an application of h differentiability to generalized complementarity problems over symmetric cones in this paper we focus on a generalized complementarity problems over symmetric cone gsccp f g when the underlying functions f and g are h differentiable by introducing the concepts of relatively uniform cartesian p property relatively cartesian p p 0 property the cartesian semimonotone e 0 property strictly cartesian semimonotone e property and the relatively regular point with respect to the merit function j x we extend various similar results proved in gcp f g to generalized complementarity problems over symmetric cone gsccp f g and establish various conditions on f and g to get a solution to gsccp f g

gaps in the differential forms spectrum on cyclic coverings we are interested in the spectrum of the hodge de rham operator on a mathbb z covering x over a compact manifold m of dimension n 1 let be a hypersurface in m which does not disconnect m and such that m is a fundamental domain of the covering if the cohomology group hn 2 is trivial we can construct for each n in mathbb n a metric g gn on m such that the hodge de rham operator on the covering x g has at least n gaps in its essential spectrum if h n 2 sigma ne 0 the same statement holds true for the hodge de rham operators on p forms provided p notin n 2 n 2 1

cartesian p property and its applications to the semidefinite linear complementarity problem we introduce a cartesian p property for linear transformations between the space of symmetric matrices and present its applications to the semidefinite linear complementarity problem sdlcp with this cartesian p property we show that the sdlcp has gus property i e globally unique solvability and the solution map of the sdlcp is locally lipschitzian with respect to input data our cartesian p property strengthens the corresponding p properties of gowda and song 15 and allows us to extend several numerical approaches for monotone sdlcps to solve more general sdlcps namely sdlcps with the cartesian p property in particular we address important theoretical issues encountered in those numerical approaches such as issues related to the stationary points in the merit function approach and the existence of newton directions and boundedness of iterates in the non interior continuation method of chen and tseng 6

necessary conditions controllability and the value function for differential difference inclusions on deduit des conditions necessaires pour la commande optimale d un systeme contraint par des inclusions differentielles aux differences

asymptotic behavior of a nonlinear kirchhoff type equation with spring boundary conditions in this paper we consider the initial boundary value problem for a nonlinear kirchhoff type equation with the damping term and spring boundary conditions we establish the global existence and uniqueness of solutions to this problem in time and give an example and simulation to illustrate our results for the proof we use the faedo galerkin approximate method finally we study the asymptotic behavior of solutions and some of its simulation results results of this paper are able to apply industrial parts such as a typical model widely used to represent threads wires magnetic tapes belts band saws and so on

merit functions for semi definite complementarity problems merit functions such as the gap function the regularized gap function the implicit lagrangian and the norm squared of the fischer burmeister function have played an important role in the solution of complementarity problems defined over the cone of nonnegative real vectors we study the extension of these merit functions to complementarity problems defined over the cone of block diagonal symmetric positive semi definite real matrices the extension suggests new solution methods for the latter problems

some p properties for linear transformations on euclidean jordan algebras a real square matrix is said to be a p matrix if all its principal minors are positive it is well known that this property is equivalent to the nonsign reversal property based on the componentwise product of vectors the order p property based on the minimum and maximum of vectors uniqueness property in the standard linear complementarity problem lipschitzian homeomorphism property of the normal map corresponding to the nonnegative orthant in this article we extend these notions to a linear transformation defined on a euclidean jordan algebra we study some interconnections between these extended concepts and specialize them to the space s n of all n n real symmetric matrices with the semidefinite cone s n and to the space r n with the lorentz cone

uniqueness and differentiability of solutions of parametric nonlinear complementarity problems we derive conditions for the local uniqueness of solutions of nonlinear complementarity problems ncp we then prove the existence continuity and directional differentiability of a locally unique parametric solution of the parametric ncp under stronger assumptions in the absence of degeneracy this parametric solution is also shown to be continuously differentiable

