Numerical Method Based on Compatible Manifold Element for Thin Plate Bending

The typical quadrangular and triangular elements for thin plate bending based on Kirchhoff assumptions are the non- conforming elements with low computational accuracy and limitative application range in fmite element method（FEM）. Some compatible elements can be developed by the means of supplementing correction functions, increasing nodes in element or on the boundaries, expanding nodal degrees of freedom（DOF）, etc, but these elements are inconvenient to apply in practice for the high calculation complexity. In this paper, in order to overcome the defects of thin plate bending finite element, numerical manifold method（NMM） was introduced to solve thin plate bending deformation problem. Rectangular mesh was adopted as mathematical mesh to form f＇mite element cover system, and then 16-cover manifold element was proposed. Numerical manifold formulas were constructed on the basis of minimum potential energy principle, displacement boundary conditions are implemented by penalty function method, and all the element matrixes were derived in details. The 16-cover element has a simple calculation process for employing only the transverse displacement cover DOFs as the basic unknown variables, and has been proved to meet the requirements of completeness and full compatibility. As an application, the presented 16-cover element has been used to analyze bending deformation of square thin plate under different loads and boundary conditions, and the results show that numerical manifold method with compatible element, compared with finite element method, can improve computational accuracy and convergence greatly.

Simple Minimum(K_4-e)-coverings of Complete Multipartite Graphs

A decomposition of K_(n(g))∪Γ, the complete n-partite equipartite graph over gn vertices union a graph Γ(called the excess) that is a subgraph of K_(n(g)), into edge disjoint copies of a graph G is called a simple minimum group divisible covering of type g^n with G if Γ contains as few edges as possible. We examine all possible excesses for simple minimum group divisible(K_4-e)-coverings.Necessary and sufficient conditions are established for their existence.

Applications of k-covers

We investigate a role of k-covers in selection principles theory. Some results about relationships between Ramsey theory and game theory and selection principles that involve k-covers are also given.

Toughness for Fractional (2, b, k)-Critical Covered Graphs

Let h:E(G)→[0,1]be a function.If a≤∑e∋xh(e)≤b holds for each x∈V(G),then we call G[Fh]a fractional[a,b]-factor of G with indicator function h,where Fh={e:e∈E(G),h(e)>0}.A graph G is called a fractional[a,b]-covered graph if for every edge e of G,there is a fractional[a,b]-factor G[Fh]with h(e)=1.Zhou,Xu and Sun[S.Zhou,Y.Xu,Z.Sun,Degree conditions for fractional(a,b,k)-critical covered graphs,Information Processing Letters 152(2019)105838]defined the concept of a fractional(a,b,k)-critical covered graph,i.e.,for every vertex subset Q with|Q|=k of G,G−Q is a fractional[a,b]-covered graph.In this article,we study the problem of a fractional(2,b,k)-critical covered graph,and verify that a graph G withδ(G)≥3+k is a fractional(2,b,k)-critical covered graph if its toughness t(G)≥1+1b+k2b,where b and k are two nonnegative integers with b≥2+k2.

A Generalization of σ-Permutability

Throughout this paper,all groups are finite and G always denotes a finite group;σis some partition of the set of all primes P.A group G is said to beσ-primary if G is aπ-group for someπ∈σ.Aπ-semiprojector of G[29]is a subgroup H of G such that HN/N is a maximalπ-subgroup of G/N for all normal subgroups N of G.LetП⊆σ.Then we say thatχ={X_(1),...,X_(t)}is aП-covering subgroup system for a subgroup H in G if all members of the setχareσ-primary subgroups of G and for eachπ∈Пwithπ∩π(H)≠φthere are an index i and aπ-semiprojector U of H such that U≤X_(i).We study the embedding properties of subgroups H of G under the hypothesis that G has aП-covering subgroup systemχsuch that H permutes with X^(x)for all X∈χand x∈G.Some well-known results are generalized.

一类单调斜积半流的ω-极限集的提升动力学行为

本文研究了一类具有极小基流的单调斜积半流.在假定半流存在一个半连续的半平衡的前提下,我们证明了具有某种一致稳定性的正半轨线的ω-极限集具有1-covering性质,这为理解系统的全局动力学提供了几何洞察.

A Result on Fractional(a,b,k)-critical Covered Graphs

A fractional[a,b]-factor of a graph G is a function h from E(G)to[0,1]satisfying a≤d^(h)_(G)(v)≤b for every vertex v of G,where d^(h)_(G)(v)=∑e∈E(v)h(e)and E(v)={e=uv:u∈V(G)}.A graph G is called fractional[a,b]-covered if G contains a fractional[a,b]-factor h with h(e)=1 for any edge e of G.A graph G is called fractional(a,b,k)-critical covered if G—Q is fractional[a,b]-covered for any Q⊆V(G)with∣Q∣=k.In this article,we demonstrate a neighborhood condition for a graph to be fractional(a,b,k)-critical covered.Furthermore,we claim that the result is sharp.

INJECTIVE PRECOVERS AND MODULES OF GENERALIZED INVERSE POLYNOMIALS

This paper is motivated by S. Park [10] in which the injective cover of left R[x]- module M[x? ] of inverse polynomials over a left R-module M was discussed. The 1 author considers the ?-covers of modules and shows that if η : P ?→ M is an ?- cover of M, then [ηS, ] : [PS, ] ?→ [MS, ] is an [?S, ]-cover of left [[RS, ]]-module ≤ ≤ ≤ ≤ ≤ [MS, ], where ? is a class of left R-modules and [MS, ] is the left [[RS, ]]-module of ≤ ≤ ≤ generalized inverse polynomials over a left R-module M. Also some properties of the injective cover of left [[RS, ]]-module [MS, ] are discussed. ≤