Generalized symmetry of graphs — A survey

Symmetry of graphs has been extensively studied over the past fifty years by using automorphisms of graphs and group theory which have played and still play an important role for graph theory, and promising and interesting results have been obtained, see for examples, [L.W. Beineke, R.J. Wilson, Topics in Algebraic Graph Theory, Cambridge University Press, London, 2004; N. Biggs, Algebraic Graph Theory, Cambridge University Press, London, 1993; C. Godsil, C. Royle, Algebraic graph theory, Springer-Verlag, London, 2001; G. Hahn, G. Sabidussi, Graph Symmetry: Algebraic Methods and Application, in: NATO ASI Series C, vol. 497, Kluwer Academic Publishers, Dordrecht, 1997]. We introduced generalized symmetry of graphs and investigated it by using endomorphisms of graphs and semigroup theory. In this paper, we will survey some results we have achieved in recent years. The paper consists of the following sections.

1. Introduction

2. End-regular graphs

3. End-transitive graphs

4. Unretractive graphs

5. Graphs and their endomorphism monoids.

Variational analysis of extended generalized equations via coderivative calculus in Asplund spaces

This paper is devoted to the development of variational analysis and generalized differentiation in the framework of Asplund spaces. We mainly concern the study of a special class of set-valued mapping given in the form

where both F and Q are set-valued mappings between Asplund spaces. Models of this type are associated with solutions maps to the so-called (extended) generalized equations and play a significant role in many aspects of variational analysis and its applications to optimization, stability, control theory, etc. In this paper we conduct a local variational analysis of such extended solution maps S and their remarkable specifications based on dual-space generalized differential constructions of the coderivative type. The major part of our analysis revolves around coderivative calculus largely developed and implemented in this paper and then applied to establishing verifiable conditions for robust Lipschitzian stability of extended generalized equations and related objects.     

The generalized relaxed proximal point algorithm involving -maximal-relaxed accretive mappings with applications to Banach spaces

A general design for the relaxed proximal point algorithm using the notion of A-maximal-relaxed accretiveness is developed, and then the convergence analysis for this algorithm in the context of solving a general class of nonlinear inclusion problems is examined along with some other results of interest involving A-maximal-relaxed accretive mappings in a real Banach space setting.     

Stability in Generalized Differentiability Based on a Set Convergence Principle

In this paper, we are concerned with epiconvergent sequences of nonsmooth functions. From a general principle of upper set convergence of set-valued maps we derive stability results for various objects in generalized differentiability. In particular, we establish stability results for the Clarke generalized gradient of locally Lipschitz functions, respectively for the generalized Hessian of C ^1,1 functions.      

一种新型的N部件串联可修系统及其可靠性分析

本文研究一种Ⅳ部件串联可修系统的一个新模型，该模型在经典。部件串联可修系统中引入了修理工可多重延误休假的概念，并且考虑了修理工使用修理设备在修理失效部件过程中可能因修理设备失效而立即更换修理设备对整个系统可靠性造成的影响,假定修理工的延误休假时间、部件的寿命和修理设备的寿命均服从指数分布，部件的修理时间、修理设备的更换时间和修理工的休假时间均服从一般连续型分布，通过使用补充变量法和广义马尔可夫过程方法得到了系统和修理设备的一些重要可靠性指标．     

Generalized convexity and inequalities

Let R₊=(0,∞) and let M be the family of all mean values of two numbers in R₊ (some examples are the arithmetic, geometric, and harmonic means). Given m₁,m₂∈M, we say that a function is (m₁,m₂)-convex if f(m₁(x,y))?m₂(f(x),f(y)) for all x,y∈R₊. The usual convexity is the special case when both mean values are arithmetic means. We study the dependence of (m₁,m₂)-convexity on m₁ and m₂ and give sufficient conditions for (m₁,m₂)-convexity of functions defined by Maclaurin series. The criteria involve the Maclaurin coefficients. Our results yield a class of new inequalities for several special functions such as the Gaussian hypergeometric function and a generalized Bessel function.     

一类E-Vandermonde矩阵的求逆及逆的迭代公式

本文给出一类E-Vandermonde矩阵和广义E-Vandermonde矩阵可逆的条件及逆的矩阵表达式，并给出了求逆的迭代公式．     

SMALL SAMPLE PROPERTIES OF THE POWER FUNCTION OF F TESTS IN TWO-WAY ERROR COMPONENT REGRESSION

1.IntroductionThetwcawayerrorcomponentregressionmodelmsybeexpressedasif=o

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