增长和扩散现象的数学模式和应用（英文版）

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.

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 Term
7 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

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as nume..