Über zwei von Hamel herrührende Extremumsätze der Funktionentheorie

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Robust branch-cut-and-price for the Capacitated Minimum Spanning Tree problem over a large extended formulation

This paper presents a robust branch-cut-and-price algorithm for the Capacitated Minimum Spanning Tree Problem (CMST). The variables are associated to q-arbs, a structure that arises from a relaxation of the capacitated prize-collecting arborescence problem in order to make it solvable in pseudo-polynomial time. Traditional inequalities over the arc formulation, like Capacity Cuts, are also used. Moreover, a novel feature is introduced in such kind of algorithms: powerful new cuts expressed over a very large set of variables are added, without increasing the complexity of the pricing subproblem or the size of the LPs that are actually solved. Computational results on benchmark instances from the OR-Library show very significant improvements over previous algorithms. Several open instances could be solved to optimality.     

Beweis für die Invarianz des ebenen Gebiets

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Effect of non-associated electrolyte solutions on the behaviour of poly(vinyl alcohol)-based hydrogels

The aim of this paper is to present the behaviour of the poly(vinyl alcohol) hydrogels [PVA-HG] in sodium and potassium chlorides aqueous solutions, due to their interactions. The tested [PVA-HG]-s have been obtained by repeated freezing and thawing cycles. White, heterogeneous hydrogels have been obtained. These hydrogels exhibit a mechanical active behaviour at their contact with electrolytes aqueous solutions, manifested by important changing in mass, volume and density of the hydrogel samples. These modifications could be explained by water elimination from the hydrogels that initially reached the equilibrium of swelling. The kinetic of the water desorption and the reversibility of this process, have been studied and some of the factors that influence this behaviour have been evidenced. The sensitivity of PVA hydrogels to electrolyte nature and concentration could be used in sensors design and also could explain some aspects of electrolytes diffusion through PVA membranes and targeted drugs delivery.     

A formula with some applications to the theory of Lyapunov exponents

We prove an elementary formula about the average expansion of certain products of 2 by 2 matrices. This permits us to quickly re-obtain an inequality by M. Herman and a theorem by Dedieu and Shub, both concerning Lyapunov exponents. Indeed, we show that equality holds in Herman’s result. Finally, we give a result about the growth of the spectral radius of products. Financial support from Pronex-Dynamical Systems, CNP_q 001/2000 and from Faperj is gratefully acknowledged.     

Banach envelopes of vector valued H spaces

In the paper we describe the Banach envelopes of Hardy spaces of analytic functions of several variables on polydiscs taking values in quasi-Banach spaces.