Mathematical Modelling in Science and Technology (eBook)

The Fourth International Conference, Zurich, Switzerland, August 1983

Xavier J.R. Avula, Rudolf E. Kalman, Anthanasios I. Liapis (Herausgeber)

eBook Download: PDF

2014 | 1. Auflage
1022 Seiten
Elsevier Science (Verlag)
978-1-4831-9059-4 (ISBN)

Infos

Mathematical Modelling in Science and Technology: The Fourth International Conference covers the proceedings of the Fourth International Conference by the same title, held at the Swiss Federal Institute of Technology, Zurich, Switzerland on August 15-17, 1983. Mathematical modeling is a powerful tool to solve many complex problems presented by scientific and technological developments. This book is organized into 20 parts encompassing 180 chapters. The first parts present the basic principles, methodology, systems theory, parameter estimation, system identification, and optimization of mathematical modeling. The succeeding parts discuss the features of stochastic and numerical modeling and simulation languages. Considerable parts deal with the application areas of mathematical modeling, such as in chemical engineering, solid and fluid mechanics, water resources, medicine, economics, transportation, and industry. The last parts tackle the application of mathematical modeling in student management and other academic cases. This book will prove useful to researchers in various science and technology fields.

Inhalt

Front Cover 1
Mathematical Modelling in Science and Technology: The Fourth International Conference 4
Copyright Page 5
Table of Contents 6
THE FOURTH INTERNATIONAL CONFERENCE ON MATHEMATICAL MODELLING 14
FOREWORD 16
PART I: INVITED GENERAL LECTURES 18
CHAPTER 1. DETERMINISTIC CONTROL OF UNCERTAIN SYSTEMS 18
Abstract 18
Keywords 18
INTRODUCTION 18
UNCERTAINTIES WITH KNOWN BOUNDS 19
UNCERTAINTIES WITH UNCERTAIN BOUNDS 21
REFERENCES 22
CHAPTER 2. THE USE OF INTERACTIVE GRAPHICS IN THE ANALYSIS AND DESIGN OF COMPLEX FEEDBACK SYSTEMS 27
Abstract 27
Keywords 27
INTRODUCTION 27
COGNITIVE ASPECTS OF INTERACTIVE COMPUTING 27
COMPUTER-AIDED DESIGN PACKAGES 28
CONTROL STRUCTURES AND CAD 28
USE OF PARAMETER GROUP DECOMPOSITIONS TO GENERATE NYQUIST-TYPE LOCI 29
FRAME ALIGNMENT AND NORMALITY 29
CONCLUSION 31
REFERENCES 31
CHAPTER 3. GENERAL SOFTWARE FOR COMPUTER-AIDED SYNTHESIS OF CONTROL FOR MANIPULATION ROBOTS 33
Abstract 33
Keywords 33
INTRODUCTION 33
I BLOCK FOR SETTING DATA ON MANIPULATOR CONFIGURATION 36
II BLOCK FOR CALCULATING DESIRED KINEMATIC TRAJECTORY 36
III BLOCK FOR SETTING DYNAMIC PARAMETERS 37
IV BLOCK FOR SETTING DATA ON ACTUATORS 37
V BLOCK FOR SYNTHESIS OF NOMINAL DYNAMICS 37
VI BLOCK FOR SETTING CONTROL TASK 38
VII BLOCK FOR SYNTHESIS OF LOCAL CONTROL 38
VIII BLOCK FOR STABILITY ANALYSIS 38
IX BLOCK FOR GLOBAL CONTROL SYNTHESIS 39
X BLOCK FOR TIME-DISCRETE CONTROL SYNTHESIS 39
XI BLOCK FOR SIMULATION 40
EXAMPLE 40
REFERENCES 42
CHAPTER 4. MULTICRITERION DECISIONS IN SYSTEMS WITH FEEDBACK 43
Abstract 43
Keywords 43
INTRODUCTION 43
TWO EXAMPLES OF HIERARCHIES 43
QUESTIONS TO ASK 46
HIERARCHIES WITH CYCLES 46
SYSTEMS WITH FEEDBACK 47
REFERENCES 53
CHAPTER 5. MATHEMATICAL MODELING AND LONG RANGE PLANNING 54
Abstract 54
Keywords 54
INTRODUCTION 54
LONG RANGE PLANNING IN UNCERTAIN TIMES 55
LONG RANGE PLANNING AND MATHEMATICAL MODELING 57
DOW JONES INDUSTRIALS (16 YEAR TIME HORIZON) 59
REFERENCES 60
CHAPTER 6. MODELING AND IDENTIFICATION 61
Abstract 61
CHAPTER 7. STATISTICAL METHODS FOR EXPERIMENTAL PLANNING IN CHEMICAL ENGINEERING 62
Abstract 62
PART II: METHODOLOGY 63
CHAPTER 8. DIRECT COMPUTER MODELING 63
Abstract 63
Keywords 63
INTRODUCTION 63
2. THE GENERAL ALGORITHM 63
3. TEMPERATURE WAVES IN A HEATED BAR 64
4. FREE SURFACE LIQUID MOTION 64
5. MODELS WITH SELF-REORGANIZATION 64
6. CONCLUDING REMARKS 65
REFERENCES 65
CHAPTER 9. INTERPOLATION METHODS FOR TENSOR FUNCTIONS 69
Abstract 69
Keywords 69
INTRODUCTION 69
TENSOR FUNCTION OF ONE VARIABLE 69
TENSOR FUNCTION OF TWO VARIABLES 71
INTERPOLATION AT COINCIDENT POINTS 72
POLYNOMIALS OF SECOND-ORDER AND FOURTH-ORDER TENSORS 72
EXAMPLES 73
REFERENCES 73
APPENDIX 74
CHAPTER 10. AN AUTOREGRESSIVE MODEL WITH VARYING COEFFICIENTS WITH APPLICATION TO PREDICTION 75
Abstract 75
Keywords 75
SERIES TRANSFORMATIONS AND PREDICTION 75
THE e-TRANSFORMATION - AR MODEL 76
THE d-TRANSFORMATION - ARTV MODEL 76
TWO-DIMENSIONAL TRANSFORMATIONS AND AR MODELS 78
REFERENCES 78
Chapter 
79 
Abstract 79
Keywords 79
GROWING USE AND DECREASING CREDIBILITY OF MATHEMATICAL MODELLING 79
USUAL EXPLANATIONS OF THE MODELLING CRISIS 79
TWO DIFFERENT CHAINS OF METHODS IN THE INNERMATHEMATICAL TREATMENT OF MODELS 80
THE EXTRAMATHEMATICAL SCIENTIFIC STATUS OF A MODEL 81
MATHEMATICAL MODELS - A PROBLEM FOR SOCIETY 81
REFERENCES 82
CHAPTER 12. SEARCHING FOR STRUCTURE: THE GMDH ALGORITHM 83
Abstract 83
Keywords 83
INTRODUCTION 83
THE GMDH ALGORITHM 83
OBSERVATIONS ON THE GMDH ALGORITHM 85
GMDH AND LONG-RANGE PREDICTION 86
REFERENCES 87
PART III: SYSTEMS THEORY 88
CHAPTER 13. CONTRIBUTIONS TO A STATE SPACE THEORY FOR LINEAR PARTIAL DIFFERENTIAL EQUATION MODELS 88
Abstract 88
Keywords 88
INTRODUCTION 88
MODEL FORMULATION 89
STATE SPACE 89
GREEN'S FUNCTION REPRESENTATION 90
STATE TRANSITION OPERATOR 91
SPECTRAL DECOMPOSITION 92
RIEMANN REPRESENTATION 92
EXAMPLES 94
SUMMARY 96
NOMENCLATURE 96
REFERENCES 97
APPENDIX 98
CHAPTER 14. COMPLEX DYNAMICAL SYSTEMS 99
Abstract 99
Keywords 99
INTRODUCTION 99
COMPLEX DYNAMICS 99
SIMPLE NETWORKS 100
EXEMPLARY APPLICATIONS 101
SIMULATION TECHNIQUES 102
CONCLUSION 102
REFERENCES 103
CHAPTER 15. ON EQUILIBRIUM PROGRAMMING 104
Abstract 104
INTRODUCTION 104
THE EQUILIBRIUM PROGRAMMING PROBLEM 104
EXAMPLES OF EP 105
VARIATIONAL INEQUALITIES AND EQUILIBRIUM PROBLEMS: COMPUTATIONAL STRATEGIES 106
FINAL REMARKS 107
REFERENCES 108
CHAPTER 16. A DECOMPOSITION ALGORITHM FOR SOLVING SPARSE SYSTEMS OF SIMULTANEOUS EQUATIONS 109
Abstract 109
Keywords 109
INTRODUCTION 109
STRUCTURAL ANALYSIS OF NON-SIMULTANEOUS SYSTEMS 110
A FIRST TEARING ALGORITHM FOR SIMULTANEOUS SYSTEMS 110
THE CONCEPT OF HIERARCHY 110
FOUNDATIONS OF THE HIERARCHIC ALGORITHM 111
DEFINITION OF THE HIERARCHIC ALGORITHM 112
PROPERTIES OF THE PRE-INVERSE [A-l] AND CONCLUSION 112
REFERENCES 113
