on the geometric properties of vandermonde s mapping and on the problem of moments on demontre que le domaine d hyperbolicite du polynome x n 2 x n 2 3 x n 3 n i r coupe par le demi plan 2 1 a la propriete de whitney on montre que les valeurs x 1 x 2 x n d une variable aleatoire sont determinees de facon unique par les probabilites correspondantes et par les u premiers moments

the fu yau equation with negative slope parameter the fu yau equation is an equation introduced by fu and yau as a generalization to arbitrary dimensions of an ansatz for the strominger system as in the strominger system it depends on a slope parameter alpha prime the equation was solved in dimension 2 by fu and yau in two successive papers for alpha prime 0 and for alpha prime 0 in the present paper we solve the fu yau equation in arbitrary dimension for alpha prime 0 to our knowledge these are the first non trivial solutions of the fu yau equation in any dimension strictly greater than 2

new entire positive solution for the nonlinear schrodinger equation coexistence of fronts and bumps in this paper we construct new kinds of positive solutions of delta u u u p 0 quad rm on bbb r 2 when p 2 these solutions have the following asymptotic behavior u x z sim omega x f z sum i 1 infty omega 0 x z xi i vec e 1 as l rightarrow infty where omega is a unique positive homoclinic solution of omega omega omega p 0 in bbb r omega 0 is the two dimensional positive solution and vec e 1 1 0 and xi j are points such that xi j jl cal o 1 for all j geq 1 this represents a first result on the it coexistence of fronts and bumps geometrically our new solutions correspond to it triunduloid in the theory of cmc surface

monotonicity of rotationally invariant convex and rank 1 convex functions let f m n n r be a function on the space m n n of n by n matrices that is invariant with respect to the left and right multiplication by proper orthogonal tensors it is shown that f a f if f is convex and the partial sums of the singular values of a m n n satisfy certain ordering inequalities the same holds if f is rank 1 convex and the partial products of the singular values satisfy analogous inequalities the proofs emphasize the roles of the ordered forces inequalities and the baker ericksen inequalities for invariant convex and rank 1 convex functions as an application the evaluation of the convex and lamination convex hulls of fully rotationally invariant sets by dacorogna and tanteri is simplified and similar results are given for sets invariant only with respect to the proper orthogonal group

algebra homomorphisms defined via convoluted semigroups and cosine functions abstract transform methods are used to establish algebra homomorphisms related to convoluted semigroups and convoluted cosine functions such families are now basic in the study of the abstract cauchy problem the framework they provide is flexible enough to encompass most of the concepts used up to now to treat cauchy problems of the first and second order in general banach spaces starting with the study of the classical laplace convolution and a cosine convolution along with associated dual transforms natural algebra homomorphisms are introduced which capture the convoluted semigroup and cosine function properties these correspond to extensions of the cauchy functional equation for semigroups and the abstract d alembert equation for the case of cosine operator functions the algebra homomorphisms obtained provide a way to prove hille yosida type generation theorems for the operator families under consideration

index growth of hypersurfaces with constant mean curvature in this paper we give the precise index growth for the embedded hypersurfaces of revolution with constant mean curvature cmc 1 in mathbb r n delaunay unduloids when n 3 using the asymptotics result of korevaar kusner and solomon we derive an explicit asymptotic index growth rate for finite topology cmc 1 surfaces with properly embedded ends similar results are obtained for hypersurfaces with cmc bigger than 1 in hyperbolic space

integrated semigroups and linear partial differential equations with delay abstract we study existence and uniqueness of solutions for linear partial differential equations with delay in l p spaces using an approach of batkai and piazzera and a recent perturbation result for integrated semigroups we apply our result to an equation with delay in the highest order derivatives

regularized solutions for abstract volterra equations abstract we introduce a two kernel dependent family of strong continuous operators defined in a banach space which allows us to consider in an unified treatment the notions of among others c 0 semigroups of operators cosine families n times integrated semigroups resolvent families and k generalized solutions the results are applied to the study of existence and uniqueness of solutions for the volterra equation of convolution type u f a au in the case a is not necessarily densely defined examples for equations defined in l p spaces are also given

