequences Spaces Ali M. Akhmedov Faculty of Mechanical-Mathematics, Baku StateUniversity, Baku, Azerbaijan [email protected]

Abstract: In this paper, we give the new method for the investigation of fine spectrum of a class generalized difference-operator matrixs acting in some sequences spaces. According to it we probe the convergence of the iterative process for an infinite family of bounded linear operators on a Banach space. We apply the main result presented in this paper for certain problem in summability theory. The obtained results generalize some similar consequences of the spectral properties of known works ([1]-[3]). Keywords: Iterative process; Convergence; Bounded linear operator; Banach space. References: [1] P. D. Srivastava, S. Kumar, “On the fine spectrum of the generalized difference operator Dv over the sequence space c 0 ”, Commun. Math. Anal., 2009, 6, no.1, p. 8-21. [2] A.M. Akhmedov, S.R. El-Shabrawy, “On the spectrum of the generalized difference operator D a ,b over the sequence space

c 0 ”, Baku Univ. News J., Phys. Math. Sci. Ser., 2010, no. 4, p. 12-21.

[3] A.M. Akhmedov, S.R. El-Shabrawy, “On the fine spectrum of the operator D a ,b over the sequence space c”, Comput. Math. Appl., 2011, 61, p. 2994-3002.

17

On Compactness of the Hardy Operator in the Weighted Lp(.) (0, ¥) Space Lutfi Akin and Yusuf Zeren Yildiz Technical University, Departmant of Mathematics, Turkey [email protected], [email protected]

Abstract: The last century, several changes of mechanical structures discovered in a private environment . In this project, which is close to their concrete problems linking species been investigated the effects of natural environments and fluids processes shape the conditions of growth of non-standard types of non-linear parabolic and elliptic partial differential equations leads to the examination. There are solutions to the equations of this type are collected in the natural functional space 𝑝𝑝(𝑥𝑥) index variable type space 𝐿𝐿𝑝𝑝(𝑥𝑥) . A lot of the characteristics of these spaces, for example, the structure of joint space, reflection, smooth functions wherever compactness, continuity and compact embedding question adequately studied. Let Let

B(0, ¥) = { x Î R n : x < ¥} be in Euclidean space R n . r : B(0, ¥) ® (1, ¥) and u : B(0, ¥) ® (-¥ , +¥) be measurable functions. Denote by Lr (.),u (B(0, ¥)) the

space of all measurable functions f : B(0, ¥) ® R n such that

ò

f (y)

r (y )

u(y)dy < ¥ . This is a Banach space

y 0 : ò ç ý. ÷ l è ø B (0,¥ ) ïî ïþ p (.),w Hardy operator Hf ( x) = ò v(y)dy to be compact from L (B(0, ¥)) to space Lq (.),v (B(0, ¥)) it is necessary

y 1, å ÷ k = n +1 ø [ ln ]

and 1

n æ öq 1 (m) q÷ (1 - l ) limsup ç ( ( )) = o(1), l ® 1- , q > 1, u w å k,p ç ÷ P P n è n [ ln ] k =[ ln ]+1 ø are satisfied, and certain conditions on ( pn ) are hold, then (u n ) is slowly oscillating.

Keywords: Tauberian theorems; Weighted means; Weighted general control modulo; Slowly decreasing sequence. References: [1] G. H. Hardy, “Divergent series”, Clarendon Press, Oxford, 1949. [2] I. Canak, U. Totur, “Some Tauberian theorems for the weighted mean methods of summability”, Comput. Math. Appl., 62 (2011), 2609-2615. [3] U. Totur,I. Canak, “Some general Tauberian conditions for the weighted mean summability method”, Comput. Math. Appl., 63 (2012), 999-1006. [4] R. Schmidt, “Über divergente Folgen und lineare Mittelbildungen”, Math. Z., 22 (1925) , 89-152. [5] I. Canak, U. Totur, “An Extended Tauberian theorem for the weighted mean method of summability”, Ukrainian Math. J., 65 (2013), 1032-1041.

229

A Tauberian Theorem for the Power Series Method of Summability Umit Totur and Ibrahim Canak Department of Mathematics, Adnan Menderes University, Aydin, Turkey Department of Mathematics, Ege University, Izmir, Turkey [email protected], [email protected]

Abstract: Let (𝑢𝑢𝑛𝑛 ) be a sequence of real numbers. Assume that p = (pn ) be a sequence of nonnegative numbers ∞ k k with p0 > 0, that Pn : = ∑nk=0 pk → ∞ as n → ∞, and that p(x) = ∑∞ k=0 pk x < ∞ 𝑓𝑓𝑓𝑓𝑓𝑓 0 ≤ 𝑥𝑥 < 1. If ∑k=0 pk uk x is convergent for 0 ≤ x < 1, and 1 k ∑∞ limx→1− k=0 pk uk x = s, p(x)

then we say that (un ) is summable to s by the power series method (J, p). In this work, we introduce a one-sided Tauberian condition in terms of the weighted general control modulo of integer order 𝑚𝑚 ≥ 1 for the power series method of summability. Keywords: Weighted means; Weighted general control modulo; Slowly decreasing sequence; Tauberian theorems; Power series method. References: [1] G. A. Mikhalin, “Theorem of Tauberian type for (𝑱𝑱, 𝒑𝒑𝒏𝒏 ) summation methods”, Ukrain. Mat. Zh. 29 (1977), 763– 770. English translation: Ukrain. Math. J. 29 (1977), 564–569. [2] U. Totur, I. Canak, “Some general Tauberian conditions for the weighted mean summability method”, Comput. Math. Appl. 63 (5) (2012), 999–1006. [3] I. Canak, U. Totur, “Tauberian theorems for the (𝑱𝑱, 𝒑𝒑) summability method”, Appl. Math. Lett. 25 (10) (2012), 1430–1434. [4] G. H. Hardy, “Divergent series”, Clarendon Press, Oxford, 1949. [5] H. Tietz, “Schmidtsche Umkehrbedingungen für Potenzreihenverfahren”, Acta Sci.Math.,54 (3-4)(1990)355-365.

