闭正则模糊拟阵的子拟阵的正则性

研究了闭正则模糊拟阵的子拟阵的正则性等性质.得到了闭正则模糊拟阵的两种子拟阵的正则性等性质,即k-子拟阵为闭正则模糊拟阵,限制子拟阵不是闭正则模糊拟阵,给出了闭正则模糊拟阵的收缩拟阵为闭正则模糊拟阵等结论.     

初等模糊拟阵与基本截片模糊拟阵的若干性质

对两种初等模糊拟阵和基本截片模糊拟阵的定义进行了比较,研究了它们之间的关系.研究了初等模糊拟阵的若干性质,得到了初等模糊拟阵和基本截片模糊拟阵为闭正则模糊拟阵等结论,给出了初等模糊拟阵的等价刻画以及初等模糊拟阵与其截拟阵之间的关系.     

准模糊图拟阵基图的最大权基与字典序最大的基

模糊拟阵的基图是模糊拟阵的基本概念.在准模糊图拟阵的基础上,给出了准模糊图拟阵基图的最大权基与字典序最大的基的性质,这将有利于模糊拟阵从基础研究逐渐转向应用研究.     

准模糊图拟阵基图的性质

模糊拟阵的基图是模糊拟阵的基本概念.在准模糊图拟阵的基础上,讨论了准模糊图拟阵基图的一些基本性质,得到了相关的几个结论,这些结论有利于进一步研究模糊拟阵的其它性质.     

准模糊图拟阵的次限制最小基

模糊拟阵的基图是模糊拟阵的基本概念.在准模糊图拟阵的基础上,给出了准模糊图拟阵基图的次限制最小基的一些性质,这将有利于进一步研究模糊拟阵的其它性质.     

准模糊图拟阵的相邻的次限制最小基

模糊拟阵的基图是模糊拟阵的基本概念.在准模糊图拟阵的基础上,给出了准模糊图拟阵基图的相邻的次限制最小基的一些性质.将为深入研究模糊拟阵的内在本质,进一步研究模糊拟阵的算法奠定了基础.     

由上近似数诱导的拟阵及其特征

拟阵理论与粗糙集理论之间有很多相似之处,近年来,探讨这二者之间的联系成为一个研究热点.首先利用基于等价关系的上近似数诱导了一系列拟阵结构,然后刻画了这类拟阵的独立集、基集、秩函数以及闭包等,讨论了与其它拟阵之间的一些联系.     

准模糊图拟阵基的交换

本文讨论了准模糊图拟阵基的交换定理,在此基础上给出了基有序的准模糊图拟阵的一些性质.     

闭模糊拟阵模糊基的判定

通过讨论闭模糊拟阵的导出拟阵序列和模糊基的结构,找到了判定闭模糊拟阵的模糊基的一个充要条件。根据此充要条件,给出了从导出拟阵序列得到闭模糊拟阵的模糊基的一种算法。     

关于G-V模糊拟阵的对偶模糊拟阵概念的推广

模糊拟阵的研究方法之一就是通过基本序列和导出拟阵序列将模糊拟阵问题转化为普通拟阵问题来进行研究。本文正是采用这个研究方法,主要完成了三项工作:一是给出并证明了闭正规模糊拟阵和正规模糊拟阵的几个充要条件;二是将对偶模糊拟阵概念从闭正规模糊拟阵推广到正规模糊拟阵并讨论了有关性质和计算;三是证明了除正规模糊拟阵外,其他模糊拟阵不存在这样的对偶模糊拟阵。     

两类带有确定潜伏期的SEIS传染病模型的分析

通过研究两类带有确定潜伏期的SEIS传染病模型,发现对种群的常数输入和指数输入会使疾病的传播过程产生本质的差异．对于带有常数输入的情形,找到了地方病平衡点存在及局部渐近稳定的阈值,证明了地方病平衡点存在时一定局部渐近稳定,并且疾病一致持续存在．对于带有指数输入的情形,发现地方病平衡点当潜伏期充分小时是局部渐近稳定的,当潜伏期充分大时是不稳定的．     

基于规模的企业竞争力蜘蛛图法评价研究

科学合理的规模结构不仅是实现规模经济的基本条件,而且是提高经济效益、降低交易成本、获得较高的企业竞争力的重要保证.基于规模理论,从生产规模、资本规模、市场规模以及效益规模四大因素入手,提出了一套基于规模的企业竞争力评价指标体系,运用蜘蛛图法建立了基于规模的企业竞争力评价模型,并结合具体的数据分析说明了企业竞争力的大小强弱.此种方法具有直观形象、定量化、可操作性强的特点.     