four applications of majorization to convexity in the calculus of variations abstract the resemblance between the horn thompson theorem and a recent theorem by dacorogna marcellini tanteri indicates that schur convexity and the majorization relation are relevant for applications in the calculus of variations and its related notions of convexity such as rank one convexity or quasiconvexity in theorem 6 6 we give simple necessary and sufficient conditions for an isotropic objective function to be rank one convex on the set of matrices with positive determinant majorization is used in order to give a very short proof of a theorem of thompson and freede r c thompson l j freede eigenvalues of sums of hermitian matrices iii j res nat bur standards b 75b 1971 115 120 ball j m ball constitutive inequalities and existence theorems in nonlinear elastostatics in r j knops ed nonlinear analysis and mechanics heriot watt symposium vol 1 res notes math 17 pitman 1977 pp 187 241 or le dret h le dret sur les fonctions de matrices convexes et isotropes cr acad sci paris serie i 310 1990 617 620 concerning the convexity of a class of isotropic functions which appear in nonlinear elasticity next we prove theorem 7 3 a lower semicontinuity result for functionals with the form w d x d x with w f h ln v f here f r f u f v f r f is the usual polar decomposition of f gl n r and ln v f is hencky s logarithmic strain we close this paper with a compact proof of dacorogna marcellini tanteri theorem based only on classical results about majorization the mentioned resemblance of this theorem with the horn thompson theorem is thus explained

constitutive theory for some constrained elastic crystals abstract some of the observations of a 15 superconductors near cubic tetragonal phase transformations suggest treating them as thermoelastic bodies subject to certain material constraints here we begin to develop a theory of this kind

on duality and spectral properties of a k regularized resolvents we construct a duality theory for a k regularized resolvents extending some of the known theorems for dual semigroups we present several classes of spaces which in the semigroup case correspond to the favard class and the sun dual space by duality arguments spectral inclusions theorems for regularized resolvents are also obtained

the cauchy problem for critical and subcritical semilinear parabolic equations in lr ii initial data in critical sobolev spaces abstract by presenting some time space l p l r estimates we will establish the local and global existence and uniqueness of solutions for semilinear parabolic equations with the cauchy data in critical sobolev spaces of negative indices our results contain the complex derivative ginzburg landau equation and the cahn hilliard equation as special cases

l2 regularity for parabolic partial integrodifferential equations with delay in the highest order derivatives abstract a partial integrodifferential equation is studied in which the derivatives of highest order also contain a discrete and a distributed delay by means of abstract regularity results global existence and uniqueness of a strict solution are obtained moreover a characterization of the infinitesimal generator of the solution operator is given

curvature contraction of convex hypersurfaces by nonsmooth speeds the research of the second author was supported by an australian postgraduate award the research of the first third fourth and fifth authors was supported by discovery project grant dp120100097 of the australian research council

quasiconvexity at the boundary positivity of the second variation and elastic stability for one dimensional problems of the calculus of variations there is a well developed theory relating the positivity of the second variation at a critical point i e linearized stability to strong relative minima these results largely due to weierstrass are usually proved by the method of fields of extremals as is described in bolza 1904 and morrey 1966 or by an argument involving a careful use of taylor series as in hestenes 1966 chapter 3 14

the global structure of constant mean curvature surfaces in a recent ground breaking paper kapouleas constructed this century s first examples of complete finite topology properly embedded surfaces with non zero constant mean curvature ka l geometrically these surfaces are quite easy to visualize as we explain below the purpose of the present paper is to characterize the extent to which kapouleas examples are typical of all embedded constant mean curvature surfaces first and throughout this paper we scale space so that the constant mean curvature the trace of the second fundamental form of our surface l is identically one and we call such a surface an mc1 surface the only complete embedded mc1 surfaces of finite topology known before kapouleas work arise from the 1parameter family of axially symmetric and periodic examples found by delaunay in 1841 using the maximum axial radius r of such a surface as a parameter this family begins with the cylinder r 1 and evolves through embedded periodic surfaces until the family degenerates to a linear chain of touching spheres r 2 the delaunay family continues for all r 2 as periodic immersions kapouleas construction of embedded surfaces begins with a piecewise linear graph in r 3 having the property that edges are either finite segments with length a multiple of 4 or half infinite rays and with the further property that at each vertex some linear combination of their direction vectors with positive coefficients adds to zero see fig 1 he constructs an approximate solution to the problem by centering radius r 2 spheres at all vertices and connecting these smoothly by delaunay segments having r 2 but near 2 with axes along the graph edges since the periods of the delaunay surfaces are slightly longer than 4 he must assume also a flexibility condition on the graph to guarantee that such a gluing

