增長和擴散現(xiàn)象的數(shù)學(xué)模式和應(yīng)用

內(nèi)容概要

Permutation groups arguably form the oldest part of group theory. Their study dates back to the early years of the nineteenth century and, indeed, for a long time groups were always understood to be permutation groups. Although, of course, this is no longer true, permutation groups continue to play an important role in modern group theory through the ubiquity of group actions and the concrete representations which permutation groups provide for abstract groups. Today, both finite and infinite permutation groups are lively topics of research.

書籍目錄

1  Introduction                   2  Some Basic Frameworks                     2.1  Exponential Function   2.2  Logistic Distribution   2.3  Confined Exponential Distribution   2.4  Combination of the Logistic Distribution and the Confined Exponential Distribution                   2.5  Normal Probability Distribution   2.6  Power Law Logistic Distribution   2.7  Logistic Growth with Migration  2.8  Epidemics and Technology Transfer  2.9  Some Modifications of the Logistic Distribution 3  Some Additional Frameworks   3.1  Gompertz Distribution               3.2  Weibull Distribution   3.3  A Generalized Distribution   3.4  Hyperlogistic Distribution    3.5  Various Other Distributions                    4  Phenomena with Variable Growth Coefficients                4.1  Linearly Variable Growth Coefficient   4.2  Hyperbolically Variable Growth Coefficient   4.3  Exponentially Variable Growth Coefficient   4.4  Sinusoidally Variable Growth Coefficient 5  Phenomena with Variable Carrying Capacities                5.1  Exponentially Variable Carrying Capacity   5.2  Logistically Variable Carrying Capacity   5.3  Linearly Variable Carrying Capacity   5.4  Hyperbolically Variable Carrying Capacity   5.5  Sinusoidally Variable Carrying Capacity   5.6  Power Law Logistic with a Power Law Logistically Variable Carrying Capacity                6  Phenomena with Time Delays  6.1  Discrete Time Delay in the Exponential Equation   6.2  Discrete Time Delay in the Logistic Equation    6.3  Distributed Time Delay: Delay Integral in the Crowding Term     6.4  Distributed Time Delay: Delay Integral in a Pollution Term7  Phenomena with Spatial Diffusion   7.1  Diffusion from Instantaneous Sources   7.2  Diffusion from Continuous Source     7.3  Diffusion with Reaction in a Finite Region   7.4  Diffusion with Convection and Reaction   7.5  Diffusion with Confined Exponential Growth   7.6  Diffusion with Logistic Growth 8  Conclusion References Author Index                   Subject Index

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