Wehrung, Friedrich

It is well known that the real spectrum of any commutative unital ring, and the ℓ-spectrum of any Abelian lattice-ordered group with order-unit, are all completely normal spectral spaces. We prove the following results: (1) Every real spectrum can be embedded, as a spectral subspace, into some ℓ-spectrum. (2) Not every real spectrum is an ℓ-spectru...

magnot, jean-pierre

We examine how implicit functions on ILB-Fréchet spaces can be obtained without metric or norm estimates which are classically assumed. We obtain implicit functions defined on a domain D which is not necessarily open, but which contains the unit open ball of a Banach space. The corresponding inverse functions theorem is obtained, and we finish with...

Bernard, J.M.L.

We develop here an efficient method for the reduction of surface radiation integrals to contour integrals, when we suppose known, as in Physical Optics (PO), the analytic expression of surface currents whose electromagnetic radiation is calculated. Although many authors have studied this problem, we present here an original solution, general and pr...

Abergel, Rémy Moisan, Lionel

We propose a computational procedure to evaluate the generalized incompletegamma function ∫_{x}^{y} s^{p-1} e^{-μs} ds, for0 ≤ x

Wehrung, Friedrich

A compact topological space X is spectral if it is sober (i.e., every irreducible closed set is the closure of a unique singleton) and the compact open subsets of X form a basis of the topology of X, closed under finite intersections. Theorem. A topological space X is homeomorphic to the spectrum of some countable Abelian ℓ-group with unit (resp., ...

Wehrung, Friedrich
Published in
Semigroup Forum

The interval monoid Υ(P)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Upsilon ({P})$$\end{document} of a poset P is defined by generators [x, y], where x≤y\documentc...

Dumitrescu, Cristian

In this paper, we study an extension of Schöning's algorithm [Schöning, 1991] for 3SAT, the clustered Sparrow algorithm. We also present strong arguments that this algorithm is polynomial.

Franc, Alain Blanchard, Pierre Coulaud, Olivier

Distance Geometry Problem (DGP) and Nonlinear Mapping (NLM) are two well established questions: Distance Geometry Problem is about finding a Euclidean realization of an incomplete set of distances in a Euclidean space, whereas Nonlinear Mapping is a weighted Least Square Scaling (LSS) method. We show how all these methods (LSS, NLM, DGP) can be ass...

Demichel, Yann

One of the easiest and common ways of generating fractal sets in ${\mathbb R}^D$ is as attractors of affine iterated function systems (IFS). The classic theory of IFS's requires that they are made with contractive functions. In this paper, we relax this hypothesis considering a new operator $H_\rho$ obtained by renormalizing the usual Hutchinson op...

Bartzos, Evangelis Borrelli, Vincent Denis, Roland Lazarus, Francis Rohmer, Damien Thibert, Boris
Published in
Foundations of Computational Mathematics

Spheres are known to be rigid geometric objects: they cannot be deformed isometrically, i.e., while preserving the length of curves, in a twice differentiable way. An unexpected result by Nash (Ann Math 60:383–396, 1954) and Kuiper (Indag Math 17:545–555, 1955) shows that this is no longer the case if one requires the deformations to be only contin...