weighted gradient estimates for elliptic problems with neumann boundary conditions in lipschitz and semi convex domains abstract let n 2 and be a bounded lipschitz domain in r n in this article the authors investigate global weighted norm estimates for the gradient of solutions to neumann boundary value problems of second order elliptic equations of divergence form with real valued bounded measurable coefficients in more precisely for any given p 2 two necessary and sufficient conditions for w 1 p estimates of solutions to neumann boundary value problems respectively in terms of a weak reverse holder inequality with exponent p or weighted w 1 q estimates of solutions with q 2 p and some muckenhoupt weights are obtained as applications for any given p 1 and a p r n the class of muckenhoupt weights the authors establish weighted w 1 p estimates for solutions to neumann boundary value problems of second order elliptic equations of divergence form with small bmo coefficients on bounded semi convex domains as further applications the global gradient estimates are obtained respectively in weighted lorentz spaces lorentz morrey spaces weighted orlicz spaces and variable lebesgue spaces

rank revealing qr factorizations abstract an algorithm is presented for computing a column permutation pi and a qr factorization a pi qr of an m by n m or n matrix a such that a possible rank deficiency of a will be revealed in the triangular factor r having a small lower right block for low rank deficient matrices the algorithm is guaranteed to reveal the rank of a and the cost is only slightly more than the cost of one regular qr factorization a posteriori upper and lower bounds on the singular values of a are derived and can be used to infer the numerical rank of a keywords qr factorization rank deficient matrices least squares computation subset selection rank singular values

commutativity preserving linear maps and lie automorphisms of triangular matrix algebras abstract in this article we classify linear maps from the algebra t n of n upper triangular matrices into itself satisfying ab ba 0 if and only if ab ba 0 in particular we show that for n 2 any such map is either the sum of an algebra automorphism and a map into the centre or the sum of the negative of an algebra anti automorphism and a map into the centre as a consequence lie automorphisms of the algebra t n are also classified

on singular implicit linear dynamical systems we investigate properties of existence unicity representation of the causal solutions of implicit linear systems or generalized systems when the underlying matrix pencil is singular we relate the geometric and the algebraic approaches the main conclusion is that if the underlying matrix pencil is column singular i e has a nonempty set of column minimal indices the causal solutions when they exist can exactly be represented as the output of a classical two player dynamical system where the second player accounts for the nonunicity properties of the equivalent system are related to those of the singular matrix pencils made with the given matrices

linear preservers on upper triangular operator matrix algebras abstract in this paper we obtain several characterizations of rank preserving linear maps and completely rank nonincreasing linear maps on upper triangular hilbert space operator matrix algebras and apply them to get some algebraic results we show that every automorphism of an upper triangular operator matrix algebra is inner and every weakly continuous surjective local automorphism is in fact an automorphism a weakly continuous linear bijection on an upper triangular operator matrix algebra is idempotent preserving if and only if it is a jordan homomorphism and in turn if and only if it is an automorphism or an anti automorphism as an application we also obtain a result concerning the asymptotic joint similarity of matrix tuples

controllability observability and duality in singular systems the concepts of controllability and observability for systems of the form e dot x ax bu y cx e singular are considered a theory is presented which unifies the three main approaches to this topic already existing in the literature the development includes a generalization of the duality theorem from state space theory

boundary layers on sobolev besov spaces and poisson s equation for the laplacian in lipschitz domains we study inhomogeneous boundary value problems for the laplacian in arbitrary lipschitz domains with data in sobolev besov spaces as such this is a natural continuation of work in jerison and kenig j funct anal 1995 16 219 where the inhomogeneous dirichlet problem is treated via harmonic measure techniques the novelty of our approach resides in the systematic use of boundary integral methods in this regard the key results are establishing the invertibility of the classical layer potential operators on scales of sobolev besov spaces on lipschitz boundaries for optimal ranges of indices applications tolp based helmholtz type decompositions of vector fields in lipschitz domains are also presented