230

Some Tauberian Theorems for the Logarithmic Integrability Method Umit Totur and Muhammet Ali Okur Department of Mathematics, Adnan Menderes University, Efeler, Aydin, Turkey [email protected] 𝑥𝑥

Abstract: Let 𝑓𝑓 be a real valued function which is continuous on [1, ∞] and 𝑠𝑠(𝑥𝑥) = ∫1 𝑓𝑓(𝑡𝑡)𝑑𝑑𝑑𝑑. The logarithmic mean of 𝑠𝑠(𝑥𝑥) is defined by 𝜎𝜎𝑙𝑙 (𝑥𝑥) =

𝑥𝑥 𝑠𝑠(𝑡𝑡) 1 𝑑𝑑𝑑𝑑. ∫ log 𝑥𝑥 1 𝑡𝑡

∞

The integral ∫1 𝑓𝑓(𝑡𝑡)𝑑𝑑𝑑𝑑 is said to be integrable by logarithmic

method to a finite number 𝑠𝑠 if (1) lim𝑥𝑥→∞ 𝜎𝜎𝑙𝑙 (𝑥𝑥) = 𝑠𝑠. If the integral ∞ ∫1 𝑓𝑓(𝑡𝑡)𝑑𝑑𝑑𝑑 = 𝑠𝑠 (2) exist, then limit (1) also exist. The converse is not always true. However, with some additional conditions it can be true. These conditions and theorems are called as Tauberian conditions and Tauberian theorems, respectively. In this paper, we give some Tauberian theorems for the logarithmic integrability of 𝑠𝑠(𝑥𝑥) with some Tauberian conditions. Keywords: Tauberian theorem; Tauberian condition; Logarithmic method; Slowly oscillating sequence; Slowly decreasing sequence; One-sided condition. References: [1] K. Ishiguro, “Tauberian theorems concerning the summability method of logarithmic type”, Proc. Japan. Acad. 39 1963 156-159. [2] B. Kwee, “A Tauberian theorem for the logarithmic method of summations”, Proc. Cambridge Philos. Soc. 63 1966 401-405 [3] B. Kwee, “Some Tauberian theorems for the logarithmic method of summability”, Canad. J. Math. 20 1968 13241331. [4] B. Kwee, “On generalized logarithmic methods of summation”, J. Math. Anal. Appl. 35 1971 83-89. [5] I. Canak, U. Totur, “Tauberian conditions for Cesàro summability of integrals”, Appl. Math. Lett. 24 (6) (2011) 891-896.

231

Eigenvalues for Kaehler Graphs of Connected Product Type Yaermaimaiti Tuerxunmaimaiti Division of Mathematics & Mathematical Science, Nagoya Institute of Technology, Japan [email protected]

Abstract: Graphs which consist of sets of vertices and sets of edges are considered as discrete models of Riemannian manifolds of nonpositive curvature, and paths on graphs are regards as geodesics. In [4] we introduced discrete models of Riemannian manifolds admitting magnetic fields. We call a graph Kaehler if its set of edges is divided into two disjoint subsets, the set of principal edges and the set of auxiliary edges. Just like motions of electric charged particles, paths on the principal graph is bended under the influence of magnetic fields. In order to show how paths are bended we use paths on the auxiliary graph. We defined Laplacians of a Kaehler graph by use of adjacency operators and transition operators of the principal and the auxiliary graphs. In this paper we give some ways to construct Kaehler graphs and study their eigenvalues. As an application we give some examples of isospectral pairs of Kaehler graphs. Keywords: Kaehler graphs; Principal graphs; Auxiliary graphs; Laplacians; Isospectrality; Regular graphs; Bipartite double; Product graphs. References: [1] A.E. Brouwer, W.H. Haemers, “Spectra of graphs”, Springer 2012. [2] H. Fujii, A. Katsuda, “Isospectral graphs and the isoperimetric constant”, Discrete Math. 207(1999), 33-52. [3] T. Sunada, “Riemannian covering and isospectral manifolds”, Ann. Math. 121(1985), 169-186. [4] T. Yaermaimaiti, T. Adachi, “Isospectral Kaehler graphs”, preprint.

232

Generalized Weighted Norlund Mean and Ideal Convergence Orhan Tug and Feyzi Basar Department of Mathematical Education, Ishik University, Erbil, Iraq Department of Mathematics, Fatih University, Turkey [email protected], [email protected]

Abstract: In this work, we introduce the generalized weighted Nörlund mean as a new summability method. We give some properties of this method and obtain some results by using ideal convergence and Nörlund mean. References: [1] B.Altay, F.Başar, Some Euler sequence spaces of non-absolute type, Ukrainian Math. J. 57 (1) (2005), 1-17. [2] F.M. Mears, The inverse Nörlund mean, Ann. Math. 44 (3) (1943), 401-409. [3] C.S. Wang. On Nörlund sequence space, Tamkang J. Math. 9 (1978), 269-274. [4] F.M. Mears, Some multiplication theorems for the Nörlund mean, The Ggeorge Washington University, Decemberr,1935, 875-880. [5] B. Altay, F. Başar, Certain topological properties and duals of the matrix domain of a triangle matrix in a sequence space, J. Math. Anal. Appl. 336 (1) (2007), 632-645. [6] A. Wilansky, Summability through Functional Analysis, North-Holland Mathematics Studies 85, Amsterdam ∙ Newyork ∙ Oxford, 1984. [7] J. Boos, Classical and Modern Methods in Summability, Oxford University Press, New York, 2000. [8] F. Başar, Summability Theory and Its Applications, Bentham Science Publishers, e-books, Monographs, İstanbul, 2012. [9] E.A. Aljimi, V. Loku, Generalized weighted Nörlund-Euler statistically convergence, Int. J. Math. Anal. 8 (7) (2014), 345-354. [10] E.A. Aljimi, V. Loku, The rate of weighted Nörlund-Euler statistically convergence, Int. J. Math. Anal. 8 (26) (2014), 1297-1304.

