Mathematical Analysis and Its Applications (eBook)

Proceedings of the International Conference on Mathematical Analysis and its Applications, Kuwait, 1985

N. S. Faour, A. Hamoui, S. M. Mazhar (Herausgeber)

eBook Download: PDF

2014 | 1. Auflage
442 Seiten
Elsevier Science (Verlag)
978-1-4831-4811-3 (ISBN)

Infos

Mathematical Analysis and its Applications covers the proceedings of the International Conference on Mathematical Analysis and its Applications. The book presents studies that discuss several mathematical analysis methods and their respective applications. The text presents 38 papers that discuss topics, such as approximation of continuous functions by ultraspherical series and classes of bi-univalent functions. The representation of multipliers of eigen and joint function expansions of nonlocal spectral problems for first- and second-order differential operators is also discussed. The book will be of great interest to researchers and professionals whose work involves the use of mathematical analysis.

Inhalt

Front Cover 1
Mathematical Analysis and its Applications 4
Copyright Page 5
Table of Contents 10
Organizing Committee 6
Preface 8
CHAPTER 1. AN ESTIMATE FOR THE RATE OF CONVERGENCE OF A GENERAL CLASS OF ORTHOGONAL POLYNOMIAL EXPANSIONS OF FUNCTIONS OF BOUNDED VARIATION 14
REFERENCES 29
CHAPTER 2. AN ESTIMATE OF THE RATE OF CONVERGENCE OF CESARO MEANS OF FOURIER SERIES OF FUNCTIONS OF BOUNDED VARIATION 30
REFERENCES 35
CHAPTER 3. APPROXIMATION OF CONTINUOUS FUNCTIONS BY ULTRASPHERICAL SERIES 36
REFERENCES 41
CHAPTER 4. MODIFIED SZASZ OPERATORS 42
1. Introduction 42
2. Auxiliary Results 42
3. Main Results 45
REFERENCES 54
CHAPTER 5. APPROXIMATION BY WALSH SERIES 56
1. Introduction 56
2. Definitions and Notations 57
3. The Degree of Approximation by De la Vallée Poussin Mean of Walsh Fourier series 58
4. Identification of the space 61
5. Conclusion 64
REFERENCES 64
CHAPTER 6. ON SOME CLASSES OF BI-UNIVALENT FUNCTIONS 66
1. Introduction 66
2. The Class Ss[.] 66
3. The Class Ss(ß) 69
4. The Class Cs(ß) 71
REFERENCES 73
CHAPTER 7. SOME APPLICATIONS OF GENERALIZED CALCULUS TO DIFFERENTIAL AND INTEGRO DIFFERENTIAL EQUATIONS 74
1. SOME EQUIVALENCE PROPERTIES 75
2. SOME METHODS OF SOLUTIONS AND PARTICULAR EQUATIONS OF SPECIAL FUNCTIONS 82
REFERENCES 89
CHAPTER 8. A BOUNDARY VALUE PROBLEM FOR HEAT AND MASS TRANSFER IN POROUS MEDIA 90
Introduction 90
1. The System of Equations Governing Heat and Mass Transfer in Porous Media 91
2. Transformation of Equations 94
3. Generalized Solutions of System I 96
4. Generalized Solutions of the Regularized System I ,eh 98
5. Existence of a Generalized Solution of Ieh 100
6. THEOREM (Compactness principle) (see [1]) 102
7. Apriori Estimates and Passage to the Limit with Respect to h 107
8. Apriori Estimates and Passage to the Limit with Respect to e 110
REFERENCES 113
CHAPTER 9. REPRESENTATION OF MULTIPLIERS OF EIGEN AND JOINT FUNCTION EXPANSIONS OF NONLOCAL SPECTRAL PROBLEMS FOR FIRST AND SECOND ORDER DIFFERENTIAL OPERATORS 114
1. Preliminaries 114
2. Multipliers Connected with First Order Differential Operators 117
3. Multipliers Connected with Second Order Differential Operators 124
REFERENCES 130
CHAPTER 10. COMPARISON METHODS FOR EIGENVALUES OF SEMILINEAR ELLIPTIC OPERATORS 132
REFERENCES 137
CHAPTER 11. RÉGULARITÉ DES SOLUTIONS DE L'EQUATION DES MILIEUX POREUX EN UNE DIMENSION D'ESPACE 138
Introduction 138
I. - Position du problème et notation 139
2 . - Solutions Régulières et Estimations à priori 142
