weighted estimates for the helmholtz equation and some applications we characterize the radial functionsvin rnfor which the a priori inequality u1 2 2 k uv1 2 2 c v 1 2 k2 u 2holds with constant independent ofk the condition is forvto have the x rays transform everywhere bounded we apply these estimates to the well posedness of evolution schrodinger equations with time dependent drift terms and to the restriction of the fourier transform to euclidean spheres

quantum instruments i extreme instruments the structure of completely positive quantum instruments is analyzed thoroughly we characterize the extreme points of the convex set of instruments the characterization holds also for nondiscrete instruments in infinite dimensions and is applied to quantum observables channels and preparations which are special cases of instruments we show that extreme instruments are discrete in finite dimensions

a method of finite element tearing and interconnecting and its parallel solution algorithm a novel domain decomposition approach for the parallel finite element solution of equilibrium equations is presented the spatial domain is partitioned into a set of totally disconnected subdomains each assigned to an individual processor lagrange multipliers are introduced to enforce compatibility at the interface nodes in the static case each floating subdomain induces a local singularity that is resolved in two phases first the rigid body modes are eliminated in parallel from each local problem and a direct scheme is applied concurrently to all subdomains in order to recover each partial local solution next the contributions of these modes are related to the lagrange multipliers through an orthogonality condition a parallel conjugate projected gradient algorithm is developed for the solution of the coupled system of local rigid modes components and lagrange multipliers which completes the solution of the problem when implemented on local memory multiprocessors this proposed method of tearing and interconnecting requires less interprocessor communications than the classical method of substructuring it is also suitable for parallel vector computers with shared memory moreover unlike parallel direct solvers it exhibits a degree of parallelism that is not limited by the bandwidth of the finite element system of equations

domain decomposition method for harmonic wave propagation a general presentation in this paper we give a general presentation of non overlapping domain decomposition methods for harmonic wave propagation models our abstract framework leads to concise convergence proofs and contains some recent developments about the use of non local transmission conditions it also includes applications to acoustic electromagnetic or elastic waves as well as the treatment of space discretization

carleman inequalities for the dirac and laplace operators and unique continuation on demontre les meilleures inegalites de type carleman possibles dans le cas de l operateur de dirac on obtient la propriete de prolongement unique pour d v ou v l loc r n 3n 2 2 n 3

optimal discrete transmission conditions for a nonoverlapping domain decomposition method for the helmholtz equation this paper is dedicated to recent developments of a two lagrange multipliers domain decomposition method for the helmholtz equation c farhat et al comput methods appl mech engrg 184 2000 pp 213 240 m j gander f magoules and f nataf siam j sci comput 24 2002 pp 38 60 involving an additional augmented operator along the interface between the subdomains most methods for optimizing the augmented interface operator are based on the discretization of approximations of the continuous transparent operator b despres proceedings of the second international conference on mathematical and numerical aspects of wave propagation r kleinman et al eds siam philadelphia 1993 pp 197 206 j d benamou and b despres j comput phys 136 1997 pp 68 82 p chevalier and f nataf domain decomposition methods 10 ams providence ri 1998 pp 400 407 m j gander proceedings of the 12th international conference on domain decomposition methods chiba japan ddm org 2000 pp 247 254 m j gander f magoules and f nataf siam j sci comput 24 2002 pp 38 60 at the discrete level the optimal operator can be proved to be equal to the schur complement of the outer domain this schur complement can be directly approximated using purely algebraic techniques like sparse approximate inverse methods or incomplete factorization the main advantage of such an algebraic approach is that it is much easier to implement in existing code without any information on the geometry of the interface and the finite element formulation used convergence results and parallel efficiency of several algebraic optimization techniques of an interface operator for acoustic analysis applications will be presented

