Modern Statistical And Mathematical Methods in Reliability可靠性中的现代统计与数学方法
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作者： Alyson G. Wilson等著
出 版 社：
出版时间： 2005-10-1字数：版次： 1页数： 409印刷时间： 2005/10/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9789812563569包装： 精装内容简介
This volume contains extended versions of 28 carefully selected and reviewed papers presented at The Fourth International Conference on Mathematical Methods in Reliability in Santa Fe, New Mexico, June 21–25, 2004, the leading conference in reliability research. The meeting serves as a forum for discussing fundamental issues on mathematical methods in reliability theory and its applications. A broad overview of current research activities in reliability theory and its applications is provided with coverage on reliability modeling, network and system reliability, Bayesian methods, survival analysis, degradation and maintenance modeling, and software reliability. The contributors are all leading experts in the field and include the plenary session speakers, Tim Bedford, Thierry Duchesne, Henry Wynn, Vicki Bier, Edsel Pena, Michael Hamada, and Todd Graves.
目录
Series Preface
Preface
1 Introduction
1.1 Basic Mathematical Questions
1.1.1 Existence
1.1.2 Multiplicity
1.1.3 Stability
1.1.4 Linear Systems of ODES and Asymptotic Stability
1.1.5 Well-Posed Problems
1.1.6 Representations
1.1.7 Estimation
1.1.8 Smoothness
1.2 Elementary Partial Differential Equations
1.2.1 Laplace's Equation
1.2.2 The Heat Equation
1.2.3 The Wave Equation
2 Characteristics
2.1 Classification and Characteristics
2.1.1 The Symbol of a Differential Expression
2.1.2 Scalar Equations of Second Order
2.1.3 Higher-Order Equations and Systems
2.1.4 Nonlinear Equations
2.2 The Cauchy-Kovalevskaya Theorem
2.2.1 Real Analytic Functions
2.2.2 Majorization
2.2.3 Statement and Proof of the Theorem
2.2.4 Reduction of General Systems
2.2.5 A PDE without Solutions
2.3 Holmgren's Uniqueness Theorem
2.3.1 An Outline of the Main Idea
2.3.2 Statement and Proof of the Theorem
2.3.3 The Weierstraß Approximation Theorem
3 Conservation Laws and Shocks
3.1 Systems in One Space Dimension
3.2 Basic Definitions and Hypotheses
3.3 Blowup of Smooth Solutions
3.3.1 Single Conservation Laws
3.3.2 The p System
3.4 Weak Solutions
3.4.1 The Rankine-Hugoniot Condition
3.4.2 Multiplicity
3.4.3 The Lax Shock Condition
3.5 Riemann Problems
3.5.1 Single Equations
3.5.2 Systems
3.6 Other Selection Criteria
3.6.1 The Entropy Condition
3.6.2 Viscosity Solutions
3.6.3 Uniqueness
4 Maximum Principles
4.1 Maximum Principles of Elliptic Problems
4.1.1 The Weak Maximum Principle
4.1.2 The Strong Maximum Principle
4.1.3 A Priori Bounds
4.2 An Existence Proof for the Dirichlet Problem
4.2.1 The Dirichlet Problem on a Ball
4.2.2 Subharmonic Functions
4.2.3 The Arzela-Ascoli Theorem
4.2.4 Proof of Theorem 4.13
4.3 Radial Symmetry
4.3.1 Two Auxiliary Lemmas
4.3.2 Proof of the Theorem
4.4 Maximum Principles for Parabolic Equations
4.4.1 The Weak Maximum Principle
4.4.2 The Strong Maximum Principle
5 Distributions
6 Function Spaces
7 Sobolev Spaces
8 Operator Theory
9 Linear Elliptic Equations
10 Nonlinear Elliptic Equations
11 Energy Methods for Evolution Problems
12 Semigroup Methods
A References
Index
