Preface......Page 6
Acknowledgements......Page 8
Contents......Page 10
About the Editors......Page 14
Optimal Strategies of the Psoriasis Treatment by Suppressing the Interaction Between T-Lymphocytes and Dendritic Cells......Page 16
2 Optimal Control Problem......Page 17
3 Pontryagin Maximum Principle......Page 19
4 Properties of the Switching Function......Page 20
5 Numerical Results......Page 23
6 Conclusions......Page 24
References......Page 26
1 Introduction......Page 27
2 Theoretical Part......Page 28
3 Identification of Dominant Subnetworks......Page 31
4 Determination of Parameters Based on Stoichiometric Constraints......Page 32
4.1 Formulation of the Constraint Equations......Page 34
4.2 Solving the Constraint Equations......Page 35
References......Page 36
1 Introduction......Page 38
2 Preliminaries......Page 39
3 Main Results......Page 40
References......Page 45
Impact of Tobacco Smoking on the Prevalence of Tuberculosis Infection: A Mathematical Study......Page 46
2 Model Formulation......Page 47
3 The Basic Reproduction Number and Existence of Equilibria......Page 50
4 Stability Analysis......Page 51
5 Numerical Simulation......Page 55
6 Optimal Control Problem......Page 58
7 Simulation of Optimal Control Model......Page 60
8 Discussion......Page 61
9 Conclusion......Page 63
References......Page 64
Modelling the Effects of Stigma on Leprosy......Page 65
1 Introduction......Page 66
2 The Model......Page 68
3.1 Equilibria......Page 71
3.2 Basic Reproduction Number......Page 73
4 Numerical Simulations......Page 74
5 Discussion......Page 78
References......Page 79
1 Introduction......Page 81
2 Lotka-Volterra Models of Interacting Species......Page 83
2.1 Analysis of the Models of Interacting Species......Page 84
2.2 Illustration of the Interacting Species Models Dynamics......Page 85
3 Influence Function Depending on One Variable Only......Page 86
3.1 Analysis of System (4)......Page 87
3.2 Illustration of the Dynamics of System (4)......Page 88
4 Influence Function of the Form xig(xixj)......Page 92
4.1 Analysis and Illustration of the Model Dynamics for the Case Considered by Foryś et al. ch6complexity......Page 93
5 Conclusions......Page 94
References......Page 95
Reliability Analysis of Multi-state Two-Dimensional System by Universal Generating Function......Page 96
1 Introduction......Page 97
2.2 Universal Generating Function......Page 98
2.4 Mean Time to Failure......Page 99
3 Reliability, MTTF and Component’s Sensitivity Analysis of Two Dimensional System by UGF......Page 100
4 Illustration......Page 103
4.1 Reliability......Page 104
5 Conclusion......Page 107
References......Page 110
1 Introduction......Page 112
2 Basic Definitions and Terminologies......Page 113
3.1 Examples of Genuine Quantum Symmetries of Classical Non-smooth Spaces......Page 115
4 The No-go Results and Open Questions for Quantum Symmetries on Smooth Spaces......Page 116
References......Page 118
1 Introduction......Page 120
1.1 Groups as Geometric Objects......Page 121
2 Quasi-isometric Rigidity......Page 123
2.1 Lattices in Semisimple Lie Group......Page 125
References......Page 127
Existence of Compositional Square-Roots of Functions......Page 128
2 Square Roots of Bijections......Page 129
3 Its All About the Domain......Page 132
References......Page 134
On Generalized Statistical Convergence and Strongly Summable Functions of Weight g......Page 135
1 Definition and Preliminaries......Page 136
2 Main Results......Page 137
References......Page 142
1 Introduction......Page 143
3 Main Definitions and Results......Page 145
References......Page 153
1 Introduction......Page 155
2 Stability Results......Page 157
References......Page 159
1 Introduction......Page 160
2 Technical Preliminaries......Page 163
3 Union of Balls......Page 164
4 Compact Subsets of Certain Real Analytic Variety......Page 167
References......Page 170
Solution of Large-Scale Multi-objective Optimization Models for Saltwater Intrusion Control in Coastal Aquifers Utilizing ANFIS Based Linked Meta-Models for Computational Feasibility and Efficiency......Page 171
1 Introduction......Page 172
2.1 Numerical Model......Page 173
2.3 Management Model......Page 174
3 Application of the Developed Methodology......Page 175
