Mathematics Across Contemporary Sciences: AUS-ICMS, Sharjah, UAE, April 2015 (Springer Proceedings in Mathematics & Statistics Book 190)

This work presents invited contributions from the second "International Conference on Mathematics and Statistics"; the conference, held at American University of Sharjah on April 2 5, 2015, was jointly organized by the AUS (American University of Sharjah) and the AMS (American Mathematical Society). Addressing several research fields across the mathematical sciences, all of the papers were prepared by faculty members at universities in the Gulf region or prominent international researchers. The current volume is the first of its kind in the UAE and is intended to set new standards of excellence for collaboration and scholarship in the region." Preface......Page 6 Contents......Page 8 About the Editors......Page 10 1 Introduction......Page 12 2 Differentiable Stacks and Lie Groupoids......Page 13 3 Lusternik-Schnirelmann Category for Lie Groupoids......Page 21 4 Lusternik-Schnirelmann Category of a Differentiable Stack......Page 23 References......Page 25 1 Introduction......Page 27 2 Existence Theorems......Page 30 References......Page 41 1 Introduction......Page 42 2 Partially Independent (p.i.) Random Variables......Page 44 3.1 Existence Conditions......Page 46 3.2 Decidability......Page 50 3.4 Related Works......Page 51 4.1 Binary Variables......Page 52 4.2 Ternary Variables......Page 56 5 Countably Many p.i. Random Variables......Page 58 6 Dutch Books......Page 60 References......Page 65 1 Introduction......Page 66 2 Literature Review......Page 67 3.1 Theoretical Background......Page 71 3.2 Sobol Sensitivity for Machine Learning......Page 74 4 Application and Comparisons......Page 77 5 Conclusion......Page 81 References......Page 83 1 Introduction......Page 85 2 Basic Definitions......Page 86 3 Bloch-Crouch Formulation of LC Circuit Dynamics......Page 87 4 Basis Independent Formulation of mathcalD......Page 91 References......Page 97 1 Introduction......Page 99 2.1 Discrete Function Spaces......Page 103 2.3 Schwarz Symmetrization in hmathbbZ......Page 104 3 Discrete Symmetrization Inequalities......Page 108 4 Discrete Fractional Constained Variational Problem......Page 111 5 Some Applications......Page 115 References......Page 116 1 Introduction......Page 118 1.1 Definitions and Properties......Page 119 1.3 Constructions......Page 121 2 Orthogonal Arrays and Coding Theory......Page 123 3 Difference Schemes and Hadamard Matrices......Page 128 4 Mixed Orthogonal Arrays......Page 132 5 Application in Factorial Experiments......Page 134 6.1 Orthogonal Latin Hypercube Designs......Page 136 6.2 Sliced Orthogonal Arrays......Page 137 7.1 Latin Squares and F-Squares......Page 139 7.2 Compound Orthogonal Arrays......Page 141 References......Page 142 1 Introduction......Page 143 2.1 Digraphs......Page 144 2.2 Association Schemes......Page 145 3 Hoffman's Bound for Normal Digraphs......Page 146 4 A Characterization of Skew-Bush-type Hadamard Matrices......Page 148 5 Regular Biangular Matrices and Association Schemes......Page 149 6 Twin Asymmetric Designs and Association Schemes......Page 151 References......Page 156 1 Introduction......Page 157 2 Preliminaries......Page 161 3 Well-Posedness......Page 163 4 Stability......Page 168 References......Page 170 1 Introduction......Page 172 2 Constructing Suitable Pricing Functions......Page 173 3 An Illustrative Example......Page 175 4.1 Model-Free Hedge Ratios......Page 177 5 Conclusion......Page 178 References......Page 180 1 Introduction......Page 181 2.1 Category of Diagrams......Page 182 2.2 Equivalence of Categories Between mathscrMn and mathscrDe......Page 185 3 Stable Homotopy Groups of Moore Spaces......Page 190 References......Page 196 Notes on Quasi-Cyclic Codes with Cyclic Constituent Codes......Page 197 2 The Circulant Matrix Decomposition of a Cyclic Code......Page 198 3 Quasi-cyclic Codes with Cyclic Constituent Codes......Page 200 4 The Generator Polynomial of θ(mathscrC)......Page 204 5 General Equivalences......Page 206 6 Application Examples......Page 209 References......Page 210 1 Introduction......Page 211 2.1 Motivation......Page 214 2.2 A Special Case: A Markov Chain......Page 216 2.3 The General Case......Page 218 3 Pathological Bayesian Networks......Page 219 4 Non-pathological Situations and Bayesian Networks of Level Two......Page 227 5 Conclusion......Page 229 References......Page 230 1 Introduction......Page 231 2 Problem Statement......Page 232 3 The Switched System......Page 234 4.1 Moment and Localizing Matrices......Page 236 4.2 Semidefinite Programs Using Moments Approach......Page 238 5 Numerical Implementation......Page 239 6 Numerical Simulation......Page 240 7 Conclusion......Page 242 References......Page 243 1 Introduction......Page 245 2 The Stationary Problem and Important Results for BV Functions......Page 251 3 Time Flow of the Weak Solution......Page 255 4 Conclusion......Page 260 References......Page 261