233

On Convergence Methods of Functions Defined on Time Scales Ceylan Turan and Oktay Duman Department of Mathematics, TOBB Economics and Technology University, Sogutozu, Ankara, Turkey [email protected], [email protected]

Abstract: In [4], [5], we introduced the concepts of statistical convergence and lacunary statistical convergence of a function defined on a time scale, which cover the classical ones examined in [1], [2], [3]. The main purpose of this presentation is to give some recent results on these convergence methods and to discuss their applications. Keywords: Time Scale; Statistical Convergence; Lacunary statistical convergence. References: [1] H. Fast, “Sur la convergence statistique”, Colloq. Math. 2 (1951), 241-244. [2] J. A. Fridy, C. Orhan, “Lacunary statistical convergence”, Pacific J. Math. 160 (1993), 43-51. [3] F. Móricz, “Statistical limits of measurable functions”, Analysis 24 (2004), 207-219. [4] C. Turan, O. Duman, “Statistical convergence on time scales and its characterizations”, Springer Proc. Math. Stat. 41 (2013), 57-71. [5] C. Turan, O. Duman, “Convergence methods on time scales”, AIP Conf. Proc. 1558 (2013), 1120-1123.

234

Classification of Integral Curves of a Linear Vector Field on (2n+1) Dimensional Semi Euclidean Space Tunahan Turhan and Nihat Ayyildiz Seydişehir Vocational School, Necmettin Erbakan University, Seydisehir, Konya, Turkey Department of Mathematics, Suleyman Demirel University, Isparta, Turkey [email protected], [email protected]

Abstract: In this work, we give some results on classification of integral curves or flow lines of a linear vector field in (2n+1)-dimensional semi-Euclidean space The skew symmetric matrix has been found depending on the number of timelike vectors are odd or even. Taking into consideration of the structure, we obtained the linear first order system of differential equations. Then, we give solution of these systems and some examples. 2n 1 E .  Keywords: Integral curve, linear vector field, semi-Euclidean space, skew-symmetric matrix. References: [1] A., Acratalishian, On the Linear Vector Field in E²ⁿ⁺¹, Commun. Fac. Sci. Ank., 1989, 39, 21-35. [2] A., Galbis M., Maestre, Vector Analysis Versus Vector Calculus, Springer, London, 2012, 375 pp. [3] A., Karger, J., Novak, Space Kinematics and Lie Groups, Gordon and Breach Science Publishers, 1978, 422 pp. [4] A., Yücesan, A.C., Çöken, N., Ayyıldız, G.S., Manning, On the Relaxed Elastic Line on Pseudo-Hypersurfaces in Pseudo-Euclidean Spaces, Applied Mathematics and Computation (AMC), 2004, 155(2), 353-372. [5] B., O'Neill, Semi-Riemann Geometry: with Applictions to Relativity. Academic Pres, New York, 1983, 469 pp. [6] T., Yaylacı, Linear Vector Fields and Applications, MSc thesis, Ankara Üniversity, The Institute of Science, Ankara, 2006, 49 pp.

235

More Results on the Upper Solution Bounds of the Continuous Algebraic Riccati Matrix Equation Zubeyde Ulukok Selçuk University, Science Faculty, Department of Mathematics, 42075, Konya, Turkey. [email protected]

Abstract. The algebraic Riccati and Lyapunov matrix equations are widely used and play an important role in various of engineering such as control system design and analysis [7, 8, 11, 14], and signal processing [17]. The continuous algebraic Riccati and Lyapunov matrix equations that we generally encounter in the literature are defined as below: The continuous algebraic Riccati matrix equation (CARE) is

PA + A P - PBB P = -Q T

where A Î ¡

n´ n

T

and B Î ¡

n´ m

(1)

are constant matrices, Q Î ¡

n´ n

is a given positive semidefinite matrix, and the

n´ n

matrix P Î ¡ is the unique positive semidefinite solution of the CARE (1). When B = 0 and A is stable matrix, the CARE (1) becomes the continuous algebraic Lyapunov matrix equation (CALE)

A P + PA = -Q . T

(2)

It is well known that the unique positive semidefinite solution P to the CARE (1) exists if the pair

(

12

controllable (stabilizable) and the pair A, Q

) is observable (detectable).

( A, B )

is

The computing of these equations’s analytic solutions are rather complicated in applications when the dimensions of system matrices are high. Therefore, in order to save time and decrease the burden of computation, instead of the exact solution, only the bounds as an approximation of the exact solution are sometimes needed. For example, for some applications such as stability analysis [16], without the burden of hard calculations, bounds are needed only for solution matrices. Furthermore, the solution bounds of the CARE (1) can be used to treat many control problems [4]. In this study, by constructing different equivalent forms of the continuous algebraic Riccati matrix equation (CARE) and using some linear algebraic techniques, we present the upper matrix bounds which depend on any positive definite matrix for the solution of the CARE. Based on these bounds, we develope iterative algorithms to obtain more sharper solution bounds. Furthermore, we give numerical examples to demonstrate that the new bounds are tighter than previous results in many cases. Keywords: Continuous algebraic Riccati matrix equation, Continuous algebraic Lyapunov matrix equation, Matrix bound. References: [1] M. Basin, J. Rodriguez-Gonzaleza, and L. Fridman, “Optimal and Robust Control for Linear State-Delay Systems”, Journal of the Franklin Institute, 344, (2007), 830-845. [2] D. S. Bernstein, Matrix Mathematics: “Theory, Facts and Formulas with Application to Linear Systems Theory”, Princeton University Press, Princeton, NJ, USA, 2005. [3] C. Y. Chen, C. H. Lee, “Explicit Matrix Bounds of the Solution for the Continuous Riccati Equation”, ICIC Express Letters, 3, (2009), 147-152. [4] R. Davies, P. Shi, and R. Wiltshire, “New Upper Solution Bounds for Perturbed Continuous Algebraic Riccati Equations Applied to Automatic Control”, Chaos, Solutions and Fractals, 32, (2007), 487-495. [5] R. Davies, P. Shi, R. Wiltshire, “New Upper Matrix Bounds for the Solution of the Continuous Algebraic Riccati Matrix Equation”, Internat. J. of Control, Automat. and Systems, 6,(2008), 776-784. [6] S.W. Kim, P.G. Park, “Upper Bounds of the Continuous ARE Solution”, IEICE Trans. Fundam. Electron. Comm.

