Preface......Page 6
Contents......Page 12
1 Introduction......Page 14
2 Two Lemmas......Page 18
3 Main Results and Applications......Page 23
4 Operator Expressions and Some Examples......Page 32
References......Page 39
1 Introduction......Page 41
2 General Solution of Functional Equations (1), (2), (3) and (4)......Page 43
3 Stability of the Additive Functional Equation (1)......Page 46
4 Stability of the Quadratic Functional Equation (2)......Page 49
5 Stability of the Cubic Functional Equation (3)......Page 52
6 Stability of Quartic Functional Equation (4)......Page 55
7 Stability of Functional Equations (1), (2), (3) and (4) Using Fixed Point Method......Page 58
References......Page 70
1 Introduction and Preliminaries......Page 72
2 Statistically Weighted widetildemathcalNΔ(α,β)-Summability Based on Generalized (p, q)-Difference Operator......Page 75
3 Some Inclusion Relations......Page 80
4 Korovkin-Type Approximation Theorem......Page 86
5 Rate of Statistically Weighted widetildemathcalNΔ(α,β)-Summability of Double Sequences......Page 91
References......Page 94
1 Preliminaries......Page 97
2 Background of the Conjecture and the Work of Rainer Brück......Page 101
3 Brück's Conjecture for Functions of Finite Order and Extensions......Page 104
4 Brück's conjecture and Nevanlinna theory......Page 112
References......Page 130
Nonlinear Magneto-Elasticity: Direct and Inverse Problems......Page 133
1 Introduction......Page 134
2.1 Direct Problem......Page 135
2.2 Inverse Problem......Page 144
3.1 Direct Problem......Page 151
3.2 Inverse Problem......Page 160
References......Page 161
Note on Periodic and Asymptotically Periodic Solutions of Fractional Differential Equations......Page 162
2 No Periodics for FDEs with Finite Lower Limits......Page 163
3 S-Asymptotically Periodics for FDEs with Finite Lower Limits......Page 172
4 Periodic BVP for FDEs......Page 182
5 Periodics for FDEs with Infinite Lower Limits......Page 189
References......Page 193
Mathematics of Wavefields......Page 195
1 Introduction......Page 196
2.1 Some Basics......Page 197
2.2 Mean Value Theorem......Page 199
2.3 Improper Integral......Page 200
2.4 Domain Differentiation......Page 202
2.5 A Brief Resume of Generalized Functions......Page 204
2.6 The Fourier Transform......Page 209
2.7 Divergence and Green's Theorems......Page 211
3.1 The Scalar Equations......Page 212
3.2 Electromagnetics......Page 216
3.3 Green's Functions......Page 219
4.1 The Second Derivative of The Fundamental Solution......Page 229
4.2 Derivatives of The Potential......Page 232
5 A Brief Digression......Page 235
References......Page 237
1 Introduction......Page 240
2 Stationary Maxwell Equations Coupled with a Linear Constitutive Relation......Page 241
2.1 One Oscillating Microscale l(h)......Page 243
2.2 Two Oscillating Microscales l1(h) and l2(h)......Page 248
3 Stationary Maxwell Equations Coupled with a Power Law Constitutive Relation on Laminate Microstructures......Page 250
3.1 Examples......Page 256
4 Time-Dependent Maxwell Equations Coupled with Linear Constitutive Relations......Page 258
4.1 Example......Page 265
References......Page 272
The Narimanov–Moiseev Multimodal Analysis of Nonlinear Sloshing in Circular Conical Tanks......Page 274
1 Introduction......Page 275
2 Statement......Page 279
2.1 Free-Boundary Problem......Page 280
2.3 Bateman-Luke Variational Formulation......Page 281
2.4 Miles-Lukovsky Modal Equations......Page 282
3.1 Natural Sloshing Modes......Page 284
3.2 Alternative Form of the Miles-Lukovsky Modal Equations......Page 286
4 Generic Weakly-Nonlinear Modal Equations......Page 288
5.1 Modal Equations......Page 291
5.2 Secondary Resonances......Page 294