a non overlapping domain decomposition method with non matching grids for modeling large finite antenna arrays a non overlapping domain decomposition method ddm is proposed herein to solve maxwell equations in r 3 in this work the maxwell equations are discretized using a vector finite element method with hierarchical h curl vector basis functions there are two major ingredients in the proposed non overlapping ddm a a proper 1st order transmission condition to enforce field continuity across domain boundaries and b a cement technique to allow non matching grids for neighboring domains moreover a detail fourier analysis of the transmission condition for a canonical half space example is presented the analysis provides significant insights into the convergence behavior of the proposed non overlapping ddm for solving electromagnetic radiation problems such as the large finite antenna arrays particularly for the antenna arrays the proposed non overlapping ddm is extremely efficient since the formulation can easily incorporate geometrical repetitions exponentially tapered notch vivaldi antenna arrays with size up to 100x100 elements are solved on a common pc to validate the proposed non overlapping ddm

optimized schwarz methods without overlap for the helmholtz equation the classical schwarz method is a domain decomposition method to solve elliptic partial differential equations in parallel convergence is achieved through overlap of the subdomains we study in this paper a variant of the schwarz method which converges without overlap for the helmholtz equation we show that the key ingredients for such an algorithm are the transmission conditions we derive optimal transmission conditions which lead to convergence of the algorithm in a finite number of steps these conditions are however nonlocal in nature and we introduce local approximations which we optimize for performance of the schwarz method this leads to an algorithm in the class of optimized schwarz methods we present an asymptotic analysis of the optimized schwarz method for two types of transmission conditions robin conditions and transmission conditions with second order tangential derivatives numerical results illustrate the effectiveness of the optimized schwarz method on a model problem and on a problem from industry

reconstruction of singularities from full scattering data by new estimates of bilinear fourier multipliers we prove that the singularities of a complex valued potential q in the schrodinger hamiltonian q can be reconstructed from the linear born approximation for full scattering data by averaging in the extra variables we prove that with this procedure the accuracy in the reconstruction improves the previously known accuracy obtained from fixed angle or backscattering data in particular for q in w alpha 2 for 0 in 2d we recover the main singularity of q with an accuracy of one derivative in 3d the accuracy is epsilon 1 2 increasing with this gives a mathematical basis for diffraction tomography the proof is based on some new estimates for multidimensional bilinear fourier multipliers of independent interest

decomposition of any quantum measurement into extremals we design an efficient and constructive algorithm to decompose any generalized quantum measurement into a convex combination of extremal measurements we show that if one allows for a classical post processing step only extremal rank 1 positive operator valued measures are needed for a measurement with n elements on a d dimensional space our algorithm will decompose it into at most n 1 d 1 extremals whereas the best previously known upper bound scaled as d2 since the decomposition is not unique we show how to tailor our algorithm to provide particular types of decompositions that exhibit some desired property

abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity critical point theorems and applications to some nonlinear problems with strong resonance at infinity p bartolo and v benci istituto di matematica applicata via re david x0 bari ital and istituto di analisi matematica palazzo ateneo l ia scolai 2 bari italy received in revised form 20 december 1952

classical randomness in quantum measurements similarly to quantum states also quantum measurements can be mixed corresponding to a random choice within an ensemble of measuring apparatuses such mixing is equivalent to a sort of hidden variable which produces a noise of purely classical nature it is then natural to ask which apparatuses are indecomposable i e do not correspond to any random choice of apparatuses this problem is interesting not only for foundations but also for applications since most optimization strategies give optimal apparatuses that are indecomposable mathematically the problem is posed describing each measuring apparatus by a positive operator valued measure povm which gives the statistics of the outcomes for any input state the povms form a convex set and in this language the indecomposable apparatuses are represented by extremal points the analogous of pure states in the convex set of states differently from the case of states however indecomposable povms are not necessarily rank one e g von neumann measurements in this paper we give a complete classification of indecomposable apparatuses for discrete spectrum by providing different necessary and sufficient conditions for extremality of povms along with a simple general algorithm for the decomposition of a povm into extremals as an interesting application informationally complete measurements are analysed in this respect the convex set of povms is fully characterized by determining its border in terms of simple algebraic properties of the corresponding povms