CHAPTER 17. THE STRUCTURAL COMPLEXITY OF CONTINUOUSLY FUNCTIONING MULTI-GOAL SYSTEMS 114
Abstract 114
Keywords 114
INTRODUCTION 114
THE DERIVATION OF THE FORMULA: THE n-S-BLOCK SYSTEM 116
THE INDIVIDUALISATION 118
APPENDIX A 118
APPENDIX B 118
APPENDIX C 118
APPENDIX D 119
CHAPTER 18. MATHEMATICAL MODELLING OF MULTIDIMENSIONAL SYSTEMS AND THEIR APPLICATIONS 120
Abstract 120
Keywords 120
INTRODUCTION 120
STATE SPACE MODELS 120
STATE SPACE REDUCTION 121
STATE SPACE MODELS FOR SEQUENTIAL MACHINES 121
PETRI NET APPROACH TO STATE SPACE MODELS AND CONCURRENCY 121
2-D SYSTEMS 122
3-D SYSTEMS 123
CONCLUSION 123
REFERENCES 124
CHAPTER 19. CATEGORY OF SPACES OF AVAILABLE STATES WITH APPLICATION TO MODELLING OF COMPUTER LANGUAGES 125
Abstract 125
Keywords 125
INTRODUCTION 125
CATEGORIES OF SPACES OF AVAILABLE STATES 125
FINITE ORDERED SPACES OF AVAILABLE STATES 127
APPLICATION TO MODELING THE COMPUTER IBM/4341 128
CONCLUSION 129
REFERENCES 129
CHAPTER 20. MODELLING THE APPLE II USING CATEGORIES OF SPACES OF AVAILABLE STATES 130
Abstract 130
Keywords 130
INTRODUCTION 130
MODELLING THE APPLE II ON THE MACHINE LANGUAGE LEVEL 130
MODELLING THE APPLE II ON THE ASSEMBLY LANGUAGE LEVEL 133
MODELLING THE ASSEMBLER 134
CONCLUSION 135
REFERENCES 135
CHAPTER 21. APPLICATION OF BIFURCATION DIAGRAMS TO THE MODELLING OF STABILITY PROBLEMS 136
Abstract 136
Keywords 136
INTRODUCTION 136
STRUCTURAL STABILITY 136
BIFURCATION DIAGRAMS 138
APPLICATIONS IN MECHANICAL ENGINEERING 139
CONCLUSION 141
REFERENCES 141
CHAPTER 22. QUALITATIVE METHODS IN SOCIAL SYSTEMS MODELLING 142
Abstract 142
Keywords 142
I. INTRODUCTION 142
II. BIFURCATION ANALYSIS 143
III. BIFURCATION ANALYSIS AND SENSITIVITY 144
IV. BIFURCATION ANALYSIS AND SPATIAL STRUCTURE 146
V. QUALITATIVE CHANGE IN SYSTEM DYNAMICS MODELS 147
CONCLUSIONS 148
REFERENCES 148
CHAPTER 23. AN EVALUATION PROCEDURE FOR ELECTRONICS EQUIPMENT LIFE CYCLE COSTS 150
Abstract 150
Keywords 150
INTRODUCTION 150
THE EVALUATION PROCEDURE 150
EXAMPLE USING THE LCC PROCEDURE 152
CONCLUSION 153
REFERENCES 155
CHAPTER 24. AN EXTENSION OF THE CONCEPT OF STRUCTURAL SENSITIVITY IN AN URBAN MODEL 156
Abstract 156
Keywords 156
INTRODUCTION 156
SUBDIVISION OF THE MODEL 157
RESULTS 158
CONCLUSION 159
ACKNOULEDGEMENTS 159
REFERENCES 159
PART IV: PARAMETER ESTIMATION AND SYSTEM IDENTIFICATION 160
CHAPTER 25. ON MEASURES OF NONLINEARITY FOR DYNAMIC STOCHASTIC SYSTEMS 160
Abstract 160
Keywords 160
INTRODUCTION 160
DEGREE OF NONLINEARITY BETWEEN VECTOR VALUED RANDOM VARIABLES 161
NONLINEARITY DEGREE BETWEEN STATIONARY PROCESSES 161
MEASURES OF NONLINEARITY FOR URYSON SYSTEMS 162
SIMPLE TESTS FOR LINEARITY OF DISCRETE SYSTEMS 163
NONLINEARITY ANALYSIS FOR DISCRETE URYSON SYSTEMS 164
REFERENCES 165
Chapter 
166 
Abstract 166
Keywords 166
INTRODUCTION 166
STATEMENT OF THE PROBLEM 166
SUFFICIENT CONDITIONS 167
DETERMINING THE LIAPUNOV FUNCTIONS 169
CONSTANT PARAMETER CASE 169
REFERENCES 170
CHAPTER 27. SINGULAR PERTURBATION APPROACH TO STIFF ESTIMATION 171
Abstract 171
Keywords 171
OCCURRENCE OF STIFF ENZYME KINETIC SYSTEMS 171
SCALING TO IDENTIFY STIFF SYSTEMS 171
SINGULAR PERTURBATION APPROACH 172
DATA SIMULATION AND ESTIMATION SOFTWARE 172
NUMERICAL EXPERIMENTS 172
CONCLUSION 174
REFERENCES 174
NOTATION 175
SUBSCRIPTS 175
SUPERSCRIPTS 175
CHAPTER 28. SYSTEM IDENTIFICATION OF SHIP STEERING DYNAMICS WITHOUT YAW MEASUREMENT 177
Abstract 177
Keywords 177
INTRODUCTION 177
DETERMINISTIC DESCRIPTION OF SHIP MANEUVERING MOTION 177
PARAMETER ESTIMATION BY EXTENDED KALMAN FILTERING 178
APPLICATION OF EXTENDED KALMAN FILTERING TO SHIP STEERING DYNAMICS 178
RESULT AND DISCUSSION 179
CONCLUSION 181
ACKNOWLEDGEMENT 181
NOMENCLATURE 181
REFERENCES 182
CHAPTER 29. IDENTIFICATION OF MULTIVARIABLE MODEL FOR COMMERCIAL VEHICLES 183
Abstract 183
Keywords 183
INTRODUCTION 183
MULTIVARIABLE MODEL FOR IDENTIFICATION 184
ESTIMATION OF THE NUMBER OF NATURAL FREQUENCIES AND THE PARAMETERS IN THE MULTIVARIABLE MODEL 185
COMPUTATION OF THE NATURAL FREQUENCIES OF THE CONTINUOUS TIME SYSTEM FROM THE ESTIMATED POLES 186
EXPERIMENTAL CONDITIONS AND IDENTIFICATION RESULTS 186
CONCLUSION 187
REFERENCES 187
CHAPTER 30. DYNAMIC MODELS OF URBAN AND REGIONAL SYSTEMS: SOME CONCEPTUAL AND METHODOLOGICAL ISSUES 189
Abstract 189
Keywords 189
1. INTRODUCTION 189
2. THE STATE OF THE ART IN DYNAMIC MODELING OF URBAN AND REGIONAL SYSTEMS 190
3. METHODOLOGICAL PROBLEMS IN URBAN AND REGIONAL DYNAMIC-MODELING 191
4. CONCEPTUAL ISSUES 192
5. DIRECTIONS FOR FURTHER RESEARCH 192
6. REFERENCES 193
CHAPTER 31. BIOCYBERNETICAL MODEL OF SOME STATES OF CONSCIOUSNESS IN HUMANS 195
Abstract 195
Keywords 195
INTRODUCTION 195
PROBLEM FORMULATION 196
MUTUAL INFORMATION AND REDUNDANCY 197
PARAMETER ESTIMATION 198
FEEDBACK CONTROL AND STATE ESTIMATE 198
ALGORITHM 199
CONCLUSION 199
REFERENCES 200
APPENDIX 201
Chapter 
202 
Abstract 202
Keywords 202
INTRODUCTION 202
TEXT RECOGNITION SYSTEM 203
ALGORITHMS AND THE TEXT RECOGNITION EXPERIMENTS 204
CONCLUSION 205
REFERENCES 206
CHAPTER 33. KALMAN FILTERING AND PARAMETER ESTIMATION IN THE ELEMENTARY GAUSSIAN PROCESS CASE 207
Abstract 207
PART V: OPTIMIZATION 208
CHAPTER 34. ON SOME ISSUES CONCERNING OPTIMIZATION AND DECISION TREES 208
Abstract 208
Keywords 208
INTRODUCTION 208
ON DECISION TREES AND CERTAIN PROPERTIES OF THEIRS 210
FINAL COMMENTS AND CONCLUSIONS 211
ACKNOWLEDGMENTS 211
REFERENCES 211
CHAPTER 35. MAXIMIZATIONS WITH RESPECT TO CONES IN MATHEMATICAL MODELLING 213
Abstract 213
Keywords 213
INTRODUCTION 213
THEORY 214
COMPUTATIONS 216
CONFLICT MODELS 216
MULTIPLE OBJECTIVE MODELS 217
CONCLUSIONS 217
REFERENCES 218
CHAPTER 36. PRODUCTION-INVENTORY SYSTEMS WITH STATE CONSTRAINTS - CONTROL POLICIES AND OBJECTIVE FUNCTIONS 219
Abstract 219
Keywords 219
INTRODUCTION 219
STATEMENT OF THE CONTROL PROBLEMS AND NECESSARY CONDITIONS 219
CONTROL POLICIES FOR PRODUCTION-INVENTORY SYSTEMS 220
CONCLUSION 224
REFERENCES 224
CHAPTER 37. THE DESIGN OF OPTIMAL RELATIONAL DATA MODEL 225
Abstract 225
Keywords 225
INTRODUCTION 225
DECOMPOSITION VERSUS SYNTHETIC APPROACH 225
FUNCTIONAL DEPENDENCIES AND SCHEMA OPERATIONS 226
THE ITERATIVE DESIGN ALGORITHM 228
COMPARISON OF ALGORITHMS 230
CONCLUSION 231
REFERENCES 231
CHAPTER 38. A MARKOV PROCESS MODEL FOR CASH MANAGEMENT 232
Abstract 232
