Constructions of Solid Hulls

For each concrete category (K,U) an extension LIM(K,U) is constructed and under certain 'smallness conditions' it is proved that LIM(K,U) is a solid hull of (K,U), i.e., the least finally dense solid extension of (K,U). A full subcategory of Top ₂ is presented which does not have a solid hull.     

A characterization of partial directed line graphs

Can a directed graph be completed to a directed line graph? If possible, how many arcs must be added? In this paper we address the above questions characterizing partial directed line (PDL) graphs, i.e., partial subgraph of directed line graphs. We show that for such class of graphs a forbidden configuration criterion and a Krausz's like theorem are equivalent characterizations. Furthermore, the latter leads to a recognition algorithm that requires O(m) worst case time, where m is the number of arcs in the graph. Given a partial line digraph, our characterization allows us to find a minimum completion to a directed line graph within the same time bound.The class of PDL graphs properly contains the class of directed line graphs, characterized in [J. Blazewicz, A. Hertz, D. Kobler, D. de Werra, On some properties of DNA graphs, Discrete Appl. Math. 98(1-2) (1999) 1-19], hence our results generalize those already known for directed line graphs. In the undirected case, we show that finding a minimum line graph edge completion is NP-hard, while the problem of deciding whether or not an undirected graph is a partial graph of a simple line graph is trivial.     

各机器具有相同加工时间的Flow Shop 成组排序问题

本文讨论了m台机器的Folw Shop成组排序问题，工件在不同机器上的加工时间相同，目标函数为极小化完工时间和。给出了一个多项式时间可解的最优算法。     

The classical monotone convergence theorem of Beppo Levi fails in noncommutative -spaces

Let be a complex Hilbert space and let be a von Neumann algebra over equipped with a faithful, normal state . Then is a prehilbert space with respect to the inner product , whose completion is given by the Gelfand-Naimark-Segal representation theorem, according to which there exist a one-to-one -homomorphism of into the algebra of all bounded linear operators acting on and a cyclic, separating vector such that for all . Given any separable Hilbert space , we construct a faithful, normal state on and an increasing sequence of positive operators acting on such that is bounded, but fails to converge both bundlewise and in -norm. We also present an example of an increasing sequence of positive operators which has a subsequence converging both bundlewise and in -norm, but the whole sequence fails to converge in either sense. Finally, we observe that our results are linked to a previous one by R. V. Kadison.

     

Minimizing total completion time for UET tasks with release time and outtree precedence constraints

Brucker et al. (Math Methods Oper Res 56: 407–412, 2003) have given an O(n ²)-time algorithm for the problems , outtree and , outtree . In this note, we show that their algorithm admits an O(n log n)-time implementation.     

Data completion via an energy error functional

We propose, in this Note, a new procedure for data completion based on the minimization of an energy like error functional. The efficiency of the proposed method is illustrated by a thermostatic application. To cite this article: S. Andrieux et al., C. R. Mecanique 333 (2005).     

Complexity results for scheduling chains on a single machine

We investigate the computational complexity of deterministic sequencing problems in which unit-time jobs have to be scheduled on a single machine subject to chain-like precedence constraints. NP-hardness is established for the cases in which the number of late jobs or the total weighted tardiness is to be minimized, and for several related problems involving the total weighted completion time criterion.     

On rectangular products of topological spaces

Several results on rectangular products in the sense of B.A. Pasynkov will be obtained, one of which asserts that for a Tychonoff space X, X × Y is rectangular for any space Y iff X is locally compact and paracompact.     

An Equivalence of Two Categories of sl(n,C)-Modules

We prove that the following two categories of sl(n,C)-modules are equivalent: (1) the category of modules with integral support filtered by submodules of Verma modules and complete with respect to Enright's completion functor; (2) the category of all subquotients of modules FM, where F is a finite-dimensional module and M is a fixed simple generic Gelfand–Zetlin module with integral central character. Our proof is based on an explicit construction of an equivalence which, additionally, commutes with translation functors. Finally, we describe some applications of this both to certain generalizations of the category O and to Gelfand–Zetlin modules.     

Image completion based on creative design of massive images

How can we complete massive images with some missing region? In this paper, we present a new image completion algorithm. Our goal is to finish the uncompleted image with missing region more creative and seamless. In other words, we not only complete the missing region semantic valid but also make the completed image more seamless and consistent.