a domain decomposition method for the vector wave equation a nonoverlapping domain decomposition method ddm is presented for the finite element fe solution of electromagnetic scattering problems by inhomogeneous three dimensional 3 d bodies the computational domain is partitioned into concentric subdomains on the interfaces of which conformal vector transmission conditions are prescribed and that can be implemented in the inhomogeneous part the ddm is numerically implemented when a conformal vector absorbing boundary condition abc is utilized on the outer boundary terminating the fe mesh while employing the standard edge based fe formulation then numerical experiments are performed on a sphere and a cone sphere that emphasize the advantages of this technique in terms of memory storage and computing times especially when the total number of unknowns is very large also these numerical experiments serve as a severe test for the performances of the abc

multi bump solutions for a strongly indefinite semilinear schrodinger equation without symmetry or convexity assumptions abstract in this paper we study the following semilinear schrodinger equation with periodic coefficient u v x u f x u u h 1 r n the functional corresponding to this equation possesses strongly indefinite structure the nonlinear term f x t satisfies some superlinear growth conditions and need not be odd or increasing in t using a new variational reduction method and a generalized morse theory we proved that this equation has infinitely many geometrically different solutions furthermore if the solutions of this equation under some energy level are isolated then we can show that this equation has infinitely many m bump solutions for any positive integer m 2

positive sesquilinear form measures and generalized eigenvalue expansions positive operator measures with values in the space of bounded operators on a hilbert space and their generalizations mainly positive sesquilinear form measures are considered with the aim of providing a framework for their generalized eigenvalue type expansions though there are formal similarities with earlier approaches to special cases of the problem the paper differs e g from standard rigged hilbert space constructions and avoids the introduction of nuclear spaces the techniques are predominantly measure theoretic and hence the hilbert spaces involved are separable the results range from a naimark type dilation result to direct integral representations and a fairly concrete generalized eigenvalue expansion for unbounded normal operators

ground state solutions for some indefinite variational problems abstract we consider the nonlinear stationary schrodinger equation u v x u f x u in r n here f is a superlinear subcritical nonlinearity and we mainly study the case where both v and f are periodic in x and 0 belongs to a spectral gap of v inspired by previous work of li et al 2006 11 and pankov 2005 13 we develop an approach to find ground state solutions i e nontrivial solutions with least possible energy the approach is based on a direct and simple reduction of the indefinite variational problem to a definite one and gives rise to a new minimax characterization of the corresponding critical value our method works for merely continuous nonlinearities f which are allowed to have weaker asymptotic growth than usually assumed for odd f we obtain infinitely many geometrically distinct solutions the approach also yields new existence and multiplicity results for the dirichlet problem for the same type of equations in a bounded domain

multiple solutions of schrodinger equations with indefinite linear part and super or asymptotically linear terms abstract based on new information concerning strongly indefinite functionals without palais smale conditions we study existence and multiplicity of solutions of the schrodinger equation u v x u g x u for x r n u x 0 as x where v and g are periodic with respect to x and 0 lies in a gap of v supposing g is asymptotically linear as u and symmetric in u we obtain infinitely many geometrically distinct solutions we also consider the situation where g is super linear with mild assumptions different from those studied previously and establish the existence and multiplicity

