## Content

### June 2018, Volume 10, Issue 3

**1-6 Operations Research, Economic Development, and Social Mobility***by*Aniekan A. Ebiefung & Michael M. Kostreva**7-14 Subjective Probability and Geometry: Three Metric Theorems Concerning Random Quantities***by*Pierpaolo Angelini & Angela De Sanctis**15-19 Some New Inequalities With Proofs and Comments on Applications***by*Xingbo WANG & Zhikui DUAN & Wen WAN**20-34 Dialectical Logic K-model: On Multidimensional Discrete Dynamical Sampling System and Further Properties of Kirchhoff Matrices***by*Yaozhi Jiang**35-41 Applications of Pell Polynomials in Rings***by*Yasemin TASYURDU & Devran ?iF?i & ?m¨¹r DEVECi**42-52 A Classroom Note on Twice Continuously Differentiable Strictly Convex and Strongly Quasiconvex Functions***by*Giorgi Giorgio**53-58 Brief Summary on Frequently-used Properties about Divisibility of Two's Power Plus-minus One***by*Jian Hui Li**59-62 Gravity, Mass and the Cosmological Constant: All Can Have the Same Origin***by*Hubert J. Veringa**63-76 Application of Extended Geometrical Criterion to Population Model with Two Time Delays***by*Suqi Ma**77-96 Return Levels Approach and Periods of Currency Crises***by*Mouridi M. HAMIDOU & Joseph K. Mung'atu & George O. Orwa**97-110 A Modified Characteristics-mixed Finite Element for Semiconductor Device of Heat Conduction and Numerical Analysis***by*Yirang Yuan**111-117 Modules Whose Nonzero Endomorphisms Have E-small Kernels***by*Abdoul Djibril DIALLO & Papa Cheikhou DIOP & Mamadou BARRY

### April 2018, Volume 10, Issue 2

**1-23 A Deeper Analysis on a Generalization of Fermat¡äs Last Theorem***by*Leandro Torres Di Gregorio**24-28 Regularity and Green's Relations for Generalized Semigroups of Transformations with Invariant Set***by*Lei Sun**29-35 Periodic Properties of Solutions of Certain Second Order Nonlinear Differential Equations***by*Akinwale Olutimo**36-54 Algorithms for Asymptotically Exact Minimizations in Karush-Kuhn-Tucker Methods***by*Koudi Jean & Guy Degla & Babacar Mbaye Ndiaye & Mamadou Kaba Traor¨¦**55-65 Stability and Oscillation for a Coupled Hamiltonian Duffing Oscillator Model with Delays***by*Chunhua Feng**66-76 Convergence Theorems of Modified Proximal Algorithms for Asymptotical Quasi-nonexpansive Mappings in CAT(0) Spaces***by*Shengquan Weng & Dingping Wu**77-87 Efficiency of MOMA-plus Method to Solve Some Fully Fuzzy L-R Triangular Multiobjective Linear Programs***by*Abdoulaye Compaor¨¦ & Kounhinir Som¨¦ & Joseph Poda & Blaise Som¨¦**88-99 Dialectical Logic K-Model: the Discrete Time Dynamical Sampling System, Multidimensional Logic Variable and Associate Database(ADB)***by*Yaozhi Jiang**100-103 Characterization of Orlicz Sobolev Spaces***by*Tiziano Granucci**104-121 Characterization of Orlicz Sobolev Spaces***by*Tiziano Granucci**122-128 Route Planning Based on Genetic Algorithm***by*Lin Li & Yuhua Zhang**129-139 The Analysis for the Scale and Efficiency of China¡¯s Major Automotive Enterprises Based on DEA Model***by*Zheng Fei & Li L. Z**140-150 An Empirical Analysis of the Relationship Between Urbanization and Fiscal Policy --- Taking Jiangxi Province of China As an Example***by*Xiao-Ying Wan**151-161 Mathematical Model for the Dynamics of Neisseria Gonorrhea Disease with Natural Immunity and Treatment Effects***by*Ibrahim Isa Adamu & Sulaiman Usman**166-181 An Approached Solution of Wave Equation with Cubic Damping by Homotopy Perturbation Method (HPM), Regular Pertubation Method (RPM) and Adomian Decomposition Method (ADM)***by*Moussa BAGAYOGO & Youssouf PARE & Youssouf MINOUNGOU