a combined smoothing and regularization method for monotone second order cone complementarity problems the second order cone complementarity problem soccp is a wide class of problems containing the nonlinear complementarity problem ncp and the second order cone programming problem socp recently fukushima luo and tseng siam j optim 12 2001 pp 436 460 extended some merit functions and their smoothing functions for ncp to soccp moreover they derived computable formulas for the jacobians of the smoothing functions and gave conditions for the jacobians to be invertible in this paper we propose a globally and quadratically convergent algorithm which is based on smoothing and regularization methods for solving monotone soccp in particular we study strong semismoothness and jacobian consistency which play an important role in establishing quadratic convergence of the algorithm furthermore we examine the effectiveness of the algorithm by means of numerical experiments

global existence and uniform decay for wave equation with dissipative term and boundary damping in this paper we prove the existence uniqueness and uniform stability of strong and weak solutions of the nonlinear wave equation u t email protected b x u t f u 0 in bounded domains with nonlinear damped boundary conditions given by email protected email protected g u t 0 with restrictions on function f u g u t and b x we prove the existence by means of the glerkin method and obtain the asymptotic behavior by using of the multiplier technique from the idea of kmornik and zuazua see 7

the adiabatic limit of schrodinger operators on fibre bundles we consider schrodinger operators h delta g varepsilon v on a fibre bundle m mathop rightarrow limits pi b with compact fibres and a metric g varepsilon that blows up directions perpendicular to the fibres by a factor varepsilon 1 gg 1 we show that for an eigenvalue lambda of the fibre wise part of h satisfying a local gap condition and every n in mathbb n there exists a subspace of l 2 m that is invariant under h up to errors of order varepsilon n 1 the dynamical and spectral features of h on this subspace can be described by an effective operator on the fibre wise lambda eigenspace bundle mathcal e rightarrow b giving detailed asymptotics for h

local soltutions for a nonlinear degenerate hyperbolic equation on etudie l existence et l unicite des solutions locales pour le probleme mixte associe a l equation hyperbolique degenere du type 2 u 2 m u x t 2 dx u 0 ou est un ouvert borne de r n a frontiere lisse et x est un vecteur de r n

spectral sequences and adiabatic limits a taylor series analysis of the laplacian as the underlying manifold is demormed leads to a hodge theoretic derivation of the leray spectral sequence

collapsing and the differential form laplacian the case of a smooth limit space we analyze the limit of the p form laplacian under a collapse with bounded sectional curvature and bounded diameter to a smooth limit space as an application we characterize when the p form laplacian has small positive eigenvalues in a collapsing sequence

a boundary of the set of the riemannian manifolds with bounded curvatures and diameters on etudie la structure de la fermeture de l ensemble constitue par des classes d isometrie de varietes de riemann a courbures et diametres bornes

applications of second order cone programming in a second order cone program socp a linear function is minimized over the intersection of an affine set and the product of second order quadratic cones socps are nonlinear convex problems that include linear and convex quadratic programs as special cases but are less general than semidefinite programs sdps several efficient primaldual interior point methods for socp have been developed in the last few years after reviewing the basic theory of socps we describe general families of problems that tan be recast as socps these include robust linear programming and robust leastsquares problems problems involving sums or maxima of norms or with convex hyperbolic constraints we discuss a variety of engineering applications such as filter design antenna array weight design truss design and grasping forte optimization in robotics we describe an efficient primaldual interior point method for solving socps which shares many of the features of primaldual interior point methods for linear program

uniform energy decay rates for nonlinear viscoelastic wave equation with nonlocal boundary damping abstract in this paper we consider the uniform decay estimates of solutions for the viscoelastic wave equation u t t 0 u 0 t g t s div a x u s d s b x h u t 0 in 0 under weak assumptions on the functions g h and f we prove the energy functional decays exponentially or polynomially to zero as the time goes to infinity by introducing brief lyapunov functions and precise priori estimates

smoothing functions for second order cone complementarity problems smoothing functions have been much studied in the solution of optimization and complementarity problems with nonnegativity constraints in this paper we extend smoothing functions to problems in which the nonnegative orthant is replaced by the direct product of second order cones these smoothing functions include the chen mangasarian class and the smoothed fischer burmeister function we study the lipschitzian and differential properties of these functions and in particular we derive computable formulas for these functions and their jacobians these properties and formulas can then be used to develop and analyze noninterior continuation methods for solving the corresponding optimization and complementarity problems in particular we establish the existence and uniqueness of the newton direction when the underlying mapping is monotone

