Mathematics in Science and Engineering

Volume 206

By: Viktor V. Ivanov, Natalya V. Ivanova

Write A Review

Hardcover | 1 June 2006

At a Glance

Hardcover
354 Pages

Dimensions(cm)
22.86 x 1.27 x 3.86

Hardcover

$591.75

or 4 interest-free payments of $147.94 with

Ships in 10 to 15 business days

Preface
List of abbreviations
List of notation s
Introduction: Evolutionary Systems and Development Modeli ng
Part 1: SURVE Y OF MM OF CAO
Chapter 1: General Methods of Inlet and Analysis of MM
Chapter 2: MM of Enzyme Reactions
Ch apter 3: MM of Kinetic Cellular Theory
Chapter 4: Some Othe r MM
Part 2: MM OF DEVELOPMENTSTRON G>
Chapter 5: Base MM
Chapter 6: Examples of CAO and Their MM
Ch apter 7: MM of the Cell
Chapter 8: MM of the Immune Netw ork
Chapter 9: MM of Some Other CAO
P art 3: INTRODUCTION TO APPLICATIONS
Chapte r 10: AIDS
Chapter 11: Cancers
Chapter 12 : On Life Longevity Problems
Chapter 13: On MM of a Disease
Appendix: MATHEMATICS OF DEVELOPMENT

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

Orders over $49.00 qualify for free shipping.

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

You Can Find This Book In

Non-Fiction Mathematics Applied Mathematics Computing & I.T.Computer Science Science Biology, Life Sciences Cellular Biology Physics Calculus & Mathematical Analysis Integral Calculus & Equations Computer Programming & Software Development