computing the state difference equations for discrete overdetermined linear m d systems we derive an algorithm that computes the state difference equations for a given set of poles of linear discrete overdetermined autonomous m d systems these difference equations allow the realization of the dynamical system by means of delay multiplication and addition elements in simulation diagrams in doing so we generalize the classical cayley hamilton theorem to multivariate polynomial ideals and provide a system theoretic interpretation to the notion of polynomial ideals leading monomials and grobner bases furthermore we extend the problem to include poles at infinity and so arrive at a description of overdetermined descriptor systems this results in a new state space description of autonomous m d descriptor systems in addition we discuss the separation of the state variables of singular m d systems into a regular and singular part a sufficient condition under which these two state vector parts can be interpreted as a forward evolving regular part and a backward evolving singular part is given the robustness and efficiency of the developed algorithms are demonstrated via numerical experiments

linear preserver problems a brief introduction and some special techniques abstract linear preserver problems concern the characterization of linear operators on matrix spaces that leave certain functions subsets relations etc invariant the earliest papers on linear preserver problems date back to 1897 and a great deal of effort has been devoted to the study of this type of question since then we present a brief picture of the subject aiming at giving a gentle introduction to the reader then we describe some techniques used in our recent papers on this type of problem

on classical adjoint commuting mappings between matrix algebras abstract let f be a field and let m and n be integers with m n 3 let m n denote the algebra of n n matrices over f in this note we characterize mappings m n m m that satisfy one of the following conditions 1 f 2 or f n 1 and adj a b adj a b for all a b m n and f with i n 0 2 is surjective and adj a b adj a b for every a b m n here adj a denotes the classical adjoint of the matrix a and i n is the identity matrix of order n we give examples showing the indispensability of the assumption i n 0 in our results

computation of transfer function matrices of generalized state space models a reliable computational algorithm is proposed for the evaluation of the transfer function matrices of linear multivariable systems described by generalized state space models the algorithm is based on a new efficient and numerically stable procedure for computing irreducible state space realizations of generalized state space models for each input output channel the proposed algorithm computes an irreducible realization using this procedure then the parameters of the corresponding transfer function gain poles zeros are determined from the resulting irreducible model

w1 p estimates for elliptic problems with neumann boundary conditions in lipschitz domains abstract we study w 1 p estimates in lipschitz domains for second order elliptic equations and systems of divergence form with real valued bounded measurable coefficients for any fixed p 2 we prove that a weak reverse holder inequality implies the w 1 p estimates for solutions with neumann boundary conditions as a result we are able to show that if the coefficient matrix of elliptic equation is symmetric and in vmo r n the w 1 p estimate holds for 3 2 e p 3 e if n 3 and for 4 3 e p 4 e if n 2 and for elliptic systems the w 1 p estimate is true for 2 n n 1 e p 2 n n 1 e

jordan isomorphisms of triangular matrix algebras over a connected commutative ring abstract let c be a 2 torsionfree commutative ring with identity 1 and let t r c r 2 be the algebra of all upper triangular r r r 2 matrices over c then c contains no idempotents except 0 and 1 if and only if every jordan isomorphism of t r c onto an arbitrary algebra over c is either an isomorphism or an anti isomorphism

linear operators preserving idempotent matrices over fields abstract suppose f is a field we show that if the characteristic of the field is not 2 then the semigroup of linear operators on the n n matrices over f that preserve idempotence is the group g f generated by transposition and similarity chan lim and tan have previously established that theorem for the real and complex fields by other methods we also show that the semigroup l f of linear operators on the n n matrices over f that preserve both idempotence and nonidempotence is g f when the characteristic of f is not 2 we determine the structure of l f when the characteristic of f is 2 and present some open problems

a note on algebra automorphisms of strictly upper triangular matrices over commutative rings abstract in this note we explicitly describe the automorphism group of the r algebra of strictly upper triangular n n matrices over an arbitrary commutative ring

elliptic equations with bmo coefficients in reifenberg domains the inhomogeneous dirichlet problems concerning divergence form elliptic equations are studied optimal regularity requirements on the coefficients and domains for the w1 p theory 1 p are obtained the principal coefficients are supposed to be in the john nirenberg space with small bmo seminorms the domain is a reifenberg domain these conditions for the w1 p theory not only weaken the requirements on the coefficients but also lead to a more general geometric condition on the domains in fact these domains might have fractal dimensions 2004 wiley periodicals inc