a return map algorithm for general isotropic elasto visco plastic materials in principal space we describe a methodology for solving the constitutive problem and evaluating the consistent tangent operator for isotropic elasto visco plastic models whose yield function incorporates the third stress invariant the developments presented are based upon original results proved in the paper concerning the derivatives of eigenvalues and eigenprojectors of symmetric second order tensors with respect to the tensor itself and upon an original algebra of fourth order tensors obtained as second derivatives of isotropic scalar functions of a symmetric tensor argument the analysis initially referred to the small strain case is then extended to a formulation for the large deformation regime for both cases we provide a derivation of the consistent tangent tensor which shows the analogy between the two formulations and the close relationship with the tangent tensors of the lagrangian description of large strain elastoplasticity copyright 2004 john wiley sons ltd

on multiplier sequences in the present paper we consider real polynomials in one real variable of a given degree n such a polynomial is called hyperbolic if it has only real roots a finite multiplier sequence of lengthn 1 fms n 1 is a tuple c 0 c n c email protected r such that if i 0 nb ix n i b email protected r is a hyperbolic polynomial then i 0 nc ib ix n i is also such a polynomial the set of fms n 1 coincides with the set of tuples such that i 0 nc n ic ix n i is a hyperbolic polynomial with all roots of the same sign in the paper we prove several geometric properties of the set of fms n 1 formulated in terms of its stratification defined by the multiplicity vectors of the polynomials and of the whitney property the curvilinear distance to be equivalent to the euclidean one

on the development of explicit robust schemes for implementation of a class of hyperelastic models in large strain analysis of rubbers the issue of developing effective and robust schemes to implement a class of the ogden type hypereiastic constitutive models for large strain analysis of rubber like materials is addressed to this end explicit forms for the corresponding material tangent stiffness tensors are developed and these are valid for the entire deformation range i e with both distinct as well as repeated principal stretch values throughout the analysis the various implications of the underlying property of separability of the strain energy functions are exploited thus leading to compact final forms of the tensor expressions in particular this facilitated the treatment of the complex cases of uncoupled volumetric deviatoric formulations for incompressible materials which are becoming increasingly popular in recent years the forms derived are also amenable for use with symbolic manipulation packages for systematic code generation

poincare like approach to landau theory i general theory we discuss a procedure to simplify the landau potential based on michel s reduction to orbit space and poincare normalization procedure and illustrate it by concrete examples the method makes use as in poincare theory of a chain of near identity coordinate transformations with homogeneous generating functions using michel s insight one can work in orbit space it is shown that it is possible to control the choice of generating functions so to obtain a in many cases substantial simplification of the landau polynomial including a reduction of the parameters it depends on several examples are considered in detail

a uniqueness theorem in kahler geometry we consider compact kahler manifolds with their kahler ricci tensor satisfying f ric constant under the nonnegative bisectional curvature assumption and certain conditions on f we prove that such metrics are in fact kahler einstein

global c2 estimates for convex solutions of curvature equations we establish a c2 a priori estimate for convex hypersurfaces whose principal curvatures 1 n satisfy k x f x x the weingarten curvature equation we also obtain such an estimate for admissible 2 convex hypersurfaces in the case k 2 our estimates resolve a longstanding problem in geometric fully nonlinear elliptic equations 2015 wiley periodicals inc

approximation of local convoluted semigroups abstract we extend the trotter kato theorem on c 0 semigroups to local convoluted semigroups on dual spaces and apply these results to the general banach space setting compared to known results we obtain weaker convergence assumptions on the resolvent

asymptotic behaviour of integrated semigroups abstract in this paper we investigate the asymptotic behaviour of cauchy problems which are not governed by strongly continuous semigroups we obtain interesting generalizations in terms of integrated semigroups of classical abelian and tauberian theorems the results are applied to the solution of the schrodinger equation in l p spaces