Keywords 232
INTRODUCTION 232
SHORT TERM CASH MANAGEMENT 232
THE COST FUNCTION 233
RESULTS 234
CONCLUSIONS 235
REFERENCES 235
CHAPTER 39. MODELLING MANPOWER ALLOCATION OF MIXED MULTIPRODUCT ASSEMBLY LINE 237
Abstract 237
Keywords 237
INTRODUCTION 237
MANPOWER ALLOCATION 237
DISCUSSION OF IMPLEMENTATION 239
Conclusion 239
REFERENCES 240
CHAPTER 40. A MATHEMATICAL TECHNIQUE TO OPTIMIZE A MECHANICAL DESIGN WITH MANY PARAMETERS 241
Abstract 241
Keywords 241
NOMENCLATURES 241
INTRODUCTION 241
MATHEMATICAL MODEL AND METHOD OF ANALYSIS 242
SAMPLE EXAMPLE 242
DISCUSSION OF RESULTS 243
REFERENCES 244
CHAPTER 41. MULTIPLE OBJECTIVE OPTIMIZATION APPLIED TO MISSILE SYSTEM DESIGN 245
Abstract 245
Keywords 245
INTRODUCTION 245
VECTOR OPTIMIZATION FOR PRODUCING OPTIMAL DESIGN 245
OPTIMIZATION APPLICATION 246
SUMMARY 249
REFERENCES 249
CHAPTER 42. REDUCTION OF THE NUMBER OF PATTERNS IN A CUTTING PROGRAM 251
Abstract 251
Keywords 251
INTRODUCTION 251
THE PROBLEM 251
THE LITERATURE 252
A POST-OPTIMIZATION PROCEDURE 253
NUMERICAL RESULTS 254
REFERENCES 255
APPENDIX 256
CHAPTER 43. OPTIMAL DESIGN OF HEAT CONDUCTING STRUCTURAL ELEMENTS 257
Abstract 257
Keywords 257
INTRODUCTION 257
SHAPE OPTIMIZATION PROBLEM 257
MATERIAL DERIVATIVE FOR SHAPE DESIGN SENSITIVITY ANALYSIS 258
OPTIMAL DESIGN OF A THERMAL DIFFUSER 258
NUMERICAL EXAMPLE 260
CONCLUSIONS 260
REFERENCES 261
CHAPTER 44. MATHEMATICAL MODELS FOR POWER CONVERTER DESIGN OPTIMIZATION 263
Abstract 263
Keywords 263
INTRODUCTION 263
CLASSIFICATION OF MATHEMATICAL MODELS 263
MODELING CONSIDERATIONS 264
SINGLE OBJECTIVE MODEL 264
NONLINEAR PROGRAMMING SOFTWARE 267
MULTIOBJECTIVE MODEL 268
NUMERICAL RESULTS 269
CONCLUSIONS 270
REFERENCES 270
CHAPTER 45. MODELS FOR ELECTRIC GENERATING SYSTEM DEVELOPMENT — ACCELERATION OF TECHNOLOGY DEVELOPMENT AND INTERACTION ANALYSIS 271
Abstract 271
Keywords 271
INTRODUCTION 271
GENERATING CAPACITY BALANCE AND ACCELERATION 271
EVALUATION INDICES 272
INTEGRATED DEVELOPMENT MODELS 273
CONCLUSIONS 274
REFERENCES 274
CHAPTER 46. A COMPARISON OF THE ALGORITHMS FOR AUTOMATED DATA ADJUSTMENT AND MATERIAL BALANCE AROUND MINERAL PROCESSING EQUIPMENT 277
Abstract 277
Keywords 277
INTRODUCTION 277
THE MATERIAL BALANCE PROBLEM 277
THE METHODS 278
RESULTS 280
DISCUSSION 280
CONCLUSIONS 280
REFERENCES 281
CHAPTER 47. A COMPUTER MODEL IN SOLID WASTE MANAGEMENT 282
Abstract 282
Keywords 282
INTRODUCTION 282
FORMULATIONS OF THE MODEL 282
UNBALANCED SYSTEM 285
SOLUTION ALGORITHM 285
DATA REQUIREMENTS 286
COMPUTER PROGRAM 286
EXAMPLE PROBLEM 286
CONCLUSIONS 286
REFERENCES 286
CHAPTER 48. APPLICATION OF OPERATIONS RESEARCH IN PAPER PROCUREMENT 288
Abstract 288
Keywords 288
THE OPERATIONS RESEARCH STUDY 290
REFERENCES 294
PART VI: STOCHASTIC MODELLING 295
CHAPTER 49. TOPOLOGICAL INVARIANCE IN STOCHASTIC ANALYSIS 295
Abstract 295
Keywords 295
THE ANALYSIS OF STOCHASTIC PROCESSES 295
MAPPINGS AND STOCHASTIC PROCESSES 296
AFFINE STATIONARY AND PROJECTIVE STATIONARY PROCESSES 298
CONCLUDING REMARKS 299
REFERENCES 300
CHAPTER 50. LINEAR SYSTEMS SUBMITTED TO NONLINEAR TRANSFORMATIONS OF GAUSSIAN PROCESSES A RITZ-GALERKIN APPROACH 301
Abstract 301
Keywords 301
INTRODUCTION (1) 301
MODELLING WHITE NOISES (2) 301
FIRST ORDER LINEAR SYSTEMS (3) 302
EXPONENTIAL APPROXIMATION OF PROBABILITY DENSITIES (4) 302
A GENERALIZED F-P-K EQUATION (5) 304
REFERENCES 304
ANNEXE 304
CHAPTER 51. RELIABILITY ASSESSMENT BASED ON POINT ESTIMATES OF PROBABILITY MOMENTS 306
Abstract 306
Key Words 306
INTRODUCTION 306
THE POINT ESTIMATE METHOD 307
THREE, OR MORE, POINT REPRESENTATIONS 307
FUNCTIONS OF TWO, OR MORE, RANDOM VARIABLES 308
RELIABILITY ASSESSMENT BASED ON THE POINT ESTIMATE METHOD 309
DISCUSSION 309
REFERENCES 310
CHAPTER 52. USING STOCHASTIC OPTIMAL CONTROL TO FIND SHORTEST PATHS IN NETWORKS 312
Abstract 312
Keywords 312
INTRODUCTION 312
STOCHASTIC CONTROL MODEL 312
APPLICATION TO NETWORKS 314
CONCLUSIONS 315
REFERENCES 315
CHAPTER 53. MARKOV PROCESS MODELS: A GENERAL FRAMEWORK FOR ESTIMATION AND INFERENCE IN THE ABSENCE OF STATE TRANSITION DATA 316
Abstract 316
Keywords 316
INTRODUCTION 316
A REVIEW OF THE STATISTICAL INFERENCE METHODOLOGY 317
POWER 318
REFERENCES 321
CHAPTER 54. A STORAGE PROCESS WITH NON-CONSTANT INFLOW AND OUTFLOW 322
Abstract 322
Keywords 322
INTRODUCTION 322
MATHEMATICAL MODEL 322
THE STORAGE PROCESS 323
ANALYTICAL SOLUTION 323
NUMERICAL SOLUTION 324
NUMERICAL EXAMPLE 325
CONCLUSION 326
REFERENCES 327
CHAPTER 55. A STOCHASTIC MATHEMATICAL MODEL ON THE KINETIC THEORY OF TEST PARTICLES IN THE FLOW FIELD OF THE DISCRETE BOLTZMANN EQUATION 328
Abstract 328
Keywords 328
INTRODUCTION 328
THE MATHEMATICAL MODEL 328
ANALYSIS 329
DISCUSSION AND APPLICATION 330
REFERENCES 331
CHAPTER 56. MATHEMATICAL MODELLING OF SURFACE TEMPERATURES 333
Abstract 333
Keywords 333
INTRODUCTION 333
DATA 333
BOX-JENKINS METHOD 334
HARMONIC ANALYSIS 334
COMPARISON OF FORECASTS 335
CONCLUDING REMARKS 335
ACKNOWLEDGEMENT 336
REFERENCES 336
CHAPTER 57. ON THE DYNAMICS OF DUMBBELL SATELLITES IN TWO GRAVITATIONAL FIELDS 337
Abstract 337
Keywords 337
INTRODUCTION 337
THE MATHEMATICAL MODEL 337
ANALYSIS AND DISCUSSION 340
REFERENCES 342
58. A STOCHASTIC TREATMENT OF A DYNAMIC MODEL FOR AN INTERACTING CITIES SYSTEM 343
Abstract. 343
Keywords. 343
INTRODUCTION 343
A STOCHASTIC NONLINEAR MODEL 343
QUASI-ANALYTICAL SOLUTION OF THE MODEL EQUATION 344
STATISTICAL MEASURES 345
CONCLUSIONS 346
REFERENCES 347
CHAPTER 59. EVENTS WITH APPLICATIONS TO QUEUEING NETWORKS CROSS CORRELATIONS IN DECOMPOSED STREAMS OF 348
Abstract 348
PART VII: SIMULATION 350
CHAPTER 60. MULTIDISCIPLINARY MATHEMATICAL MODELING WITH ADVANCED SIMULATION LANGUAGES 350
Abstract 350
Keywords 350
INTRODUCTION 350
SINGLE INSTRUCTION PROGRAMMING 351
OTHER ACSL FEATURES 351
MODELING OF VEHICLES OR STRUCTURES IN HOSTILE ENVIRONMENTS 353
COMPUTER HARDWARE TRENDS 355
CONCLUSIONS 355
ACKNOWLEDGEMENTS 355
REFERENCES 355
CHAPTER 61. MAPLIS - A MATRIX ORIENTED LANGUAGE FOR MODELLING AND INTERACTIVE SIMULATION 356
Abstract 356
Keywords 356
INTRODUCTION 356
AN EXAMPLE 357
INTERACTION AS A NEW DECISION-MAKING AID 359
CHARACTERISTICS OF THE SIMULATION LANGUAGE MAPLIS 359
THE STATE OF DEVELOPMENT 361
REFERENCES 361
CHAPTER 62. MWR-BASED MODELLING AND SIMULATION OF MULTIDIMENSIONAL DISTRIBUTED PARAMETER SYSTEMS WITH CURVILINEAR BOUNDARY 362