uniform regularity estimates in homogenization theory of elliptic system with lower order terms abstract in this paper we extend the uniform regularity estimates obtained by m avellaneda and f lin in 3 6 to the more general second order elliptic systems in divergence form l e e 0 with rapidly oscillating periodic coefficients we establish not only sharp w 1 p estimates holder estimates lipschitz estimates and non tangential maximal function estimates for the dirichlet problem on a bounded c 1 domain but also a sharp o e convergence rate in h 0 1 by virtue of the dirichlet correctors moreover we define the green s matrix associated with l e and obtain its decay estimates we remark that the well known compactness methods are not employed here instead we construct the transformations 1 11 to make full use of the results in 3 6

linear operators strongly preserving r potent matrices over semirings abstract we consider the problem of characterizing those linear operators l on the matrices over a semiring such that l x is idempotent if and only if x is complete characterizations are obtained for many semirings including the nonnegative reals the nonnegative integers the two element boolean algebra and the fuzzy scalars

some linear preserver problems on block triangular matrix algebras in this article we classify rank one nonincreasing maps on n square block triangular matrix algebras with the assumption that in is of rank n as applications we obtain complete classifications of adjugate commuting maps and compound commuting maps on block triangular matrix algebras

pole zero representation of descriptor systems we present an algorithm for computing the pole zero representation of descriptor systems whose generalized state space models are described by the 5 tuple e a b c d where e may be a singular matrix but del a e 0 the proposed algorithm uses only orthogonal transformations hence the computed results are numerically reliable numerical examples are included to illustrate the proposed results

classical adjoint commuting mappings on hermitian and symmetric matrices let m and n be integers such that m n 3 and let f and k be fields which possess involutions of f and of k respectively let hnf be the k linear space n n hermitian matrices over f in this note we address the general description of mappings satisfying one of the following conditions 1 hn f hm k with either k 2 or f k 3 and f and k of characteristic 2 if and are the identity maps and is surjective satisfying adj a b adj a b for every a b hn f 2 hn f hm f with either f 2 or f n 1 and adj a b adj a b for every a b hn k and f 3 hn f hm k is additive with adj a adja for every a hn f here f a f a a and k a k a a are the fixed fields with respect to the involutions of f and of k respectively and adja denotes the classical adjoint of the matrix a

notes on exterior lp boundary value problems for nonhomogeneous elliptic operators abstract in terms of non smooth domains and non homogeneous elliptic operators this paper is devoted to study non tangential maximal function estimates for exterior l p regular problems we do not repeat the layer potential arguments which is a possible way instead appealing to a radial maximal function we can employ the results on homogeneous operators to make the proof much easier nevertheless this method relies on an exterior w 1 p estimate which is established in the course of the proof

on the long time stability of a temporal discretization scheme for the three dimensional viscous primitive equations in this article a semi discretized euler scheme to solve the three dimensional viscous primitive equations is studied based on suitable assumptions on the initial data and forcing terms the long time stability of the proposed scheme is proven by showing that the h 1 norm in space variables of the solutions is bounded at each time step when the time step satisfies certain smallness condition

the conormal derivative problem for elliptic equations with bmo coefficients on reifenberg flat domains we study the inhomogeneous conormal derivative problem for the divergence form elliptic equation assuming that the principal coefficients belong to the bmo space with small bmo semi norms and that the boundary is delta reifenberg flat these conditions for the w 1 p theory not only weaken the requirements on the coefficients but also lead to a more general geometric condition on the domain in fact the reifenberg flatness is the minimal regularity condition for the w 1 p theory

linear preservers on triangular matrices abstract let t n f denote the vector space of all n n upper triangular matrices over a field f we characterize those linear transformations t on t n f that satisfy one of the following properties 1 t preserves rank one matrices 2 t preserves both singular and nonsingular matrices 3 t is nonsingular and t adj a adj t a for all a t n f

linear operators preserving adjoint matrix between matrix spaces abstract we characterize the linear operators from the linear space of n n matrices into the linear space of m m matrices over any field f that preserve adjoint matrix where n 3