on critical point theory for indefinite functionals in the presence of symmetries we consider functionals which are not bounded from above or from below even modulo compact perturbations and which exhibit certain symmetries with respect to the action of a compact lie group we develop a method which permits us to prove the existence of multiple critical points for such functionals the proofs are carried out directly in an infinite dimensional hilbert space and they are based on minimax arguments the applications given here are to hamiltonian systems of ordinary differential equations where the existence of multiple time periodic solutions is established for several classes of hamiltonians symmetry properties of these hamiltonians such as time translation invariancy or evenness are exploited introduction many variational problems which arise from physics or mathematical physics are indefinite in the sense that the functionals involved are not bounded from below or from above however some of these functionals defined in an appropriate function space are semidefinite in the sense that they are bounded from below or from above if perturbed with a weakly continuous functional this paper deals with functionals which are not semidefinite usually problems involving indefinite functionals are more difficult to handle and only very recently a method has been developed which permits us to treat such problems directly in an infinite dimensional function space 7 in 7 some theorems have been proved which establish the existence of at least one nontrivial critical point for such functionals in many physical situations there are problems which have symmetries with respect to the action of some lie group in this case we expect the existence of many critical points this has been established for semidefinite functionals cf e g 8 and 3 for even functionals 9 for a zp action with p prime numbers 15 16 10 and 6 for an s action in this paper we develop a method which allows us to estimate the number of critical points of indefinite functionals in the presence of symmetries more precisely received by the editors july 16 1980 and in revised form june 26 1981 1980 mathematics subject classification primary 58e05 70h05 secondary 34c25

a partial answer to a conjecture of b simon concerning unique continuation in his survey paper on schrijdinger semigroups s b simon formulated the following conjecture see s p 5193 let ve kfp the local kato class of potentials then the time independent schrddinger operator h d v has the unique continuation property ucp by this it is meant that given any connected open subset 52 c r the only solution u of hu 0 in 52 that can vanish in an open subset 52 c sz is u 0 a measurable function v on r is said to belong to the kato class k if

inverse scattering problem for a two dimensional random potential we study an inverse problem for the two dimensional random schrodinger equation q k 2 u 0 the potential q x is assumed to be a gaussian random function whose covariance operator is a classical pseudodifferential operator we show that the backscattered field obtained from a single realization of the random potential q determines uniquely the principal symbol of the covariance operator of q the analysis is carried out by combining harmonic and microlocal analysis with stochastic methods

l p l q estimates for electromagnetic helmholtz equation abstract in space dimension n 3 we consider the electromagnetic schrodinger hamiltonian h i a x 2 v and the corresponding helmholtz equation i a x 2 u u v x u f in r n we extend the well known l p l q estimates for the solution of the free helmholtz equation to the case when the electromagnetic hamiltonian h is considered

decay estimates and strichartz estimates of fourth order schrodinger operator abstract we study time decay estimates of the fourth order schrodinger operator h 2 v x in r d for d 3 and d 5 we analyze the low energy and high energy behaviour of resolvent r h z and then derive the jensen kato dispersion decay estimate and local decay estimate for e i t h p a c under suitable spectrum assumptions of h based on jensen kato type decay estimate and local decay estimate we obtain the l 1 l estimate of e i t h p a c in 3 dimension by ginibre argument and also establish the endpoint global strichartz estimates of e i t h p a c for d 5 furthermore using the local decay estimate and the georgescu larenas soffer conjugate operator method we prove the jensen kato type decay estimates for some functions of h

unique continuation and absence of positive eigenvalues for schrodinger operators on considere l operateur de laplace sur r n et une fonction v x sur un sous ensemble connexe ouvert de r n on montre que si n 3 une propriete de prolongement unique est vraie pour v l loc n 2 r n dans l espace de sobolev h loc 2 q r n avec q 2n n 2

uniform resolvent estimates for schrodinger operator with an inverse square potential abstract we study the uniform resolvent estimates for schrodinger operator with a hardy type singular potential let l v v x where is the usual laplacian on r n and v x v 0 r 2 where r x x x and v 0 c 1 s n 1 is a real function such that the operator v 0 n 2 2 4 is a strictly positive operator on l 2 s n 1 we prove some new uniform weighted resolvent estimates and also obtain some uniform sobolev estimates associated with the operator l v

analysis and optimization of the generalized schwarz method for elliptic problems with application to fluid structure interaction we propose a unified convergence analysis of the generalized schwarz method applied to a linear elliptic problem for a general interface flat cylindrical or spherical in any dimension in particular we provide the exact convergence set of the interface symbols related to the operators involved in the transmission conditions we also provide a general procedure to obtain estimates of the optimized interface symbols within the constants we apply such general results to a simple fluid structure interaction model problem given by the interaction between an incompressible inviscid fluid and the wave equation finally we assess the effectiveness of the theoretical findings through three dimensional numerical experiments in the haemodynamic context obtained by solving the coupling between the navier stokes equations and the linear infinitesimal elasticity