Abstract 362
Keywords 362
INTRODUCTION 362
PROBLEM FORMULATION 362
SOLUTION OF THE EQUILIBRIUM STATE PROBLEM 363
SOLUTION OF THE DYNAMICAL PROBLEM 363
EXAMPLE 364
SOME GENERALIZATIONS 365
REFERENCES 365
CHAPTER 63. FUZZY SIMULATION PROGRAMMING SYSTEM-CONFUCIUS 368
Abstract 368
Keywords 368
INTRODUCTION 368
FUZZY MODELS 368
EVALUATION 369
MIXED MODELS 370
CONFUCIUS 370
FUZZY APPROXIMATION 371
FUZZY RECOMMENDATION 371
PRACTICAL RESULTS 372
CONCLUSION 372
REFERENCES 372
CHAPTER 64. MISSION PLANNING FOR THE VOYAGER 2 ENCOUNTER WITH URANUS -MATHEMATICAL MODELLING APPLICATIONS 373
Abstract 373
Keywords 373
INTRODUCTION 373
SYSTEM DESCRIPTION 373
MATHEMATICAL MODEL 374
RESULTS 376
CONCLUSIONS 378
REFERENCES 378
ACKNOWLEDGEMENT 378
CHAPTER 65. GRAPHICS BASED SIMULATION SYSTEM (GBSS) FOR MICROCOMPUTERS 381
Abstract 381
PART VIII: NUMERICAL MODELLING 382
CHAPTER 66. FINITE DIFFERENCE METHODS FOR MODELLING ELASTICALLY DISSIMILAR STRATA 382
Abstract 382
Keywords 382
INTRODUCTION 382
SIMULATION OF ELASTIC BEHAVIOUR 382
ADAPTATION OF THE MODEL PROGRAM TO THE MINING ENVIRONMENT 384
FIELD INVESTIGATIONS 384
DISCUSSION OF IN-SITU AND MODEL RESULTS 386
CONCLUSIONS 387
ACKNOWLEDGEMENTS 387
REFERENCES 387
CHAPTER 67. NUMERICAL IMPLEMENTATION OF ELASTO-PLASTIC MODEL 388
Abstract 388
Keywords 388
INTRODUCTION 388
THEORETICAL CONCEPTS OF THE MODEL 388
MATERIAL TESTING 389
MATERIAL MODELLING 389
NON-ASSOCIATIVE BEHAVIOR 389
CORRECTION FUNCTION 389
ALGORITHM FOR NONASSOCIATIVE MODEL 390
CONCLUSION 390
REFERENCES 390
CHAPTER 68. FINITE ELEMENT MODELLING OF CONTAMINANT TRANSPORT IN SATURATED AQUIFERS 394
Abstract 394
Keywords 394
INTRODUCTION 394
MATHEMATICAL FORMULATION 394
PROBLEM DEFINITION 395
RANGES OF VALUES OF VARIOUS FIELD PARAMETERS 396
RESULTS AND DISCUSSION 396
CONCLUSIONS 398
ACKNOWLEDGEMENTS 398
REFERENCES 399
CHAPTER 69. A NON-ITERATIVE PERFORMANCE MODELLING METHOD FOR SUPERCHARGED HEATER CYCLE 400
Abstract 400
Keywords 400
INTRODUCTION 400
DESCRIPTION OF COMBUSTION PRODUCT COMPOSITION 400
SUPERCHARGED HEATER CYCLE MODEL 401
CLOSED-FORM SOLUTION OF THE ENERGY BALANCE EQUATION 402
PERFORMANCE CHARACTERISTIC 402
THERMODYNAMIC DATA 403
COMPUTATION EXAMPLE 403
CONCLUSIONS 403
ACKNOWLEDGEMENT 403
REFERENCES 403
CHAPTER 70. NUMERICAL SOLUTION OF ELECTRICAL POWER SYSTEMS USING DIAKOPTICS 406
Abstract 406
Keywords 406
INTRODUCTION 406
ANALYSIS OF A SIMPLE POWER NETWORK 407
APPLICATION TO PRACTICAL POWER SYSTEMS 408
CONCLUSIONS 408
REFERENCES 408
CHAPTER 71. FINITE ELEMENT MODELLING OF THE TEMPERATURE HISTORIES IN ARC WELDING 412
Abstract 412
Keywords 412
INTRODUCTION 412
FINITE ELEMENT FORMULATION 412
RESULTS AND DISCUSSIONS 415
CONCLUSION 417
REFERENCES 417
CHAPTER 72. MATHEMATICAL MODELING OF UNBOUNDED MEDIA UNDERGOING WAVE MOTION 418
Abstract 418
Keywords 418
INTRODUCTION 418
MATHEMATICAL FORMULATION 419
CONCLUSIONS 421
REFERENCES 422
ACKNOWLEDGEMENT 422
CHAPTER 73. NUMERICAL MODELING OF D-MAPPINGS WITH APPLICATIONS TO CHEMICAL KINETICS 424
Abstract 424
Keywords 424
INTRODUCTION 424
D-MATRICES AND D-MAPPINGS 424
LOCALLY LINEARIZED D-MAPPING 424
PERTURBED FUNCTIONAL ITERATION 425
A DEGENERATE IMPLICIT CODE 426
APPLICATIONS 426
CONCLUSION 426
ACKNOWLEDGMENT 426
REFERENCES 426
CHAPTER 74. TRANSPORT AND ACCUMULATION OF FRAZIL ICE SUSPENSIONS IN RIVERS 429
Abstract 429
Keywords 429
INTRODUCTION 429
THE FINITE-ELEMENT SCHEME 430
RESULTS AND CONCLUSIONS 432
ACKNOWLEDGEMENT 433
REFERENCES 433
CHAPTER 75. A THREE DIMENSIONAL MODEL OF ESTUARINE HYDRAULICS 435
Abstract 435
Keywords 435
INTRODUCTION 435
MATHEMATICAL MODEL 435
NUMERICAL SCHEME AND COMPUTATION 437
APPLICATION AND DISCUSSION 438
CONCLUSIONS 438
REFERENCES 438
CHAPTER 76. SOME USEFUL FORMULAS FOR MULTI-VARIABLE INTERPOLATION AND INTEGRATION 441
Abstract 441
Keywords 441
INTRODUCTION 441
NOTATIONS 441
MULTI-VARIABLE INTERPOLATION FORMULAE IN THE SENSE OF LaGRANGE 441
MULTI-VARIABLE LINEAR INTERPOLATION FORMULA 443
MULTI-VARIABLE NUMERICAL INTEGRATIONS 444
CONCLUSION 446
CHAPTER 77. FINITE ELEMENT ANALYSIS OF CALENDERING 447
Abstract 447
Keywords 447
INTRODUCTION 447
THE FINITE ELEMENT METHOD 448
RESULTS AND DISCUSSION 449
CONCLUSIONS 450
REFERENCES 450
CHAPTER 78. A MATHEMATICAL MODEL FOR COMPUTING RUN-UP OF BREAKING WAVES 452
Abstract 452
Keywords 452
INTRODUCTION 452
NUMERICAL MODEL 452
CONCLUSION 454
ACKNOWLEDGMENT 454
REFERENCES 454
CHAPTER 79. MATHEMATICAL MODELLING OF SPARK IGNITION ENGINE COMBUSTION 455
Abstract 455
Keywords 455
INTRODUCTION 455
THE SPARK IGNITION ENGINE COMBUSTION PROCESS 455
COMBUSTION MODEL CLASSIFICATION 456
CONCLUSIONS 461
REFERENCES 461
NOTATION 462
CHAPTER 80. A BOUNDARY ELEMENT METHOD FOR ANALYZING MINING INDUCED STRESSES AND DISPLACEMENTS 464
Abstract 464
INTRODUCTION 464
CONCLUSIONS AND DISCUSSION 468
ACKNOWLEDGEMENTS 469
REFERENCES 469
PART IX: CHEMICAL ENGINEERING 470
CHAPTER 81. CONVERSION ESTIMATES FOR GAS-SOLID REACTIONS 470
Abstract 470
Keywords 470
INTRODUCTION 470
ASYMPTOTIC RESULTS IN THE GENERAL CASE 471
REDUCTION TO A SCALAR PROBLEM IN CASE (2b) 471
THE PSEUDO-STEADY-STATE PROBLEM 472
CONVERSION ESTIMATES 472
CONCLUSIONS 473
REFERENCES 473
CHAPTER 82. MATHEMATICAL MODEL OF A FREELY-BUBBLING FLUIDIZED BED 474
Abstract 474
Keywords 474
INTRODUCTION 474
THE MATHEMATICAL MODEL 475
THE EXPERIMENTS 479
DISCUSSION 479
CONCLUSIONS 479
NOTATION 479
GREEK SYMBOLS 479
REFERENCES 480
CHAPTER 83. MICROSTRUCTURAL MODELS FOR IMMISCIBLE MIXTURES: MATHEMATICAL MODELING METHODS 484
Abstract 484
Keywords 484
INTRODUCTION 484
WELL-POSEDNESS AND VON NEUMANN STABILITY 484
ANALYSIS OF MICROSTRUCTURAL MODELING METHODS 485
EXTENSIONS AND APPLICATIONS 488
CONCLUSION 488
ACKNOWLEDGEMENTS 489
REFERENCES 489
CHAPTER 84. IGNITION OF A COMBUSTIBLE SOLID WITH VARIABLE ACTIVATION ENERGY 490
Abstract 490
Keywords 490
INTRODUCTION 490
LARGE ACTIVATION ENERGY ANALYSIS 491
INTEGRAL EQUATION FOR IGNITION TIME 493
IGNITION CRITERIA 493
REFERENCES 493
CHAPTER 85. CONCENTRATION WAVES - EFFECTS OF AN ELECTRIC FIELD 494
Abstract 494
Keywords 494
INTRODUCTION 494
MATHEMATICAL MODEL 494
EXPERIMENTS 495
RESULTS OF THE MATHEMATICAL MODELLING 495
EXCITABLE PULSES 495
WAVE FRONTS 497
DISCUSSION 498
REFERENCES 498
