Strong Unicity of Restricted p-Centers

Given a continuous seminorm p on a separated locally convex linear topological space X, we study in this paper strong uniqueness of the so-called restricted p-centers of sets. First we explore finite extremal characterizations of strongly unique restricted p-centers of subsets of X from its finite dimensional subspaces. Our main goal here is to investigate strong uniqueness of restricted p-centers of certain sets from the so-called p-RS sets, which are defined as closed convex sets that are obtained by imposing convex side constraints arising from boundedness of coefficients on translates of certain subspaces of X.     

Complex-valued preplaces and the nonring cmc subsets of a ring

We show that the torsion free Krull-Schmidt-Azumaya Theorem holds for the integral group ring Z D ₈ Were D ₈ is the group of order 8, but torsion free cancellation (and hence also the torsion free Krull-Schmidt-Azumaya theorem) fails for the integral group ring Z D ₃₂ We summarize the cases for which the integral group ring Z G is known to satisfy the torsion free Krull-Schmidt-Azumaya Theorem, Z D ₁₆ being the only open case.     

新型多孔芳香骨架材料用于硝基爆炸物的检测

采用付玫瑰苯胺与对苯二甲醛通过希夫碱偶联反应制备了新型的多孔芳香骨架材料.经过FTIR,TGA,PXRD,SEM,TEM和Ar吸附等分析方法对多孔芳香骨架材料的成键方式和骨架结构进行了表征.分析结果显示,该多孔芳香骨架材料具有优异的热稳定性(350℃仅失重5%)和溶剂稳定性,其Langmuir比表面积约为472m~2/g.紫外光谱和荧光光谱测试分析表明,该材料在苯、甲苯和氯苯等芳香化合物环境中无明显的荧光强度变化.然而在硝基爆炸物环境中会发生灵敏的、专一的荧光淬灭现象.该多孔材料可应用于硝基爆炸物的检测.     

A unique continuation result for the plate equation and an application

In this paper, we prove the unique continuation property for the weak solution of the plate equation with the low regular coefficient. Then, we apply this result to study the global attractor for the semilinear plate equation with a localized damping. Copyright © 2015 John Wiley & Sons, Ltd.     

<Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript> estimates and asymptotic behavior of extremal function to Hardy-Sobolev type inequality on the H-type group*

This paper is devoted to discuss the regularity of the weak solution to a class of non-linear equations corresponding to Hardy-Sobolev type inequality on the H-type group. Combining the Serrin's idea and the Moser's iteration, L^p estimates of the weak solution are obtained, which generalize the results of Garofalo and Vassilev in [6, 14]. As an application, asymptotic behavior of the weak solution has been discussed. Finally, doubling property and unique continuation of the weak solution are given. *This material is based upon work funded by Zhejiang Provincial Natural Science Foundation of China under Grant No. Y606144.     

Identification of Cavities Inside Two-Dimensional Heterogeneous Isotropic Elastic Bodies

In this paper, we discuss the uniqueness in determining cavities (i.e., nonrectilinear cracks) in a heterogeneous isotropic elastic medium in two dimensions. Our main result asserts that there is at most one cavity in the elastic medium which yields the same surface displacements and stresses on an arbitarily small portion of the boundary. The boundaries of cavities are assumed to be piecewise smooth and admit edges where no net force is exerted. The key of the proof is the unique continuation for the isotropic Lamé system and geometric considerations. This revised version was published online in August 2006 with corrections to the Cover Date.     

两相同部件冷贮备可修系统的定性分析

用纯分析的方法给出了两相同部件冷贮备可修系统解的存在惟一性证明.     

Unique factorization of compositive hereditary graph properties

A graph property is any class of graphs that is closed under isomorphisms. A graph property P is hereditary if it is closed under taking subgraphs; it is compositive if for any graphs G1, G2 ∈ P there exists a graph G ∈ P containing both G1 and G2 as subgraphs. Let H be any given graph on vertices v1, . . . , vn, n ≥ 2. A graph property P is H-factorizable over the class of graph properties P if there exist P 1 , . . . , P n ∈ P such that P consists of all graphs whose vertex sets can be partitioned into n parts, possibly empty, satisfying: 1. for each i, the graph induced by the i-th non-empty partition part is in P i , and 2. for each i and j with i = j, there is no edge between the i-th and j-th parts if vi and vj are non-adjacent vertices in H. If a graph property P is H-factorizable over P and we know the graph properties P 1 , . . . , P n , then we write P = H [ P 1 , . . . , P n ]. In such a case, the presentation H[ P 1 , . . . , P n ] is called a factorization of P over P. This concept generalizes graph homomorphisms and (P 1 , . . . , P n )-colorings. In this paper, we investigate all H-factorizations of a graph property P over the class of all hered- itary compositive graph properties for finite graphs H. It is shown that in many cases there is exactly one such factorization.