estimates for schrodinger evolution equations on demontre que pour des donnees de cauchy dans l 1 r n la solution d une equation d evolution de schrodinger a coefficients constants d ordre 2m est uniformement bornee pour t 0 de borne 1 t c ou c est un entier c n 2m 1

a family of metric strains and conjugate stresses prolonging usual material laws from small to large transformations abstract a new family of simple generalized strains and conjugate stresses based on the material metric right cauchy green tensor is proposed it includes an interesting quasilinear pair it is a close approximation of the seth hill family with the advantage of being easier to calculate it extends the realm of application of the classical theories of linear elasticity and perfect plasticity from small to large transformations for isotropic and anisotropic materials without any modification

cartesian currents weak diffeomorphisms and existence theorems in nonlinear elasticity in this paper we introduce some new classes of functions among these a class of weak diffeomorphisms in these classes we prove by direct methods the existence of minimizers for several kinds of variational integrals in particular we prove the existence of one to one orientation preserving maps that minimize suitable energies associated with hyperelastic materials the minimizers are also proved to satisfy equilibrium equations finally radial deformations are discussed in connection with cavitation

an interior estimate for convex solutions and a rigidity theorem abstract we establish an interior c 2 estimate for k 1 convex solutions to dirichlet problems of k hessian equations we also use such estimate to obtain a rigidity theorem for k 1 convex entire solutions of k hessian equations in euclidean space

laplace transforms and integrated regularized semigroups in locally convex spaces abstract in this paper we consider the vector valued laplace transforms r times r 0 integrated semigroups and regularized semigroups in the context of sequentially complete locally convex spaces our theorems develop the corresponding results in 1 11 including the well known integrated version of the classical widder s representation theorem of laplace transforms for functions taking values in banach spaces moreover we study a class of differential operators on certain function spaces optimal conditions making them the generators of integrated or regularized semigroups are obtained we finally show some applications to abstract cauchy problems

geometry and topology of some overdetermined elliptic problems we study necessary conditions on the geometry and the topology of domains in r2 that support a positive solution to a classical overdetermined elliptic problem u f u 0in u 0on u constanton the ideas and tools we use come from constant mean curvature surface theory in particular we obtain a partial answer to a question posed by h berestycki l caffarelli and l nirenberg in 1997 we investigate also some boundedness properties of the solution u some of our results generalize to higher dimensions

a basis free formula for time rate of hill s strain tensors abstract in this paper we use the method to obtain a basis free formula for the time rate e of hill s strain tensor e u i i n ni here u is the right stretch tensor i are its eigenvalues and ni is a lagrangian triad of orthonormal eigenvectors subordinate to i is a smooth strictly increasing scalar function that satisfies 1 0 1 1 our formula is generally valid provided that u is a c1 function of time and is of class c3 until now all other basis free formulae for e in the literature have been burdened by one or other of the following deficiencies i valid only under various special circumstances ii a complete proof is wanting the formula derived herein is free of these difficulties

integrated semigroups and the cauchy problem for systems in lp spaces abstract in this note we prove that under suitable hypotheses every homogeneous differential operator on lp r n n corresponding to a system which is well posed in l2 r n n generates an times integrated semigroup on lp r n n 1 n 1 2 1 p for some special systems of mathematical physics such as the wave equation or maxwell s equations this constant can be improved to be n 1 1 2 1 p

constant mean curvature surfaces with three ends abstract we announce the classification of complete almost embedded surfaces of constant mean curvature with three ends and genus zero they are classified by triples of points on the sphere whose distances are the asymptotic necksizes of the three ends

rank 1 perturbations of cosine functions and semigroups abstract let a be the generator of a cosine function on a banach space x in many cases for example if x is a umd space a b generates a cosine function for each b l d a 1 2 x if a is unbounded and 1 2 1 then we show that there exists a rank 1 operator b l d a x such that a b does not generate a cosine function the proof depends on a modification of a baire argument due to desch and schappacher it also allows us to prove the following if a b generates a distribution semigroup for each operator b l d a x of rank 1 then a generates a holomorphic c 0 semigroup if a b generates a c 0 semigroup for each operator b l d a x of rank 1 where 0 1 then the semigroup t generated by a is differentiable and t t o t as t 0 for any 1 this is an approximate converse of a perturbation theorem for this class of semigroups

