The character and the wave front set correspondence in the stable range

We relate the distribution characters and the wave front sets of unitary representation for real reductive dual pairs of type I in the stable range.     

On generalized perfect difference sets constructed from Sidon sets

Let $\mathbb{N}$ be the set of positive integers. For a nonempty set A of integers and every integer u, denote by $d_A(u)$ the number of $(a,a^{\prime })$ with $a,a^{\prime }\in A$ such that $u=a-a^{\prime }$. For a sequence S of positive integers, let $S(x)$ be the counting function of S. The set $A\subseteq \mathbb{N}$ is called a perfect difference set if $d_A(u)=1$ for every positive integer u. In 2008, Cilleruelo and Nathanson (2008) [4] constructed dense perfect difference sets from dense Sidon sets. In this paper, as a main result, we prove that: let $f:\mathbb{N}\to \mathbb{N}$ be an increasing function satisfying $f(n)\ge 2$ for any positive integer n, then for every Sidon set B and every function $\omega (x)\to \infty$, there exists a set $A\subseteq \mathbb{N}$ such that $d_A(u)=f(u)$ for every positive integer u and $B(x/3)-\omega (x)\le A(x)\le B(x/3)+\omega (x)$ for all $x\ge C_{f,B,\omega }$.     

基于串联两阶段网络DEA模型的供应链规模收益分析

数据包络分析(DEA)是评价供应链系统(Supply chain system)间相对有效性的一种重要的工具,但是传统的DEA不考虑供应链的内部结构,对系统效率评价偏高;而本文所研究两阶段串联供应链系统,考虑把部分中间产品作为最终产品输出,增加额外中间投入的情形.基于所提出的供应链系统结构,本文建立相应的串联结构下的网络DEA模型,并针对所建立模型进行相关理论的研究,给出了串联结构下的生产可能集和规模收益情况判定方法.最后,进行数值实验,以验证我们提出的结论.     

Characterization and linear-time detection of minimal obstructions to concave-round graphs and the circular-ones property

A graph is concave-round if its vertices can be circularly enumerated so that the closed neighborhood of each vertex is an interval in the enumeration. In this study, we give a minimal forbidden induced subgraph characterization for the class of concave-round graphs, solving a problem posed by Bang-Jensen, Huang, and Yeo [SIAM J. Discrete Math., 13 (2000), pp. 179–193]. In addition, we show that it is possible to find one such forbidden induced subgraph in linear time in any given graph that is not concave-round. As part of the analysis, we obtain characterizations by minimal forbidden submatrices for the circular-ones property for rows and for the circular-ones property for rows and columns and show that, also for both variants of the property, one of the corresponding forbidden submatrices can be found (if present) in any given matrix in linear time. We make some final remarks regarding connections to some classes of circular-arc graphs.     

Definition and detection of data-based uniqueness in evaluating bilinear (two-way) chemical measurements

Multivariate curve resolution methods, frequently used in analyzing bilinear data sets, result in ambiguous decomposition in general. Implementing the adequate constraints may lead to reduce the so-called rotational ambiguity drastically, and in the most favorable cases to the unique solution. However, in some special cases, non-negativity constraint as minimal information of the system is a sufficient condition to resolve profiles uniquely. Although, several studies on exploring the uniqueness of the bilinear non-negatively constrained multivariate curve resolution methods have been made in the literature, it has still remained a mysterious question. In 1995, Manne published his profile-based theorems giving the necessary and sufficient conditions of the unique resolution. In this study, a new term, i.e., data-based uniqueness is defined and investigated in details, and a general procedure is suggested for detection of uniquely recovered profile(s) on the basis of data set structure in the abstract space. Close inspection of Borgen plots of these data sets leads to realize the comprehensive information of local rank, and these argumentations furnish a basis for data-based uniqueness theorem. The reported phenomenon and its exploration is a new stage (it can be said fundament) in understanding and describing the bilinear (matrix-type) chemical data in general.     

Cycle and circle tests of balance in gain graphs: Forbidden minors and their groups

We examine two criteria for balance of a gain graph, one based on binary cycles and one on circles. The graphs for which each criterion is valid depend on the set of allowed gain groups. The binary cycle test is invalid, except for forests, if any possible gain group has an element of odd order. Assuming all groups are allowed, or all abelian groups, or merely the cyclic group of order 3, we characterize, both constructively and by forbidden minors, the graphs for which the circle test is valid. It turns out that these three classes of groups have the same set of forbidden minors. The exact reason for the importance of the ternary cyclic group is not clear. © 2005 Wiley Periodicals, Inc. J Graph Theory     

Necessary Conditions for Differentiability of Distance Functions

Necessary conditions for the Gâteaux differentiability of the distance function to a set are considered. A series of characterizing results is obtained.     

The push-out region of an immersed manifold

We consider immersions: and construct a subspace of which corresponds to a set of embedded manifolds which are either parallel to f, tubes around f or, in general, partial tubes around f. This space is invariant under the action of the normal holonomy group, We investigate the case where is non-trivial and obtain some results on the number of connected components of . Received 24 March 2000.