The strain energy criterion of mixed-mode brittle fracture

In this paper, we proposed a new cr tenon or mixea-moae brittle fracture, i.e., the strain energy criterion, which can be stated as (K_Ⅰ/K_Ⅰc)² +(K_Ⅰ/K_Ⅰc)²+(K_Ⅱ/K_Ⅱc)²=1. This criterion is shown to be in good agreement with known experimental data.In this paper, an experimental criterion:(K_Ⅰ/K_Ⅰc)^m+(K_Ⅱ/K_Ⅱc)ⁿ=1, 1≤_n^m≤2.is also proposed.     

定义在分形集上函数的H-导数

 分形的生成含有降维与升维两种形式,采用适当的方式总可以对分形集加以定向化,分形的内禀测度是Hausdorff测度。因此,定义在分形集上的函数可以看作是在Hausdorff测度下定义在区间[0, h]。在函数图像也是分形的前提下,依函数的Hausdorff测度的定义,给出了定义在分形集上的函数f(p)关于Hausdorff测度p的导数以及一些性质。     

A POLYNOMIAL ALGORITHM FOR FINDING THE MINIMUM FEEDBACK VERTEX SET OF A 3-REGULAR SIMPLE GRAPH

1IntroductionLetG=(VE)beaconnectedsimplegraph.AsubsetFofvertexsetViscalIedafeedbackvertexsetofGifthegraPhGFisaf0rest.ThecardinaIity0faminimumfeedbackvertexset0fGisdenotedbyf(G).AvertexsubsetJofvertexsetViscaJledallonseparatingindependentsetofG,ifJisanilldependentsetofVandGJisconnected.Thema-xiammcardinalityofnollseparatingindependelltsetofGisden0tedbyz(G)andiscalledthenonseparatingindepelldentnumberofG,AgraphGiscalledacactusifGisc0nnectedandanytwocyclesofGaredisjoint.Avertexvofacon…     

A Characterization Theorem for the Canonical Basis of a Closure Operator

The purpose of this paper is to provide a characterization result for the canonical basis of an arbitrary closure operator. This theorem strengthens the result of Burosch, Demetrovics and Katona, who propose a characterization of the generating system of a closure operator defined by the quasi-closed sets of the closure operator.     

Graphs with Branchwidth at Most Three

In this paper we investigate both the structure of graphs with branchwidth at most three, as well as algorithms to recognise such graphs. We show that a graph has branchwidth at most three if and only if it has treewidth at most three and does not contain the three-dimensional binary cube graph as a minor. A set of four graphs is shown to be the obstruction set for the class of graphs with branchwidth at most three. Moreover, we give a safe and complete set of reduction rules for the graphs with branchwidth at most three. Using this set, a linear time algorithm is given that verifies if a given graph has branchwidth at most three, and, if so, outputs a minimum width branch decomposition.     

N指标d维广义Wiener过程的极性

本文讨论了N指标d维广义Wiener过程的极性,并得到了一个集合为极集的充分必要条件．     

Dulac函数的构造及其应用(Ⅰ)

本文研究（Ⅰ）和（Ⅱ）类系统Dulac函数的构造问题,作为应用,讨论此两类系统的极限环的不存在性问题,得到了一些新结果．     

A Technique for Stochastic Control Problems with Unbounded Control Set

We describe a change of time technique for stochastic control problems with unbounded control set. We demonstrate the technique on a class of maximization problems that do not have optimal controls. Given such a problem, we introduce an extended problem which has the same value function as the original problem and for which there exist optimal controls that are expressible in simple terms. This device yields a natural sequence of suboptimal controls for the original problem. By this we mean a sequence of controls for which the payoff functions approach the value function.     

Strong Cardinals and Sets of Reals in Lω1(ℝ)

We generalize results of [3] and [1] to hyperprojective sets of reals, viz. to more than finitely many strong cardinals being involved. We show, for example, that if every set of reals in L_ω (?) is weakly homogeneously Souslin, then there is an inner model with an inaccessible limit of strong cardinals.     

On a Class of Recursively Enumerable Sets

We define a class of so-called ∑(n)-sets as a natural closure of recursively enumerable sets W_n under the relation “∈” and study its properties.