Mathematics and Computing: ICMC 2018, Varanasi, India, January 9-11, Selected Contributions (Springer Proceedings in Mathematics & Statistics Book 253)

This book discusses recent advances and research in applied mathematics, statistics and their applications in computing. It features papers presented at the fourth conference in the series organized at the Indian Institute of Technology (Banaras Hindu University), Varanasi, India, on 9 – 11 January 2018 on areas of current interest, including operations research, soft computing, applied mathematical modelling, cryptology, and security analysis. The conference has emerged as a powerful forum, bringing together leading academic scientists, experts from industry, and researchers and offering a venue to discuss, interact and collaborate to stimulate the advancement of mathematics and its applications in computer science. The education of future consumers, users, producers, developers and researchers of mathematics and its applications is an important challenge in modern society, and as such, mathematics and its application in computer science are of vital significance to all spectrums of the community, as well as to mathematicians and computing professionals across different educational levels and disciplines. With contributions by leading international experts, this book motivates and creates interest among young researchers. Preface......Page 7 Contents......Page 9 Contributors......Page 13 1 Introduction......Page 18 2 Amalgamations and Hamilton Decompositions......Page 21 3 Embeddings of Edge-Colorings into Hamilton Decompositions......Page 23 References......Page 27 1 Introduction......Page 29 2.1 Pseudoconvexity and Quasiconvexity......Page 30 2.2 Strong Convexity and Strong Monotonicity of Order σ......Page 31 3 Strongly Pseudoconvexity of Order σ and Strongly Pseudomonotonicity of Order σ......Page 32 4 Strongly Quasiconvexity and Strongly Quasimonotonicity of Order σ......Page 34 References......Page 38 1 Introduction......Page 39 2 Model Description and Notation......Page 41 3 The Steady-State Analysis......Page 42 3.2 The Steady-State Probability Vector......Page 44 3.3 Rate Matrix (R)......Page 45 3.4 Busy Probabilities at Arbitrary Time......Page 46 3.5 Steady-State Probability at Departure Epoch......Page 47 4.1 The Steady-State Analysis—Classical Non-preemptive Priority Queueing Model......Page 49 5 Comparison of the Two Models......Page 52 6 Numerical Examples......Page 53 7 Concluding Remarks......Page 57 References......Page 58 1 Introduction......Page 59 2 Definitions and Notations......Page 60 3 Inclusion Theorems......Page 63 References......Page 66 1.1 Mullins Models of Thermal Diffusion Grooving......Page 68 2.1 Single-Integration Approach......Page 70 3.1 Transformation to Nonlinear Diffusion Problem......Page 71 3.2 Assumed Profile......Page 72 3.4 Penetration Depth......Page 73 3.5 Approximate Profile (Solution)......Page 74 4.2 Approximation of the Diffusion Term......Page 76 4.3 Optimal Exponents with Linear Approximation of arctan(aΘa)......Page 77 4.4 Brief Notes......Page 78 5 Numerical Simulations......Page 79 References......Page 80 1 Introduction......Page 82 2 Equilibrium Problems......Page 83 3 Optimal Control Problem......Page 87 References......Page 91 1 Introduction......Page 93 2 Main Results......Page 96 3 Numerical Example......Page 99 References......Page 100 1 Introduction......Page 101 2 Preliminaries......Page 102 3 Degree Reduction of Bézier Curves......Page 103 4 Applications......Page 104 References......Page 108 1 Introduction......Page 110 2 Cyber Situational Awareness......Page 111 3 Attack Graphs......Page 113 3.1 Topological Vulnerability Analysis......Page 118 3.2 A Network Security Planning Architecture......Page 119 3.3 Multihost, Multistage, Vulnerability Analysis......Page 121 4 Conclusion......Page 122 References......Page 123 10 A Solid Transportation