a new dual primal domain decomposition approach for finite element simulation of 3 d large scale electromagnetic problems a novel dual primal non overlapping domain decomposition method ddm for the finite element solution of three dimensional 3d large scale electromagnetic problems is proposed this method reduces the computational complexity from solving the original 3d problem to an equivalent interface problem by utilizing the idea of the dual primal finite element tearing and interconnecting feti dpem method the new method which is referred to as the feti dpem2 combines the dual primal idea with two lagrange multipliers and implements robin type transmission condition at the subdomain interfaces to significantly improve the convergence of the interface solution in the high frequency region similar to the original version a global coarse problem related to the degrees of freedom at the subdomain corner edges is designed to propagate the residual error to the whole computational domain at each iteration which further increases the convergence numerical examples are presented to demonstrate the validity and the capability of this method the results show that the proposed method produces fast solutions to large scale problems in any frequency band

a fast domain decomposition method for the solution of electromagnetic scattering by large objects a nonoverlapping domain decomposition method is proposed for the finite element solution of the scattering problem by electrically large inhomogeneous infinite cylinders of arbitrary cross section to minimize the size of the total computational domain a second order absorbing boundary condition abc is applied upon an outer boundary of arbitrary shape which may be conformal to the surface of the scatterer this domain is then partitioned into concentric subdomains circumscribing the object a second order transmission condition derived from the abc is prescribed upon the interfaces between two adjacent subdomains this particular configuration is responsible for the fast convergence of the domain decomposition iterative algorithm which is parallelizable numerical results obtained with a nonparallelized computer code are presented which emphasize the superiority of this technique in terms of memory storage requirements and computing times over the standard finite element approach as well as over the rigorous hybrid finite element integral equation formulation

generalized coherent states and extremal positive operator valued measures we present a correspondence between positive operator valued measures povms and sets of generalized coherent states povms describe quantum observables and similar to quantum states quantum observables can also be mixed we show how the formalism of generalized coherent states leads to a useful characterization of extremal povms we prove that covariant phase space observables related to squeezed states are extremal while those related to number states are not extremal this article is part of a special issue of journal of physics a mathematical and theoretical devoted to coherent states mathematical and physical aspects

dual variational methods and nonvanishing for the nonlinear helmholtz equation we set up a dual variational framework to detect real standing wave solutions of the nonlinear helmholtz equation u k2u q x u p 2u u w2 p rn with n 3 2 n 1 n 1 p 2nn 2 and nonnegative q l rn we prove the existence of nontrivial solutions for periodic q as well as in the case where q x 0 as x in the periodic case a key ingredient of the approach is a new nonvanishing theorem related to an associated integral equation the solutions we study are superpositions of outgoing and incoming waves and are characterized by a nonlinear far field relation

on the degrees of freedom of scattered fields starting from the observation that fields differing less than a prescribed error cannot be resolved as distinct entities the degrees of freedom of the scattered field are introduced and then computed the degrees of freedom are shown to be practically equal to the nyquist number appropriate to the effective spatial bandwidth of the scattered field and to the extension of the observation domain accordingly a finite number of elements of information can be used to determine the scattered field to a prescribed approximation error it is also shown that the field representation can be made in terms of field values and simple sampling functions provided that a marginal increase in the approximation error is tolerated the results not only completely justify the use of sampling interpolation for representing scattering fields but also demonstrate that such representation is practically an optimal one an algorithm for the reconstruction of scattered fields given the maximum allowed error is then produced