gradient estimates for elliptic systems in non smooth domains we obtain the global w 1 p 1 p estimate for the weak solution of an elliptic system with discontinuous coefficients in non smooth domains without using maximal function approach it is assumed that the boundary of a bounded domain is well approximated by hyperplanes at every point and at every scale and that the tensor coefficients belong to bmo space with their bmo semi norms sufficiently small

a generalized state space for singular systems systems of the form e dot x ax bu y cx with e singular are studied of particular interest are the impulsive modes that may appear in the free response of such systems when arbitrary initial conditions are permitted modes that are associated with natural system frequencies at infinity a generalized definition of system order that incorporates these impulsive degrees of freedom is proposed and concepts of controllability and observability are defined for the impulsive modes allowable equivalence transformations of such singular systems are specified the present framework is shown to overcome several difficulties inherent in other treatments of singular systems and to extend in a natural and satisfying way many results previously known only for regular state space systems

maps on matrix spaces it is well known that every automorphism of the full matrix algebra is inner we give a short proof of this statement and discuss several extensions of this theorem including structural results for multiplicative maps on matrix algebras characterizations of monotone and orthogonality preserving maps on idempotent matrices some nonlinear preserver results and some recent theorems concerning geometry of matrices we show that all these topics are closely related and point out the connections with physics and geometry several open problems are posed

uniform regularity estimates in homogenization theory of elliptic systems with lower order terms on the neumann boundary problem abstract in this paper we mainly employed the idea of the previous paper 34 to study the sharp uniform w 1 p estimates with 1 p for more general elliptic systems with the neumann boundary condition on a bounded c 1 domain arising in homogenization theory based on the skills developed by z shen in 27 and by t suslina in 31 32 we also established the l 2 convergence rates on a bounded c 1 1 domain and a lipschitz domain respectively here we found a rough version of the first order correctors see 1 12 which can unify the proof in 27 and 32 it allows us to skip the corresponding convergence results on r d that are the preconditions in 31 32 our results can be regarded as an extension of 23 developed by c kenig f lin z shen as well as of 32 investigated by t suslina

spectrum and commutativity preserving mappings on triangular matrices we give the description of continuous mappings on the algebra of all upper triangular complex matrices that preserve spectrum and commutativity

the lp boundary value problems on lipschitz domains abstract let be a bounded lipschitz domain in r n we develop a new approach to the invertibility on l p of the layer potentials associated with elliptic equations and systems in as a consequence for n 4 and 2 n 1 n 1 e p 2 where e 0 depends on we obtain the solvability of the l p neumann type boundary value problems for second order elliptic systems the analogous results for the biharmonic equation are also established

on w1 p estimates for elliptic equations in divergence form first we will apply the method to study w 1 p regularity for a nonlinear elliptic operator in divergence form we would like to point out that in the particular case of a linear elliptic equation this method gives an alternative proof to the classical one which uses the general theory of singular integrals the utility of the method that we describe below is that hypotheses a and b are obtained directly by studying the deviation of the coefficients of a from the coefficients of a0 and this is usually not a difficult task a more interesting application of this kind of approximation method is to elliptic homogenization problems for which we obtain results that give w 1 p estimates with a weak hypothesis of regularity in the coefficients for instance we are able to study the following cases

lipschitz estimates in almost periodic homogenization we establish uniform lipschitz estimates for second order elliptic systems in divergence form with rapidly oscillating almost periodic coefficients we give interior estimates as well as estimates up to the boundary in bounded c1 domains with either dirichlet or neumann data the main results extend those in the periodic setting due to avellaneda and lin for interior and dirichlet boundary estimates and later kenig lin and shen for the neumann boundary conditions in contrast to these papers our arguments are constructive and thus the constants are in principle computable and the results for the neumann conditions are new even in the periodic setting since we can treat nonsymmetric coefficients we also obtain uniform w1 p estimates 2015 wiley periodicals inc

computation of transfer function matrices of linear multivariable systems abstract this paper is concerned with the computation of transfer function matrices of linear multivariable systems described by their state space equations the algorithm proposed here performs orthogonal similarity transformations to find the minimal order subsystem corresponding to each input output pair and uses some determinant identities to determine the elements of the transfer function matrices numerical examples are included to illustrate the performance of the proposed algorithm