4.1 Performance of ANFIS Meta-Models......Page 176
4.2 Management Model Performance......Page 177
References......Page 178
1 Introduction......Page 180
2.1 Specifications of Demand Response Participants......Page 181
2.2 Objective Function......Page 182
3 Particle Swarm Optimization......Page 183
4 Results and Discussions......Page 186
4.2 Case 1B......Page 188
4.3 Case 2A......Page 189
4.4 Case 2B......Page 190
References......Page 191
1 Introduction......Page 193
2 Model Description......Page 194
3 Boundedness......Page 196
4 Global Exponential Stability......Page 197
5 Numerical Simulations and Results......Page 199
6 Conclusions......Page 201
References......Page 202
1 Introduction......Page 203
2 DNA as a Spin Chain......Page 205
3 Topological Properties of a DNA Molecule......Page 207
References......Page 212
1 Introduction......Page 214
1.1 Importance of Microphytobenthos......Page 215
2.1 Nitrogen Uptake by Microphytobenthos......Page 216
3 Factors Affecting Microphytobenthos Productivity......Page 217
4.1 Mechanisms of BPC......Page 218
5 Microphytobenthos and Benthic Pelagic Coupling......Page 219
6 Microphytobenthos Dynamics (Modelling Approach)......Page 220
7 Modelling Studies Focusing on Both MPB and BPC......Page 223
9 Future Prospects......Page 224
References......Page 225
Overview of Ecological Economics and Ecosystem Services Consequences from Shrimp Culture......Page 230
2 Mari-Culture as New Form of Aquaculture......Page 231
4 Ecosystem Services and Ecological Economics......Page 232
4.1 Forms of Ecosystem Services......Page 233
4.2 Valuation of Services Provided by the Ecosystem......Page 234
5 Farmer's Manipulation in Shrimp Culture......Page 235
6 Alteration of Ecosystem Services by Shrimp Culture......Page 236
7 Eco-Economic Analysis of Loss of Ecosystem Services and Economic Gain by Shrimp Culture......Page 237
8 Ecosystem Service, Ecological Economics, Policy Making and Ecosystem Based Fisheries Management (EBFM)......Page 238
9 Conclusion......Page 239
References......Page 240
Recent Trends of Ecosystem Health and Biodiversity Status of Pelagic-Benthic Coupled System in Indian Estuaries with Special Emphasis on Hooghly Estuary, India......Page 242
1 Introduction......Page 243
2 Studies on Indian Estuaries......Page 244
3 Hooghly Estuary......Page 245
4 Modelling Studies on Ecosystem Health and Biodiversity Status of Hooghly Estuary, India......Page 247
4.1 Process Based Dynamic Modelling Approaches......Page 248
4.2 Static Modelling Approaches Regarding Ecosystem Health......Page 249
5 Future Prospects......Page 251
References......Page 253
Guanotrophication by Waterbirds in Freshwater Lakes: A Review on Ecosystem Perspective......Page 257
1 Introduction......Page 258
2 Faecal Matter Analysis......Page 259
3 Effect of Nutrient Loading by Waterbird on Water Quality......Page 261
4.2 Phosphorus Loading Model by Gremillion and Malone ch22sps20......Page 263
4.4 Bioenergetics Model by Hahn et al. ch22sps3,ch22sps15......Page 264
6 Factors Affecting Allochthonous Nutrient Input by Waterbirds......Page 265
8.1 Cycling of Nitrogen......Page 266
8.2 Cycling of Phosphorous......Page 268
9 Conclusion......Page 269
References......Page 270
1 Introduction......Page 274
2 Model Principle......Page 275
3 Empirical Analysis......Page 277
4 Conclusion......Page 280
References......Page 281
1 Introduction......Page 282
2 The Mathematical Model with Diffusion and Its Analysis......Page 284
3 Analysis in Presence of Diffusion of the System (2.2): Turing Bifurcation......Page 287
4 Numerical Simulation Results: Spatiotemporal Pattern......Page 288
4.1 The Effect of Unequal Diffusion Coefficients d1 and d2......Page 289
4.3 The Effect of m in Absence of Harvesting......Page 290
5 Conclusion and Discussion......Page 291
References......Page 294
1 Introduction......Page 296
2 Notations and Assumptions......Page 298
3.1 Retailer's Perspective......Page 299
3.2 Manufacturer's Perspective......Page 302
3.3 Integrated Supply Chain......Page 303
4 Model Analysis......Page 304
5 Numerical Results......Page 305
6 Sensitivity Analysis......Page 306
References......Page 308
1 Introduction......Page 310
2 Formulation of the Model with Proper Justification......Page 312