A sufficient condition for DP-4-colorability

DP-coloring of a simple graph is a generalization of list coloring, and also a generalization of signed coloring of signed graphs. It is known that for each $k\in \{3,4,5,6\}$, every planar graph without $C_k$ is 4-choosable. Furthermore, Jin et al. (2016) showed that for each $k\in \{3,4,5,6\}$, every signed planar graph without $C_k$ is signed 4-choosable. In this paper, we show that for each $k\in \{3,4,5,6\}$, every planar graph without $C_k$ is 4-DP-colorable, which is an extension of the above results.     

Problems on matchings and independent sets of a graph

Let $G$ be a finite simple graph. For $X?V\left(G\right)$, the difference of $X$, $d\left(X\right)?\left|X\right|?\left|N\left(X\right)\right|$ where $N\left(X\right)$ is the neighborhood of $X$ and $max\{d\left(X\right):X?V\left(G\right)\}$ is called the critical difference of $G$. $X$ is called a critical set if $d\left(X\right)$ equals the critical difference and $\ker \left(G\right)$ is the intersection of all critical sets. $\mathrm{diadem}\left(G\right)$ is the union of all critical independent sets. An independent set $S$ is an inclusion minimal set with$d\left(S\right)>0$ if no proper subset of $S$ has positive difference.A graph $G$ is called a König–Egerváry graph if the sum of its independence number $\alpha \left(G\right)$ and matching number $\mu \left(G\right)$ equals $\left|V\left(G\right)\right|$.In this paper, we prove a conjecture which states that for any graph the number of inclusion minimal independent set $S$ with $d\left(S\right)>0$ is at least the critical difference of the graph.We also give a new short proof of the inequality $\left|\ker \left(G\right)\right|+\left|\mathrm{diadem}\left(G\right)\right|\le 2\alpha \left(G\right)$.A characterization of unicyclic non-König–Egerváry graphs is also presented and a conjecture which states that for such a graph $G$, the critical difference equals $\alpha \left(G\right)?\mu \left(G\right)$, is proved.We also make an observation about $\ker \left(G\right)$ using Edmonds–Gallai Structure Theorem as a concluding remark.     

Some aspects of dimension theory for topological groups

We discuss dimension theory in the class of all topological groups. For locally compact topological groups there are many classical results in the literature. Dimension theory for non-locally compact topological groups is mysterious. It is for example unknown whether every connected (hence at least 1-dimensional) Polish group contains a homeomorphic copy of $[0,1]$. And it is unknown whether there is a homogeneous metrizable compact space the homeomorphism group of which is 2-dimensional. Other classical open problems are the following ones. Let $G$ be a topological group with a countable network. Does it follow that $\dim G=\mathrm{ind}G=\mathrm{Ind}G$? The same question if $X$ is a compact coset space. We also do not know whether the inequality $\dim (G\times H)\le \dim G+\dim H$ holds for arbitrary topological groups $G$ and $H$ which are subgroups of $\sigma$-compact topological groups. The aim of this paper is to discuss such and related problems. But we do not attempt to survey the literature.     

Milnor方图中的w-凝聚性

整环R称为ω-凝聚整环,是指R的每个有限型理想是有限表现型的.本文证明了ω-凝聚整环是v-凝聚整环,且若(RDTF,M)是Milnor方图,则在Ⅰ型情形,R是ω-凝聚整环当且仅当D和T都是ω-整环,且T_M是赋值环;对于Ⅱ-型情形,R是ω-凝聚整环当且仅当D是域,[F:D]<∞,M是R的有限型理想,T是ω-凝聚整环,且R_M是凝聚整环.     