5.3 Steady-State (Periodic) Solutions and Their Stability......Page 295
5.4 Illustrative Response Curves......Page 301
6 Concluding Remarks......Page 302
A.1 Generalised Coordinate β0(t)......Page 303
A.2 Integrals AMip and Amir Defined by (28)......Page 304
A.3 Integrals ANK Defined by (29)......Page 306
A.4 Generalised Velocities PCd and Rcd......Page 308
A.5 Integrals li......Page 309
A.6 The d-, g-, t-Coefficients in (35)......Page 311
A.7 Coefficients of the Modal System (38)......Page 313
References......Page 315
1 Introduction......Page 317
2 The CIMA Reaction–Diffusion Model......Page 319
3 Stability of the Lengyel–Epstein System......Page 321
3.1 Local Stability in the ODE Sense......Page 322
3.2 Local Stability in the PDE Sense......Page 324
3.3 Turing Instability......Page 328
3.4 Activator–Inhibitor Nature......Page 331
3.5 Global Asymptotic Stability......Page 333
4.1 Hopf–Bifurcation Theory......Page 336
4.2 Hopf–Bifurcation of the Lengyel–Epstein Model......Page 340
5 Modified Lengyel–Epstein Systems......Page 342
6 Generalizations of the Lengyel–Epstein Model......Page 346
7 Numerical Results......Page 347
8 Open Problems......Page 350
References......Page 355
Abstract......Page 358
1 Introduction......Page 359
2 Related Works......Page 361
3 Problem Statement......Page 364
4 Method to Solve the Direct Bifurcation Problem......Page 367
5 The Existence of a Solution to the First Inverse Bifurcation Problem......Page 369
6 Method to Solve the First Inverse Bifurcation Problem......Page 371
7 Method to Solve the Second Bifurcation Problem......Page 373
8 Solutions of the First Inverse Bifurcation Problem......Page 376
9 Solutions of the Second Inverse Bifurcation Problem......Page 381
10 Conclusions and Directions of Future Research......Page 382
References......Page 383
1 Introduction......Page 387
2 Construction of Layer Adapted Meshes......Page 388
2.1 Bakhvalov Mesh......Page 389
2.2 Shishkin Mesh......Page 392
4 Discussion and Conclusion......Page 399
References......Page 407
Use of Galerkin Technique in Some Water Wave Scattering Problems Involving Plane Vertical Barriers......Page 409
1 Oblique Scattering by a Thin Vertical Barrier in Deep Water......Page 412
1.1 Mathematical Formulation of the Problem......Page 413
1.2 Method of Solution......Page 415
1.3 Upper and Lower Bounds for C......Page 417
1.4 Partially Immersed Vertical Barrier......Page 420
1.5 Submerged Barrier Extending Infinitely Downwards......Page 424
1.6 Oblique Scattering by a Thin Vertical Plate......Page 430
References......Page 435
Dynamics of a Class of Leslie–Gower Predation Models with a Non-Differentiable Functional Response......Page 437
1 Introduction......Page 438
2 The Model......Page 440
3 Main Results......Page 443
3.1 Case 1: Kolmogorov Type System......Page 444
3.2 Case 2: Non-Kolmogorov Type System......Page 450
4 Numerical Simulations......Page 454
5 Conclusions......Page 458
References......Page 460
1 Context and the Diffusion Model......Page 462
2 Radial Symmetry of Solutions to Diffusion Systems and Historical Notes......Page 466
3 Statement of the Problem......Page 468
4 The Mathematical Results......Page 471
5 The Arzelà–Ascoli Theorem......Page 474
6.1 The Solvability of the System with no Boundary Conditions......Page 475
8 Open Problem......Page 485
References......Page 486
Abstract......Page 489
2 Background: Multiple Objective Programming......Page 490
3 Goal Programming Models: Some of the Existing Variants......Page 491
3.2 Stochastic Goal Programming......Page 492
3.4 Other GP Variants......Page 495
4.1 A SGP Model with Satisfaction Function for Portfolio Management......Page 496
4.2 Strategic Marketing Decisions Using GP with Satisfaction Function......Page 501