Algorithms & Data Structures

Preface	p. xv
List of abbreviations	p. xviii
List of notations	p. xix
Introduction: Evolutionary Systems and Development Modeling	p. 1
Evolutionary Systems (ES)	p. 1
Artificial ES	p. 1
Natural ES	p. 4
Joined ES	p. 6
Generalized Structure of ES	p. 7
Generalized Structure of Two ES Interactions	p. 8
Generalized Structure of CAO	p. 10
On Development Modeling	p. 12
Base simplest MM of development	p. 12
Comparison with classical MM	p. 14
A history, in short	p. 16
Survey of MM of Cao	p. 17
General Methods of Inlet and Analysis of MM	p. 19
Methods of Simplification of the Systems of Kinetic Equations	p. 19
On the Qualitative Theory for the Systems of the Second Order	p. 21
MM of cell cycles, I	p. 24
MM of hyper-cycle	p. 27
MM of cell excitable membranes	p. 28
MM of Spatial Systems	p. 30
MM of tumor angiogenesis	p. 33
Mechanical models for mesenchymal morphogenesis	p. 35
Possibility for Description of Biological Events on Molecular Level	p. 36
MM of traffic through cell membranes	p. 39
Passive transport	p. 39
Active transport	p. 40
On the problem of structure and protein folding	p. 41
Simple kinetic MM in protein folding	p. 42
Theories of reaction rates	p. 42
Application to the protein folding without barriers	p. 43
Physical model of DNA	p. 44
MM of Enzyme Reactions	p. 47
Method of Graphs	p. 47
MM of Open Reactions with Substratum Inhibition	p. 49
MM of Two-Substratum Reactions with Inhibition	p. 50
On Multi-enzyme Systems	p. 52
General notions	p. 52
Simple MM of energetic metabolism	p. 53
Effects of pH and T on the Reaction Rates	p. 56
MM of Cell-to-Cell Interactions	p. 58
MM of Kinetic Cellular Theory	p. 61
Assumption 1	p. 61
Assumption 2	p. 61
Assumption 3	p. 61
Assumption 4	p. 63
Assumption 5	p. 63
Assumption 6	p. 63
Assumption 7	p. 64
Assumption 8	p. 66
Assumption 9	p. 66
Assumption 10	p. 67
Assumption 11	p. 67
On Generalized Kinetic Models in Applied Sciences	p. 68
Some Other MM	p. 69
Delay Differential Equations	p. 69
Mathematics in Population Biology	p. 69
Some Problems and MM in Computational Biology and Bioinformatics	p. 72
On the Theory Catastrophes	p. 75
On the Respective Software	p. 78
MM of Development	p. 79
Base MM	p. 81
Base Minimal MM	p. 81
More General MM	p. 85
Additional MM	p. 88
On Comparison with Well-Known MM	p. 89
Methods for Estimation of MM Input Data	p. 89
On the Problem of MM Completeness	p. 91
Methods of CAO de- and aggregation	p. 92
Detailing the CAO structure	p. 92
Case of self-development of the indices [alpha]- and [beta]-types	p. 92
Case of the additional "executive" subsystem (E)	p. 94
Case of the additional "recreation" subsystem (R)	p. 95
Further factorization of the indices [alpha]- and [beta]-types	p. 96
On introduction of dimensionless relations	p. 96
On using extreme concepts	p. 96
Statement of the Modeling Problems	p. 98
Examples of CAO and Their MM	p. 101
On Hyper-Cycle, Origin of Life and DNA Code	p. 101
Dehydration Synthesis and Hydrolysis	p. 103
ATP Synthesis	p. 104
Biosynthesis	p. 109
On Pattern Formation	p. 111
MM of Regulatory Processes in Cells	p. 113
Biological background	p. 113
Proteins turn genes on or off	p. 113
Differentiated cells has a particular pattern of genes	p. 114
Complex protein control transcription	p. 116
RNA adds a cap and poly-A tail and removes non-coding segments	p. 116
Multiple mechanisms control gene expression	p. 117
Gene expression and cell-to-cell signaling	p. 119
Signal-transduction pathways	p. 119
MM of turning genes on or off	p. 120
MM of DNA transcription and mRNA translation	p. 122
MM of signal-transduction pathways	p. 122
MM of molecular pumps	p. 123
MM of the Cell	p. 125
On Cell Biology	p. 125
Molecular constituents of cells	p. 125
Structure and functions of cells	p. 127
On cell metabolism	p. 131
On control of gene expression	p. 132
Summing up	p. 133
Base MM of a Cell	p. 134
MM of cell structure and functions	p. 135
MM of a cell with regard to its given spatial structure	p. 136
MM of developing cell	p. 137
MM of cell bio-field	p. 139
On the Protein Folding Problem	p. 140
MM of Cell Cycle, II	p. 142
Biological background	p. 142
The respective MM	p. 145
MM of Morphogenesis	p. 146
Biological background	p. 146
The respective MM	p. 149
MM of the Immune Network	p. 151
Introduction	p. 151
Cells of the Immune System	p. 152
On the immune system	p. 152
Properties of the immune network cells	p. 154
Continuous MM	p. 157
On the Classical and the New Approach	p. 163
Some Results of Investigation	p. 166
Conclusion	p. 167
MM of Some Other CAO	p. 169
Function of Special Cells	p. 169
MM of Stem Cells	p. 170
MM of Thymus and Spleen	p. 172
MM of the Immune and Blood System Cells	p. 173
MM of Endothelial Cells	p. 175
Conclusion	p. 175
Introduction to Applications	p. 177
AIDS	p. 179
Introduction	p. 179
Immune Status of an Organism	p. 179
Viruses	p. 181
Main properties of viruses	p. 181
On retroviruses and HIV	p. 181
Pattern of HIV infection	p. 183
MM of Viruses	p. 183
Base MM	p. 183
MM of HIV	p. 184
Qualitative investigation of MM of HIV	p. 185
More complicated MM of HIV and its qualitative investigation	p. 188
MM of HIV population	p. 189
MM of HIV population inside of the host cell	p. 189
MM of HIV free population	p. 190
MM of AIDS	p. 192
Qualitative investigation of MM of AIDS	p. 196
On AIDS immune therapy	p. 198
Conclusion	p. 200
Cancers	p. 201
On Study of a Cancer at the Molecular Level	p. 201
MM of a Cancer Cell	p. 203
Base MM of a cell at the start of proliferation	p. 203
More complicated MM	p. 204
MM of developing daughter cell	p. 206
MM of a cancer cell bio-field	p. 207
Qualitative Investigation of MM of a Cancer Cell	p. 208
Investigation of MM (1)-(5)	p. 208
Investigation of MM (6)-(8)	p. 210
Investigation of MM (9), (10)	p. 212
MM of a Cancer	p. 213
Base MM of interaction of a cancer with host organism	p. 216
Qualitative investigation of MM of a cancer	p. 217
Investigation of MM (37)-(43)	p. 217
Investigation of MM (44), (45)	p. 221
On Immune Therapy of Cancers	p. 224
On Gene Therapy of Cancers	p. 225
Conclusion	p. 227
On Life Longevity Problems	p. 229
Clock of Cellular Aging	p. 229
Error accumulation theory	p. 229
Programmed dearth theory	p. 229
Winding back the clock	p. 230
Modeling of Cell Longevity Problems	p. 231
Modeling of error accumulation	p. 231
Modeling of programmed death	p. 232
Modeling of winding back the clock	p. 233
On Modeling of Organism Longevity Problems	p. 234
Certain Perspectives	p. 235
On MM of a Disease	p. 237
Introduction	p. 237
Conception of the Norm and Pathology	p. 238
Norm Restoration Problems	p. 239
On Optimization Problems	p. 240
On the Problems of Individualization of MM	p. 241
On MM of Doctor's Business	p. 242
Mathematics of Development	p. 245
Investigation of Equations	p. 247
Examples of Analytic Solutions	p. 247
Existence and Uniqueness of Solutions	p. 249
Cases of Non-Uniqueness of Solutions	p. 259
On Stability of Solutions	p. 260
Cases of Oscillating, Wave, and Some Other Solutions	p. 262
Asymptotic Properties of Solutions	p. 266
Some Additions and Remarks	p. 267
Investigation of Optimization Problems	p. 269
Preliminary Concepts and Results	p. 269
Examples of Analytical Solutions	p. 274
Existence and Uniqueness of Solutions	p. 276
On Stability of Solutions	p. 280
On Investigation of Solution Structure	p. 283
Case of Non-Uniqueness of Solutions	p. 286
Asymptotic Properties of Solutions	p. 288
Additions and Remarks	p. 290
Numerical Methods and Software	p. 293
On the Solution with the Pre-Assigned Accuracy	p. 293
Second kind of Volterra equations	p. 293
Inherent errors	p. 293
Method errors	p. 297
Round-off errors	p. 302
Analysis of the total errors	p. 303
First kind of Volterra equations	p. 304
Two main approaches	p. 304
Quasi-solution method	p. 305
Estimate of continuity modules for reciprocal operators	p. 306
On regularization for linear equations	p. 307
Reduction to Volterra-Type Equations	p. 309
Mathematical programming problems	p. 309
Some other problems	p. 312
On Optimal Numerical Methods	p. 313
Approximation of functions	p. 313
On the solution of other applied problems	p. 314
On Algorithms and Software	p. 317
Summary	p. 319
Bibliography	p. 321
Index	p. 329
About the Authors	p. 333
Table of Contents provided by Ingram. All Rights Reserved.