a hybrid finite element and integral equation domain decomposition method for the solution of the 3 d scattering problem abstract a domain decomposition method ddm is presented for the solution of the time harmonic electromagnetic scattering problem by inhomogeneous 3 d objects the computational domain is partitioned into concentric subdomains on the interfaces of which robin type transmission conditions are prescribed on the outer boundary terminating the computational domain the radiation condition is accounted for by employing an integral equation ie formulation the ddm decouples the interior problems that correspond to the solution of maxwell s equations inside each subdomain and are formulated by using a finite element method from the exterior problem solved by employing the ie it has been shown that the solutions of this ddm algorithm converge to those of the original problem a particular ie is used that allows the implementation of a very simple and fully iterative solver the main advantage offered by this technique is a reduction in memory requirements various numerical examples are presented that illustrate its potential

square integrability modulo a subgroup we prove a weak form of the frobenius reciprocity theorem for locally compact groups as a consequence we propose a definition of square integrable representation modulo a subgroup that clarifies the relations between coherent states wavelet transforms and covariant localisation observables a self contained proof of the imprimitivity theorem for covariant positive operator valued measures is given

on the periodic and asymptotically periodic nonlinear helmholtz equation abstract in the first part of this paper the existence of infinitely many l p standing wave solutions for the nonlinear helmholtz equation u u q x u p 2 u in r n is proven for n 2 and 0 under the assumption that q be a nonnegative periodic and bounded function and the exponent p lies in the helmholtz subcritical range in a second part the existence of a nontrivial solution is shown in the case where the coefficient q is only asymptotically periodic

non overlapping schwarz methods with optimized transmission conditions for the helmholtz equation abstract the development of efficient transmission conditions for the schwarz method without overlap is an important area of current research the techniques developed in recent years mainly consist of algebraic approximations of the discrete transparent operator or optimized approximations of the continuous transparent operator these optimized approximations are currently based on an analytical approach involving a minimization problem over all the available frequencies and using the l norm in this paper new numerical optimization techniques are investigated these original approaches allow selection of the frequency range for the minimization problem which is based on the l p norm new numerical experiments performed on a model problem demonstrate the performance and the robustness of the proposed optimization techniques in the particular cases p 1 and p applications to industrial automotive problems confirm the efficiency of these techniques when using arbitrary mesh partitions

singular value decomposition of the radiation operator application to model order and far field reduction the time harmonic electromagnetic scattering or radiation problem is considered the singular value decomposition svd is applied to the radiation operator that maps the set of electric and magnetic currents defined on the surface of an inhomogeneous object onto the set of the far fields scattered or radiated from this object the svd yields orthonormal bases for both sets because the radiation operator is compact and regularizing it is demonstrated that the far field calculated from the series expansions of the currents on these bases converges exponentially fast to the exact one if a sufficient number of terms is considered in these series this number is closely related to the degrees of freedom that characterize the far field the latter can be computed from a reduced number of unknowns in the discretized integral equation that links electric and magnetic surface currents by writing it in the new currents bases also it allows the reduction of the far field in a given angular sector the numerical complexity of this technique is addressed and 2d numerical examples are presented that illustrate its potentialities

optimized schwarz methods for the diffusion reaction problem with cylindrical interfaces in this work we consider the optimized schwarz method for the three dimensional 3d diffusion reaction problem in particular we treat the case of cylindrical interfaces between the subdomains and we provide a convergence analysis of the schwarz method both in the case of dirichlet interface conditions and in that of general transmission conditions this allows us to recover for the latter case optimal symbols for the interface conditions which are supposed to work well for geometries which feature cylindrical interfaces moreover starting from these optimal symbols we propose effective and easily computable constant interface parameters derived both from taylor expansions and from an optimization procedure we finally present several 3d numerical results aiming at validating the theoretical findings

