Problème de Cauchy non autonome pour des équations d'évolution

Nous étudions dans un espace de Banach le problème de Cauchy pour des équations d'évolution gouvernées par des opérateurs dépendant du temps dans un cadre plus général que les hypothèses d'accrétivité. D'une part, ce cadre s'adapte bien à des perturbations continues vérifiant des conditions de type Osgood, d'autre part, l'essentiel des résultats de la théorie moderne des équations d'évolution abstraites se trouve prolongé à ce nouveau contexte.     

On Metric and Calmness Qualification Conditions in Subdifferential Calculus

The paper contains two groups of results. The first are criteria for calmness/subregularity for set-valued mappings between finite-dimensional spaces. We give a new sufficient condition whose subregularity part has the same form as the coderivative criterion for “full” metric regularity but involves a different type of coderivative which is introduced in the paper. We also show that the condition is necessary for mappings with convex graphs. The second group of results deals with the basic calculus rules of nonsmooth subdifferential calculus. For each of the rules we state two qualification conditions: one in terms of calmness/subregularity of certain set-valued mappings and the other as a metric estimate (not necessarily directly associated with aforementioned calmness/subregularity property). The conditions are shown to be weaker than the standard Mordukhovich–Rockafellar subdifferential qualification condition; in particular they cover the cases of convex polyhedral set-valued mappings and, more generally, mappings with semi-linear graphs. Relative strength of the conditions is thoroughly analyzed. We also show, for each of the calculus rules, that the standard qualification conditions are equivalent to “full” metric regularity of precisely the same mappings that are involved in the subregularity version of our calmness/subregularity condition. The research of Jiří V. Outrata was supported by the grant A 107 5402 of the Grant Agency of the Academy of Sciences of the Czech Republic.     

Generalized Dirichlet Normal Ordering in Open Bosonic Strings

Generally, open string boundary conditions play a nontrivial role in string theory. For example, in the presence of an antisymmetric tensor background field, they will lead the spacetime coordinates noncommutative. In this paper, we mainly discuss how to build up a generalized Dirichlet normal ordered product of open bosonic string embedding operators that satisfies both the equations of motion and the generalized Dirichlet boundary conditions at the quantum level in the presence of an antisymmetric background field, as the generalized Neumann case has already been discussed in the literature. Further, we also give a brief check of the consistency of the theory under the newly introduced normal ordering.     

A multigrid procedure for Cartesian ghost‐cell methods

This paper proposes a multigrid technique for Cartesian grid flow solvers. A recently developed ghost body‐cell method for inviscid flows is combined with a nested‐level local refinement procedure, which employs multigrid to accelerate convergence to steady state. Different from standard multigrid applications for body‐fitted grids, a fictitious residual needs to be defined in the ghost cells to perform a correct residual collection and thus to avoid possible stalling of the multigrid procedure. The efficiency of the proposed local refinement multigrid Cartesian method is demonstrated for the case of the inviscid subsonic flow past a circular body. Copyright © 2008 John Wiley & Sons, Ltd.     

Sequential optimality conditions for composed convex optimization problems

Using a general approach which provides sequential optimality conditions for a general convex optimization problem, we derive necessary and sufficient optimality conditions for composed convex optimization problems. Further, we give sequential characterizations for a subgradient of the precomposition of a K-increasing lower semicontinuous convex function with a K-convex and K-epi-closed (continuous) function, where K is a nonempty convex cone. We prove that several results from the literature dealing with sequential characterizations of subgradients are obtained as particular cases of our results. We also improve the above mentioned statements.     

On a comparison principle for delay coupled systems with nonlocal and nonlinear boundary conditions

This paper is concerned with delay coupled systems of parabolic equations with nonlocal and nonlinear boundary conditions. For them, a new and general comparison principle is established, which is more general and useful than the existing results.     

Defining the size and location of the slit in rainbow holography

A simple method is described for defining the size and location of the slit in a rainbow holography optical system in order to guarantee the optimal observation conditions of the reconstructed image. A brief explanation of the basic principles of rainbow holography is given and the projection of viewing slits and pseudoscopic, or orthoscopic, images is considered. An application of the method for afocal systems used in rainbow holography is presented.     

A theorem on upper-lower solutions for nonlinear elliptic systems and its applications

We report on a result of upper-lower solutions for nonlinear elliptic systems without the assumption of quasi-monotonicity. An application is described involving the existence of positive steady states of a certain interaction system arising in biology and medical sciences.     

Bounded sets of Lagrange multipliers for vector optimization problems in infinite dimension

The aim of this paper is to point out some sufficient constraint qualification conditions ensuring the boundedness of a set of Lagrange multipliers for vectorial optimization problems in infinite dimension. In some (smooth) cases these conditions turn out to be necessary for the existence of multipliers as well.     

Laws of Influence of Structural Characteristics on the Strength and Crack Resistance of Aging Metallic Materials

The structural characteristics (the volume fraction, size, and shape of and the distance among hardening-phase particles) of aging alloys and steels, which define the behavior of the critical stress intensity factor during thermal hardening, are determined using the structural-mechanical approach we have developed. It is experimentally demonstrated for maraging steels that our approach is capable of proving the correlations of strength, plasticity, and crack- resistance with the structural characteristics, which were varied by changing the chemical composition of steel and thermokinetic aging conditions__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 1, pp. 94–101, January 2005.