3 . - Existence, Unicité et Régularité de la Solution de (C) 150
BIBLIOGRAPHIE 154
CHAPTER 12. THE SMOOTHNESS OF THE HEAT EQUATION SOLUTION IN A SINGULAR DOMAIN OF Rn+1 156
1. Introduction 156
2. The Study of the Regularized Problem 157
3. Proof of Theorem 1 160
REFERENCES 162
CHAPTER 13. SEQUENCES OF FOURIER–YOUNG COEFFICIENTS OF A FUNCTION OF WIENER'S CLASS 164
1. Introduction 164
REFERENCES 170
CHAPTER 14. MULTIPLIERS AND ISOMETRIES OF ORLICZ SPACES 172
1. Introduction 172
2. Multipliers of L. 173
3. Multiplication Isometries of L. 174
4. Isometries of L. 175
REFERENCES 178
CHAPTER 15. CONE ABSOLUTELY (p,q) — SUMMING OPERATORS FROM BANACH LATTICES TO BANACH SPACES AND THEIR ADJOINTS 180
1. Introduction 180
2. Banach Space–Valued Sequence Spaces 181
3 . Lattice Summable Sequences from a Banach Lattice 182
4. Cone Absolutely (p,q) — Summing and (p,q) — Majorising Operators 185
REFERENCES 187
CHAPTER 16. THE STABILITY OF LINEAR MAPPINGS ANDSOME PROBLEMS ON ISOMETRIES 188
1 . The Stability of Linear Mappings in Banach Spaces 188
2. Isometries 193
REFERENCES 197
CHAPTER 17. GLOBAL THEORIES OF THE LINEARIZING PROJECTION WITH APPLICATIONS 198
1. Introduction 198
2. The Polynomial Theory 200
REFERENCES 207
CHAPTER 18. ON ONE-PARAMETER GROUPS OF AUTOMORPHISMS OF VON NEUMANN ALGEBRAS 208
1 . Introduction and Background 208
2. Results 209
REFERENCES 211
CHAPTER 19. ON THE EULER–MACLAURIN SUMMATION FORMULA FOR ALTERNATING SERIES AND A NEW PROOF OF THE FUNCTIONAL EQUATION FOR .(x) 212
1. Introduction 212
2. The Euler-Maclaurin Formula for Alternating Series 213
3. The Theta-Series T(x) 216
REFERENCES 223
CHAPTER 20. A FINITE ELEMENT APPROACH TO NONLINEAR TRANSIENT PROBLEMS 224
1. Introduction 224
2. The Features of the General Model 226
3. The Finite Element Technique 227
4. A Quasi-Linear Convection Dominated Diffusion Equation 229
5. Nonlinear Diffusion-Reaction Problem 231
6. Quasi–Linear Advection–Diffusion Equation 233
7. Discussion 237
8. Conclusions 239
REFERENCES 240
CHAPTER 21. NUMERICAL SOLUTION OF MULTI-DIMENSIONAL STEFAN PROBLEM 242
1. Introduction 242
2. Statement of the First Problem 243
3. Statement of the Second Problem 248
4. Analysis of the Method 249
5. Conclusion 253
REFERENCES 254
CHAPTER 22. A SELF-CONSISTENT FINITE-DIFFERENCE TREATMENT OF THE MOVING BOUNDARY FOR LONG WAVES IN SHALLOW WATER 256
1. Introduction 256
2. Study of the Unidimensional Case 257
3. The Algorithm of Solution 258
4. Numerical Results 260
5. Conclusion 261
REFERENCES 261
CHAPTER 23. RATIONAL AND POLYNOMIAL APPROXIMATIONS FROM ULTRASPHERICAL SERIES FOR LINEAR DIFFERENTIAL EQUATIONS 264
1. Introduction 264
2. Solution of Linear Differential Equations in Ultraspherical Polynomials 267
3. Extension of the Method in the Complex Domain 269
4. Numerical Example 270
5 Conclusion 272
REFERENCES 273
CHAPTER 24. THE ASYMPTOTIC BEHAVIOUR OF SOME SEMI-DISCRETE AND FULLY-DISCRETE FINITE ELEMENT SCHEMES FOR THE EVOLUTION NAVIER-STOKES EQUATIONS 274
1. Introduction 274
2. Proof of Theorem 1 277
3. Proof of Theorem 2 278
REFERENCES 280
CHAPTER 25. ITERATIONS D'ALGORITHMES D'ACCELERATION DE LA CONVERGENCE 282
Abstract 282
RESUMÉ 282
Introduction 282
1 Notations et Définitions 283
2. Presentation du Probleme 284
3. Resultats Theoriques 284
4. Applications 286
5. Resultats Numériques 288
BIBLIOGRAPHIE 292
CHAPTER 26. A THIRD ORDER FINITE-DIFFERENCE METHOD FOR TWO DIMENSIONAL PARABOLIC EQUATIONS 294
1. Introduction 294
2. Third Order L0–Stable Method 295
