State theory of linear hereditary differential systems

AbstractIn this paper we present a state theory for a class of linear functional differential equations of the retarded type considered by Delfour and Mitter (J. Differential Equations, 18 1975, 18–28) with initial functions in the product space Mp = X × Lp(−b, 0; X). Roughly speaking, the state at time t is a piece of trajectory defined over an interval [t − b, t] for a fixed b > 0. From a study of the properties of the state in Mp an operational differential equation, the so-called state equation, is derived in order to describe its evolution. An adjoint state equation is also introduced for the adjoint state and the connection between solutions of the hereditary adjoint system and those of the adjoint state equation is established. All this provides the appropriate framework for the solution and the numerical approximation of the associated linear-quadratic optimal control and filtering problems

Function spaces with a projective limit structure

AbstractVector spaces of functions and equivalence classes of functions for which a natural projective limit structure exists are studied in a systematic manner. The theory is illustrated by a series of examples arising from specific applications to the stability of feedback systems and the theory of hereditary differential systems

A Topology-Preserving Level Set Method for Shape Optimization

The classical level set method, which represents the boundary of the unknown geometry as the zero-level set of a function, has been shown to be very effective in solving shape optimization problems. The present work addresses the issue of using a level set representation when there are simple geometrical and topological constraints. We propose a logarithmic barrier penalty which acts to enforce the constraints, leading to an approximate solution to shape design problems.Comment: 10 pages, 4 figure

Sharp interface limit for a phase field model in structural optimization

We formulate a general shape and topology optimization problem in structural optimization by using a phase field approach. This problem is considered in view of well-posedness and we derive optimality conditions. We relate the diffuse interface problem to a perimeter penalized sharp interface shape optimization problem in the sense of $\Gamma$-convergence of the reduced objective functional. Additionally, convergence of the equations of the first variation can be shown. The limit equations can also be derived directly from the problem in the sharp interface setting. Numerical computations demonstrate that the approach can be applied for complex structural optimization problems

Cochabamba (Bolivie): Hacer ciudad, Hacer Sociedad, du rêve à la réalité

Il s’agit du récit d’un échec, celui de l’approbation du Plan Municipal de Ordenación del territorio (PMOT), d’autant plus cuisant que l’adéquation inédite entre le projet d’aménagement du territoire mené par la municipalité de Cochabamba (province de Cercado-Bolivie) et la construction d’un nouveau modèle du vivre ensemble dans un environnement plurinational (Nouvelle Constitution Politique de l’Etat- NPCE) portaient à croire que ce serait une réussite. Quelles sont les raisons de cet échec ? Le volet politique (idéologique) a-t-il prévalu au détriment du volet sociétal ? Bref, peut-on « Faire ville » et « Faire société » dans un pays où la prégnance des villes et des régions a très souvent orienté la politique nationale ?Se trata del relato de un fracaso, el de la aprobación del Plan de Ordenación del Territorio (PMOT), tanto más doloroso que la adecuación entre el proyecto de ordenación municipal de Cochabamba (provincia de Cercado-Bolivia) llevado por la municipalidad y la construcción de un nuevo modelo para vivir juntos en un entorno plurinacional (Nueva Constitución Política del Estado – NCPE) presagiaban un éxito. ¿Cúales son las razones de este fracaso? ¿Lo político (ideológico) prevaleció en detrimento de lo societal? ¿Es factible “Hacer ciudad” y “Hacer sociedad” en un país donde la fuerza de las ciudades y de las regiones ha orientado con frecuencia la política nacional

Éditorial

Le numéro 9 de la revue L’Âge d’or, de l’équipe « Écritures des mondes hispaniques » (EMHIS), se compose de deux dossiers consacrés aux innovations politiques et culturelles dans les pays andins. Cette aire géographique dont la cordillère des Andes − dénominateur physique commun − est au long de l’histoire de l’Amérique espagnole puis de l’Amérique indépendante terre(s) d’innovations. Depuis 1998, en Bolivie, en Équateur, au Venezuela mais également au Pérou des acteurs nouveaux, auto-désigné..

Locally optimal unstructured finite element meshes in 3 dimensions

This paper investigates the adaptive finite element solution of a general class of variational problems in three dimensions using a combination of node movement, edge swapping, face swapping and node insertion. The adaptive strategy proposed is a generalization of previous work in two dimensions and is based upon the construction of a hierarchy of locally optimal meshes. Results presented, both for a single equation and a system of coupled equations, suggest that this approach is able to produce better meshes of tetrahedra than those obtained by more conventional adaptive strategies and in a relatively efficient manner