CHAPTER 86. MATHEMATICAL MODELS OF HEAT AND MASS TRANSFER IN CAPILLARY-POROUS BODIES DRYING PROCESS 500
Abstract 500
Keywords 500
INTRODUCTION 500
TRANSFER EQUATIONS 500
MATHEMATICAL MODELS 501
CONCLUSION 504
REFERENCES 504
NOMENCLATURE 505
CHAPTER 87. REACTION KINETIC PARAMETERS OBTAINED FROM DIFFERENTIAL SCANNING CALORIMETRIC DATA 506
Abstract 506
Keywords 506
INTRODUCTION 506
ASSUMPTIONS 506
TEMPERATÜRE INTEGRAL 507
PEAK OF THE DSC-CURVE 508
SHAPE OF THE DSC-CURVE 509
AREA UNDER THE DSC-CURVE 510
CONCLUSIONS 511
ACKNOWLEDGEMENT 511
REFERENCES 511
CHAPTER 88. MODELING OF BASE-CATALYZED PHENOLIC POLYMERIZATION 512
ABSTRACT 512
KEYWORDS 512
INTRODUCTION 512
BACKGROUND 512
CHEMISTRY 513
KINETICS 514
FORMULATION 514
RESULTS AND DISCUSSION 515
SUMMARY 516
REFERENCES 516
CHAPTER 89. FUZZY MODELS IN CAPITAL COST ESTIMATION OF CHEMICAL PLANTS 517
Abstract 517
Keywords 517
INTRODUCTION 517
FUZZY MODELLING 518
A FUZZY MODEL FOR PRELIMINARY COST ESTIMATION 519
DISCUSSION AND EXAMPLES OF ESTIMATION 519
CONCLUSIONS 521
REFERENCES 521
PART X: SOLID MECHANICS 524
CHAPTER 90. ON DELAMINATION IN PLATES: A UNILATERAL-CONTACT APPROACH 524
ABSTRACT 524
INTRODUCTION 524
THEORY AND FORMULATION 524
FINITE-ELEMENT MODEL 525
DISCUSSION OF NUMERICAL RESULTS 526
CONCLUSIONS 528
REFERENCES 528
CHAPTER 91. APPLICATION OF LAGRANGE'S EQUATION TO CRACK PROPAGATION PROBLEMS 530
Abstract 530
Keywords 530
INTRODUCTION 530
CRACK MODEL 530
CRACK PATH ANALYSIS BY LAGRANGE'S EQUATION 532
DISCUSSION AND CONCLUSION 532
ACKNOWLEDGEMENT 533
REFERENCES 533
APPENDIX. ELASTIC ANALYSIS BY THE CONTINUOUSLY DISTRIBUTED DISLOCATIONS MODEL 533
CHAPTER 92. MODELLING THE QUASISTATIC GROWTH OF CURVED INTERFACE CRACKS IN THERMAL STRESSED FIBER REINFORCED COMPOSITES BY A MODIFIED CRACK CLOSURE INTEGRAL 536
Abstract 536
Keywords 536
INTRODUCTION 536
A UNIT CELL WITH AN INTERFACE CRACK AND THE RELATED MIXED BOUNDARY VALUE PROBLEM 536
THE NUMERICAL METHOD OF THE MODIFIED CRACK CLOSURE INTEGRAL 537
EFFECTS OF DIFFERENT TYPES OF FINITE ELEMENTS 538
EFFECTS OF THE NET TOPOLOGY 540
CONCLUSIONS 541
REFERENCES 541
CHAPTER 93. FORCED TRANSIENT TORSIONAL WAVES IN A FLAWED ELASTIC COMPOSITE 542
ABSTRACT 542
Keywords 542
INTRODUCTION 542
CONCLUSION 546
REFERENCES 546
CHAPTER 94. COMPUTATIONAL MODELING OF CUMULATIVE DAMAGE FORMATION IN POLYMERIC MATERIALS 547
Abstract 547
Keywords 547
COMPUTATIONAL MODEL DEVELOPMENT 547
RESULTS 548
CONCLUSION 551
REFERENCES 551
CHAPTER 95. STRUCTURAL DAMPING OF STRANDED CABLE 554
Abstract 554
Keywords 554
INTRODUCTION 554
BENDING MODE OF COIL DEFORMATION 554
TWISTING MODE OF COIL DEFORMATION 555
TOTAL FRICTIONAL LOSSES 556
BENDING OF STRANDED CANTILEVER CABLE 557
CONCLUSION 558
ACKNOWLEDGEMENT 558
REFERENCES 558
CHAPTER 96. ENERGY ABSORPTION IN LARGE PANEL STRUCTURAL JOINTS 559
Abstract 559
Keywords 559
INTRODUCTION 559
THE KEY-JOINT 559
THE VERTICAL LOCK-JOINT 561
ENERGY ABSORPTION ON LOCK-JOINT 563
THE HORIZONTAL JOINT 564
ENERGY ABSORPTION ON HORIZONTAL JOINT 565
CONCLUSION 566
REFERENCES 566
Chapter 
567 
Abstract 567
Keywords 567
INTRODUCTION 567
EXPERIMENTAL WORK 568
PARTIAL SLIP DAMPING 569
CONCLUSION 570
REFERENCES 570
CHAPTER 98. THE QUASI-ELASTIC METHOD IN CREEP STABILITY ANALYSIS 571
Abstract 571
Keywords 571
INTRODUCTION 571
BIFURCATION BUCKLING 571
SNAPTHROUGH BUCKLING 573
ANALYSIS OF RESULTS 574
NUMERICAL EXAMPLES 574
CONCLUSION 576
ACKNOWLEDGEMENTS 576
REFERENCES 576
CHAPTER 99. ON THE THEORETICAL MODELING OF HUMAN JOINTS 577
Abstract 577
Keywords 577
INTRODUCTION 577
FORMULATION OF AN ARTICULATING JOINT MODEL 578
NUMERICAL METHOD OF SOLUTION 580
RESULTS AND DISCUSSION 580
REFERENCES 582
CHAPTER 100. THEORETICAL ANALYSIS OF IMPACT OF A FLUID-FILLED SPHERICAL SHELL WITH A SHALLOW SHELL: A MODEL FOR HEAD IMPACT 583
Abstract 583
Keywords 583
NOMENCLATURE 583
INTRODUCTION 584
FORMULATION OF THE IMPACT PROCESS 584
ALGORITHM FOR NUMERICAL SOLUTION 586
RESULTS AND CONCLUDING REMARKS 587
REFERENCES 588
APPENDIX 588
CHAPTER 101. MATHEMATICAL MODEL OF WRINKLING PHENOMENON IN STRUCTURES 590
Abstract 590
Keywords 590
INTRODUCTION 590
CONCLUSIONS 594
ACKNOWLEDGMENTS 595
REFERENCES 595
CHAPTER 102. PLANE WAVE PROPAGATION IN DISCRETE SOLIDS BY THE MONTE CARLO SIMULATION 596
Abstract 596
Keywords 596
INTRODUCTION 596
MATHEMATICAL MODEL OF WAVE PROPAGATION 596
THE MONTE CARLO SIMULATION 598
CONCLUSIONS 600
REFERENCES 600
CHAPTER 103. A SIMPLIFIED MODEL FOR THE DAMAGED SEGMENT OF A LONGITUDINALLY VIBRATING UNIFORM BEAM 602
Abstract 602
Keywords 602
ANALYTICAL RESULTS 602
EXPERIMENTAL RESULTS 603
CONCLUSIONS 603
REFERENCES 604
CHAPTER 104. A MODEL OF A FRACTURED CANINE RADIUS BASED ON THE STRUCTURAL FREQUENCY RESPONSE FUNCTION 606
Abstract 606
Keywords 606
INTRODUCTION 606
BACKGROUND 606
PRESENT INVESTIGATION 606
CONCLUSION 608
REFERENCES 608
CHAPTER 105. MODELING OF MAGNETIC FIELD, POOL PROFILES, TEMPERATURE FIELD IN COLD CRUCIBLE INDUCTION MELTING 610
Abstract 610
Keywords 610
INTRODUCTION 610
FORMULATION 610
RESULTS 612
CONCLUSIONS 613
REFERENCES 613
APPENDICES 613
CHAPTER 106. MATHEMATICAL MODEL AND PARAMETRIC STUDIES OF FOUNDATIONS ON PILES 616
Abstract 616
Keywords 616
INTRODUCTION 616
MATHEMATICAL MODELLING 616
SUGGESTED MODEL 617
PARAMETRIC STUDIES AND EXPERIMENTAL VERIFICATION 617
CONCLUSION 621
ACKNOWLEDGEMENT 621
REFERENCES 621
PART XI: FLUID MECHANICS 622
CHAPTER 107. NUMERICAL MODEL OF THE ARRESTED TOPOGRAPHIC WAVE 622
Abstract 622
Keywords 622
INTRODUCTION 622
THE ANALYTICAL MODEL 622
THE NUMERICAL MODEL 623
THE SEA BREEZE MODEL 623
THE COASTAL PROMONTORY 626
CONCLUSION 626
ACKNOWLEDGMENT 626
REFERENCES 626
CHAPTER 108. THE OIL-WAVE INTERACTION 627
Abstract 627
Keywords 627
INTRODUCTION 627
FORMULATION OF THE PROBLEM 627
SOLUTION OF THE PROBLEM 628
DISCUSSION 631
REFERENCES 632
CHAPTER 109. COMPARISON OF A DISTRIBUTED PARAMETER AND A BOUNDARY INTEGRAL MODEL OF LONG PERIOD OCEAN WAVES 633
Abstract 633
Keywords 633
INTRODUCTION 633
DISTRIBUTED PARAMETER MODEL 634
BOUNDARY INTEGRAL DYNAMIC MODEL 634
NUMERICAL APPLICATION 635
CONCLUSIONS 637
ACKNOWLEDGEMENTS 637
REFERENCES 638
CHAPTER 110. FAR-FIELD CONTAMINANT DISPERSION IN ENVIRONMENTAL FLOWS 639
Abstract 639
Keywords 639
INTRODUCTION 639
RATIONALE FOR THE BASIC MODEL 640
THE MATHEMATICAL MODEL 641
DISCUSSION OF THE MODEL 642