Mathematics in Science and Engineering

Volume 206

At a Glance

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

More in Integral Calculus & Equations

Multivariable Calculus Set Free

Infinitesimals Ride Again

Multivariable Calculus Set Free

Infinitesimals Ride Again

An Illustrative Guide to Multivariable and Vector Calculus

Theoretical and Computational Contact Micromechanics

Solid Mechanics and Its Applications

Universal Key: Fourier Transformation Innovative

Applications in Science and Technology

The Mittag-Leffler and Gamma Function

Oxford Mathematical Monographs

Choquet Integral and Monotone Sublinear Operators

Frontiers in Mathematics

Nonlinear Complex Systems II

Attractors, Solitons, and Waves

Convergence in Measure and in Category

Lecture Notes in Mathematics

Advanced Topics on Caputo Tempered Fractional Di?erential Equations with Applications

Measure and Integration

An Introductory Path Toward Functional Analysis and Probability

Periodic Elliptic Partial Differential Operators

The Main Structures

Measure Theory for Analysis and Probability

Indian Statistical Institute Series

A Problem-Solving Approach to Multi-Variable Calculus

Volume I

Tbilisi Analysis and PDE Seminar

Extended Abstracts of the 2024 Seminar Talks

Digital Twin-Driven Manufacturing System

Key Technologies and Opportunities

From Classical Analysis to Analysis on Fractals

A Tribute to Robert Strichartz, Volume 2

Why Don't Rabbits Rule The World?

Mathematical answers to life's key questions

Symmetry Analysis of Differential Equations

An Introduction

Mathematical Epidemiology and Fractional Calculus Applications

Industrial and Applied Mathematics

Integral Equations of the First Kind

Series on Soviet and East European Mathematics

Integral Equations and Boundary Value Problems : Proceedings of the International Conference

Proceedings of the International Conference

Lectures on Ergodic Theory

Dover Books on Mathematics

Elements Of Functional Analysis And Operator Theory

This product is categorised by