On equivalent stability properties in semi-infinite optimization

This paper studies noncompact feasible sets of a semi-infinite optimization problem which are defined by finitely many equality constraints and infinitely many inequality constraints. The main result is the equivalence of the overall validity of the Extended Mangasarian Fromovitz Constraint Qualification with certain (topological) stability conditions. Furthermore, two perturbation theorems being of independent interest are presented.This work was supported by the Deutsche Forschungsgemeinschaft under grant Gu 304/1-2.     

随机集的独立性与同分布性的刻划

本文绘出了随机集的独立性与同分布性的刻化，所给出的准则比Hess[4]，[5]更易于验证．     

L─fts中的导集和导算子

本文首先讨论了Ｌ─ｆｔｓ中ＬＦ集的聚点的分布；其次讨论了ＬＦ集的导集的一些性质，并给出了一般的Ｌ─ｆｔｓ中类似于杨忠道定理的结果；本文最后引进了导算子的概念，并用其刻划一般的Ｌ─ｆｔｓ．     

Analytical solution of Everett integral using Lorentzian Preisach function approximation

In this paper, we take in to account the Lorentzian function, already proposed as analytical function approximation in scalar Preisach-type modeling of hysteresis of soft magnetic materials. Preliminarily, we point out the properties of the Lorentzian function and the physical and mathematical meaning of its parameters. Successively, we show how the use of the Lorentzian function approximation allows to solve in complete analytical way the Everett's integral. In particular, we present in the paper the analytical expression in closed form of the first magnetization curve, of the symmetric and non-symmetric minor loops, and of the first- and second-order reversal curves. In addition, we show the use of the complete analytical formulas of the symmetric magnetic loops above-mentioned, applied to a simple identification procedure of the Lorentzian function parameters, by the knowledge of the measured major loop. Finally, in order to show the practical use of the analytical expression found, some computation examples and comparisons with experimental data are shown.     

New large sets of t‐designs with prescribed groups of automorphisms

In this article, we investigate the existence of large sets of 3‐designs of prime sizes with prescribed groups of automorphisms PSL(2,q) and PGL(2,q) for q < 60. We also construct some new interesting large sets by the use of the computer program DISCRETA. The results obtained through these direct methods along with known recursive constructions are combined to prove more extensive theorems on the existence of large sets. © 2006 Wiley Periodicals, Inc. J Combin Designs 15: 210–220, 2007     

Additive and multiplicative Sidon sets

Summary Inspired by a paper of Sárk?zy [4] we study sets of integers and sets of residues with the property that all sums and all products are distinct.     

Threshold start-up control policy for polling systems

A threshold start-up policy is appealing for manufacturing (service) facilities that incur a cost for keeping the machine (server) on, as well as for each restart of the server from its dormant state. Analysis of single product (customer) systems operating under such a policy, also known as the N-policy, has been available for some time. This article develops mathematical analysis for multiproduct systems operating under a cyclic exhaustive or globally gated service regime and a threshold start-up rule. It pays particular attention to modeling switchover (setup) times. The analysis extends/unifies existing literature on polling models by obtaining as special cases, the continuously roving server and patient server polling models on the one hand, and the standard M/G/1 queue with N-policy, on the other hand. We provide a computationally efficient algorithm for finding aggregate performance measures, such as the mean waiting time for each customer type and the mean unfinished work in system. We show that the search for the optimal threshold level can be restricted to a finite set of possibilities. This revised version was published online in June 2006 with corrections to the Cover Date.     

Self-organization driven by broad band light

We show that strong incoherent broad band light transports electrons in random media in opposite to the electric force eE direction. Current flows against the voltage drop and static polarization is generated reversed to the applied electric field. This unusual response amplifies the internal electric fields and drives self-organization phenomena in wide class of disordered materials. The model proposed gives an idea on how the life on Earth could have emerged.     

Clustering reduced interval data using Hausdorff distance

Summary  In the last decade, factorial and clustering techniques have been developed to analyze multidimensional interval data (MIDs). In classic data analysis, PCA and clustering of the most significant components are usually performed to extract cluster structure from data. The clustering of the projected data is then performed, once the noise is filtered out, in a subspace generated by few orthogonal variables. In the framework of interval data analysis, we propose the same strategy. Several computational questions arise from this generalization. First of all, the representation of data onto a factorial subspace: in classic data analysis projected points remain points, but projected MIDs do not remains MIDs. Further, the choice of a distance between the represented data: many distances between points can be computed, few distances between convex sets of points are defined. We here propose optimized techniques for representing data by convex shapes, for computing the Hausdorff distance between convex shapes, based on an L ₂ norm, and for performing a hierarchical clustering of projected data.