区间数相似度研究

对区间数相似性问题进行了探讨.定义了区间数相似度的概念,给出了度量区间数相似度的一个简洁公式,详细研究了它的一些优良性质,如:自反性、对称性和传递性等,并且研究了区间数相似度公式与区间数排序的可能度公式之间的关系,从而为区间数的实际应用奠定了理论基础.     

基于关联度的灰色模糊综合评判

针对被评判对象的特点,根据灰色模糊数学的理论,将隶属度和灰度综合起来表示灰色模糊数,并结合灰色关联度的应用,建立了基于关联度分析的灰色模糊综合评判的数学模型,此方法能使评判结果更加客观可信.     

The maximum and minimum degrees of random bipartite multigraphs

In this paper the authors generalize the classic random bipartite graph model, and define a model of the random bipartite multigraphs as follows:let m = m（n） be a positive integer-valued function on n and ζ（n,m;{pk}） the probability space consisting of all the labeled bipartite multigraphs with two vertex sets A ={a₁,a₂,...,a_n} and B = {b₁,b₂,...,b_m}, in which the numbers t_ai,b_j of the edges between any two vertices a_i∈A and b_j∈ B are identically distributed independent random variables with distribution P{t_ai,b_j=k}=pk,k=0,1,2,...,where pk ≥0 and ∞Σk=0 pk=1. They obtain that X_c,d,A, the number of vertices in A with degree between c and d of G_n,m∈ζ（n, m;{pk}） has asymptotically Poisson distribution, and answer the following two questions about the space ζ（n,m;{pk}） with {pk} having geometric distribution, binomial distribution and Poisson distribution, respectively. Under which condition for {pk} can there be a function D（n） such that almost every random multigraph G_n,m∈ζ（n,m;{pk}） has maximum degree D（n）in A? under which condition for {pk} has almost every multigraph G（n,m）∈ζ（n,m;{pk}） a unique vertex of maximum degree in A?     

Corrigendum to “Probabilistic properties of the relative tensor degree of finite groups” [Indag. Math. (N.S.) 27 (2016) 147–159]

We clarify Theorems 5.1 and 5.4 of our paper “Probabilistic properties of the relative tensor degree of finite groups”, published in Indagationes Mathematicae 27 (2016), 147–159.     

Lukasiewicz n值命题逻辑中命题的真度理论

利用势为 n的均匀概率空间的无穷乘积在 Lukasiewicz n值命题逻辑中引入了公式的真度概念,当3≤n≤17时证明了全体公式的真度值之集在[0,1]上是稠密的,并给出了公式真度的表达通式;利用真度定义了公式间的相似度,进而导出了全体公式集上的一种伪距离,为n值Lukasiewicz命题逻辑系统的近似推理理论提供了一种可能的框架。     

基于整体性思想的数据分析

通过对风险函数的分解,首先得到了传统上在独立同分布模型或线性模型假定下被忽视的度量复杂系统非线性程度的重要指标-扭曲度,然后对如何降低风险进行了讨论.逐步引出了干扰度、偏离度和信息分解比,它们与风险函数和扭曲度一起组成五个指标;最后权衡这五个指标,达到对稳定中心度量指标的控制.这也是用整体性思想进行数据分析的一种尝试.     

Lukasiewicz 命题逻辑系统一种新的理论的相容度

根据演绎定理和完备性定理,应用公式真度理论在Lukasiewicz命题模糊逻辑系统中讨论理论Γ的相容性,根据矛盾式■是Γ-结论的真度的大小,提出了一种新的极指标和相容度的概念.给出了理论Γ相容、不相容及其它相关结论的充分必要条件,并且获得了相容度与发散度之间联系的重要关系式.     

Sequences that Preserve the Homological Degree

The homological degree is a cohomological degree generalizing the classical degree function of a module. Given a finitely generated graded module M, over a standard graded ring A, this note is concerned with the question of when, for an element x in the augmentation ideal of A that is not in any associated prime of M other than the augmentation ideal itself, the homological degree of M is equal to the homological degree of M/xM. This question is answered when the dimension of M is one or two.     

c-Quasiminimal Enumeration Degrees

The notion of a C-quasiminimal set, with C an arbitrary subset of the naturals, was introduced by Sasso and presents a relativization of the well-known notion of quasiminimal set which was first constructed by Medvedev for proving the existence of nontotal enumeration degrees. In this article we study the local properties of the partially ordered set of the enumeration degrees containing C-quasiminimal sets. In particular, we prove for arbitrary enumeration degrees c and a that if c<a and a is a total e-degree then each at most countable partial order embeds isomorphically into the partially ordered set of c-quasiminimal e-degrees lying below a.     

