基于正极性或-符合展开的易测性网络

为提高数字电路的可测性,提出了可实现任意逻辑函数的正极性或-符合网络的易测性实现,并给出了测试网络中所有单固定故障的通用测试集．该实现基于逻辑函数的正极性或-符合展开,网络的同或部分分别采用了串联和树形结构．为提高可测性,同或串的实现结构只需增加1个控制端及1个观察端,同或树的实现结构只需增加3个控制端及1个观察端．对于1个n变量的逻辑函数,两种实现结构下通用测试集的基数分别为（n＋4）和（n＋5）．这样短的通用测试集非常适合用内建自测试实现,从而有效地缩短测试时间．     

Equivalence of positive Hausdorff measure and the open set condition for self-conformal sets

A compact set is self-conformal if it is a finite union of its images by conformal contractions. It is well known that if the conformal contractions satisfy the ``open set condition' (OSC), then has positive -dimensional Hausdorff measure, where is the solution of Bowen's pressure equation. We prove that the OSC, the strong OSC, and positivity of the -dimensional Hausdorff measure are equivalent for conformal contractions; this answers a question of R. D. Mauldin. In the self-similar case, when the contractions are linear, this equivalence was proved by Schief (1994), who used a result of Bandt and Graf (1992), but the proofs in these papers do not extend to the nonlinear setting.

     

Good ideals in Gorenstein local rings

Let be an -primary ideal in a Gorenstein local ring (, ) with , and assume that contains a parameter ideal in as a reduction. We say that is a good ideal in if is a Gorenstein ring with . The associated graded ring of is a Gorenstein ring with if and only if . Hence good ideals in our sense are good ones next to the parameter ideals in . A basic theory of good ideals is developed in this paper. We have that is a good ideal in if and only if and . First a criterion for finite-dimensional Gorenstein graded algebras over fields to have nonempty sets of good ideals will be given. Second in the case where we will give a correspondence theorem between the set and the set of certain overrings of . A characterization of good ideals in the case where will be given in terms of the goodness in their powers. Thanks to Kato's Riemann-Roch theorem, we are able to classify the good ideals in two-dimensional Gorenstein rational local rings. As a conclusion we will show that the structure of the set of good ideals in heavily depends on . The set may be empty if , while is necessarily infinite if and contains a field. To analyze this phenomenon we shall explore monomial good ideals in the polynomial ring in three variables over a field . Examples are given to illustrate the theorems.

     

Curvatures and Currents for Unions of Sets with Positive Reach, II

A class of subsets of ^d which can berepresented as locally finite unions of sets with positive reach isconsidered. It plays a role in PDE's on manifolds with singularities.For such a set, the unit normal cycle (determining the d – 1curvature measures) is introduced as a (d – 1)-currentsupported by the unit normal bundle and its properties are established.It is shown that, under mild additional assumptions, the unit normalcycle (and, hence, also the curvature measures) of such a set can beapproximated by that of a close parallel body or, alternatively, by themirror image of that of the closure of the complement of the parallelbody (which has positive reach). Finally, the mixed curvature measuresof two sets of this class are introduced and a translative integralgeometric formula for curvature measures is proved.     

复迭代映射z_(n 1)= c的 广义Mandelbrot集研究

研究了复迭代映射ｚ（ｎ＋１）＝／ｚｎｍ＋ｃ的广义Ｍａｎｄｅｌｂｒｏｔ集,指出其关于实轴是对称的,并且具有ｍ＋１次的旋转对称性,得出周期轨道的稳定性条件及一周期轨道的稳定区域的边界方程．利用逃逸时间算法和周期点查找的算法构造Ｍａｎｄｅｌｂｒｏｔ集,可以更清楚地了解Ｍａｎｄｅｌｂｒｏｔ集的结构．     

THE ＇HYBRID＇ TECHNIQUE FOR RISK ANALYSIS OF SOME DISEASES

Based on the data obtained from a survey recently made in Shanghai, this paper presents the hybrid technique for risk analysis and evaluation of some diseases. After determination of main risk factors of these diseases by analysis of variance, the authors introduce a new concept ‘Illness Fuzzy Set‘ and use fuzzy comprehensive evaluation to evaluate the risk of suffering from a disease for residents. Optimal technique is used to determinethe weights wi in fuzzy comprehensive evaluation, and a new method ‘Improved Information Distribution‘ is also introduced for the treatment of small sample problem. It is shown that the results obtained by using the hybrid technique are better than by using single fuzzy technique or single statistical method.     

Similarity in soft set theory

We introduce and study the concept of similarity between soft sets, which is an extension of the equality for soft set theory. We also introduce the concepts of conjunction parameter (α∧β) and disjunction parameter (α∨β) of ordered pair parameter 〈α,β〉 for soft set theory, and we investigate modified operations of soft set theory in terms of ordered parameters.     

The intersection of all maximum stable sets of a tree and its pendant vertices

A stable set in a graph G is a set of mutually non-adjacent vertices, α(G) is the size of a maximum stable set of G, and is the intersection of all its maximum stable sets. It is known that if G is a connected graph of order n≥2 with 2α(G)>n, then , [V.E. Levit, E. Mandrescu, Combinatorial properties of the family of maximum stable sets of a graph, Discrete Applied Mathematics 117 (2002) 149-161; E. Boros, M.C. Golumbic, V.E. Levit, On the number of vertices belonging to all maximum stable sets of a graph, Discrete Applied Mathematics 124 (2002) 17-25]. When we restrict ourselves to the class of trees, we add some structural properties to this statement. Our main finding is the theorem claiming that if T is a tree of order n≥2, with 2α(T)>n, then at least two pendant vertices an even distance apart belong to .