REFERENCES 642
CHAPTER 111. A MATHEMATICAL MODEL FOR THE DRAWING OF A SOLID CONTINUUM THROUGH NEWTONIAN FLUID FILLED TUBULAR ORIFICE 644
Abstract 644
Keywords 644
INTRODUCTION 644
ANALYSIS 644
NOTATIONS 647
RESULTS 647
CONCLUSIONS 648
REFERENCES 648
CHAPTER 112. GEOTHERMAL AQUIFER MODELLING: A LOW TEMPERATURE PRODUCTION/DISPOSAL SYSTEM 651
Abstract 651
Keywords 651
INTRODUCTION 651
GENERAL MODEL 652
MODEL IMPLEMENTATION 653
NUMERICAL RESULTS 654
CONCLUSIONS 655
ACKNOWLEDGEMENTS 656
BIBLIOGRAPHY 656
CHAPTER 113. THE NUMERICAL SOLUTION OF THE NATURAL CONVECTION FLOW IN A SQUARE CAVITY 657
Abstract 657
Keywords 657
INTRODUCTION 657
SPLINE FORMULATION 657
EQUATIONS OF NATURAL CONVECTION 658
NUMERICAL SOLUTION 658
RESULTS 659
CONCLUSIONS 660
APPENDIX 660
REFERENCES 660
CHAPTER 114. EXPERIMENTAL AND THEORETICAL STUDY OF NON-DARCY FLOW THROUGH POROUS MEDIA 663
Abstract 663
Keywords 663
INTRODUCTION 663
MATHEMATICAL FORMULATION AND SOLUTIONS 663
NUMERICAL SOLUTIONS 664
EXPERIMENTAL WORK 665
CONCLUSIONS 665
REFERENCES 667
CHAPTER 115. STABILITY OF FLOW IN A ROTATING POROUS MEDIUM IN THE FORM OF AN ANNULUS: THE WIDE-GAP PROBLEM 668
Abstract 668
Keywords 668
INTRODUCTION 668
BASIC FLOW 668
STABILITY ANALYSIS 669
NUMERICAL SOLUTION OF THE PROBLEM 669
DISCUSSION OF RESULTS 671
ACKNOWLEDGEMENTS 672
REFERENCES 672
CHAPTER 116. A THEORETICAL ANALYSIS OF NONISOTHERMAL FLOW OF TWO SUPERIMPOSED FLUIDS IN A CONVERGING GEOMETRY 674
Abstract 674
Keywords 674
INTRODUCTION 674
DESCRIPTION OF THE FLOW PROBLEM 675
RESULTS AND DISCUSSION 676
CONCLUSION 677
NOMENCLATURE 677
REFERENCES 677
CHAPTER 117. MODELLING AND OPTIMIZATION PROBLEMS FOR STOCHASTIC CONSTRAINED FUNCTIONALS IN THE KINETIC THEORY OF AERODYNAMICAL SHAPES 681
Abstract 681
Keywords 681
INTRODUCTION 681
MATHEMATICAL MODELLING AND STATEMENT OF THE PROBLEM 682
ANALYSIS 683
APPLICATION 684
CONCLUSIONS 685
REFERENCES 685
PART XII: WATER RESOURCES 686
CHAPTER 118. NUMERICAL SOLUTION OF THE SHALLOW WATER EQUATIONS WITH A MACCORMACK TYPE FINITE DIFFERENCE SCHEME 686
Abstract 686
Keywords 686
INTRODUCTION 686
SHALLOW WATER EQUATIONS 686
NUMERICAL METHOD 687
RESULTS AND DISCUSSION 688
CONCLUSION 688
REFERENCES 689
CHAPTER 119. DEVELOPMENT AND VERIFICATION OF THE EDDY DIFFUSION THERMAL STRATIFICATION MODEL, 'U.S.E.D.' 691
Abstract 691
Key Words 691
INTRODUCTION 691
MODEL DEVELOPMENT 692
EDDY DIFFUSION COEFFICIENTS 693
REFORMULATION OF EDDY DIFFUSIVITY 693
HYDROCLIMATIC SIMULATIONS 695
CONCLUSIONS 696
REFERENCES 696
CHAPTER 120. MATHEMATICAL MODELLING & SIMULATION OF THE PASSAIC RIVER BASIN IN NEW JERSEY
Abstract 698
Keywords 698
BACKGROUND 698
THE PASSAIC RIVER BASIN SYSTEM EXAMPLE OF DATA USED IN MODEL DEVELOPMENT 699
JERSEY CITY SYSTEM 699
THE PASSAIC RIVER BASIN MATHEMATICAL MODEL 700
CONCLUSIONS 701
PART XIII: BIOMEDICAL MODELS 702
Chapter 
702 
Abstract 702
Key Words 702
1. Introduction 702
2. Definitions and Notation 703
3. Active Memory in Neural Networks 705
References 707
Chapter 
708 
Abstract 708
Keywords 708
INTRODUCTION 708
STRUCTURAL MINIMALITY 709
MINIMALITY FROM BOND GRAPHS 710
EXAMPLE OF ELECTRIC CIRCUIT 711
EXAMPLES OF BIOLOGICAL INTEREST 711
CONCLUSIONS 712
ACKNOWLEDGEMENTS 713
REFERENCES 713
CHAPTER 123. REDUCED MODELS OF THE PULMONARY ARTERIAL TREE: A CASE STUDY IN MODELLING METHODOLOGY 714
Abstract 714
Keywords 714
INTRODUCTION 714
THE METHODOLOGY 715
THE CASE STUDY 717
CONCLUSIONS 718
ACKNOWLEDGEMENTS 719
REFERENCES 719
CHAPTER 124. ANALYSIS OF FLOW THROUGH STENOSED BLOOD VESSELS 720
Abstract 720
Keywords 720
INTRODUCTION 720
METHODS OF PROCEDURE 720
RESULTS AND DISCUSSIONS 722
REFERENCES 723
CHAPTER 125. MATHEMATICAL MODEL OF AORTIC VALVE VIBRATION 726
Abstract 726
Keywords 726
INTRODUCTION 726
II. DEVELOPMENT OF THE MODEL 726
III. NUMERICAL RESULTS AND DISCUSSION 729
REFERENCES 731
CHAPTER 126. VARIATIONAL SOLUTION FOR PULSATILE FLOW IN RIGID TUBES 732
Abstract 732
Keywords 732
INTRODUCTION 732
VARIATIONAL SOLUTION 732
RESULTS AND DISCUSSION 734
REFERENCES 734
CHAPTER 127. THRESHOLD AND CONDUCTION PROPERTIES OF A DIFFUSION MODEL OF A MYELINATED AXON 736
Abstract 736
Keywords 736
INTRODUCTION 736
THE MODEL 736
PROPAGATION 737
CONCLUSION 738
ACKNOWLEDGEMENT 739
REFERENCES 739
CHAPTER 128. COMPUTER SIMULATION OF ARTERIAL BRANCH FLOW 740
Abstract 740
Keywords 740
INTRODUCTION 740
METHODS 741
RESULTS AND DISCUSSION 741
References 742
Acknowledgement 742
CHAPTER 129. MATHEMATICAL MODELS OF RENAL FUNCTION 746
Abstract 746
Keywords 746
INTRODUCTION 746
COMPUTER ALGORITHMS 747
CONCLUDING REMARKS 748
REFERENCES 748
CHAPTER 130. THE INTRINSIC GEOMETRY OF BIOLOGICAL SURFACE GROWTH 750
Abstract 750
Keywords 750
INTRODUCTION 750
A MODELLING STRATEGY 751
AXISYMMETRIC GROWTH 751
A GENERAL MODEL 752
THE DEVELOPMENT OF CORTICAL FOLDING 754
SUMMARY 755
REFERENCES 755
CHAPTER 131. INSTABILITIES IN STEM CELL SYSTEMS 756
Abstract 756
Keywords 756
0. INTRODUCTION 756
1. THE MODEL 757
2. THE CRITICAL BEHAVIOUR OF THE SC PROXIMITY PROCESS 758
3. FINAL COMMENTS 760
REFERENCES 760
CHAPTER 132. NEIGHBORHOOD COMPLEXITIES AND SYMMETRY OF CHEMICAL GRAPHS AND THEIR BIOLOGICAL APPLICATIONS 762
Abstract 762
Keywords 762
INTRODUCTION 762
PRELIMINARIES OF GRAPHS AND THEIR INFORMATION CONTENT 762
GROUPS OF A CHEMICAL GRAPH AND RELATED INFORMATION CONTENT 764
SAMPLE CALCULATION OF INFORMATION - THEORETIC INDICES FROM A CHEMICAL GRAPH 765
BIOLOGICAL APPLICATIONS 766
CONCLUSIONS 767
REFERENCES 767
ACKNOWLEDGMENT 767
CHAPTER 133. MODEL FORMULATION, IDENTIFICATION AND VALIDATION: AN INTEGRATED APPROACH FOR THE STUDY OF PHYSIOLOGICAL SYSTEMS 768
Abstract 768
Keywords 768
INTRODUCTION 768
THE MODELLING PROCESS 768
THE PURPOSE OF MODELLING 768
MODEL BASIS IN THEORY AND DATA 768
MODEL FORMULATION 768
MODEL IDENTIFICATION 769
MODEL VALIDATION 770
CONCLUSIONS 773
ACKNOWLEDGEMENTS 773
REFERENCES 773
CHAPTER 134. FINITE ELEMENT ANALYSIS OF ENZYMATIC REMOVAL OF ADP FROM BLOOD PLATELETS DURING FLOW 774
Abstract 774
Keywords 774
INTRODUCTION 774
EXPERIMENTAL 775
MATHEMATICAL MODELLING 775
FINITE ELEMENT FORMULATION 775
RESULTS OF FINITE ELEMENT ANALYSES 776
DISCUSSION 777
ACKNOWLEDGEMENTS 777
REFERENCES 777
CHAPTER 135. MATHEMATICAL MODELING IN ENZYME SYSTEMS 779
Abstract 779
Keywords 779
INTRODUCTION 779
