Approximation Methods by Regular Functions

This paper is a survey of approximation results and methods by smooth functions in Banach spaces. The topics considered in the paper are the following: approximation by polynomials by C^k-functions using the method of smooth partitions of unity, approximation by the fine topology, analytic approximation and regularization in Banach spaces using the infimal convolution method.     

An Approach to Shape Optimization with State Constraints

We introduce a new approach to solve shape optimization problems with state constraints. The problem is reformulated on a fixed reference domain using conformal pull-back. The shape dependence is then hidden in the conformal parameter. The problem is discretized using FEM and solved as an NLP. Finally the optimal shape can be reconstructed from the optimal conformal parameter. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Closed hypersurfaces of S4(1) with constant mean curvature and zero Gauß–Kronecker curvature

We consider a closed hypersurface $M^3?{\mathbb{S}}^4(1)$ with identically zero Gauß–Kronecker curvature. We prove that if $M^3$ has constant mean curvature H, then $M^3$ is minimal, i.e., $H=0$. This result extends Ramanathan's classification (Math. Z. 205 (1990) 645–658) result of closed minimal hypersurfaces of ${\mathbb{S}}^4(1)$ with vanishing Gauß–Kronecker curvature. To cite this article: T. Lusala, A. Gomes de Oliveira, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Topological representation for monadic implication algebras

In this paper, every monadic implication algebra is represented as a union of a unique family of monadic filters of a suitable monadic Boolean algebra. Inspired by this representation, we introduce the notion of a monadic implication space, we give a topological representation for monadic implication algebras and we prove a dual equivalence between the category of monadic implication algebras and the category of monadic implication spaces.      

Complex impure systems: Sheaves,freeways, and chains

Fundamental to the approach of Complex Impure Systems is the definition of the concept of an s‐impure set as a set of perceptual beliefs or denotative significances (relative beings) of material and/or energetic real objects (absolute beings). But any Subject not only the subject S perceives objects O as significances, and he perceives the existing relations between these significances or, alternatively, he infers them. The study of these relations, conceived not as a singular relation between singular objects, but as sheaves of relations in both directions and forming relational freeways, will be studied here. In this work, we approach the structure of the system, from a synchronous point of view, as a first approach to this class of systems. © 2016 Wiley Periodicals, Inc. Complexity 21: 387–400, 2016     

Asymptotic stability and bifurcations of 3D piecewise smooth vector fields

The paper deals with the analysis of the behavior of a nonsmooth three-dimensional vector field around a typal singularity. We focus on a class of generic one-parameter families \({Z_{\lambda}}\) of Filippov systems and address the persistence problem for the asymptotic stability when the parameter varies near the bifurcation value \({\lambda = 0}\).