时标上的推广的Pachpatte型不等式及其在边值问题中的应用

该文利用单调化技巧研究了时标上的推广的Pachpatte型不等式, 该不等式右端有一个非常数项和三个包含未知函数与没有假设单调性的非线性函数的复合函数的积分项, 不等式左端是未知函数与非线性函数的复合函数. 所得不等式不仅把Pachpatte型不等式的离散形式和连续形式统一起来, 而且推广了已有的时标上的相应不等式. 最后, 用得到的结果研究时标上边值问题解的估计.     

一类两个变量的弱奇性Wendroff积分不等式的推广

建立了一类有两个变量的非线性弱奇性Wendroff型积分不等式解的估计,所得结果推广了过去关于非线性弱奇性Wendroff型积分不等式的相关结果,所给出的解的估计更具有一般性.     

带有无穷求和的非线性离散不等式的推广及应用

本文研究一类带有多个非线性项和无穷求和的二元离散不等式,借助数学归纳法,给出这类不等式中未知函数的估计,所得结果推广了一些已有结果.最后,本文利用此结果得到一个差分方程解的上界.     

含有n个无关变元的欧阳型非线性离散不等式

讨论N^n上的Ou—Iang型离散不等式，得到了几个非线性离散不等式．并将所得结论用于研究一类非线性时滞偏差分方程解的有界性．     

一类新的弱奇性Volterra 积分不等式解的估计

收稿研究了一类新的含有多个非线性项的弱奇性Volterra积分不等式解的估计,所得结果推广了过去关于弱奇性Volterra型积分不等式的相关结果,并用实例给出了解的估计.     

一类三变量非线性和差分不等式中未知函数的估计

Gronwall-Bellman型积分不等式的离散形式及其推广形式是研究和差分方程解的存在性、有界性和唯一性等定性性质的重要工具.研究了一类六重非线性和差分不等式,和号外含非常数因子,和项外包含了非常数项.利用差分算子的性质、求和技巧、变量替换技巧和积分中值定理等分析手段,给出了和差分不等式中未知函数的上界估计,推广了已有结果.最后举例说明所得结果可以用来研究三独立变量差分方程解的定性性质.     

抛物型变分不等式的一类全离散非协调有限元方法

讨论了抛物型变分不等式的一类全离散非协调有限元方法,得到了相应的最优误差估计,改进了以往文献的结果.     

弱奇性Volterra积分不等式解的估计

Medved对弱奇性Gronwall型和Henry型积分不等式解的估计提出一种新方法，本文将他的方法稍加改进用来研究更广的Volterra型弱奇性线笥及非线性积分不等式解的估计，导出解的先验逐点界公式，并举例说明了结果的应用。     

一类非线性积分不等式组中未知函数的估计

研究了一类二维非线性积分不等式组,该不等式组积分号外有非常数因子,不能用向量形式的Gronwall-Bellman型积分不等式进行估计.先利用Bernoulli不等式把非线性问题转化成线性问题,利用变量替换技巧和放大技巧研究只含有一个未知函数的积分不等式,接着利用两个引理和变量替换技巧和放大技巧给出不等式组中两个未知函数的估计.结果可用于研究积分、微分动力系统解的性质.     

一类非线性时滞Volterra-Fredholm型积分不等式及其应用

在文献马庆华和J.Pecǎri,2008的基础上,建立了一个新的VolterraFredholm型非线性时滞积分不等式.把参考文献中不等式右端被积因子w(u)推广成w_1(u)u和w_1(u)w_2(u)的非线性函数.运用放大技巧、积分微分技巧、变量替换技巧、反函数技巧、常量与变量的辩证关系,给出了不等式中未知函数的估计.推广了文献中相应不等式的结果.最后,用所得结果给出了Volterra-Fredholm积分方程解的估计.     

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.