AMYLASE-CATALYZED REACTION OF LINEAR MALTOOLIGOSACCHARIDES AND AMYLOSE 779
HYDROLYSIS OF MICROCRYSTALLINE CELLULOSE (MCC) BY CELLULASE 781
ATP REGENERATION FROM ADENOSINE BY ENZYMES OF ALCOHOL FERMENTATION AND KINASES OF YEAST USING GLUCOSE AS AN ENERGY SOURCE 782
THERMAL INACTIVATION OF COVALENTLY BOUND IMMOBILIZED ENZYME 783
CONCLUSION 784
REFERENCES 784
CHAPTER 136. INVERSE SOLUTIONS FOR AUDITORY EVOKED POTENTIAL FIELDS 785
Abstract 785
Keywords 785
INTRODUCTION 785
AUDITORY EVOKED BRAINSTEM POTENTIALS 785
MODELLING THE SOURCES 785
MODELING THE HEAD 786
CONCLUSIONS 787
REFERENCES 787
CHAPTER 137. A FUNDAMENTAL PROBLEM IN PLANT MORPHOGENESIS FROM THE STANDPOINT OF DIFFERENTIAL GROWTH 791
Abstract 791
Keywords 791
PHYLLOTAXIS: DEFINITIONS AND NOTATIONS 791
ALLOMETRY: IN PHYLLOTAXIS 792
DISCUSSION 793
CONCLUSION 794
ACKNOWLEDGEMENTS 794
REFERENCES 794
PART XIV: MODELLING IN ECONOMICS 795
CHAPTER 138. A GENERALIZED TEST FOR FOUR TYPES OF REGRESSION SPECIFICATION ERROR 795
Abstract 795
Keywords 795
INTRODUCTION 795
TESTS FOR SPECIFICATION ERROR 795
PRACTICAL APPLICATION OF THE TESTS 797
ILLUSTRATIVE EXAMPLE 798
CONCLUSIONS 799
REFERENCES 800
CHAPTER 139. ESTIMATION AND PREDICTION OF TIME-VARYING PARAMETER ECONOMIC MODELS 801
Abstract 801
Key Words 801
I. INTRODUCTION 801
II. KALMAN FILTER ESTIMATION METHOD 801
III. PREDICTION USING KALMAN FILTER METHOD 803
IV. CONCLUSIONS 805
REFERENCES 805
FOOTNOTES 805
CHAPTER 140. A DYNAMIC MODEL OF AN INFORMATIONALLY DISAGGREGATE ECONOMY 806
Abstract 806
Keywords 806
THE ECONOMY 806
THE MODELS 807
THE OPTIMAL PROGRAMS AND THEIR SOLUTIONS 808
THE MICRO-MACRO MODEL OF THE ECONOMY 809
CONCLUSIONS 810
LIST OF VARIABLES AND DEFINITIONS 810
REFERENCES 811
ACKNOWLEDGEMENTS 811
REFERENCES 811
ADDENDUM 811
CHAPTER 141. MODELLING NON-PRICE COMPETITION AND MARKET SHARE 812
Abstract 812
Keywords 812
INTRODUCTION 812
THE MODEL AND ITS SOLUTION 812
THE CONSTRAINED MODEL 813
CONCLUSION 814
REFERENCES 814
CHAPTER 142. BOOM TOWNS: QUEUE UP OR BUST A WELFARE ECONOMY ANALYSIS 816
Abstract 816
Keywords 816
INTRODUCTION 816
THE PLANNING MODEL 816
THE MARKET MODEL 817
CONCLUSION 818
REFERENCES 818
CHAPTER 143. MODELLING THE ECONOMIC DEVELOPMENT BY MEANS OF IMPULSIVE CONTROL TECHNIQUES 819
Abstract 819
Keywords 819
INTRODUCTION 819
THE STOPPING TIME PROBLEM 820
THE IMPULSIVE CONTROL PROBLEM 822
CONCLUSIONS 823
REFERENCES 823
CHAPTER 144. FINAL DEMAND CONVERSION COEFFICIENTS FOR THE 1972 UNITED STATES INPUT-OUTPUT TABLE AND THEIR USE IN MICROECONOMIC MODELLING 824
Abstract 824
Keywords 824
INTRODUCTION 824
DEFINITIONS AND DATA 824
CONSTRUCTION OF COEFFICIENTS 825
USE IN MODELLING 828
EXAMPLE 829
CONCLUSIONS 830
ACKNOWLEDGEMENTS 830
REFERENCES 830
CHAPTER 145. IMPACT OF SUBSIDIES AND OF TAX DEDUCTIONS ON CONSUMER'S ENERGY SAVINGS - THE BELGIAN CASE 832
Abstract 832
Keywords 832
A. DESCRIPTION OF THE MEASURES 832
B. EVALUATION OF THE COST OF INSULATION 833
C. IMPACT OF THE VARIOUS MEASURES 834
D. REDISTRIBUTIVE EFFECTS OF THE VARIOUS MEASURES 836
E. MACRO-ECONOMIC IMPACT 837
REFERENCES 837
CHAPTER 146. SYSTEM IDENTIFICATION AND ANALYSIS OF INFLATION IN BRAZIL 839
Abstract 839
Keywords 839
INTRODUCTION 839
BOX-JENKINS METHODOLOGY 839
MODEL IDENTIFICATION AND ANALYSIS OF BRAZILIAN INFLATION 841
FORECASTING OF INFLATION 843
CONCLUSION 843
REFERENCES 844
CHAPTER 147. A METHOD OF GETTING APPROXIMATE INPUT-OUTPUT TABLE FOR LESS DEVELOPED COUNTRIES 845
Abstract 845
Keywords 845
NATIONAL ACCOUNTS AND BASIC DATA 845
STEPS FOR THE MAKING ACCOUNTS SYSTEM 845
REMARKS ON RAS METHOD 848
CONCLUSION 849
ACKNOWLEDGEMENT 849
REFERENCES 849
CHAPTER 148. SUBSTITUTIONS IN THE FRENCH FOOD INDUSTRY FROM A TRANSLOG COST FUNCTION MODEL 850
Abstract 850
Keywords 850
INTRODUCTION 850
THE MODEL 850
APPLICATION TO THE FRENCH FOOD INDUSTRY 852
CONCLUSION 853
REFERENCES 853
CHAPTER 149. IMPERFECT PRICE ADJUSTMENT, CONTROLLED PRICE AND MULTIMARKET RATIONING MODELS: THEIR POTENTIAL APPLICATION TO THE MODELLING OF TRADE IN KING AND TANNER CRAB PRODUCTS 854
Abstract 854
Keywords 854
INTRODUCTION 854
RATIONING MODELS 854
IMPERFECT PRICE ADJUSTMENT MODELS 855
CONTROLLED PRICE MODELS 857
MULTIMARKET MODELS 859
CONCLUSIONS 859
REFERENCES 860
PART XV: TRANSPORTATION 861
CHAPTER 150. RISK ANALYSIS OF RAILROAD FREIGHT TRANSPORTATION DISASTERS 861
Abstract 861
Keywords 861
INTRODUCTION 861
THE RISK PROFILES f(x) and .(x) 861
MODELING AND COMPUTATION OF g(x) 861
MODELING AND COMPUTATION OF f(x) and .(x) 863
CONCLUSIONS 863
CHAPTER 151. MODELING COMMUNITY REACTIONS TO TRANSPORTATION IMPACTS 864
Abstract 864
Keywords 864
INTRODUCTION 864
STUDY OBJECTIVE 864
THEORETICAL APPROACH 864
APPLICATION 866
MODELING RESULTS 867
CONCLUSIONS AND FUTURE RESEARCH 868
ACKNOWLEDGEMENT 868
REFERENCES 869
CHAPTER 152. INTEGRATION OF CHOICE SET REDUCTION IN BEHAVIORAL CHOICE TRAVEL DEMAND MODELS 870
Abstract 870
Keywords 870
INTRODUCTION 870
PROBLEMS AND ISSUES RELATED TO INDIVIDUAL CHOICE SETS 870
THEORETICAL FRAMEWORK 872
MODEL FORMULATION 873
VALIDATION AND TESTING 875
CONCLUSION 876
REFERENCES 876
CHAPTER 153. A TOUR MANAGEMENT SYSTEM FOR THE INDUSTRIAL CARRIER PROBLEMS 877
Abstract 877
Keywords 877
INTRODUCTION 877
THE INDUSTRIAL CARRIERS 877
FREIGHTS REGROUPING ALGORITHM 878
TOUR COMPUTATION ALGORITHM 880
SYSTEM IMPLEMENTATION 882
ACKNOWLEDGEMENTS 882
REFERENCES 882
CHAPTER 154. MODELLING THE FUTURE AIR TRAFFIC DEMANDS IN SAUDI ARABIA 883
Abstract 883
Keywords 883
INTRODUCTION 883
MAIN RESULTS 883
METHODOLOGY OF MODEL BUILDING 883
MODEL STRUCTURE 885
SIMULATION WITH THE MODEL 886
DISCUSSION 887
REFERENCES 888
CHAPTER 155. ROUTING IN STRATEGIC AIRLIFT: A STUDY IN BOTTLENECK ROUTING 889
Abstract 889
Keywords 889
INTRODUCTION 889
MATHEMATICAL FORMULATION 890
AN EXACT SOLUTION PROCEDURE 891
RESULTS AND CONCLUSION 892
REFERENCES 892
CHAPTER 156. A BRANCH AND BOUND MODEL FOR THE TRANSPORTATION ROUTING PROBLEM 894
Abstract 894
Keywords 894
INTRODUCTION 894
DEVELOPMENT OF THE ALGORITHM 895
APPLICATION TO GAS DISTRIBUTION 898
CONCLUSION 899
REFERENCES 899
PART XVI: INDUSTRIAL APPLICATIONS 900
CHAPTER 157. MODELLING AND GENERALIZED SOLUTION FOR THE KINEMATICS OF MULTI - AXIS ROBOT'S SKELETON 900
Abstract 900
Keywords 900
INTRODUCTION 900
THE MECHANICAL - MATHEMATICAL MODEL 900
APPENDIX 905
REFERENCES 907
