Epi-拓扑的某些性质

Throughout this paper R denotes the set of all real numbers.An extended real valued function j f X-[--oo, +oc] is called lower semicontinuouson X if fOr each real Q, {x' f(x) > o} is open in X. Clearly, f is lower semicontinuous ifand only if, its epigraph eghf = {(x, a) f f(x) 5 cr} is closed in X x R. f is caJ1ed proper ifit is somewhere finite, and its values lie in (--co, +oc]. We denote by LSC(X) the set of ajlproper lower semicontinuous functions.In the sequel, we identify lower se…     

Classification of Spherical Fusion Categories of Frobenius-Schur Exponent 2

In this paper,we propose a new approach towards the classification of spherical fusion categories by their Frobenius-Schur exponents.We classify spherical fusion categories of Frobenius-Schur exponent 2 up to monoidal equivalence.We also classify modular categories of Frobenius-Schur exponent 2 up to braided monoidal equivalence.It turns out that the Gauss sum is a complete invariant for modular categories of FrobeniusSchur exponent 2.This result can be viewed as a categorical analog of Arf's theorem on the classification of non-degenerate quadratic forms over fields of characteristic 2.     

关于MH中的Lie双代数和余Poisson-Hopf代数

本文研究余三角Ｈｏｐｆ代数余模范畴中的Ｌｉｅ双代数和余ＰｏｉｓｓｏｎＨｏｐｆ代数,我们主要讨论余三角Ｈｏｐｆ代数余模范畴中的Ｌｉｅ双代数和余Ｐｏｉｓｓｏｎ－Ｈｏｐｆ代数之间的关系。     

三维编织复合材料模量的双尺度有限元计算

针对三维编织复合材料的力学性能进行了双尺度有限元(TSA)数值计算,给出了计算模型和算法过程,并将数值结果与文献中的实验数据进行了比较,验证了算法的物理准确性。编织复合材料的力学性能不仅依赖于材料的基本组份,也与细观构造相关。双尺度有限元计算可以数值模拟出三维编织复合材料的整体力学性能,从而为材料的研发提供指导。本文的双尺度有限元三维数值计算方法可以推广到其他增强／孔隙等多相复合材料的数值模拟。     

The Generic Stability and Existence of Essentially Connected Components of Solutions for Nonlinear Complementarity Problems

The aim of this paper is to develop the general generic stability theory for nonlinear complementarity problems in the setting of infinite dimensional Banach spaces. We first show that each nonlinear complementarity problem can be approximated arbitrarily by a nonlinear complementarity problem which is stable in the sense that the small change of the objective function results in the small change of its solution set; and thus we say that almost all complementarity problems are stable from viewpoint of Baire category. Secondly, we show that each nonlinear complementarity problem has, at least, one connected component of its solutions which is stable, though in general its solution set may not have good behaviour (i.e., not stable). Our results show that if a complementarity problem has only one connected solution set, it is then always stable without the assumption that the functions are either Lipschitz or differentiable.     

Lipschitz functions with maximal Clarke subdifferentials are generic

We show that on a separable Banach space most Lipschitz functions have maximal Clarke subdifferential mappings. In particular, the generic nonexpansive function has the dual unit ball as its Clarke subdifferential at every point. Diverse corollaries are given.

     

The near centre of Doi-Hopf module categoryA M (H) C

It is known that any strict tensor category (C⊗I) determines a braided tensor categoryZ(C), the centre ofC. WhenA is a finite dimension Hopf algebra, Drinfel’d has proved thatZ(_A M) is equivalent to _D(A) M as a braided tensor category, whereA ^M is the left A-module category andD(A) is the Drinfel’d double ofA. For a braided tensor category, the braidC _U,v is a natural isomorphism for any pair of object (U,V) in. If weakening the natural isomorphism of the braidC _U,V to a natural transformation, thenC _U,V is a prebraid and the category with a prebraid is called a prebraided tensor category. Similarly it can be proved that any strict tensor category determines a prebraided tensor category Z∼ (C), the near centre of. An interesting prebraided tensor structure of the Yetter-Drinfel’d category _C*A YD ^C*A given, whereC # A is the smash product bialgebra ofC andA. And it is proved that the near centre of Doi-Hopf module _A M(H) ^C is equivalent to the Yetter-Drinfel’ d _C*A YD ^C*A as prebraided tensor categories. As corollaries, the prebraided tensor structures of the Yetter-Drinfel’d category _A YD ^A , the centres of module category and comodule category are given.     

范畴MΔ中的正合列

本文研究域上矩阵给出的范畴,给出了正合性的等价刻画,提出了将正合列理论应用于矩阵论的途径．     

Metric,Fractal Dimensional and Baire Results on the Distribution of Subsequences

Let X be a locally compact metric space. One important object connected with the distribution behavior of an arbitrary sequence x on X is the set M( x ) of limit measures of x . It is defined as the set of accumulation points of the sequence of the discrete measures induced by x . Using binary representation of reals one gets a natural bijective correspondence between infinite subsets of the set ℕ of positive integers and numbers in the unit interval I = 〈0, 1]. Hence to each sequence x = (x_n)_n∈ℕ ∈ X^ℕ and every a I there corresponds a subsequence denoted by a x . We investigate the set M(a x ) for given x with emphasis on the behavior for “typical” a in the sense of Baire category, Lebesgue measure and Hausdorff dimension.     

Incidence Category of the Young Lattice,Injections Between Finite Sets,and Koszulity

We study the quadratic quotients of the incidence category of the Young lattice defined by the zero relations corresponding to adding two boxes to the same row,or to the same column,or both.We show that the last quotient corresponds to the Koszul dual of the original incidence category,while the first two quotients are,in a natural way,Koszul duals of each other and hence they are in particular Koszul self-dual.Both of these two quotients are known to be basic representatives in the Morita equivalence class of the category of injections between finite sets.We also present a new,rather direct,argument establishing this Morita equivalence.