236

Global Attractors for Quasilinear Parabolic-Hyperbolic Equations Governing Longitudinal Motions of Nonlinearly Viscoelastic Rods Suleyman Ulusoy Department of Mathematics, Zirve University, Gaziantep, Turkey [email protected]

Abstract: We prove the existence of a global attractor and estimate its dimension for a general family of thirdorder quasilinear parabolic-hyperbolic equations governing the longitudinal motion of nonlınearly viscoelastic rods subject to interesting body forces and end conditions. The simplest version of the equations has the form w_{tt} = n(w_x,w_{xt})_x where n is defined on (0,\infty)\times\bb R and is a strictly increasing function of each of its arguments, with $n \to \infty$ as its first argument goes to 0. This limit characterizes a total compression, a source of technical difficulty, which new delicate a priori estimates prevent. We determine how the dimension of the attractor varies with several parameters of the problem giving conditions ensuring that the dimension is small. These estimates of dimension illuminate asymptotic analyses of the governing equation as parameters approach certain limits. This is a joint work with Stuart S. Antman. This work has been supported by TÜBİTAK grant 112T237. Keywords: Nonlinearly viscoelastic rods; Dimension of attractors; Quasilinear parabolic-hyperbolic equation. References: [1] S. S. Antman and T. I. Seidman, “Quasilinear hyperbolic-parabolic equations of one-dimensional viscoelasticity”, J. Differential Equations, 124(1996), 132-185. [2] S. S. Antman and S. Ulusoy, “The asymptotics of heavily burdened viscoelastic rods”, Quarterly J. Appl. Math, 170(2012), 437-467. [3] S. S. Antman and S. Ulusoy, “Global Attractors for Quasilinear Parabolic-Hyperbolic Equations Governing Longitudinal Motions of Nonlinearly Viscoelastic Rods”, Physica D , to appear.

237

(�)-boundedness of localization operators involving watson transform associated to regular representations and wavelet multipliers

S.K.Upadhyay Department of Mathematical Sciences, IIT (BHU) and CIMS-DST (BHU), Varanasi - 221 005 (India) E-mail address: [email protected]

Abstract : (�)-boundedness of localization operators associated to left reg-ular representations of locally compact group is investigated and using the theory of Watson Transformation relation between wavelet multipliers and localization operators is found. References: [1] F.M. Cholewinski, A Hankel convolution complex inversion. Theory. Mem. Amer. Math.Soc.58 (1965). [2] Richard R.Goldberg, Watson transform on groups, Annals of Mathematics, Second Series, 71(3) (1960), 522-528. [3] D.T. Haimo, Integral equation associated with Hankel convolution. Trans. Amer. Math.Soc.116 (1965), 330-375. [4] Hirschman Jr. I.I. Variation diminishing Hankel Transform. J. Analyse Math. 8 (1960-1961),307-336.

238

A Maximum Modulus Estimate for the Steady Stokes Equations Werner Varnhorn Institute of Mathematics, Faculty of Mathematics and Natural Sciences, Kassel University, Germany [email protected]

Abstract: In the theory of partial differential equations the classical maximum principle is well known. It states that any non-constant harmonic function u takes its maximum (and minimum) values always at the boundary ∂G of the corresponding domain G. For higher order differential equations as well as for systems of differential equations such a principle doesn’t hold in general. In these cases, however, there is some hope for a so-called maximum modulus estimate of the form max|u(x)| ≤ c max|u(x)|, G

∂G

where c denotes some constant. We prove the validity of such an estimate for the linear Stokes system via the method of the boundary integral equations. Here G ⊂ ℝn (n ≥ 2) is some bounded or unbounded open set having a compact boundary ∂G of class C1,α (0 < 𝛼𝛼 ≤ 1) Keywords: Stokes Equations; Maximum modulus estimates. References: [1] W. Varnhorn, “Maximum Modulus Estimates for the Linear Steady Stokes System”, Proc. Appl. Math. Mech., 12: 589–590. doi: 10.1002/pamm.201210283, 2012.

239

Approximation Properties of Chlodowsky-Durrmeyer Type q-Bernstein-Schurer-Stancu Operators Tuba Vedi and Mehmet Ali Ozarslan Department of Mathematics, Eastern Mediterranean University, Gazimagusa, TRNC, Mersin 10, Turkey [email protected], [email protected]

Abstract: The well known q-Durrmeyer operators and their approximation properties was studied by Gupta [7]. In this paper, we inroduce the Chlodowsky-Durrmeyer type q-Bernstein-Schurer-Stancu operators. We prove Korovkintype approximation theorems on the unbounded domain and compute the rate of convergence of the operators. Keywords: q-Durrmeyer operators, q-Chlodowsky operators, q-Beta integral, q-calculus. References: [1] Agrawal P. N., Gupta V. and Kumar A. Sathish, On q-analogue of Bernstein-Schurer-Stancu operators, Applied Mathematics and Computation, 219 (14), (2013), 7754-7764. [2] Agrawal P. N., Kumar A. Sathish and Sinha T. A. K., Stancu type generalization of modified Schurer operators based on q-integers, Applied Mathematics and Computation, 226, (2014), 765-776. [3] Büyükyazıcı İ. And Sharma H., Approximation properties of two-dimensional q-Bernstein-ChlodowskyDurrmeyer operators, Numerical Functional Analysis and Optimization, 33 (12), (2012), 1351-1371. [4] Chlodowsky, I: Sur le development des fonctions defines dans un interval infini en series de polynomes de M. S. Bernstein, Compositio Math., 4, 380-393 (1937). [5] Derriennic, M. M., Modified Bernstein polynomials and Jacobi polynomials in q-calculus, Rend. Circ. Mat. Palermo, Serie II (Suppl. 76), (2005), 269-290. [6] DeVore, RA, Lorentz, GG: Constructive Approximation, Springer-Verlag, Berlin (1993).