on the fundamental groups of manifolds of positive sectional curvature let m be an n manifold with sectional curvature 0 6 k 1 the main result asserts that the fundamental group of m has a finite normal cyclic subgroup with index less than w n 8 oc a constant depending on n and 8

the atiyah singer index theorem for families of dirac operators two heat equation proofs the purpose of this paper is to give two heat equation proofs of the index theorem of atiyah singer for a family of dirac operators

collapsing of riemannian manifolds and eigenvalues of laplace operator on etudie la perturbation des valeurs propres de l operateur de laplace sous des deformations des varietes qui ne conservent pas les dimensions

stability of spectra of hodge de rham laplacians in this paper we investigate the stability of eigenspaces of the laplace operator acting on differential forms satisfying relative or absolute boundary conditions on a compact oriented riemannian manifold with boundary this includes in particular both neumann and dirichlet conditions for the laplace beltrami operator on functions more precisely our main result is that the gap between corresponding eigenspaces precise definition will be recalled below measured using the l norm converges to zero when smooth metrics g converge to g0 in the c 1 topology it is quite well known cf 3 or 14 that the eigenvalues of the laplacian vary continuously under c 0 continuous perturbations of the metric it is perhaps less well known but implicit in the work of cheeger 3 that eigenspaces vary continuously as subspaces of l2 when the metric is perturbed c 0 continuously we reprove this c 0 l2 stability in sect 4 for completeness and in order to be able to use certain notation conventions and partial results in the proof of c 1 l stability in sect 5 the second section of the paper contains a review of the hodge theory for the laplace operator with absolute and relative boundary conditions we also state here the sobolev embedding theorems and the basic a priori estimates for the square root d of the laplacian we need to work with d rather than d 2 since the coefficients of depend on the second derivatives of the metric tensor and we allow only c 1 continuous perturbations of the metric and do not assume any bounds on the second derivatives in the third section we review following kato 12 and osborn 16 general results from functional analysis concerning perturbation theory for compact operators on banach spaces that reduce proving convergence of eigenvalues and eigenspaces

some p properties for nonlinear transformations on euclidean jordan algebras in this article we introduce the concepts of p and p0 properties for a nonlinear transformation defined on a euclidean jordan algebra and study existence of solution in the associated complementarity problems in particular we show in this general setting that if a transformation has the p0 and r0 properties then all associated complementarity problems have solutions we also describe a necessary condition for a transformation to have the global uniqueness of solution property

stabilization for the kirchhoff type equation from an axially moving heterogeneous string modeling with boundary feedback control abstract the first objective of this paper is to make the mathematical model for vibration suppression of an axially moving heterogeneous string in order to describe the geometrical nonlinearity due to finite transverse deformation the exact expression of the strain is used the mathematical modeling is derived first by using hamilton s principle and variational lemma and the derived nonlinear pde system is the kirchhoff type equation with boundary feedback control next we show the existence and uniqueness of strong solutions of the pde system via techniques of functional analysis mainly a theorem of compactness for the analysis of the approximation of the faedo galerkin method and estimate a decay rate for the energy the theoretical results are assured by numerical results of the solution s shape and asymptotic behavior for the system

strong semismoothness of the fischer burmeister sdc and soc complementarity functions we show that the fischer burmeister complementarity functions associated to the semidefinite cone sdc and the second order cone soc respectively are strongly semismooth everywhere interestingly enough the proof relys on a relationship between the singular value decomposition of a nonsymmetric matrix and the spectral decomposition of a symmetric matrix

a regularization method for the second order cone complementarity problem with the cartesian p0 property abstract we consider the tikhonov regularization method for the second order cone complementarity problem soccp with the cartesian p 0 property we show that many results of the regularization method for the p 0 nonlinear complementarity problem still hold for this important class of nonmonotone soccp for example under the more general setting every regularized problem has the unique solution and the solution trajectory generated is bounded if the original soccp has a nonempty and bounded solution set we also propose an inexact regularization algorithm by solving the sequence of regularized problems approximately with the merit function approach based on fischer burmeister merit function and establish the convergence result of the algorithm preliminary numerical results are also reported which verify the favorable theoretical properties of the proposed method