Problem with Additional Constraints Using Gaussian Type-2 Fuzzy Environments......Page 125 1 Introduction......Page 126 2.1 Notations......Page 127 2.2 Model Formulation......Page 128 2.3 Defuzzification of Gaussian Type-2 Fuzzy Variables......Page 129 2.4 Model 2: Production Cost, Unit Transportation Cost, Impurity at Demand Point are treated as Gaussian Type-2 Fuzzy Variables and Source, Demands are Crisp......Page 131 3 Solution Procedures......Page 132 3.4 Crossover......Page 133 4 Numerical Experiments......Page 134 5 Discussion......Page 135 References......Page 136 1 Introduction......Page 138 2 Voronovskaya's Formula for Composition of Operators......Page 139 3 The Operator Bn......Page 142 4 The Operator Bn-1......Page 143 References......Page 145 12 Mathematics and€Machine Learning......Page 146 2.1 Recommender Systems (Supervised Learning)......Page 147 2.2 Classifier Systems (Unsupervised Learning)......Page 148 2.3 Anomaly Detection......Page 150 2.4 Neural Networks......Page 152 2.5 Principal Component Analysis......Page 154 3.1 Linear/Logistic Regression......Page 155 3.2 Neural Networks......Page 161 References......Page 164 13 Numerical Study on the Influence of Diffused Soft Layer in pH Regulated Polyelectrolyte-Coated Nanopore......Page 165 1 Introduction......Page 166 2 Mathematical Model......Page 167 3 Numerical Schemes......Page 171 4 Results and Discussions......Page 172 References......Page 177 1 Introduction......Page 179 2 Preliminaries......Page 180 3 Main Theorem......Page 181 4 Application......Page 188 References......Page 192 1 Introduction......Page 194 2.1 Dataset......Page 195 2.3 Classification Protocol......Page 196 2.4 Optimal Balancing Protocol......Page 197 2.6 Performance Evaluation Metrics......Page 198 3 Result and Discussion......Page 199 4 Conclusion......Page 201 References......Page 204 1 Introduction......Page 206 2 Physical Model......Page 207 3 Mathematical Formulation......Page 208 5 Results and Discussion......Page 210 5.1 Flow and Temperature Field......Page 211 6 Conclusions......Page 215 References......Page 216 1 Introduction......Page 218 2 Statement of the Problem......Page 220 3.1 Finding Displacement in Anisotropic Inhomogeneous Layer......Page 221 3.2 Finding Displacement for Inhomogeneous Orthotropic Half-Space......Page 222 4 Boundary Conditions and Dispersion Equation......Page 224 5 Numerical Computations, Graphs, and Discussion......Page 226 6 Conclusion......Page 231 References......Page 232 1 Introduction and Mathematical Formulation of the Problem......Page 233 2 Method of Solution......Page 235 3 Upper and Lower Bounds for C......Page 237 4 Discussion of Numerical Results......Page 241 5 Conclusion......Page 243 References......Page 244 1 Introduction......Page 245 2 Lemmas......Page 247 3 Proof of the Main Results......Page 249 4 Remark......Page 254 References......Page 255 1 Introduction......Page 256 2.1 Joint Probability Distribution at Departure Epoch......Page 258 2.2 Joint Probability Distribution at Arbitrary Epoch......Page 260 4 Numerical Results......Page 264 5 Conclusion......Page 268 References......Page 269 21 A Fuzzy Random Continuous (Q,r,L) Inventory Model Involving Controllable Back-order Rate and Variable Lead-Time with Imprecise Chance Constraint......Page 270 1 Introduction......Page 271 2 Preliminaries......Page 273 3.1 Model and Assumptions......Page 274 3.2 Determination of the Expected Shortage......Page 278 3.3 Defuzzification of the Fuzzy Expected Total Cost Function Using Possibilistic Mean Value......Page 279 3.4 Crisp Equivalent Form of the Imprecise Chance Constraint......Page 281 4 Numerical Example......Page 282 References......Page 284 1 Introduction......Page 287 2 Unbiased Estimation and a Complete Class Result......Page 289 2.1 A Complete Class Result......Page 291 3 Asymptotic Confidence Interval for ξ......Page 292 4 Bayes Estimation......Page 