240

On Relative Homology Groups of Khalimsky Spaces Tane Vergili and Ismet Karaca Department of Mathematics, Ege University, Bornova, Izmir, Turkey [email protected], [email protected]

Abstract: In digital topology, the invariants such as the digital fundamental group [1, 2], the digital nth homotopy groups [5], the digital simplicial homology [3] and cohomology groups [4] of digital images are tools for comparing the digital images. The digital singular homology theory for Khalimsky spaces are introduced in [6] to distinguish the Khalimsky spaces regarding the functorial property. In this work, we introduce the digital relative singular homology groups and discover whether the excision, dimension, additivity and exactness axioms are valid for the digital singular homology of digital Khalimsky spaces. Keywords: digital homology groups, relative homology, Khalimsky space References: [1] E.H. Spanier, “Algebraic Topology”, Springer-Verlag, New York, (1966). [2] A. Rosenfeld, “Continuous functions on digital pictures”, Pattern Recognition Letters 4(1986), 177-184. [3] T.Y. Kong, “A digital fundamental group”, Computers and Graphics, 13(1989), 159-166. [4] L. Boxer, “A classical construction for the digital fundamental group”, Journal of Mathematical Imaging and Vision, 10(1994), 833-839. [5] L. Boxer, I. Karaca and A. Oztel, “Topological invariants in digital images”, Journal of Mathematical Sciences: Advances and Applications, 11(2011) No 2, 109-140. [6] O. Ege and I. Karaca, “Cohomology theory for digital images”, Romanian Journal of Information Science and Technology, 16(2013) No 1, 10-28. [7] T. Vergili and I. Karaca, “Some properties of higher dimensional homotopy groups for digital images”, Applied Mathematics and Information Science, (2014)(Submitted). [8] T. Vergili and I. Karaca, “On homology groups of certain digital spaces”, Mathematical Science Letters, (2014)(Submitted).

241

Stabilization in a n-Species Chemotaxis System with a Logistic Source Wang Wenjia Department of Mathematics, Southeast University, Nanjing, China [email protected]

Abstract: In this paper we consider the following system involving more than two competitive populations of biological species all of which are attracted by the same chemoattractant,

ìu1t = Du1 - c1Ñ × (u 1 Ñw) + µ1u1 (1 - å n a1i ui ), x Î W, i =1 ï ïu = Du - c Ñ × (u Ñw) + µ u (1 - n a u ), x Î W, å i =1 1i i 1 1 1 1 1 ïï 1t L íL ï n ïu1t = Du1 - c1Ñ × (u 1 Ñw) + µ1u1 (1 - å i =1 a1i ui ), x Î W, ï n x Î W, ïî-Dw + l w = å i =1 u1 , N under homogeneous Neumann boundary conditions in a bounded domain W Ì ¡ ( N We prove that if µi , c i and the following matrix

æ a11 ç a A = ç 21 ç M ç è an1

t > 0, t > 0, t > 0, t > 0,

³ 1) with smooth boundary.

a12 L a1n ö ÷ a22 L a2 n ÷ M O M ÷ ÷ an 2 L ann ø

satisfy certain properties, then all solutions of this system will stabilize towards to a positive equilibrium

{u }

* i i =1,..., n

which is globally asymptotically stable. Keywords: Keller-Segel system; Chemotaxis; Logistic source; Steady-state. References: [1] T. Cieślak, P. Laurençot, “Finite time blow-up for a one-dimensional quasilinear parabolic-parabolic chemotaxis system”, Ann. Inst. H. Poincaré Anal. Non Linéaire, 27(2010) , 437-446. [2] T. Cieślak, C. Stinner, “Finite-time blowup and global-in-time unbounded solutions to a parabolic-parabolic quasilinear Keller-Segel system in higher dimensions”, J. Differential Equations, 252(2012), 5832-5851. [3] T. Cieslak, M. Winkler, “Finite-time blow-up in a quasilinear system of chemotaxis”, Nonlinearity, 21(2008), 1057-1076.

242

Hermite-Hadamard-Fejer Type Inequalities Hatice Yaldiz Department of Mathematics, Duzce University, Duzce, Turkey [email protected]

Abstract: In this paper, we have established the left hand side of the Hermite-Hadamard-Fejer type inequalities for the class of functions whose derivatives in absolute value at certain powers are convex functions by using fractional integrals. Because of the wide application of Hermite-Hadamard type inequalities and fractional integrals, many researchers extend their studies to Hermite-Hadamard type inequalities involving fractional integrals not limited to integer integrals. Recently, more and more Hermite-Hadamard inequalities involving fractional integrals have been obtained for different classes of functions. Keywords: Convex function; Hermite-Hadamard inequality; Hermite-Hadamard-Fejer inequality; RiemannLiouville fractional integral. References: [1] M. Z. Sarikaya, “On new Hermite Hadamard Fejér type integral inequalities”, Stud. Univ. Babeş-Bolyai Math. 57 (3) (2012), 377--386. [2] M. Z. Sarikaya, E. Set, H. Yaldiz, N. Basak, “Hermite -Hadamard's inequalities for fractional integrals and related fractional inequalities”, Mathematical and Computer Modelling, DOI:10.1016/j.mcm.2011.12.048, 57 (2013) 2403-2407. [3] I. Iscan, “Hermite-Hadamard-Fejer Type Inequalities For Convex Functions Via Fractional Integrals”, 2014, arXiv:1404.7722v1. [4] M. Z. Sarikaya, H. Ogunmez, “On new inequalities via Riemann-Liouville fractional integration”, Abstract an Applied Analysis, 2012 (2012) 10 pages, Article ID 428983. doi:10.1155/2012/428983. [5] L. Fejér, “Uberdie Fourierreihen”, II Math. Naturwise. Anz Ungar. Akad., Wiss, 24 (1906), 369-390, (in Hungarian).

243

A Note on a Functional Identity on Lie Ideals Nihan Baydar Yarbil Department of Mathematics, Ege University, Bornova, Izmir, Turkey [email protected]

Abstract: A functional identity can be defined as an identical relation including elements of a ring together with functions. The aim of the functional identity (FI) theory is to characterize the form of these functions. This theory was first introduced by M. Bresar. K. I. Beidar and M. A. Chebotar has given the foundations of FI theory. Let R be a ring. An additive map of R is said to be a Lie derivation if F [ x, y ] = é F ( x ) , y ù + é x, F ( y ) ù for all x, y Î R . In this ë

û ë

û

talk, we will take two additive mappings F and D of R such that F [ x, y ] = é F ( x ) , y ù + é x, D ( y ) ù for all x, y Î L ë û ë û where L is a noncentral Lie ideal of R and determine the form of these mappings. Keywords: Prime ring, derivation , Lie derivation, functional identitity. References: [1] K. I. Beidar, M. A. Chebotar , “On functional identities and d-free subsets of Rings I”, Comm. Algebra 28 (2000), 3925-3951. [2] K. I. Beidar , On functional identities and commuting additive mappings, Comm. Algebra, 26 (6) (1998), 18191850. [3] M. Bresar, C. R. Miers, Commuting maps on Lie ideals, Comm. Algebra 23 (1995), 5339-5553. [4] M. Bresar, On generalized biderivations and related maps”, Jour. Algebra 172(3) (1995), 764-786. [5] M. Bresar, M. A. Chebotar, W. S. Martindale, “Functional identities”, Birkhauser Verlag, 2007, Basel, Switzerland.

