Matching Extension Missing Vertices and Edges in Triangulations of Surfaces

Let G be a 5‐connected triangulation of a surface Σ different from the sphere, and let be the Euler characteristic of Σ. Suppose that with even and M and N are two matchings in of sizes m and n respectively such that . It is shown that if the pairwise distance between any two elements of is at least five and the face‐width of the embedding of G in Σ is at least , then there is a perfect matching M₀ in containing M such that .     

弱Hopf代数上的Militaru-Stefan提升定理

本文研究了弱Hopf-Galois扩张的扩张模.利用忠实平坦的弱Hopf-Galois扩张理论,研究了弱Hopf代数上的Militaru-Stefan提升定理,推广了文献[10]中的相应结果.进一步地,通过诱导模的自同态环的cleft扩张刻画了弱稳定模.     

基于可拓评价的无菌医疗器具生产环境安全评价与预警研究

将可拓评价方法用于无菌医疗器具生产环境安全评价与预测研究,建立了无菌医疗器具生产环境安全可拓物元评价模型.利用关联函数动态赋权法,改进了待评物元所属安全等级特征值的计算方法,使得判别更加准确.同时也对各单项指标进行了评价与预测,可为企业决策者提供更加有效的科学依据.     

一维六方准晶压电材料中幂函数型曲线裂纹的反平面问题

依据一维六方准晶压电材料反平面问题的基本方程,利用复变函数方法,通过引入适当的保角映射,研究了一维六方准晶压电材料中幂函数型曲线裂纹的反平面问题,并利用Cauchy积分理论,得到电不可通和电可通边界条件下的应力场和位移场的复表示以及裂纹尖端场强度因子的解析表达式.     

Numerical solution of a singular integral equation arising in a cruciform crack problem

A singular integral equation arising in a cruciform crack problem is investigated in the present paper. Based on the convex technique, the piecewise Taylor-series expansion method is extended by introducing a weight parameter. An approximate solution of the singular integral equation is constructed and its convergence and error estimate are made. The variations of the approximate solutions associating with stress intensity factors are analyzed by considering internal pressures of power and sine functions, respectively. By comparing with the known methods, the observations reveal that a good approximation can be achieved using less derivative times, less discretization points, and a suitable weight parameter. The obtained results show that the crack growth is dependent on applied mechanical loadings.     

The ∞‐Besov capacity problem

A theory of ∞‐Besov capacities is developed and several applications are provided. In particular, we solve an open problem in the theory of limits of the ∞‐Besov semi‐norms, we obtain new restriction‐extension inequalities, and we characterize the pointwise multipliers acting on the ∞‐Besov spaces.     

Representability of actions in the category of (Pre)crossed modules in Leibniz algebras

We investigate the representability of actions in the category of (pre)crossed modules in Leibniz algebras. For this, we construct an actor of a (pre)cat¹-Leibniz algebra and then by using the natural equivalence of the categories of (pre)cat¹-Leibniz algebras and that of (pre)crossed modules, we construct the split extension classifier of the corresponding (pre)crossed module.     

Constacyclic codes over finite local Frobenius non-chain rings with nilpotency index 3

The main results of this paper are in two directions. First, the family of finite local Frobenius non-chain rings of length 4 (hence of nilpotency index 3) is determined. As a by-product all finite local Frobenius non-chain rings with $p^4$ elements, (p a prime) are given. Second, the number and structure of γ-constacyclic codes over finite local Frobenius non-chain rings with nilpotency index 3, of length relatively prime to the characteristic of the residue field of the ring, are determined.