3. Numerical Results 298
4. Discussion 300
REFERENCES 300
CHAPTER 27. A PARALLEL ASYNCHRONOUS RELAXATION ALGORITHM FOR OPTIMALCONTROL PROBLEMS 302
1. Introduction 302
2. General Formulation of the Problem 303
3. Sequential Algorithm: Costate Relaxation Method 304
4. Parallel Asynchronous Algorithm : Costate Relaxation Method with 304
5. Convergence Analysis 307
6. Application to Optimal Control Law Computation of a Thermic Process 313
7. Extension to more General Cases 314
REFERENCES 314
CHAPTER 28. ON THE VALIDITY AND STABILITY OF THE METHOD OF LINES FOR THE SOLUTION OFPARTIAL DIFFERENTIAL EQUATIONS 316
1. Introduction 316
2. MOL Applied to Elliptic Equations 317
3. Relation between Analytic Solution and MOL Solution 320
4. Effect of Increasing the Number of Lines N 322
5. Conclusion 323
REFERENCES 323
CHAPTER 29. CAUSALITY IN ALGORITHMS AND ARCHITECTURES 324
1. Introduction 324
2. Schedules 325
3. Algorithms 326
4. Architectures 330
5. Scheduling Algorithms in Architectures 331
6. Fundamental Algorithms and Architectures 335
REFERENCES 341
CHAPTER 30. SOME RESULTS ON FINITE-ELEMENT APPROXIMATION OF A QUASI-VARIATIONAL IN EQUALITY INSEMI-CONDUCTOR ANALYSIS 342
1. Introduction 342
2. The Semi-Conductor Model and the Finite–Element Approximation. Existence of the Galerkin Solution 343
3. Error Estimate 346
REFERENCES 348
CHAPTER 31. ASYNCHRONOUS ALGORITHMS FOR HEAT CONDUCTION IN COMPOSITE MEDIA 350
1. Introduction 350
2. Mathematical Formulation 351
3. The Method of Lines and Invariant Imbedding. 352
4. Associated Fixed Point Problem and Iterative Algorithms 355
5. Numerical Results and Conclusion 358
REFERENCES 361
CHAPTER 32. Lo-STABLE METHODS FOR CONSTANT COEFFICIENT PARABOLIC EQUATIONS 362
1. Introduction 362
2. A Second Order Method and its Extrapolation 364
3. A Third Order Method and its Extrapolation 366
4. Two Fourth Order Methods 367
5. Numerical Results 369
6. Summary 371
REFERENCES 371
CHAPTER 33. FINITE ELEMENT CALCULATION OF A PATH INTEGRAL FOR NONLINEAR FRACTURE 372
1. Introduction 372
2. Jp-integral 372
3. Calculation of the J -integral 373
4. Application to Crack Problems with Strain Hardening. 375
REFERENCES 378
CHAPTER 34. NUMERICAL TREATMENT OF SOME MATHEMATICAL MODELS DESCRIBING LONG-RANGE TRANSPORT OF AIR POLLUTION 380
1. Description of a General Air Pollution Model 381
2. Splitting of the General Air Pollution Model 383
3. Efficient Numerical Treatment of the Advection Part of the General Model 387
4. Numerical Results 393
REFERENCES 394
CHAPTER 35. FUNCTIONS MOYENNE-PERIO DI QUES ASSOCIEES A UN OPERATEUR DIFFERENTIEL DANS LE DOMAINE COMPLEXE 398
Introduction 398
I. Transformation de Fourier-Borel et Produit de Convolution associés à l'Opèrateur L 400
2) Transformation de Fourier-Borel généralisée et théoréme de Paley-Wiener associés à . Opérateur L 401
3 ) Produit de convolution généralisé associé . . 'Operateur L 402
BIBLIOGRAPHIE 414
CHAPTER 36. ON AN APPLICATION OF REGULAR VARIATION IN PROBABILITY THEORY 416
REFERENCES 423
CHAPTER 37. HILBERT SPACE STRUCTURE ON THE SOLUTION SPACE OF HELMHOLTZ EQUATION 424
1. Introduction 424
2. Canonical Form 425
3. Imbedding of the J-Function 427
4. A New Basis for Functions on the Plane 428
REFERENCES 431
CHAPTER 38. TEACHING THE ART OF APPLYING MATHEMATICS 434
REFERENCES 443

Produkt-Details

• Erscheint lt. Verlag: 17.5.2014
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Technik
• ISBN-10: 1-4831-4811-4 / 1483148114
• ISBN-13: 978-1-4831-4811-3 / 9781483148113