294 4.1 Minimaxity and Admissibility of the Pitman Estimator......Page 295 5 Numerical Comparisons......Page 297 References......Page 298 1 Introduction......Page 300 1.2 Problem Statement......Page 301 2 Existence and Uniqueness of an Equilibrium Solution......Page 302 3 Numerical Results......Page 306 3.1 Example 1......Page 307 References......Page 308 1 Introduction......Page 309 2.1 Fractional Nabla Calculus......Page 310 2.2 Volterra Difference Systems......Page 311 3 Main Results......Page 313 References......Page 318 1 Introduction......Page 319 2 Hammerstein Integral Equations......Page 321 3 Convergence Rates......Page 325 4 Numerical Examples......Page 330 References......Page 331 1 Introduction......Page 333 2 Orlicz-Taylor Sequence Spaces......Page 335 3 Matrix Operators on Orlicz-Taylor Sequence Spaces......Page 338 3.1 Generalized Hausdorff Matrix Operator......Page 339 3.2 Nörlund Matrix Operator......Page 341 References......Page 343 1 Introduction......Page 344 2 Preliminaries......Page 346 3 Fuzzy Triangle......Page 348 4 Fuzzy Trigonometry......Page 355 5 Conclusion......Page 361 References......Page 362 1 Introduction and Background......Page 363 2 Definitions and Preliminaries......Page 364 3 Main Results......Page 366 References......Page 372 1 Introduction......Page 374 1.1 Cost of€Treatment......Page 375 2 Role of€an€NGO in€Health care......Page 376 3.2 Social Service Model......Page 377 4 Methodology......Page 378 5.1 Parameter Definition......Page 380 5.2 Problem Statement......Page 381 6 Objective Function......Page 382 7 Results and€Discussion......Page 383 8 Conclusions......Page 384 References......Page 385 1 Introduction......Page 387 2.1 The Graph Transformation System Bap:Hec......Page 388 2.2 FACSP (Fuzzy Artificial Cell Systems With Proteins On Membranes) Hel:Sar......Page 389 3.1 Molecular Representation of FACSP Using Graphs......Page 390 3.2 Critical Pair Analysis for FACSP......Page 391 4 Stochastic Graph Transformation System for FACSP......Page 394 4.1 Stoichiometric Matrix for FACSP......Page 395 4.2 Place Transition Net Representing FACSP Reaction Mechanism......Page 396 References......Page 397 1 Introduction......Page 399 2 Preliminaries......Page 401 2.3 Encryption Scheme......Page 402 3 Our Scheme......Page 403 3.1 Coping with VLR and Making the Scheme Secure......Page 404 3.2 Description of Our Scheme......Page 406 4 Security Notions of the Scheme......Page 408 4.1 The Oracles......Page 409 4.3 Anonymity......Page 411 4.5 Traceability......Page 412 5.2 Non-Frameability......Page 413 References......Page 414 1 Introduction......Page 416 2.1 Access Structure and Monotone Span Program......Page 418 2.2 Function Secret Sharing......Page 419 2.3 Basis Functions......Page 420 3.1 Shamir's Threshold Secret Sharing......Page 421 4 Our Proposal......Page 422 4.1 FSS Scheme for the Fourier Basis......Page 423 4.2 General FSS Scheme for Succinct Functions......Page 424 References......Page 426 1 Introduction......Page 428 2 The Model Problem and the Analytical Solution......Page 429 3 The NIPG Method......Page 431 4 Error Analysis......Page 433 5 Numerical Result......Page 438 References......Page 439 1 Introduction......Page 440 2 Preliminaries......Page 442 3 Nash Equilibrium Strategies for Bimatrix Games......Page 443 4 Numerical Example......Page 448 References......Page 450 1 Introduction......Page 452 2.2 Method of Solution to Singular Integral Equation on mathbbR with Cauchy-Type Kernel......Page 454 2.3 Evaluation of Matrix Element......Page 455 3.1 Transformation to the Finite Range of Integration......Page 456 3.2 Legendre Multiwavelets......Page 458 3.3 Multiscale Approximation of a Function......Page 459 3.4 Evaluation of Integrals......Page 460 3.5 Multiscale Representation of the Operator mathcalL......Page 462 4 Illustrative Examples......Page 463 5 Conclusion......Page 467 References......Page 468