244

On the Higher Order Gaussian Curvatures in Lorentz Space Ayse Yasar Yavuz and F. Nejat Ekmekci Department of Mathematics Education, Necmettin Erbakan Konya University, Konya, Turkey Department of Mathematics, Ankara University, Ankara, Turkey [email protected], [email protected]

� be a parallel hypersurfaces to 𝑀𝑀. The higher order Gaussian Abstract: Let 𝑀𝑀 be hypersurfaces in 𝐸𝐸 𝑛𝑛+1 and 𝑀𝑀 � are known. We introduced higher order Gaussian curvatures of 𝑀𝑀 and 𝑀𝑀 � in 𝐸𝐸1𝑛𝑛+1 Lorentz curvatures of 𝑀𝑀 and 𝑀𝑀 Space our last studies [2] . And now in this paper we prove a new theorem in Lorentz space by using principal curvatures and higher order Gaussian curvatures in our last works. Keywords: Gaussian curvatures; Principal curvatures; Parallel hypersurfaces References: [1] B. O'Neill , “Semi Riemannıan Geometry”, Department of Mathematics University of California Los Angeles, California. 1983 [2] A. Yasar, “Higher Order Gaussian Curvatures of a Parallel Hypersurfaces in Lorentz Space”, Master Thesis Ankara University. 2010

245

On Soft Dual Space of Soft Normed Spaces Murat Ibrahim Yazar, Yilmaz Altun and Tunay Bilgin Department of Mathematics, Kafkas University, Kars, Turkey Department of Mathematics, Artvin Coruh University, Artvin, Turkey Department of Secondary Education Science and Mathematics Fields Teaching, Yuzuncu Yil University, Van, Turkey [email protected], [email protected], [email protected]

Abstract: The concept of Soft set theory introduced by Molodtsov in[1]. Soft real numbers and properties introduced in[2] and soft normed space is defined in [3]. In this study, firstly we obtain a soft normed space by defining a soft norm on ¡ (Real numbers) which is called soft normed real space. By using this normed space we define the soft linear functional and investigate some of its properties. Secondly, we introduce soft dual space and soft dual operator and investigate their properties. Finally, we state and prove the theorem about representation of soft linear functional by inner product in soft Hilbert space defined in [4]. Keywords: Soft normed spaces; Soft linear functionals; Soft dual spaces; Soft dual operators; Soft Hilbert spaces. References: [1] D. Molodtsov, “Soft set-theory-first results”, Computers and Mathematics with Applications. 37(1999), 19-31. [2] S. Das, S. K. Samanta, “Soft real sets, soft real numbers and their properties”,J. Fuzzy Math.20.3(2012), 551-576. [3] M.I. Yazar, T. Bilgin, S. Bayramov, C. Gunduz(Aras), “A new view on soft normed spaces”, International Mathematical Forum, accepted. [4] M.I. Yazar,“Soft metric and soft normed spaces”,PhD Thesis, Yüzüncü Yıl University,Institute of Sciences,2014.

246

On Some Properties of the B-Convex Functions Ilknur Yesilce and Gabil Adilov Department of Mathematics, Mersin University, Mersin, Turkey Department of Mathematics, Akdeniz University, Antalya, Turkey [email protected], [email protected]; [email protected]

Abstract:

A

subset

U

of

¡ n+

is

B-convex

if

for

all

x, y Î U

and

all l Î [ 0,1]

one

has

l x Ú y = ( max {l x1 , y1} , max {l x2 , y2 } ,..., max {l xn , yn } ) Î U . This definition is given by Briec and Horvath [1]. Also, B-convex sets are studied in [1-4]. Using B-convex set, the definition of B-convex function can be given as f : U ® ¡ È {±¥} U Ì ¡n . A function is called B-convex function if follows: Let

epif = {( x, µµµ ) : x ÎU , Î ¡, ³ f ( x )} is B-convex set. Furthermore, we can give a necessary and sufficent condition for B-convex function: Let U Ì ¡ n+ , f : U ® ¡ + È {+¥} . f is B-convex function if and only if U is Bconvex set and for all x, y Î U and all l Î [ 0,1] the following inequality holds:

f (l x Ú y ) £ l f ( x) Ú f ( y ) In this work, some properties of B-convex functions are analyzed. Keywords: B-convexity, B-convex Sets, B-convex Functions. References: [1] W. Briec and C. D. Horvath, “B-convexity”, Optimization, 53(2004), 103-127. [2] G. Adilov and A. Rubinov, “B-convex sets and functions”, Numerical Functional Analysis and Optimization, 27:3-4(2006), 237-257. [3] W. Briec, C. D. Horvath and A. Rubinov, “Seperation in B-convexity”, Pacific J. Optimiz., 1(2005), 13-30. [4] W. Briec and C. D. Horvath, “Halfspaces and HahnBanach like properties in B-convexity and Max-Plus convexity”, Pacific J. Optimiz., 4:2(2008), 293-317.

247

Statistical Convergence of Multiple Sequences on a Product Time Scale Emrah Yilmaz, Yavuz Altin and Hikmet Koyunbakan Department of Mathematics, Firat University, Elazıg, Turkey [email protected], [email protected],[email protected]

Abstract: In this study, we extend the concepts and basic results on statistical convergence from multiple sequences to any product time scales. Moreover, various characterizations about these new notions are also obtained. Keywords: Statistical Convergence; Multiple Sequences; Product Time Scales. References: [1] F. Moricz, “Statistical convergence of multiple sequences”, Archiv der Mathematik, 81 (2003), 82-89. [2] C. Turan, O. Duman, “Statistical convergence on time scales and its characterizations”, Advances in Applied Mathematics and Approximation Theory, Springer Proceedings in Mathematics & Statistics, 41 (2013), 57-71. [3] M. S. Seyyidoglu, N. Ozkan Tan, “A note on statistical convergence on time scale”, Journal of Inequalities and Applications, (2012), 219-227. [4] S. Hilger, “Analysis on measure chains-A unified approach to continuous and discrete calculus”, Results in Mathematics, 18 (1990), 19-56. [5] M. Bohner, G. Sh. Guseinov, “Multiple integration on time scales”, Dynamic Systems an Applications, 14 (2005), 579-606. [6] B. Jackson, “Partial dynamic equations on time scales”, Journal of Computational and Applied Mathematics, 186 (2006), 391--415. [7] A. Zygmund, “Trigonometric Series”, Cambridge University Press, Cambridge, UK, 1979. [8] Y. Altin, H. Koyunbakan, E. Yilmaz, “Uniform Statistical Convergence on Time Scales”, Journal of Applied Mathematics, Volume 2014, Article ID 471437, 6 pages.