improved transmission conditions for a one dimensional domain decomposition method applied to the solution of the helmholtz equation the scattering problem of a time harmonic electromagnetic wave from a perfect electric conductor pec coated with materials is considered and solved by coupling a finite element method with an integral equation prescribed on the outer boundary of the computational domain to reduce the numerical complexity a one dimensional domain decomposition method ddm is employed the computational domain is partitioned into concentric subdomains sds and robin transmission conditions tcs are prescribed on the interfaces for some configurations and or materials the convergence of the corresponding ddm algorithm happens to be slow a possible remedy is to enhance the efficiency of the tcs by approximating the exact ones more accurately to this end we first consider the simplified 2d problem of a circular pec cylinder with an homogeneous coating and up to four sds with circular interfaces thus allowing to obtain the exact tcs in closed form approximate local or non local tcs are derived from these exact ones and numerical examples demonstrate their superiority over the standard robin tcs then the case of an elliptical pec cylinder with one interface in free space is investigated also the issues pertaining to the uniqueness of the solutions and convergence of the algorithm are addressed

one way domain decomposition method with adaptive absorbing boundary condition for the solution of maxwell s equations for the solution of the time harmonic electromagnetic scattering problem by inhomogeneous 3 d objects a previously published one way domain decomposition method ddm is considered the computational domain is partitioned into concentric subdomains on the interfaces of which robin type transmission conditions tcs are prescribed with an integral equation ie on the outer boundary of the computational domain ddm ie on account of the large computing time required by the solution of the isolated ie system in this paper the ie is replaced by the integral representations irs of the fields that requires only a few matrix vector products adaptive absorbing boundary condition aabc the irs necessitate the calculation of the electric and magnetic currents on some inner surface s that is chosen to be the interface between the last two subdomains taking advantage of the tcs the unknown current on s here the magnetic current is obtained via a change of bases h rot to h div that allows the accurate computation of the ir integrals involving the surface divergence terms and permits the separate solution of the fe systems in the last two subdomains the matrix vector products in the aabc are performed only once per ddm iteration numerical results are presented that illustrate the accuracy of the ddm aabc and its superiority in terms of computing time over the ddm ie also some indications are given on how to estimate numerically the convergence rate of the ddm aabc

existence of solutions for semilinear elliptic equations with indefinite linear part we study equations on rn lu w x u p 1 ulu f u where l is an indefinite schrodinger operator 0 w x 0 as and subcritical nonlinearities we prove existence of solutions u h1 rn via an inversion to a dual variational problem

a fast domain decomposition method for solving three dimensional large scale electromagnetic problems an efficient algorithm based on domain decomposition method ddm and partial basic solution vectors pbsv technique is proposed for solving three dimensional 3 d large scale finite periodic electromagnetic problems such as photonic or electromagnetic bandgap structures frequency selective surfaces the entire computational domain is divided into many smaller nonoverlapping subdomains a robin type condition is introduced at the interfaces between subdomains to enforce the field continuity with the help of a set of dual unknowns each subdomain can be tackled independently because of geometric repetitions all the sudomains can be classified into a few building blocks which can be dealt with by an improved pbsv algorithm thus the original problem becomes a much smaller one which involves the unknowns only at the interfaces the resulting linear system of equations is solved by a block symmetric successive over relaxation ssor preconditioned krylov subspace method once the unknowns at the interfaces have been obtained the final solution on each subdomain can easily be calculated independently some numerical examples are provided and show the method is scalable with the number of subdomains

unique continuation from infinity for linear waves abstract we prove various uniqueness results from null infinity for linear waves on asymptotically flat space times assuming vanishing of the solution to infinite order on suitable parts of future and past null infinities we derive that the solution must vanish in an open set in the interior we find that the parts of infinity where we must impose a vanishing condition depend strongly on the background geometry in particular for backgrounds with positive mass such as schwarzschild or kerr the required assumptions are much weaker than the ones in the minkowski space time the results are nearly optimal in many respects they can be considered analogues of uniqueness from infinity results for second order elliptic operators this work is partly motivated by questions in general relativity