### February 2018, Volume 10, Issue 1

**1-5 Probability to Compute Divisor of a Hidden Integer***by*Xingbo Wang & Jianhui Li & Zhikui Duan & Wen Wan**6-19 Remarks on Convolutions and Fractional Derivative of Distributions***by*Chenkuan Li & Kyle Clarkson**20-24 Korovkin Approximation Theorem with ? Striped***by*Malik Saad Al-Muhja & Mohammad Mursaleen & Masnita Misiran & Zurni B. Omar & Sui Yang Khoo**25-31 Reverse Definite Integral of Algebraic Functions***by*Yogesh Mahat**32-43 Numerical Solution for Solving System of Fuzzy Nonlinear Integral Equation by Using Modified Decomposition Method***by*Alan Jalal Abdulqader**44-58 Numerical Solution of System of Three Nonlinear Volterra Integral Equations Using Implicit Trapezoidal***by*Dalal Adnan Maturi & Honaida Mohammed Malaikah**59-66 On the Trapped Surface Characterization of Black Hole Region in Vaidya Spacetime***by*Mohammed Kumah & Francis T. Oduro**67-89 The Origin of Gravity An Attempt to Answer this Question with the Help of Existing Concepts***by*Hubert J. Veringa**90-109 High-order Filtered Schemes for the Hamilton-Jacobi Continuum Limit of Nondominated Sorting***by*Warut Thawinrak & Jeff Calder**110-114 Edge-Maximal Graphs Containing No $r$ Vertex-Disjoint Triangles***by*Mohammad Hailat**115-123 Asymptotic Analysis of a Deterministic Control System via Euler's Equation Approach***by*Gladys Denisse Salgado Su¨¢rez & Hugo Cruz-Su¨¢rez & Jos¨¦ Dionicio Zacar¨ªas Flores**124-131 Existence and Uniqueness of Solution for Caginalp Hyperbolic Phase- Field System with a Polynomial Potential***by*Franck Davhys Reval Langa & Daniel Moukoko & Dieudonn Ampini & Fidle Moukamba**132-143 On the Concept of Representations of Prime Numbers and Prime Products***by*Peter Bissonnet

### December 2017, Volume 9, Issue 6

**1-13 Stabilization of Variable Coefficients Euler-Bernoulli Beam with Viscous Damping under a Force Control in Rotation and Velocity Rotation***by*Bomisso G. Jean Marc & Tour¨¦ K. Augustin & Yoro Gozo**14-23 An Instability Phenomenon in Hele-Shaw Displacements***by*Gelu Pasa**24-54 Gray Code in the Solution of the Nine Rings Chinese Game***by*Erick Ceasar Huang & Sharon Sherry Huang & Cheng-Hua Tsai**55-66 Various Proofs of the Sylvester Criterion for Quadratic Forms***by*Giorgio Giorgi**67-81 Algebraic Properties of Toeplitz Operators on the Pluri-harmonic Fock Space***by*Dieudonne Agbor**82-94 Dialectical Logic K-Model: A Mathematical Model for Machine***by*Yaozhi Jiang**95-105 Strong Goldbach Number in Goldbach¡¯s Problem***by*Pingyuan Zhou**106-111 Estimation of Causal Functional Linear Regression Models***by*J.C.S. de Miranda**112-123 Directional Method of Fundamental Solutions for Three-dimensional Laplace Equation***by*Chein-Shan Liu & Zhuojia Fu & Chung-Lun Kuo**124-143 Optimal Control of Evolution Macro-Hybrid Mixed Variational Inclusions***by*Gonzalo Alduncin**144-147 On Elliptic Operator Theory***by*Abdalla, Salih Abdalla**148-155 The Global Stability of 2-D Subsonic Circulatory Flows for the Steady Isothermal Gas***by*Dacheng Cui

### October 2017, Volume 9, Issue 5

**1-17 A Study on the Minimum and Maximum Sum of C2 Problem in IMO2014***by*Erick Ceasar Huang & Sharon Sherry Huang & Cheng-Hua Tsai**18-29 New Model for Solving Mixed Integral Equation of the First Kind with Generalized Potential Kernel***by*Shareefa Eisa Ali Alhazmi**30-36 The Separable Complementation Property and Mr¨®wka Compacta***by*Jesus Ferrer**37-45 K-loop Structures Raised by the Direct Limits of Pseudo Unitary $U(p, a_{n})$ and Pseudo Orthogonal $O(p, a_{n})$ Groups***by*Alper Bulut**46-53 Existence of Solutions for Functional Integral Equation Involving the Henstock-Kurzweil-Stieltjes Integral***by*Hui Mei & Guoju Ye & Wei Liu & Yanrong Chen**54-60 Sign of Permutation Induced by Nagata Automorphism over Finite Fields***by*Keisuke Hakuta & Tsuyoshi Takagi**61-70 Some More New Properties of Consecutive Odd Numbers***by*Xingbo Wang**71-86 Angular Vectors in the Theory of Vectors***by*Yevhen Kharchenko**87-96 On the Interval Controllability of Fractional Systems with Control Delay***by*Jiang Wei**97-107 On S-quasi-Dedekind Modules***by*Abdoul Djibril Diallo & Papa Cheikhou Diop & Mamadou Barry**108-125 Tripled Coincidence Point Results for $(\psi,\varphi)$-weakly Contractive Mappings in Partially Ordered S-matric Spaces***by*Abdolsattar Gholidahneh, & Shaban Sedghi**126-132 Exact Solitary Wave Solutions for the Generalized Schamel Korteweg¨CDe Vries Equation***by*N. O. Al Atawi**133-141 L\'{e}vy Process, Proportional Transaction Costs and Foreign Exchange***by*Obonye Doctor & Elias R. Offen & Edward M. Lungu