248

Optimality Conditions for Non-Lipschitz Optimization Nurullah Yılmaz and Ahmet Sahiner Department of Mathematics, Suleyman Demirel University, Isparta, Turkey [email protected], [email protected]

Abstract: Most of nonsmooth optimization studies deal with the Lipschitz continuous objective functions. In recent years, some interesting studies arise on non-Lipschitz optimization, because of the wide application areas in image processing [1,2,3]. In this study, we introduce optimality conditions that are one of the corner stone of the optimization theory for non-lipschitz objective functions. Keywords: Nonsmooth optimization, lp minimization, optimzality conditions. References: [1] X. Chen, L. Niu and Y. Yuan, Optimality Conditions and smoothing trust region method for nonlipschitz optimization, SIAM J. Optim., 23 (3), (2013),1528-1552. [2] X. Chen, W. Zhou, “Convergence of the reweighted l1 minimization algorithm for l2 –lp minimization”, Comput. Optim. Appl. 59(2014), 47-61. [3] H. Wang, D.-H. Li, X.-J. Zhang and L. Wu, “Optimality Conditions for constrained Lp regularization”, Optimization, (2014), Doi: 10.1080/02331934.2014.929678

249

Groups and Graphs Utku Yilmazturk Department of Mathematics, Istanbul University, Fatih, Istanbul, Turkey [email protected]

Abstract: There are several graphs related to finite groups. One of these graphs, denoted by D(G ) , is the character degree graph. The definition of this graph is the following: Let G be a finite group and let cd (G ) denote the set of the irreducible complex character degrees of G . The vertex set of the character degree graph, denoted by r (G ) , is the prime divisors of the elements of cd (G ) and there is an edge between two vertices p and q if and only if there exists an element of cd (G ) divisible by pq . In the literature, there are several studies on the relation between the invariants of the character degree graph of a finite group and the structure of that group. For example, Palfy [1] has proved that in the character degree graph of a finite solvable group any three vertices induce a non-empty graph. Lewis [2] has classified all solvable groups with disconnected character degree graph. Lewis and Meng [3] has shown that a solvable group whose character degree graph is square (the graph with four vertices and in which every vertex has degree 2) is a direct product of two subgroups. Zuccari and Paolo[4] has given a relation between the character degree graph of a finite group and fitting height of that group. In this talk we will focus on the relation between a given graph and the group admits that graph as the character degree graph. Keywords: Finite group; Character degree graph. References: [1] P. P. Palfy, “On the character degree graph of solvable groups. I. Three primes”, Period. Math. Hungar. 36 (1998), no. 1, 61-65 [2] M. L. Lewis, “Solvable groups whose degree graphs have two connected components”, J. Group Theory 4(2001), no. 3, 255-275. [3] M. L. Lewis, M. Qingyun, “Square character degree graphs yield direct products”, J. Algebra 349 (2012), 185200 [4] M. Zuccari, C. Paolo, “Fitting height and diameter of character degree graphs” Comm. Algebra 41 (2013), no. 8, 2869-2878.

250

Center Coloring and the Other Colorings Zeynep Ors Yorgancioglu and Pinar Dundar Department of Mathematics, Yasar University, Izmir, Turkey Department of Mathematics, Ege University, Izmir, Turkey [email protected], [email protected]

Abstract- For a nontrivial connected graph G , center coloring is a kind of coloring the vertices of a graph G in such a way that if vertices have different distance from the center, then they must receive different colors. Two adjacent vertices can receive the same color. The number of colors required of such a coloring is called center coloring number Cc ( G ) of G . [1] This coloring can be applied to hierarchy problems to find the number of structures, people, criteria and comparisons, etc. Moreover it can be applied to earthquake motion problems to find the number of settlements that are affected by an earthquake. In this paper, center coloring is compared with the other various colorings [2, 3, 4, 5, 6] and several bounds are established for the center coloring and the other colorings. Keywords: Center; Distance; Coloring; Center coloring. References: [1] Y. Immelman, “On The (Upper) Line-Distinguishing And (Upper) Harmonious Chromatic Numbers Of A Graph”, Dissertation, 2007. [2] Z. Yorgancıoglu, P. Dundar, M.E. Berberler, “Center Colorıng Of Graphs And Spanning Trees”, Ecco XXV European Chapter on Combinatorial Optimization, Antalya, Turkey, 2012. [3] X. Li, Y. Sun, “Rainbow Connections Of Graphs”, Springer, 2012. [4] M., Kubale, “Harmonious Coloring Of Graphs”, Graph Colorings, Contemporary Mathematics, 2002, ISSN 0271-4132; 352. [5] S. Isobe, X. Zhou, T. Nishizeki, “A Polynomial – Time Algorithm for Finding Total Colorings of Partial k-trees”, International Journal of Foundations of Computer Science 10, 100-113, 1999. [6] J. Vernold Vivin, M.M. Akbar Ali, “On Harmonious Coloring of Middle graph of C (Cn ) , C ( K1,n ) and C ( Pn ) ”, Note di Matematica, 201-211, 2009.