List star chromatic index of sparse graphs

A star edge-coloring of a graph $G$ is a proper edge coloring such that every 2-colored connected subgraph of $G$ is a path of length at most 3. For a graph $G$, let the list star chromatic index of $G$, $c{h}_s^{\prime }\left(G\right)$, be the minimum $k$ such that for any $k$-uniform list assignment $L$ for the set of edges, $G$ has a star edge-coloring from $L$. Dvo?ák et al. (2013) asked whether the list star chromatic index of every subcubic graph is at most 7. In Kerdjoudj et al. (2017) we proved that it is at most 8. In this paper we consider graphs with any maximum degree, we proved that if the maximum average degree of a graph $G$ is less than $\frac{14}{5}$ (resp. 3), then $c{h}_s^{\prime }\left(G\right)\le 2\Delta \left(G\right)+2$ (resp. $c{h}_s^{\prime }\left(G\right)\le 2\Delta \left(G\right)+3$).     

Refined weight of edges in normal plane maps

The weight $w\left(e\right)$ of an edge $e$ in a normal plane map (NPM) is the degree-sum of its end-vertices. An edge $e=uv$ is of type $(i,j)$ if $d\left(u\right)\le i$ and $d\left(v\right)\le j$. In 1940, Lebesgue proved that every NPM has an edge of one of the types $(3,11)$, $(4,7)$, or $(5,6)$, where 7 and 6 are best possible. In 1955, Kotzig proved that every 3-connected planar graph has an edge $e$ with $w\left(e\right)\le 13$, which bound is sharp. Borodin (1989), answering Erd?s’ question, proved that every NPM has either a $(3,10)$-edge, or $(4,7)$-edge, or $(5,6)$-edge.A vertex is simplicial if it is completely surrounded by 3-faces. In 2010, Ferencová and Madaras conjectured (in different terms) that every 3-polytope without simplicial 3-vertices has an edge $e$ with $w\left(e\right)\le 12$. Recently, we confirmed this conjecture by proving that every NPM has either a simplicial 3-vertex adjacent to a vertex of degree at most 10, or an edge of types $(3,9)$, $(4,7)$, or $(5,6)$.By a $k^{\left(?\right)}$-vertex we mean a $k$-vertex incident with precisely $?$ triangular faces. The purpose of our paper is to prove that every NPM has an edge of one of the following types: $(3^{\left(3\right)},10)$, $(3^{\left(2\right)},9)$, $(3^{\left(1\right)},7)$, $(4^{\left(4\right)},7)$, $(4^{\left(3\right)},6)$, $(5^{\left(5\right)},6)$, or $(5,5)$, where all bounds are best possible. In particular, this implies that the bounds in $(3,10)$, $(4,7)$, and $(5,6)$ can be attained only at NPMs having a simplicial 3-, 4-, or 5-vertex, respectively.     

Decomposability index of tournaments

Given a tournament $T$, a module of $T$ is a subset $X$ of $V\left(T\right)$ such that for $x,y\in X$ and $v\in V\left(T\right)?X$, $(x,v)\in A\left(T\right)$ if and only if $(y,v)\in A\left(T\right)$. The trivial modules of $T$ are $?$, $\left\{u\right\}$ $(u\in V\left(T\right))$ and $V\left(T\right)$. The tournament $T$ is indecomposable if all its modules are trivial; otherwise it is decomposable. The decomposability index of $T$, denoted by $\delta \left(T\right)$, is the smallest number of arcs of $T$ that must be reversed to make $T$ indecomposable. For $n\ge 5$, let $\delta \left(n\right)$ be the maximum of $\delta \left(T\right)$ over the tournaments $T$ with $n$ vertices. We prove that $?\frac{n+1}{4}?\le \delta \left(n\right)\le ?\frac{n?1}{3}?$ and that the lower bound is reached by the transitive tournaments.