CHAPTER 158. MODEL FORMULATION OF FLEXIBLE MANIPULATOR ARMS 908
Abstract 908
Keywords 908
INTRODUCTION 908
DIRECT PATH METHOD 908
BERNOUILLI-EULER BEAM MODELLING 909
FINITE-ELEMENT BASED MODELLING 910
LUMPED PARAMETER MODELLING 911
HYBRID MULTIBODY MODELLING 912
CONCLUSION 912
REFERENCES 913
CHAPTER 159. DYNAMIC FORMULATION TECHNIQUES FOR ROBOT MANIPULATORS 914
Abstract 914
Keywords 914
INTRODUCTION 914
KINEMATICS FORMULATION 915
LAGRAMGIAN FORMULATION USING HOMOGENEOUS TRANSFORMATION 917
LAGRANGIAN FORMULATION USING .3x3 ROTATIONAL MATRICES 919
LAGRANGIAN FORMULATION USING KINEMATICS OF CENTER OF MASS 920
DYNAMIC FORMULATION USING INFLUENCE COEFFICIENTS 920
NEWTON-EULER FORMULATION 921
NEWTON-EULER FORMULATION IN LINK COORDINATES 921
DUAL-EULER EQUATIONS 921
DISCUSSION 922
CONCLUSION 923
REFERENCES 923
CHAPTER 160. STOCHASTIC CHARACTERIZATION AND MODELLING OF THE ROUGHNESS OF TECHNOLOGICAL SURFACES 925
Abstract 925
Keywords 925
INTRODUCTION 925
PROBLEM ANALYSIS AND RESEARCH OBJECTIVES 926
MATHEMATICAL MODELS FOR THE DETERMINISTIC AND STOCHASTIC CHARACTERIZATION OF TECHNOLOGICAL SURFACES 927
EXPERIMENTS AND DISCUSSION 928
REFERENCES 929
CHAPTER 161. COMPUTER CONTROL SYSTEM OF INDUCTION HEATER 931
Abstract 931
Keywords 931
INTRODUCTION 931
FUNDAMENTAL EQUATIONS OF THE INDUCTION HEATING PROCESS 931
MATHEMATICAL MODEL OF THE BILLET TEMPERATURE CALCULATION 932
CONTROL SYSTEM OF THE BILLET TEMPERATURE 933
CONTROL RESULT 934
CONCLUSION 934
CHAPTER 162. INTEGRATING HUNAN FACTOR ASPECTS IN COST FUNCTION DEVELOPMENT : A QUALITY INSPECTION CASE 937
Abstract 937
INTRODUCTION 937
ASSUMPTIONS AND NOTATIONS 937
THE THREE SAMPLING PLANS 938
THE HUMAN ERRORS CONSIDERED 939
NUMERICAL EXAMPLE 940
CONCLUSIONS 941
REFERENCES 941
PART XVII: POPULATIONS 942
CHAPTER 163. STABILITY OF BIFURCATING ORBITS IN A PREDATOR PREY MODEL 942
Abstract 942
Keywords 942
INTRODUCTION 942
CONDITIONS OF A SUPERCRITICAL HOPF BIFURCATION 943
CONCLUSION 944
REFERENCES 944
CHAPTER 164. PRIMARY PRODUCTIVITY AND ECOLOGY IN COMPETITIVE PLANT COMMUNITIES 945
Abstract 945
Keywords 945
INTRODUCTION 945
SECTION 1. THE SINGLE SPECIES GOMPERTZIAN 946
SECTION 2. THE GOMPERTZIAN COMMUNITY FOR TWO 947
SECTION 3 SOLUTION OF THE n-SPECIES GOMPERTZIAN GROWTH EQUATIONS AND CONCLUSION 948
REFERENCES 949
CHAPTER 165. BALANCE OF GROWTH: CELL-POPULATION APPROACH TO IMMUNITY, HEMOPOIESIS AND CANCER 950
Abstract 950
Keywords 950
INTRODUCTION 950
SELF-RENEWAL VERSUS MATURATION 950
NORMAL AND ABNORMAL HEMOPOIESIS 951
COMPETITION LEUKEMIA AND THE BLAST CRISIS
IMMUNOLOGIC SPECIFICITY 953
KINETIC CHARACTERISTICS 954
CONCLUSION 954
REFERENCES 955
CHAPTER 166. POPULATION MODELLING BY SECOND ORDER DIFFERENTIAL SYSTEMS 956
Abstract 956
1. INTRODUCTION 956
2. MODELLING BY SECOND ORDER SYSTEMS 956
3. A PREDATOR-PREY MODEL 957
4. DISCUSSION 958
REFERENCES 958
PART XVIII: MATHEMATICAL MODELLING EDUCATION 959
CHAPTER 167. NEW APPROACHES TO TEACHING MATHEMATICAL MODELLING TO MANAGEMENT STUDENTS 959
Abstract 959
Key words 959
BACKGROUND 959
THE METHODOLOGY OF MATHEMATICAL MODELLING 960
MATHEMATICAL MODELLING IN CONTEXT 962
TECHNIQUES USED 962
RANGE OF EXAMPLES 963
PROBLEMS 964
CONCLUSION 964
REFERENCES 964
CHAPTER 168. CURRICULUM DEVELOPMENT IN MATHEMATICAL MODELLING 965
Abstract 965
Keywords 965
INTRODUCTION 965
ANALYSIS OF PHYSICAL PROBLEMS FOR MATHEMATICAL MODELLING 966
DISCONTINUOUS PHYSICAL PROCESS 966
REFERENCES 970
CHAPTER 
971 
Abstract 971
INTRODUCTION 971
A PRAGMATIC METHODOLOGY FOR MATHEMATICAL MODELLING 972
DEVELOPMENT OF APPROPRIATE TEACHING PHILOSOPHY AND FRAMEWORK 974
THE ROLE OF COMPUTING 975
TEACHING OF MATHEMATICAL MODELLING 976
ASSESSMENT 977
CONCLUSIONS 977
REFERENCES 977
CHAPTER 170. MATHEMATICAL MODELLING IN A DIFFERENTIAL EQUATIONS COURSE 981
CHAPTER 171. A GOAL PROGRAMMING APPLICATION ACADEMIC PLANNING IN A NIGERIAN UNIVERSITY 985
Abstract 985
PART XIX: GENERAL TOPICS 986
CHAPTER 172. ENERGY CONSERVATION: A POLICY MODEL FOR THE UNITED STATES 986
Abstract 986
Keywords 986
INTRODUCTION 986
AN ENERGY CONSERVATION POLICY MODEL FOR THE UNITED STATES 986
STRUCTURE OF THE HIERARCHY 987
DESCRIPTION OF THE ELEMENTS IN THE HIERARCHY 987
COMPUTING PRIORITIES 989
CONCLUSION 989
REFERENCES 991
CHAPTER 173. ON THE DETERMINANTS OF CREDIBLE ANALYSIS 992
Abstract 992
Keywords 992
BASELINE ANALYSIS 992
POLICY IMPACT ANALYSIS 993
DETERMINANTS OF A CREDIBLE BASELINE ANALYSIS 993
ANALYSIS CREDIBILITY RATING 995
RATING DESCRIPTIONS FOR CONSISTENCY ACROSS MODELS 995
RATING DESCRIPTIONS FOR SCENARIOS 995
RATING DESCRIPTIONS FOR ANALYSIS DESCRIPTION 996
RATING DESCRIPTIONS FOR USER INTERFACE 996
RATING DESCRIPTIONS FOR MODEL SELECTION 996
RATING DESCRIPTIONS FOR EXPERT ASSISTANCE AND REVIEW 996
SUMMARY 996
REFERENCES 996
CHAPTER 174. ENERGY CONSERVATION AND MODELING OF INDOOR POLLUTION 998
Abstract 998
Keywords 998
INTRODUCTION 998
INDOOR POLLUTION MODEL 999
CONCLUSION 1000
REFERENCES 1000
CHAPTER 175. SOME FECENT APPLICATIONS OF MATHEMATICAL MODELLING TO CHEMISTRY AND BIOLOGY 1002
Abstract 1002
Keywords 1002
(a) Solar energy research 1002
(b) Gastric and duodenal ulcers 1003
CHAPTER 176. A POPULATION MODEL ACCOUNTING FOR HOUSEHOLD DIMENSIONS 1005
Abstract 1005
Keywords 1005
INTRODUCTION 1005
DESCRIPTION OF THE PROBLEM 1005
A MATHEMATICAL MODEL 1006
THE SYSTEM OF RENEWAL EQUATIONS 1007
SOME CONSIDERATIONS ON THE SOLUTIONS 1008
REFERENCES 1009
Acknowledgment 1009
CHAPTER 177. VERTICAL MOTION WITH AIR RESISTANCE 1010
Abstract 1010
Keywords 1010
INTRODUCTION 1010
THE EQUATIONS OF MOTION 1010
QUALITATIVE RESULTS 1011
REFERENCES 1012
CHAPTER 178. QUANTUM MECHANICS AND THE PHENOMENA OF LIFE 1013
Abstract 1013
Keyword 1013
INTRODUCTION 1013
DEGENERACY CONSTRAINTS
CONSTRAINTS 1016
HIERARCHY 1017
CONCLUSIONS 1019
REFERENCES 1019
PART XX: LATE ABSTRACTS 1020
CHAPTER 179. ON A NEW ITERATIVE METHOD FOR MATHEMATICAL MODELLING OF ENGINEERING AND BIOMEDICAL SYSTEMS 1020
Abstract 1020
CHAPTER 180. NONCLASSICAL MEMORY PATHS IN THE DESCRIPTION OF MATERIAL RESPONSE TO EXTERNAL EXCITATIONS 1021
Abstract 1021
AUTHOR INDEX 1022

Produkt-Details

• Erscheint lt. Verlag: 9.5.2014
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik
• Themenwelt: Technik
• ISBN-10: 1-4831-9059-5 / 1483190595
• ISBN-13: 978-1-4831-9059-4 / 9781483190594