on local solutions of a mildly degenerate hyperbolic equation in this work we prove the existence of a unique nonlocal solution for the vibrations of a nonhomogeneous stretched string in sobolev spaces and without any smallness conditions on the size of the initial data

a nonmonotone line search technique and its application to unconstrained optimization a new nonmonotone line search algorithm is proposed and analyzed in our scheme we require that an average of the successive function values decreases while the traditional nonmonotone approach of grippo lampariello and lucidi siam j numer anal 23 1986 pp 707 716 requires that a maximum of recent function values decreases we prove global convergence for nonconvex smooth functions and r linear convergence for strongly convex functions for the l bfgs method and the unconstrained optimization problems in the cute library the new nonmonotone line search algorithm used fewer function and gradient evaluations on average than either the monotone or the traditional nonmonotone scheme

vibrations of elastic string with nonhomogeneous material abstract in this paper we analyze from the mathematical point of view a model for small vertical vibrations of an elastic string with fixed ends and the density of the material being not constant we employ techniques of functional analysis mainly a theorem of compactness for the analysis of the approximation of faedo galerkin method we obtain strong global solutions with restrictions on the initial data u 0 and u 1 uniqueness of solutions and a rate decay estimate for the energy

some nonlinear degenerate wave equations on etudie la resolubilite locale du probleme aux valeurs limites et initiales suivant 2 u t 2 m gradu x t 2 dx u 0 dans 0 u 0 sur w 0 u 0 0 u t 0 dans ou m r est une fonction c 1 non negative sur 0 un domaine borne de r n a frontiere lisse w

collapsing riemannian manifolds while keeping their curvature bounded i soit y n une variete de riemann connexe complete et p y n le rayon d injectivite i p de l application exponentielle en p est defini comme etant le plus petit r tel que exp p b r p n est pas un diffeomorphisme sur son image on etudie la situation dans laquelle la taille du rayon d injectivite est petite relativement a la courbure

vanishing of cohomology groups and large eigenvalues of the laplacian on p forms for collapsing of closed riemannian manifolds the first positive eigenvalue of the laplacian on p forms may or may not tend to infinity in special cases we show that the existence of the first positive eigenvalue tending to infinity is related to vanishing of cohomology groups of generic fibers

nilpotent structures and invariant metrics on collapsed manifolds let mn be a complete riemannian manifold of bounded curvature say iki 0 we put mn w n c u fn c where 1n e consists of those points at which the injectivity radius of the exponential map is e the complementary set n c is called the e collapsed part of mn if x e 4 n r e then the metric ball bx r is quasi isometric with small distortion to the flat ball b0 r in the euclidean space rn after slightly

complex dynamics of high speed axially moving systems in this paper the dynamic response of a simply supported travelling beam subjected to a transverse load is investigated in the super critical speed range the well known axially moving beam theory is considered and a simple viscous damping mechanism has been introduced the displacement field is expanded in a series of the buckling modes a sine series and different techniques have been used in analyzing the response of the dynamical system periodic oscillations are studied by means of continuation techniques while non stationary dynamics are investigated through direct simulations a comparison with the literature and a convergence test on the series expansion are performed a sample case of a physical beam is developed and numerical results are presented concerning bifurcation analysis and stability and direct simulations of global postcritical dynamics a complex scenario of alternate regular and chaotic motions is found in a large range of the main parameters

conjugacy classes of n tuples in lie algebras and algebraic groups let g be a reductive algebraic group over an algebraically closed field f of characteristic zero and let l g be the lie algebra of g then g acts on g by inner automorphisms and it acts on l g by the adjoint representation by taking the diagonal actions we get actions of g on the spaces of n tuples g n and l g in this paper we will prove a number of geometric properties of the orbits of g on these spaces of n tuples