the linear quadratic optimal regulator for descriptor systems in this paper we investigate the linear quadratic optimal regulator problem for the continuous time descriptor system e dot x ax bu where e is in general a singular matrix we solve first a general finite horizon problem by applying the calculus of variations to derive the optimal trajectory of the vector consisting of the concatenated descriptor codescriptor and control vectors from this trajectory the optimal feedback gain relating the control and descriptor variable can be computed by transforming to a coordinate system which can be computed by performing a singular value decomposition of e we derive several riccati differential equations all of which have the same solution this solution gives the optimal cost the steady state optimal feedback gain can be computed by solving an eigenvalue eigenvector problem formulated from the untransformed system parameters in general there does not exist a unique optimal feedback gain but rather the gain is constrained to lie in a linear variety whose dimension is equal to the number of inputs times the rank deficiency of e

elliptic equations in divergence form with partially bmo coefficients the solvability in sobolev spaces is proved for divergence form second order elliptic equations in the whole space a half space and a bounded lipschitz domain for equations in the whole space or a half space the leading coefficients aij are assumed to be only measurable in one direction and have locally small bmo semi norms in the other directions for equations in a bounded domain additionally we assume that aij have small bmo semi norms in a neighborhood of the boundary of the domain we give a unified approach of both the dirichlet boundary problem and the conormal derivative problem we also investigate elliptic equations in sobolev spaces with mixed norms under the same assumptions on the coefficients

commutativity preserving operators on symmetric matrices abstract if is a nonsingular linear operator on n n symmetric matrices over a formally real field n 3 and if preserves commutativity then a cu 1 au f a i where u t u and c are scalar and is a linear functional this is an extension of a result of chan and lim

linear preservers on powers of matrices abstract this paper is concerned with linear maps l on n x n matrices such that i l ak l a k for all a where k is a fixed integer 2 or ii l preserves idempotent or tripotent matrices respectively

linear preservers on matrices abstract let u denote either the vector space of n n matrices or the vector space of n n symmetric matrices over an infinite field f in this paper we characterize linear mappings l on u that satisfy one of the following properties i l adja adjl a for all a in u ii l preserves idempotent matrices and l in in where f is the real field r or the complex field c iii l ea el a for all a in u where f r or c

linear preservers and representations with a 1 dimensional ring of invariants we determine the group of linear transformations on a vector space v that preserve a polynomial function f on v for several interesting pairs v f using the theory of semisimple algebraic groups in an 1897 paper fro97 frobenius proved that every linear transformation of the n by n real matrices that preserves the determinant is of the form x 7 axb or x 7 ax t b for some a b gln r such that det ab 1 this is the basic example of a linear preserver problem lpp one is given a finite dimensional vector space v over a field k and a polynomial function f v k and one wants to determine the linear transformations of v that preserve f since frobenius many such prob lems have been solved see for example the surveys lp01 pll 92 lt92 and mar62 we develop here a general method that solves several new problems see examples 3 14 and 3 15 and corollaries 7 10 8 3 8 7 8 5 8 8 and 8 11 our method is to introduce an auxiliary group g gl v that is semisimple and such that v is an irreducible representation or weyl module of g in section 2 we determine the normalizer ngl v g of g in gl v we prove in theorem 3 2 that this subgroup equals the stabilizer of a closed g orbit o in the projective space p v i e stabgl v o ngl v g using this result in sections 7 and 8 we solve two families of lpps by reducing the problems in each family to determining this stabilizer these two families consist of representations v with a 1 dimensional ring of g invariant functions generated by f and are examples of prehomogenous vector spaces of parabolic type the two families correspond to the cases where the unipotent radical u of the parabolic subgroup is abelian i e u u 0 or u u is 1 dimensional respectively and we use the general results on representations in these families from rrs92 roh93 and hel12 besides obtaining new results we also recover many known solutions to linear preserver problems the generality of our method is in contrast to many of the proofs in the literature which typically are highly dependent on the particular choice of v and f the arguments in pd95 and gur97 are notable exceptions further we require only very weak assumptions about the field k at most we require that the characteristic is 6 2 3 and determine the preserver precisely and not just its identity component or lie algebra

