Approximation of regularized evolution operators

This paper is devoted to the approximation of a regularized evolution operator by a sequence of regularized discrete parameter evolution operators, and the results obtained here are applied to some degenerate partial differential equation.Received: 4 December 2001     

Bounded point evaluations and cyclic polynomials on the spaces $$\hat F$$

LetF be aBK space withAK and denote the set of all formal power series with such that ε F for the sequence of coefficients of . We give a necessary and sufficient condition for a point to be a bounded point evaluation on , and for a polynomial to be cyclic in . As special cases, we obtain the results for the space ℓ _p (β) in [7]. Research of the authors supported under the research project #1232 of the Serbian Ministry of Sciences and Tecnology and, in the case of the second author, also by the DAAD foundation (German Academic Exchange Service), grant 911 103 102 8.     

Some remarks on half-factorial orders

In questo articolo, si dimostra il legame fra la semi-fattorialità e la fattorialità debole nel contesto degli ordini algebrici. In particolare, si ottiene che un ordine semi-fattoriale ha il stesso numero di classi che su chiusura integrale.     

An Edge Point Gibbs Phenomenon for Fourier Series in Two Dimensions

Let f be a function periodic in its two variables x, y with period 2 and having at the origin an edge point jump discontinuity (its graph may be roughly described by a cliff with a smooth but possibly inclined rim). The Fourier series of f exhibits a Gibbs phenomenon as in the one-dimensional case but with an affine horizontal deformation depending on the compass direction of the rim at the origin.Received February 7, 2002; in revised form May 24, 2002 Published online April 4, 2003     

Unitals in Topological Affine Translation Planes Need Not Be Strictly Convex

We study the relationship of two incidence geometric convexity notions, namely, ovoids in real affine spaces and compact unitals of codimension 1 in topological affine translation planes. In [3] we showed that every ovoid in a translation plane is a unital, and we asked if the converse is true. Here we introduce the notion of a shell, which is distinctly weaker than that of an ovoid and still implies the unital property if the translation plane is properly chosen (and the shell is not too degenerate). We give an explicit example of a shell that is not an ovoid. The question remains whether or not conversely, every compact unital of codimension 1 in a translation plane is a shell.This paper was written while the third author was supported by a grant from DFG and TÜBITAK.Received March 12, 2002 Published online November 18, 2002     

Maximal <Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript>‐regularity for elliptic operators with VMO‐coefficients

In this paper we show that the parabolic problem associated with elliptic operators A having coefficients in has the property of maximal -regularity. RID="h1" ID="h1"In Memoriam Philippe Bénilan     

Empirisch begründete Idealtypenbildung. Ein methodisches Prinzip zur Theoriekonstruktion in der interpretativen mathematikdidaktischen Forschung

How does the development of ideal types contribute to an empirically based construction of theories in the interpretative research of mathematics education? Before answering this question I clarify what is meant by the termstheory andideal type. Personal ideal types, ideal types of actions andsituational ideal types are going to be distinguished. Representing research examples. I show that forming ideal types can be considered as a methodical principle for empirically grounded theory construction with common features and different heuristics.     

The Effect of the Geometry of the Particle Distribution in Ostwald Ripening

Based on [1], we derive equations for the radii and the centers that we relate to the Lifshitz-Slyozov-Wagner theory. N.D.A. and G.K. were partially supported by a ENE 99/527 interdisciplinary grant in Materials, and by a grant from the University of Athens. N.D.A. would like to thank also the people at BYU for providing extraordinary hospitality and a stimulating environment during his visit in the Fall of 2000.N.D.A. and G.K. were partially supported by a ENE 99/527 interdisciplinary grant in Materials, and by a grant from the University of Athens. N.D.A. would like to thank also the people at BYU for providing extraordinary hospitality and a stimulating environment during his visit in the Fall of 2000.     

A Stochastic Model Associated with Enskog Equation and Its Kinetic Limit

 We examine a system of particles in which the particles travel deterministically in between stochastic collisions. The collisions are elastic and occur with probability ɛ ^d when two particles are at a distance σ. When the number of particles N goes to infinity and Nɛ ^d goes to a nonzero constant, we show that the particle density converges to a solution of the Enskog Equation. Received: 29 January 2002 / Accepted: 30 July 2002 Published online: 14 November 2002 RID="*" ID="*" Research supported in part by NSF Grant DMS-0072666     

On the Structure of Stationary Solutions of the Navier-Stokes Equations

 This paper is a supplementary section to [1]. We show that without any additional hypothesis the main result in [1] (Theorem 1) can be considerably strengthened. Note. This paper cannot be read independently of [1]. The numbering of equations, theorems and propositions as well as cross-references used here have to be understood as if this paper were an additional section to [1]. Received: 7 May 2002 / Accepted: 15 October 2002 Published online: 10 February 2003 RID="*" ID="*" Supported in part by the Fonds National Suisse. Communicated by A. Kupiainen