Book contents
- Frontmatter
- Colophon
- Contents
- Preface
- 1 Semigroups of Operators and Cosine Operator Functions
- PART I REGULAR CONVERGENCE
- PART II IRREGULAR CONVERGENCE
- 26 First Examples
- 27 Extremely Strong Genetic Drift
- 28 The Nature of Irregular Convergence
- 29 Irregular Convergence Is Preserved Under Bounded Perturbations
- 30 Stein's Model
- 31 Uniformly Holomorphic Semigroups
- 32 Asymptotic Behavior of Semigroups
- 33 Fast Neurotransmitters
- 34 Fast Neurotransmitters II
- 35 From Diffusions on Graphs to Markov Chains and Back Again
- 36 Semilinear Equations, Early Cancer Modeling
- 37 Coagulation-Fragmentation Equation
- 38 Homogenization Theorem
- 39 Shadow Systems
- 40 Kinases
- 41 Uniformly Differentiable Semigroups
- 42 Kurtz's Singular Perturbation Theorem
- 43 A Singularly Perturbed Markov Chain
- 44 A Tikhonov-Type Theorem
- 45 Fast Motion and Frequent Jumps Theorems for Piecewise Deterministic Processes
- 46 Models of Gene Regulation and Gene Expression
- 47 Oligopolies, Manufacturing Systems, and Climate Changes
- 48 Convex Combinations of Feller Generators
- 49 The Dorroh Theorem and the Volkonskii Formula
- 50 Convex Combinations in Biological Models
- 51 Recombination
- 52 Recombination (Continued)
- 53 Averaging Principle of Freidlin and Wentzell: Khasminskii's Example
- 54 Comparing Semigroups
- 55 Relations to Asymptotic Analysis
- 56 Greiner's Theorem
- 57 Fish Population Dynamics and Convex Combination of Boundary Conditions
- 58 Averaging Principle of Freidlin and Wentzell: Emergence of Transmission Conditions
- 59 Averaging Principle Continued: L1-Setting
- PART III CONVERGENCE OF COSINE FAMILIES
- PART IV APPENDIXES
46 - Models of Gene Regulation and Gene Expression
from PART II - IRREGULAR CONVERGENCE
Published online by Cambridge University Press: 05 July 2016
Book contents
- Frontmatter
- Colophon
- Contents
- Preface
- 1 Semigroups of Operators and Cosine Operator Functions
- PART I REGULAR CONVERGENCE
- PART II IRREGULAR CONVERGENCE
- 26 First Examples
- 27 Extremely Strong Genetic Drift
- 28 The Nature of Irregular Convergence
- 29 Irregular Convergence Is Preserved Under Bounded Perturbations
- 30 Stein's Model
- 31 Uniformly Holomorphic Semigroups
- 32 Asymptotic Behavior of Semigroups
- 33 Fast Neurotransmitters
- 34 Fast Neurotransmitters II
- 35 From Diffusions on Graphs to Markov Chains and Back Again
- 36 Semilinear Equations, Early Cancer Modeling
- 37 Coagulation-Fragmentation Equation
- 38 Homogenization Theorem
- 39 Shadow Systems
- 40 Kinases
- 41 Uniformly Differentiable Semigroups
- 42 Kurtz's Singular Perturbation Theorem
- 43 A Singularly Perturbed Markov Chain
- 44 A Tikhonov-Type Theorem
- 45 Fast Motion and Frequent Jumps Theorems for Piecewise Deterministic Processes
- 46 Models of Gene Regulation and Gene Expression
- 47 Oligopolies, Manufacturing Systems, and Climate Changes
- 48 Convex Combinations of Feller Generators
- 49 The Dorroh Theorem and the Volkonskii Formula
- 50 Convex Combinations in Biological Models
- 51 Recombination
- 52 Recombination (Continued)
- 53 Averaging Principle of Freidlin and Wentzell: Khasminskii's Example
- 54 Comparing Semigroups
- 55 Relations to Asymptotic Analysis
- 56 Greiner's Theorem
- 57 Fish Population Dynamics and Convex Combination of Boundary Conditions
- 58 Averaging Principle of Freidlin and Wentzell: Emergence of Transmission Conditions
- 59 Averaging Principle Continued: L1-Setting
- PART III CONVERGENCE OF COSINE FAMILIES
- PART IV APPENDIXES
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- Convergence of One-Parameter Operator SemigroupsIn Models of Mathematical Biology and Elsewhere, pp. 281 - 286Publisher: Cambridge University PressPrint publication year: 2016