3 Rescaled Model......Page 314
4 Stability Analysis......Page 315
5 Numerical Simulation and Discussion of the Results......Page 316
References......Page 321
1 Introduction......Page 322
2 The Main Results......Page 324
3 Numerical Simulations and Conclusion......Page 328
References......Page 331
1 Introduction......Page 333
2 Non-cooperative N-person Finite Semi-Markov Games......Page 334
3 Action Independent Transition Semi-Markov Games......Page 340
References......Page 344
1 Introduction......Page 346
2 Notations and Definitions......Page 348
2.1 System of Multivariate Polynomial Equalities and Inequalities in the Max Algebra......Page 349
2.2 Max Algebraic Linear System and Set Covering Problem......Page 350
3 Max Version of Various Optimization Problem......Page 351
3.2 Convex Quadratic Programming......Page 352
3.3 Linear Fractional Programming Problem......Page 353
3.4 Computation Nash Equilibrium Pair in Bimatrix Games Using Max-Plus Algebra......Page 355
4 Application of Max Plus Algebra in Stochastic Games......Page 356
5 Discounted Switching Controller Stochastic Games......Page 359
6 Conclusion......Page 360
References......Page 361
1 Introduction......Page 363
2 Mathematical Model Derivation......Page 364
3 Dynamics of the System......Page 365
4 Numerical Simulation......Page 368
References......Page 370
1 Introduction......Page 371
2 Assumptions and Notations......Page 373
3.1 Buyer's Perspective......Page 374
3.2 Vendor's Perspective......Page 376
4 Numerical Illustration......Page 379
4.1 Sensitivity Analysis......Page 381
5 Conclusions......Page 382
References......Page 383
1 Introduction......Page 384
2.1 General Model Formulation with Suitable Assumptions......Page 386
2.2 Linear Functional Response......Page 387
2.3 Hyperbolic Functional Response......Page 389
3 Numerical Simulation and Discussion......Page 391
4 Conclusion......Page 395
References......Page 400
Global Dynamics of a TB Model with Classes Age Structure and Environmental Transmission......Page 401
1 Introduction......Page 402
2 The Model......Page 403
3 Equilibria and Their Local Stability......Page 408
4 The Uniform Strong Persistence of TB Bacteria......Page 414
5 Global Stability of the Disease-Free Equilibrium......Page 430
6 Global Stability of the Endemic Equilibrium......Page 434
7 Discussion......Page 443
References......Page 444
1 Introduction......Page 446
2 Geometry of Space-Time......Page 447
3 Initial Value Formulation and Gravitational Radiation......Page 448
4 Linearized and Post-Newtonian Approximation of Einstein Equations: Gravitational Waves......Page 450
5 Numerical Techniques......Page 452
6 Summary of GW Detection......Page 453
References......Page 454
Current Trends in the Bifurcation Methods of Solutions of Real World Dynamical Systems......Page 455
1 Introduction......Page 456
2.1 Poincaré Map and Displacement Function......Page 457
2.2 Hopf Bifurcation and Lyapunov Coefficients......Page 458
2.3 Reduction to the Center Manifold and the Hopf Bifurcation......Page 461
3 Turing Bifurcation......Page 469
4 Zip Bifurcation for ODE Systems Without Delay......Page 477
5 Zip Bifurcation for ODE Systems with Delay......Page 481
6 Zip Bifurcation for Reaction Diffusion Systems Without Delay......Page 484
7 Zip Bifurcation for Reaction Diffusion Systems with Delay......Page 486
8 Zip Bifurcation for Reaction Diffusion Systems with Cross-Diffusion......Page 487
8.2 Analysis of Equilibria for Model (68) on the Line LK......Page 489
References......Page 491
1 Introduction......Page 494
2 Proposed Scheme in Two Dimensions......Page 496
2.1 Numerical Illustration in Two Dimension......Page 497
3 Extension to n-Dimension......Page 499
4 Convergence Analysis of the Proposed Scheme......Page 500
5 Numerical Illustration......Page 502
References......Page 505
1 Introduction......Page 506
2 Preliminaries......Page 507
2.2 Fuzzy Logistic Prey-Predator Model......Page 509
5 Dimensionless of the Logistic Model......Page 510
6.1 Stability Analysis of System in Crisp Environment......Page 511
6.2 Logistic Prey-Predator Model in Fuzzy Environment......Page 512
7 Numerical Example......Page 515
8 Conclusion......Page 516
References......Page 518