席位分配的平均公平度方法

定义个体相对于总体的公平程度,即个体公平度与总体绝对公平度的比值,当比值趋于1时,就说明分配方案使该个体满意.利用方差的概念定义平均公平度,使个体公平程度相对于总体的公平程度的差距最小,等价于每一个个体公平度都很接近,并且趋于1,每个个体的公平程度达到最大,此时座位分配最为公平.     

Theory of truth degrees of propositions in two-valued logic

By means of infinite product of evenly distributed probabilistic spaces of cardinal 2 this paper introduces the concepts of truth degrees of formulas and similarity degrees among formulas, and a pseudo-metric on the set of formulas is derived therefrom, this offers a possible framework for developing an approximate reasoning theory of propositions in two-valued logic.     

The homological degree of a module

A homological degree of a graded module is an extension of the usual notion of multiplicity tailored to provide a numerical signature for the module even when is not Cohen-Macaulay. We construct a degree, , that behaves well under hyperplane sections and the modding out of elements of finite support. When carried out in a local algebra this degree gives a simulacrum of complexity à la Castelnuovo-Mumford's regularity. Several applications for estimating reduction numbers of ideals and predictions on the outcome of Noether normalizations are given.

     

Characterization of Digraphic Sequences with Strongly Connected Realizations

Let be a sequence of of nonnegative integers pairs. If a digraph D with satisfies and for each i with , then d is called a degree sequence of D. If D is a strict digraph, then d is called a strict digraphic sequence. Let be the collection of digraphs with degree sequence d . We characterize strict digraphic sequences d for which there exists a strict strong digraph .     

二值命题逻辑中有限理论数值特征的真度研究

以真度为基础,给出了有限理论的发散度、伪距离和有效度等数值特征的一般真度表示式,并研究了它们之间的关系.     

Vertex‐disjoint cycles containing prescribed vertices

Enomoto 7 conjectured that if the minimum degree of a graph G of order n ≥ 4k ? 1 is at least the integer , then for any k vertices, G contains k vertex‐disjoint cycles each of which contains one of the k specified vertices. We confirm the conjecture for n ≥ ck² where c is a constant. Furthermore, we show that under the same condition the cycles can be chosen so that each has length at most six. © 2003 Wiley Periodicals, Inc. J Graph Theory 42: 276–296, 2003     

带紧扰动的极大单调算子的广义度理论及其应用

本文借助于Lerar－Schauder度理论构造了带紧扰动的极大单调算子的广义度，扩展了李树杰与冯德兴相应的结果．运用新的度理论给出了某些算子方程可解性的简单证明．     

Balanced judicious bipartitions of graphs

A bipartition of the vertex set of a graph is called balanced if the sizes of the sets in the bipartition differ by at most one. B. Bollobás and A. D. Scott, Random Struct Alg 21 (2002), 414–430 conjectured that if G is a graph with minimum degree of at least 2 then V(G) admits a balanced bipartition V₁, V₂ such that for each i, G has at most |E(G)|/3 edges with both ends in V_i. The minimum degree condition is necessary, and a result of B. Bollobás and A. D. Scott, J. Graph Theory 46 (2004), 131–143 shows that this conjecture holds for regular graphs G(i.e., when Δ(G)=δ(G)). We prove this conjecture for graphs G with \begin{eqnarray*}\Delta(G)\le\frac{7}{5}\delta(G)\end{eqnarray*}; hence, it holds for graphs ]ensuremathG with \begin{eqnarray*}\delta(G)\ge\frac{5}{7}|V(G)|\end{eqnarray*}. © 2009 Wiley Periodicals, Inc. J Graph Theory 63: 210–225, 2010     

逻辑系统$G_3$中命题的真度值之集在[0,1]上的分布

利用势为3的均匀概率空间的无穷乘积在G■del三值命题逻辑中引入了公式的真度概念,给出了真度推理规则,证明了全体公式的真度值之集在[0,1]上是稠密的,并给出了公式真度的表达通式,为进一步建立三值命题逻辑的近似推理理论奠定了基础．