### August 2017, Volume 9, Issue 4

**1-10 Solving Liouville-type Problems on Manifolds with Poincar\'{e}-Sobolev Inequality by Broadening $q$-Energy from Finite to Infinite***by*Lina Wu**11-22 Some Remarks on the Stability Condition of Numerical Scheme of the KdV-type Equation***by*Chun-Te Lee & Jeng-Eng Lin & Chun-Che Lee & Mei-Li Liu**23-29 Sign of Permutations Induced by Anick and Nagata-Anick Automorphisms over Finite Fields***by*Keisuke Hakuta**30-48 Dissipative Numerical Method for a Flexible Euler-Bernoulli Beam with a Force Control in Rotation and Velocity Rotation***by*Bomisso G. Jean Marc & Tour'{e} K. Augustin & Yoro Gozo**49-68 The original problem that serves as a basis for this project comes from an American contest (PUMaC, 2014) regarding the maximum amount of enclosed spaces given a limited number of cuts on an infinite plane. In this study, we explore the same problem and extend it in the context of m dimensions given n (m-1) dimensional cuts using the recursive relationship of finite cuts and enclosed spaces in lower dimensions. Once the general formula of f(m,n)?was proven for dimensions, an Euler¡¯s inspired formula was used to check the accuracy of the formula in two and three dimensions. The Euler¡¯s formula also allowed us to derive the formula for the maximum number of unenclosed spaces in three-dimensional F(3, n). The results are as follows:***by*Erick C. Huang & Sharon S. Huang & Cheng-Hua Tsai**69-77 Cone Avoidance of Some Turing Degrees***by*Patrizio Cintioli**78-86 Modeling and Numerical Simulation of Sand Dunes Formation***by*HASSANE GANDA Rabi & HAMIDOU Haoua & SALEY Bisso**87-100 The Convergence of Calder¨®n Reproducing Formulae of Two Parameters in $L^p$, in $\mathscr S$ and in $\mathscr S'$***by*Jiang-Wei Huang & Kunchuan Wang**101-113 A Mathematical Model for the Vector Transmission and Control of Banana Xanthomonas Wilt***by*Kweyunga Eliab Horub & Tumwiine Julius**114-123 Analysis of Compression Ratio of Various Randomly Generated Images of Same Size***by*Tanvir Prince**124-134 On the Existence of Global Weak Solutions to 1D Pollutant Transport Model***by*Brahima ROAMBA & Jean de Dieu ZABSONRE & Yacouba ZONGO**135-144 Transmuted Mukherjee-Islam Distribution: A Generalization of Mukherjee-Islam Distribution***by*Loai M. A. Al-Zou'bi**145-167 The Global and Exponential Attractors for the Higher-order \\[6pt] Kirchhoff-type Equation with Strong Linear Damping***by*Guoguang Lin & Yunlong Gao**168-184 Minimum Principle-Type Necessary Optimality Conditions in Scalar and Vector Optimization. An Account***by*Giorgio Giorgi**185-195 Existence Conditions of Super-Replication Cost in a Multinomial Model***by*Mei Xing**196-199 On $FGDF$-modules***by*Alhousseynou BA & Sidy Demba Tour'e & Oumar Diankha**200-208 The First Hochschild Cohomology of Square Algebras With it's Stability***by*Feysal Hassani & Negin Salehi Oroozaki**209-230 On Theory of logarithmic Poisson Cohomology***by*Joseph Dongho & Alphonse Mbah & Shuntah Roland Yotcha**231-248 Logarithmic Differential Operators and Prequantization of Logsymplectic Poisson Structure***by*Joseph Dongho

### June 2017, Volume 9, Issue 3

**1-7 Nonexistence of Nontrivial Stationary Solutions with Decay Order for Some Nonlinear Evolution Equations***by*Jeng-Eng Lin**8-13 Quadratic form Approach for the Number of Zeros of Homogeneous Linear Recurring Sequences over Finite Fields***by*Yasanthi Kottegoda**14-22 Convergence Analysis for Mixed Finite Element Method of Positive Semi-definite Problems***by*Yirang Yuan & Changfeng Li**23-29 An Addendum on Postoptimality of Maximally Reliable Path***by*Ahmad Hosseini & Bita Kabir Baiki**30-37 Modeling and Resolution of the Allocation Problem of the Time Slots in Dakar Airport***by*Youssouf Ahamada & Salimata G. Diagne & Amadou Coulibaly & D'ethi'e Dione & N'dogotar N閘io & Youssou Gningue**38-45 The [a,b]-domination and [a,b]-total Domination of Graphs***by*Xiujun Zhang & Zehui Shao & Hong Yang**46-67 Symmetric Boundary Condition for Laplacian on Net of Regular Hexagons***by*Daniel Lee**68-74 On the Existence of Poncelet-Morley Points in Euclidean Geometry***by*Joseph Dongho & Nguimbous F. L. & Teyou M. R.**75-79 A Note on the Structure of Roller Coaster Permutations***by*William Adamczak**80-94 Minimum Hellinger Distance Estimation of a Univariate GARCH Process***by*Roger Kadjo & Ouagnina Hili & Aubin N'dri**95-111 A Fuzzy-stochastic Approach for Binary Linear Programming under Uncertainties***by*Wei Peng & Rene V. Mayorga