numerically stable algorithm for transfer function matrix evaluation a numerically stable algorithm for the evaluation of the transfer function matrix corresponding to a state space description is proposed the algorithm performs orthogonal similarity transformations on the system matrices eigenvalue computations are used for pole and zero determinations

mappings preserving spectrum and commutativity on hermitian matrices the general form of a continuous mapping acting on the real vector space of all n n complex hermitian or real symmetric matrices and preserving spectrum and commutativity is derived it turns out that is either linear or its image forms a commutative set

deflation in eigenvalue assignment of descriptor systems using state feedback it is shown how deflation by unitary equivalence transformations can be used to solve the eigenvalue assignment problem for descriptor systems using state feedback the system is first transformed to a form that reveals its controllability the uncontrollable part of the system if any is then discarded and the assignments are continued with the completely controllable part of the system to give insight into the approach a mathematical method for the solution is derived without considering numerical issues using the idea of deflation it is shown how this method can be modified to derive a numerically efficient algorithm the numerical stability of the algorithm is proved and a numerical example is presented

elliptic equations with bmo coefficients in lipschitz domains in this paper we study inhomogeneous dirichlet problems for elliptic equations in divergence form optimal regularity requirements on the coefficients and domains for the w 1 p 1 p estimates are obtained the principal coefficients are supposed to be in the john nirenberg space with small bmo semi norms the domain is supposed to have lipschitz boundary with small lipschitz constant these conditions for the w 1 p theory do not just weaken the requirements on the coefficients they also lead to a more general geometric condition on the domain

homogenization of nonlinear equations with mixed boundary conditions in this paper we will study the convergence rates of solutions for homogenization of quasilinear elliptic equations with the mixed dirichlet robin boundary conditions thanks to the smoothing operator as well as homogenization tools we could handle the different boundary conditions in a uniform fashion as a consequence we establish the sharp rates of convergence in h1 and l2 which may be regarded as an extension from the classical linear equations dirichlet or neumann problems to a nonlinear case with the mixed boundary settings in this paper we will study the convergence rates of solutions for homogenization of quasilinear elliptic equations with the mixed dirichlet robin boundary conditions thanks to the smoothing operator as well as homogenization tools we could handle the different boundary conditions in a uniform fashion as a consequence we establish the sharp rates of convergence in h1 and l2 which may be regarded as an extension from the classical linear equations dirichlet or neumann problems to a nonlinear case with the mixed boundary settings

inverse optical tomography through pde constrained optimization l infty fluorescent optical tomography fot is a new bio medical imaging method with wider industrial applications it is currently intensely researched since it is very precise and with no side effects for humans as it uses non ionising red and infrared light mathematically fot can be modelled as an inverse parameter identification problem associated with a coupled elliptic system with robin boundary conditions herein we utilise novel methods of calculus of variations in l to lay the mathematical foundations of fot which we pose as a pde constrained minimisation problem in lp and l

coherence invariant mappings on block triangular matrix spaces abstract in this paper we classify bijective mappings on the space of block upper triangular matrices such that both and 1 preserve pairs of matrices whose differences have rank one applications to rank one preservers and semi isomorphisms are considered

the characteristic polynomial of an algebra and representations we pose two new linear preserver problems first given a field k and a finite dimensional k algebra b we show that the only linear maps k d b k d b which preserve the unit and the n th roots of unity for some n 2n 2 coprime to char k char k are the algebra homomorphisms second we consider linear maps a b a b between finite dimensional k algebras which preserve the cayley hamilton relations we show that if preservation of the cayley hamilton property is understood in a certain non commutative sense and a k da k d then the only such linear mappings are the algebra homomorphisms

additive rank one preserving mappings on triangular matrix algebras abstract we classify surjective additive maps on the space of block upper triangular matrices that preserve matrices of rank one as well as linear maps preserving matrices of rank one on fairly general subspaces of matrices