4.3 Media Campaign Strategy Using GP with Satisfaction Function......Page 505
References......Page 507
Modeling Highly Random Dynamical Infectious Systems......Page 510
1 Introduction......Page 511
2 Derivation of Stochastic and Deterministic Models......Page 515
2.1 Deterministic Model......Page 516
2.2 Stochastic Model......Page 520
3 Existence and Uniqueness of Solution......Page 524
4 Existence and Stability of Equilibrium......Page 531
4.1 Existence of Equilibrium......Page 532
4.2 Stability of Equilibrium......Page 534
5 Asymptotic Behavior of the System Subjected Under Various Orders for the Intensities of Noise......Page 554
6.1 Example 1: The Effect of the Intensity of the White Noise Process on Disease Eradication......Page 563
6.2 Example 2: Effect of the Intensity of White Noise on the Trajectories of the System......Page 564
7 Conclusion......Page 576
References......Page 578
1 Introduction......Page 580
2 Preliminaries......Page 583
3 Fatou Type Convergence......Page 587
4 Rate of Pointwise Convergence......Page 601
References......Page 602
1 Introduction......Page 605
1.1 Preview and Motivation......Page 606
1.2 Overview......Page 607
2.2 p-Adic Analysis on mathbbQp......Page 608
3 Analysis on mathcalMp......Page 611
4 Representations of ( mathcalMp, p)......Page 613
5 Analysis on Mp......Page 615
6 Semigroup C-Subalgebras mathfrakSp of Mp......Page 617
7 Weighted-Semicircular Elements......Page 619
7.1 Semicircular and Weighted-Semicircular Elements......Page 620
7.2 Tensor Product Banach -Algebra mathfrakLSp......Page 622
7.3 Weighted-Semicircular Elements Qp,j in mathfrakLSp......Page 625
8 Semicircularity on mathfrakLS......Page 627
9.1 Circular Elements......Page 630
9.2 Circular Elements in mathfrakLS......Page 631
9.3 Free Distributions of Circular Elements: The Circular Law......Page 642
10 Weighted-Circular Elements of mathfrakLS Induced by mathcalQ......Page 643
11 From Numbers to the Circular Law......Page 651
References......Page 653
On Statistical Deferred Weighted mathcalB-Convergence......Page 655
1 Introduction......Page 656
2 Definitions and Regular Methods......Page 660
3 A Korovkin-Type Theorem......Page 665
4 Rate of the Deferred Weighted mathcalB-Statistical Convergence......Page 671
5 Concluding Remarks......Page 675
References......Page 677
1 Introduction......Page 679
2 Poly-Bernoulli Numbers and Polynomials with Parameters a, b, c......Page 689
3 Poly-Euler Numbers and Polynomials with Parameters a, b, c......Page 698
4 Multi Poly-Bernoulli Numbers and Polynomials with Parameters a, b, c......Page 705
5 Multi Poly-Euler Numbers and Polynomials with Parameters a, b, c......Page 711
References......Page 719
Geometric Properties of Normalized Wright Functions......Page 722
1 Introduction and Preliminaries......Page 723
1.1 Preliminaries......Page 724
2 Sufficient Conditions for the Normalized Wright Functions......Page 726
3 Sufficient Conditions for the Integrals Involving Normalized Wright Functions......Page 735
4 Close-to-Convexity of Normalized Wright Functions......Page 741
4.1 Sufficient Conditions for the Class K(α,β)......Page 744
5 Some Integral Operators of Normalized Wright Functions......Page 751
6 Univalence of Certain Integral Operators Involving Normalized Wright Functions......Page 758
7 More on Univalence of Integral Operators Involving Wright Functions......Page 770
8 Applications of a Poisson Distribution Series on the Analytic Functions......Page 778
8.1 Some Integral Operators Involving the Functions F(p,z) and G(p,z)......Page 784
References......Page 787
1 Introduction, Preliminaries and Definitions......Page 790
2 Main Results......Page 798
References......Page 808