spectra of pseudodifferential operators generating integrated semigroups consider the lp realization opp a of a pseudodifferential operator with symbol a e sp70 having constant coefficients we show that for a certain class of symbols the spectrum of opp a is independent of p this implies that opp a generates an n times integrated semigroup on lp i rn for a certain n if and only if p opp a 8 0 and the numerical range of a is contained in a left half plane our method allows us also to construct examples of operators generating integrated semigroups on lp rn if and only if p is sufficiently close to 2

principal component analysis of high frequency data we develop the necessary methodology to conduct principal component analysis at high frequency we construct estimators of realized eigenvalues eigenvectors and principal components and provide

lipschitzian semigroups and abstract functional differential equations abstract the paper is devoted to studying an abstract functional differential equation by a nonlinear semigroup approach we first prove in details the equivalence of the well posedness of an abstract functional differential equation and an associated abstract cauchy problem in the sense of strong solutions secondly a sufficient condition is derived for well posedness of the abstract functional differential equation thirdly we present principles of linearized stability for the abstract functional differential equation finally the results obtained are applied to a reaction diffusion equation with delays

a fully nonlinear flow for two convex hypersurfaces in riemannian manifolds we consider a one parameter family of closed embedded hypersurfaces moving with normal velocity g kappa big sum i j frac 1 lambda i lambda j 2 kappa big 1 where lambda 1 le cdots le lambda n denote the curvature eigenvalues and kappa is a nonnegative constant this defines a fully nonlinear parabolic equation provided that lambda 1 lambda 2 2 kappa in contrast to mean curvature flow this flow preserves the condition lambda 1 lambda 2 2 kappa in a general ambient manifold our main goal in this paper is to extend the surgery algorithm of huisken sinestrari to this fully nonlinear flow this is the first construction of this kind for a fully nonlinear flow as a corollary we show that a compact riemannian manifold satisfying overline r 1313 overline r 2323 ge 2 kappa 2 with non empty boundary satisfying lambda 1 lambda 2 2 kappa is diffeomorphic to a 1 handlebody the main technical advance is the pointwise curvature derivative estimate the proof of this estimate requires a new argument as the existing techniques for mean curvature flow due to huisken sinestrari haslhofer kleiner and brian white cannot be generalized to the fully nonlinear setting to establish this estimate we employ an induction on scales argument this relies on a combination of several ingredients including the almost convexity estimate the inscribed radius estimate as well as a regularity result for radial graphs we expect that this technique will be useful in other situations as well

schrodinger type evolution equations in lp ω abstract let ap be a strongly elliptic operator of order 2m m n in lp 1 p a bounded domain of rn with dirichlet or neumann boundary conditions of concern is the cauchy problem for schrodinger type evolution equations in lp formula by showing that iap is the generator of a c0 group on a certain interpolation space we obtain results of wellposedness for which are stronger than those derived from the regularized or integrated groups on lp as a by product it is shown that iap is the generator of a ap r regularized group 0 on lp for all formula

invariants de classe c r des groupes finis engendres par des reflexions et theoreme de chevalley en classe c r

uniqueness of regular and singular equilibria for spherically symmetric problems of nonlinear elasticity introduction 97 constitutive assumptions 99 0 the stored energy function and weak equilibrium solutions 101 1 properties of radial equilibrium solutions 105 2 uniqueness of solutions to boundary value problems for shells 111 3 uniqueness of cavitating solutions 117 4 existence of radial equilibria 121 5 asymptotic behaviour of equilibria for shells 128 6 concluding remarks 132 7 appendix 133 references 135