251

Dual Transformations and One-Paremeter Motions Gulsum Yuca and Yusuf Yayli Aksaray Üniversitesi, Sabire Yazıcı Fen Edebiyat Fakültesi, Matematik Bölümü, 68000, Aksaray, Türkiye Ankara Üniversitesi, Fen Fakültesi, Matematik Bölümü, 06100, Ankara, Türkiye [email protected], [email protected]

Abstract: In this study we examine one-parameter motions by a dual transformation. We give examples in Euclidian space and Lorentzian space. Geometric interpretations will be given for these examples. Keywords: Dual transformation, Axis of rotation, Euclidean space, Lorentzian space References: [1] Dohi, R., Maeda, Y., Mori, M., Yoshida, H. 2010. "A dual transformation between SO(n + 1) and SO(n, 1) and its geometric applications". Linear Algebra Appl., vol. 432; pp. 770-776. [2] Greub W.H., Linear Algebra, Springer-Verlag New York, 1967 [3] Karger, A., Novak, J. 1985. Space Kinematics and Lie Groups, Gordon and Breach Science Publishers, Montreux. [4] Lopez, R. 2008. Differential Geometry of Curves and Surfaces in Lorentz-Minkowski space. [5] O’Neill, B. Semi-Riemannian Geometry, with applications to relativity. Academic Press, New York, 1983

252

On Boundedness of Fractional Maximal Operator in the Weighted Lp(.) (0,1) Space Yusuf Zeren and Lutfi Akin Yildiz Technical University, Departmant of Mathematics, Turkey [email protected], [email protected]

Abstract: Investigations of variational problems with variable exponent started from the papers by V. Zhykov. Later M. Ruzicka studied the problems in the so called rheological and electrorheological fluids, which lead to spaces with variable exponent. Many mathematical models in fluid mechanics, elasticity theory, differential equations etc are naturally related to the problems with non- standard local growth.It should be stressed that historically, the boundedness of the Hardy–Littlewood maximal operator over bounded domain W was established by L. Diening. We prove a new sufficiency result for the two weighted boundedness of the fractional maximal operator in the variable exponent Lebesgue space Lp(.) (0,1) . A complete analog of the Sawyer’s condition are obtained on the weight functions assuming a usual log-Holder continuity condition on the exponent function p(.) . Keywords: Fractional Maximal Operator; Variable exponent; Two weight inequality; Boundedness. References: [1] D. Cruz Uribe, A. Fiorenza. “Variable Lebesgue Spaces”, Foundations and Harmonic Analysis (Applied and Numerical Harmonic Analysis)" , Birkhauser,2013 [2] D. Cruz Uribe, A. Fiorenza. “Variable Lebesgue spaces: Foundations and Harmonic Analysis(Applied and numerical analysis)”, Birkhauser, 2013.

253

Global Existence and Asymptotic Properties of the Solution to a Two-Species Chemotaxis System Qingshan Zhang Department of Mathematics, Southeast University, Nanjing, P. R. China [email protected]

Abstract: This paper deals with the Cauchy problem for a two-species chemotactic Keller-Segel system ìut = Du - c1Ñ·(uÑw), ï ívt = Dv - c 2 Ñ·(vÑw), ï w = Dw - g w + a u + a v 1 2 î t in ¡ 2 ´ [0, ¥), where g ³ 0, c1 , c 2 and a1 , a 2 are real numbers. We obtain the global existence of solutions if ‖u0‖1 ,‖v0‖1 , and ‖Ñw0‖2 are small, and the asymptotic behavior of the small-data solution as follows: l If g = 0 , the solution is asymptotic to a self-similar solution for large time;

l If g > 0 , the solution behaves like a multiple of the heat kernel as t ® ¥ . Keywords: Two-species chemotaxis system, Global existence, Self-similar solution, Asymptotic profile.

254

One Dimensional Model of Biodegradable Elastic Curved Rods Bojan Zugec Faculty of organization and informatics, University of Zagreb, Varazdin, Croatia [email protected]

Abstract: In this work we consider a curved elastic rod made of biodegradable material, situated in a liquid solvent. The rod is clamped in both ends. By asymptotic expansion we derive a one dimensional model of biodegradable elastic curved rod from the associated 3D problem. The model is described by two coupled equations describing behaviour of the linearized elastic curved rod and the evolution of the rod's material at time t. Two cases of biodegradation are being observed: the case where diffusion doesn't affect biodegradation, i.e. material loss, and the case where it does. In both of these cases the existence and uniqueness of the one dimensional model solution will be proved. Keywords: Biodegradation, 1D model, elasticity. References: [1] A. Göpferich. “Mechanisms of polymer degradation and erosion”. Biomaterials 17.2 (1996.), 103–114. [2] M. Jurak i J. Tambaca. “Derivation and justification of a curved rod model”. Mathematical Models and Methods in Applied Sciences 09.07 (1999.), 991–1014. [3] K. Rajagopal, A. Srinivasa i A. Wineman. “On the shear and bending of a degrading polymer beam”. International Journal of Plasticity 23 (2007.), 1618– 1636.

255

Convergence Analysis and Numerical Solution of Benjamin-Bona-Mahony Equation by Lie-Trotter Splitting Fatma Zurnaci, Nurcan Gucuyenen, Muaz Seydaoglu and Gamze Tanoglu Department of Mathematics, Izmir Institute of Technology, Urla, Izmir, Turkey Civil Engineering Department, Gediz University, Menemen, Izmir, Turkey Department of Mathematics, Ege University, Bornova, Izmir, Turkey [email protected], [email protected], [email protected], [email protected]

Abstract: In this paper, an operator splitting method is used to analyse the nonlinear Benjamin-Bona-Mahony type equations. We split the equation as an unbounded linear part and a bounded nonlinear part and then Lie-Trotter splitting method is applied to the splitted equations. The local error bounds are obtained using the similiar approaches as in [1]; [2]. The approach bases on the differential theory of operators in Banach space and the quadrature errors estimated via Lie commutator bounds. The global error estimate is obtained via Lady Windermere’s fan argument. Finally, to confirm the expected convergence order, a numerical example is studied. Keywords: Lie-Trotter splitting; Convergence analysis; Benjamin-Bona-Mahony equation. References: [1] H. Holden, K. H. Karlsen, N. H. Risebro, “Operator splitting for the KdV Equation”, Math. Comp., 80(2011), 821-846. [2] H. Holden, C. Lubich, N. H. Risebro “Operator splitting for partial differential equations with Burgers nonlinearity”, Mathematics of Computation, 82(2013), 173-185. [3] T. B. Benjamin, J. L. Bona, J. J. Mahony, “Model equations for long waves in nonlinear dispersive systems”, Philos. Trans. Roy. Soc. London, 272(1972), 47-78.

256