the dirichlet problem for nonlinear second order elliptic equations iii functions of the eigenvalues of the hessian on etudie le probleme de dirichlet dans un domaine borne de r n a frontiere lisse f d 2 u dans u sur

large deviation approach to the generalized random energy model the generalized random energy model is a generalization of the random energy model introduced by derrida to mimic the ultrametric structure of the parisi solution of the sherrington kirkpatrick model of a spin glass it was solved exactly in two special cases by derrida and gardner a complete solution for the thermodynamics in the general case was given by capocaccia et al here we use large deviation theory to analyse the model in a very straightforward way we also show that the variational expression for the free energy can be evaluated easily using the cauchy schwarz inequality

static realization of dynamic precompensators the problem of static realization of dynamic precompensators on a controllable pair a b is considered necessary and sufficient conditions for the solution of this problem in the general case are given these conditions are constructive and they apply not only to invertible precompensators but also th those which are only left invertible

nonsmooth viscosity solutions of elementary symmetric functions of the complex hessian abstract in this paper we prove the existence of nonsmooth viscosity solutions for dirichlet problems involving elementary symmetric functions of the eigenvalues of the complex hessian

on the existence of thermodynamics for the generalized random energy model derrida s generalized random energy model is considered almost sure andlp convergence of the free energy at any inverse temperature are proven for an arbitrary numbern of hierarchical levels the explicit form of the free energy is given in the most general case and the limitn is discussed

weak solutions for the levi equation and envelope of holomorphy we consider the dirichlet problem for the levi equation in c2 and we prove an existence theorem of weak solutions i e in the sense of viscosity as an application we obtain the existence of the envelope of holomorphy for certain compact 2 manifolds

the dirichlet problem for nonlinear second order elliptic equations i monge ampegre equation on considere le probleme de dirichlet pour des equations elliptiques non lineaires pour une fonction reelle u definie dans la fermeture d un domaine borne dans r n avec une frontiere c

pseudoconvex fully nonlinear partial differential operators strong comparison theorems we introduce a new class of curvature pdos describing relevant properties of real hypersurfaces of cn 1 in our setting the pseudoconvexity and the levi form play the same role as the convexity and the real hessian matrix play in the real euclidean one our curvature operators are second order fully nonlinear pdos not elliptic at any point however when computed on generalized s pseudoconvex functions we shall show that their characteristic form is nonnegative definite with kernel of dimension one moreover we shall show that the missing ellipticity direction can be recovered by taking into account the cr structure of the hypersurfaces these properties allow us to prove a strong comparison principle leading to symmetry theorems for domains with constant curvatures and to identification results for domains with comparable curvatures

solution to morgan s problem a necessary and sufficient condition is presented for the solution of the row by row decoupling problem known as morgan s problem in the general case that is without any restrictive assumption added to the system to the feedback law u fx gy g may be noninvertible this is a structural condition in terms of invariant lists of integers which are easily computable from a given state realization of the system these integers are the infinite zero orders morse s list i sub 4 and the essential orders of the system which only depend on the input output behavior and morse s list i sub 2 of the system which depends on the choice of a particular state realization

the minimal delay decoupling problem feedback implementation with stability in this paper we solve the minimal delay decoupling problem of linear multivariable systems we look for feedback implementable solutions which moreover guarantee closed loop stability we prove that dynamic state feedback decoupling with stability is achievable if the number of independent inputs is large enough to compensate the intrinsic nondecouplability of the system we introduce new feedback invariants characterizing the minimal number of infinite and unstable zeros of the decoupled system

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

fundamental theorem of state feedback for singular systems abstract the limits of state feedback in altering the dynamics of singular systems are studied a necessary and sufficient condition is given for a list of polynomials to be invariant polynomials of a proper system obtained by state feedback from the singular system the condition consists of inequalities which involve the controllability indices of the singular system and the degrees of the invariant polynomials the development is based on the properties of polynomial matrices a procedure is given for the calculation of a feedback gain which achieves the desired dynamics

nonsmooth hypersurfaces with smooth levi curvature abstract in r 3 lipschitz continuous viscosity solutions to the k prescribed levi curvature equation are smooth and strictly pseudoconvex if k is smooth and strictly positive see 5 we show here that in r 2 n 1 n 1 a similar result does not hold that is we prove the existence in c n 1 n 1 of nonsmooth pseudoconvex hypersurfaces with smooth levi curvature

realization of full column rank precompensators using stabilizing static state feedback abstract in some control problems it is convenient to use a precompensator to alter the transfer function of the system such that the transfer function of the compensated system has a specified property then if possible the action of the compensator on the system is realized by a static state feedback law applied to the system when the compensator is square and non singular the state feedback is regular and the problem has already been solved non square compensators however result in non regular state feedback in this paper necessary and sufficient conditions are presented for the compensated system to be stabilizable by such a non regular static state feedback law

generalized random energy model the formulae for the free energy when the driving distributions in generalized random energy model grem are of the form ce x gamma for 1 are derived the large deviation technique allows the use of different distributions at different levels of the grem as an illustration we consider in detail a two level grem with exponential and gaussian distributions this simple case itself leads to interesting phenomena

nonsmooth solutions for a class of fully nonlinear pde s on lie groups abstract in this paper we prove the existence of nonsmooth viscosity solutions for dirichlet problems involving a class a fully non linear operators on lie groups in particular we consider the elementary symmetric functions of the eigenvalues of the hessian built with left invariant vector fields

new results about morgan s problem some aspects of the nonsquare morgan s problem are considered in particular it is shown that the condition given by j descusse et al 1986 to solve this problem is not sufficient it is also shown that the essential orders are not necessarily preserved in the static decoupling problem a necessary and sufficient condition for static decoupling of a system without modifying the essential orders is given for the case k p 1 where p is the number of outputs and k is the rank at infinity of the proper part of the interactor

static realization of dynamic precompensators for descriptor abstract the problem of static realization of dynamic precompensators on a linear descriptor system is considered necessary and sufficient constructive solvability conditions are given in the general non square case

convergence time to equilibrium of the metropolis dynamics for the grem we study the convergence time to equilibrium of the metropolis dynamics for the generalized random energy model with an arbitrary number of hierarchical levels a finite and reversible continuous time markov process in terms of the spectral gap of its transition probability matrix this is done by deducing bounds to the inverse of the gap using a poincare inequality and a path technique we also apply convex analysis tools to give the bounds in the most general case of the model

convexity and horizontal second fundamental forms for hypersurfaces in carnot groups we use a riemannian approximation scheme to give a characterization for smooth convex functions on a carnot group in the sense of danielli garofalo nhieu or lu manfredi stroffolini in terms of the positive semidefiniteness of the horizontal second fundamental form of their graph