a closed form representation for the derivative of non symmetric tensor power series in the present paper a closed form representation for the derivative of non symmetric tensor power series is proposed particular attention is focused on the special case of repeated eigenvalues in this case a non symmetric tensor can possess no spectral decomposition in diagonal form such that the well known solutions in terms of eigenprojections as well as basis free representations for isotropic functions of symmetric tensor arguments cannot be used thus our representation seems to be the only possibility to calculate the derivative of non symmetric tensor power series in a closed form finally this closed formula is illustrated by an example being of special importance in large strain anisotropic elasto plasticity as such we consider the exponential function of the velocity gradient under simple shear right in this loading case the velocity gradient has a triple defective eigenvalue excluding the application of any other solutions based on the spectral decomposition

on isotropic rank 1 convex functions let f be a rotationally invariant function defined on the set lin of all tensors with positive determinant on a vector space of arbitrary dimension necessary and sufficient conditions are given for the rank 1 convexity of f in terms of its representation through the singular values for the global rank 1 convexity on lin the result is a generalization of a two dimensional result of aubert generally the inequality on contains products of singular values of the type encountered in the definition of polyconvexity but is weaker it is also shown that the rank 1 convexity is equivalent to a restricted ordinary convexity when f is expressed in terms of signed invariants of the deformation

lp lq estimates for dispersive equations and related applications abstract this paper is mainly concerned with the l p l q estimates of solutions for a class of general dispersive equations under the condition h b with an index b 0 1 to the end the new pointwise decay estimates of oscillatory integrals related to the fundamental solutions are proved if b 1 then the pointwise estimates are particularly consistent with the sharp results of the nondegenerate cases moreover as an application of the l p l q estimates we also show that higher order differential operator i p d v x d generates a fractionally integrated group on some l p r n from which certain l p estimates for the solutions of generalized schrodinger equations are obtained

the topology and geometry of embedded surfaces of constant mean curvature si m est une surface proprement plongee dans r 3 avec une courbure moyenne constante non nulle alors m n est pas homeomorphe a une surface fermee avec un seul point elimine soit m une surface proprement plongee dans r 3 a courbure moyenne constante non nulle si m est homeomorphe a une surface fermee avec 2 points elimines alors m est une distance bornee a partir d une ligne droite soit m une surface proprement plongee de courbure moyenne non nulle qui est homeomorphe a une surface fermee avec 3 points elimines alors m reste une distance bornee a partir d un plan

semigroups and linear partial differential equations with delay abstract we prove the equivalence of the well posedness of a partial differential equation with delay and an associated abstract cauchy problem this is used to derive sufficient conditions for well posedness exponential stability and norm continuity of the solutions applications to a reaction diffusion equation with delay are given

integrated semigroups and related partial differential equations abstract we investigate the relationship between abstract linear evolution equations of heat wave and schrodinger types in terms of well posedness in banach spaces more precisely we study our operators as generators of integrated semigroups and integrated cosine functions as applications we consider in a banach space context an abstract laplacian which generalizes the ordinary laplacian in thelp r n spaces we obtain optimal results when compared to the classical situation where the generation results were obtained by 17 using completely different methods our main tools are the boundary value theorem for holomorphic semigroups and the abstract weierstrass formula related partial differential equations have been considered previously by bragg and dettman

the complex hessian equations with gradient terms on hermitian manifolds abstract in this paper we consider the complex hessian equation involving additional gradient terms on both left and right hand sides we derive the second order estimates for plurisubharmonic solutions to this equation on compact hermitian manifolds such an estimate may be helpful to study the existence and regularity for the solution of the equation

a landau kolmogorov inequality for generators of families of bounded operators abstract a landau kolmogorov type inequality for generators of a wide class of strongly continuous families of bounded and linear operators defined on a banach space is shown our approach allows us to recover in a unified way known results about uniformly bounded c 0 semigroups and cosine functions as well as to prove new results for other families of operators in particular if a is the generator of an times integrated family of bounded and linear operators arising from the well posedness of fractional differential equations of order 1 then we prove that the inequality a x 2 8 m 2 2 2 1 2 3 x a 2 x holds for all x d a 2

basis free representations for the stress rate of isotopic materials in terms of the principal components of stress tensor and a scalar response function two kinds of basis free representation for the stress rate are obtained which only include the time rate of the strain tensor functions and invariants of the strain tensor the expressions for the stress rate valid in the cases that the eigenvalues of the strain are distinct doubly coalescent and triply coalescent respectively