one way domain decomposition method with exact radiation condition and fast gmres solver for the solution of maxwell s equations for the solution of the time harmonic electromagnetic scattering problem by inhomogeneous 3 d objects a one way domain decomposition method ddm is considered the computational domain is partitioned into concentric subdomains on the interfaces of which robin type transmission conditions tcs are prescribed an integral representation of the electromagnetic fields on the outer boundary constitutes an exact radiation condition the global system obtained after discretization of the finite element fe formulations is solved via a krylov subspace iterative method gmres it is preconditioned in such a way that essentially only the solution of the fe subsystems in each subdomain is required this is made possible by a computationally cheap h curl h div transformation performed on the interfaces that separate the two outermost subdomains the eigenvalues of the preconditioned matrix of the system are bounded by two and optimized values of the coefficients involved in the local tcs on the interfaces are determined so as to maximize the minimum eigenvalue numerical experiments are presented that illustrate the numerical accuracy of this technique its fast convergence and legitimate the choices made for the optimized coefficients

a domain decomposition method with nonconformal meshes for finite periodic and semi periodic structures we present a domain decomposition method as a preconditioner for krylov type solvers to model complex electromagnetic problems containing periodicities the method reduces memory requirements by decomposing the original problem into several nonoverlapping sub domains the 1st order transmission condition is employed on interfaces between adjacent sub domains to enforce continuity of electromagnetic fields and to ensure the sub domain problems are well posed by following the spirit of duality paring a symmetric system is obtained to reduce the computational burdens of the present method the finite element tearing and interconnecting like algorithm is adopted this algorithm results in the computation of the so called numerical green s function which can be compressed efficiently via a rank revealing matrix factorization algorithm the final system matrix is solved by krylov solvers instead of classical stationary solvers to improve the convergence of iterative solvers several robust implementation details are discussed and the choice of some popular krylov subspace solvers is studied through numerical examples

phase space observables and isotypic spaces we give necessary and sufficient conditions for the set of neumark projections of a countable set of phase space observables to constitute a resolution of the identity and we give a criteria for a phase space observable to be informationally complete the results will be applied to the phase space observables arising from an irreducible representation of the heisenberg group

improved eigenvalue bounds for schrodinger operators with slowly decaying potentials we extend a result of davies and nath j comput appl math 148 1 1 28 2002 on the location of eigenvalues of schrodinger operators with slowly decaying complex valued potentials to higher dimensions in this context we also discuss various examples related to the laptev and safronov conjecture laptev and safronov in commun math phys 292 1 29 54 2009

non trivial l q solutions to the ginzburg landau equation it is shown that the contour problem for the stationary ginzburg landau equation where x r with r x is well posed in l 4 n for a class of small data f l 2 s n 1

barycentric decomposition of quantum measurements in finite dimensions we analyze the convex structure of the set of positive operator valued measures povms representing quantum measurements on a given finite dimensional quantum system with outcomes in a given locally compact hausdorff space the extreme points of the convex set are operator valued measures concentrated on a finite set of k d2 points of the outcome space d being the dimension of the hilbert space we prove that for second countable outcome spaces any povm admits a choquet representation as the barycenter of the set of extreme points with respect to a suitable probability measure in the general case krein milman theorem is invoked to represent povms as barycenters of a certain set of povms concentrated on k d2 points of the outcome space

complete characterization of extreme quantum observables in infinite dimensions we give a complete characterization for extreme quantum observables i e for normalized positive operator valued measures povms which are extremals in the convex set of all povms the characterization is valid both in discrete and continuous cases and also in the case of an infinite dimensional hilbert space we show that sharp povms are pre processing clean i e they cannot be irreversibly connected to other povms via quantum channels

sharp resolvent estimates outside of the uniform boundedness range in this paper we are concerned with resolvent estimates for the laplacian delta in euclidean spaces uniform resolvent estimates for delta were shown by kenig et al duke math j 55 2 329 347 1987 who established rather a complete description of the lebesgue spaces allowing such estimates however the problem of obtaining sharp l p l q bounds depending on z has not been considered in a general framework which admits all possible p q in this paper we present a complete picture of sharp l p l q resolvent estimates which may depend on z we also obtain the sharp resolvent estimates for the fractional laplacians and a new result for the bochner riesz operators of negative index