on maps preserving square zero matrices the problem of characterizing linear operators on matrix algebras that leave invariant certain functions subsets or relations has attracted the attention of many mathematicians see survey papers 20 22 27 for details for instance linear operators preserving zeroproduct of matrices are studied in 15 16 29 31 linear operators preserving idempotent matrices are studied in 1 11 13 14 linear operators preserving matrices annihilated by a fixed polynomial are studied in 12 13 18 linear operators preserving nilpotent matrices are studied in 9 and linear operators preserving square zero matrices are studied in 29 most linear preserver problems were investigated in the case of matrix algebras over fields in contrast not too much is known about matrix algebras over commutative rings to the best of our knowledge beside the papers by mcdonald 25 and waterhouse 30 only bresar and semrl 11 used elementary calculations to describe linear maps preserving idempotent matrices over commutative rings the reason why people seldom study matrix algebras over commutative rings is probably that one might encounter some difficulties that are not easy to overcome for example unlike matrix algebras over fields the automorphisms on matrix algebras over commutative rings can fail to be inner see 19 28

convergence rates and interior estimates in homogenization of higher order elliptic systems abstract this paper is concerned with the quantitative homogenization of 2m order elliptic systems with bounded measurable rapidly oscillating periodic coefficients we establish the sharp o e convergence rate in w m 1 p 0 with p 0 2 d d 1 in a bounded lipschitz domain in r d as well as the uniform large scale interior c m 1 1 estimate with additional smoothness assumptions the uniform interior c m 1 1 w m p and c m 1 estimates are also obtained as applications of the regularity estimates we establish asymptotic expansions for fundamental solutions

computation of structural invariants of generalized state space systems in this paper we develop an algorithm for computing the zeros of a generalized state space model described by the matrix 5 tuple e a b c d where e may be a singular matrix but det a he 0 the characterization of these zeros is based on the system matrix of the corresponding 5 tuple both the characterization and the computational algorithm are extensions of equivalent results for state space models described by the 4 tuples a b c d we also extend these results to the computation of infinite zeros and left and right minimal indices of the system matrix several non trivial numerical examples are included to illustrate the proposed results

linear k power k potent preservers between matrix spaces abstract suppose f is a field let mn f be the linear space of all n n matrices over f and let sn f be its subspace consisting of all symmetric matrices let m n k be positive integers with k 2 and let v m n f s n f and w m m f s m f a linear map f v w is called a k power preserver if f a k f ak for every a v and a k potent preserver if f a k f a for any a v with ak a we characterize i linear k power preservers from mn f to mm f when ch f k or ch f 0 ii linear k potent preservers from mn f to mm f when f is an algebraically closed field with ch f 0 iii linear k power preservers from sn f to mm f respectively sm f when ch f k 5 or ch f 0 and iv linear k potent preservers from sn f to mm f respectively sm f when f is an algebraically closed field with ch f 0

linear additive preservers of ranks 2 and 4 on alternate matrix spaces over fields abstract let kn f be the linear space of all n n alternate matrices over a field f an operator f kn f kn f is said to be additive if f a b f a f b for any a b kn f linear if f is additive and f aa af a for every a f and a kn f and a preserver of ranks 2 and 4 on kn f if rank f x rank x for every x kn f with rank x 2 or 4 when n 4 we characterize all linear respectively additive preservers of ranks 2 and 4 on kn f over any field respectively any field that is not isomorphic to a proper subfield of itself furthermore it is also shown that the condition f is not isomorphic to a proper subfield of itself is necessary for the obtained conclusion on additive preservers of ranks 2 and 4 on kn f

characterization of jordan homomorphisms on mn using preserving properties abstract let o mn mn n 3 be a continuous mapping preserving spectrum and commutativity in both directions neither linearity nor multiplicativity of i is assumed then i is either an automorphism or an antiautomorphism the same result holds if i preserves spectrum commutativity and rank one matrices

hardy spaces and the neumann problem in l p for laplace s equation in lipschitz domains on donne des resultats optimaux pour la resolubilite du probleme de neumann dans des domaines de lipschitz a donnees dans l p on obtient des resultats du point extreme correspondant pour des espaces de hardy

the l p regularity problem for the stokes system on lipschitz domains we study the lp regularity problem for the stationary stokes system on lipschitz domains for any p 2 we show that a weak reverse holder inequality with exponent p is both necessary and sufficient for the solvability of the regularity problem with data in w1 p lnp we also obtain the w1 p estimate u lp q lp f lp in a bounded lipschitz domain rd for solutions to the dirichlet problem u q div f div u 0 in and u 0 on where 1p 12 12d e