higher order stable generalized finite element method for the elliptic eigenvalue and source problems with an interface in 1d abstract we study the generalized finite element methods gfems for the second order elliptic eigenvalue problem with an interface in 1d the linear stable generalized finite element methods sgfem were recently developed for the elliptic source problem with interfaces we first generalize sgfem to arbitrary order elements and establish the optimal error convergence of the approximate solutions for the elliptic source problem with an interface we then apply the abstract theory of spectral approximation of compact operators to establish the error estimation for the eigenvalue problem with an interface the error estimations on eigenpairs strongly depend on the estimation of the discrete solution operator for the source problem we verify our theoretical findings in various numerical examples including both source and eigenvalue problems

on adjacency distance spectral radius and spread of graphs abstract let g be a connected graph the greatest eigenvalue and the spread of the sum of the adjacency matrix and the distance matrix of g are called the adjacency distance spectral radius and the adjacency distance spread of g respectively both quantities are used as molecular descriptors in chemoinformatics we establish some properties for the adjacency distance spectral radius and the adjacency distance spread by proposing local grafting operations such that the adjacency distance spectral radius is decreased or increased hence we characterize those graphs that uniquely minimize and maximize the adjacency distance spectral radii in several sets of graphs and determine trees with small adjacency distance spreads it transpires that the adjacency distance spectral radius satisfies the requirements of a branching index

on the accuracy of the gerschgorin circle theorem for bounding the spread ofa symmetric matrix abstract the spread of a matrix with real eigenvalues is the difference between its largest and smallest eigenvalues the gerschgorin circle theorem can be used to bound the extreme eigenvalues of the matrix and hence its spread for nonsymmetric matrices the gerschgorin bound on the spread may be larger by an arbitrary factor than the actual spread even if the matrix is symmetrizable this is not true for real symmetric matrices it is shown that for real symmetric matrices or complex hermitian matrices the ratio between the bound and the spread is bounded by p 1 where p is the maximum number of off diagonal nonzeros in any row of the matrix for full matrices this is just n this bound is not quite sharp for n greater than 2 but examples with ratios of n 1 for all n are given for banded matrices with m nonzero bands the maximum ratio is bounded by m independent of the size of n this bound is sharp provided only that n is at least 2m for sparse matrices p may be quite small and the gerschgorin bound may be surprisingly accurate

positive linear maps and spreads of matrices ii abstract it is shown how positive linear maps can be used to obtain lower bounds for spreads of normal matrices some known results and some new ones are obtained in this way

eigenvalue approximation by mixed and hybrid methods note univ maryland dept math college pk md 20742 ecole polytech ctr math appl f 91128 palaiseau france univ paris 6 f 75230 paris 05 france mercier b cea limeil f 94190 villeneuve france isi document delivery no lq584times cited 29cited reference count 44 reference asn article 1981 005doi 10 2307 2007651 record created on 2006 08 24 modified on 2017 05 12

bounds for the spectrum of normal matrices abstract let a be a normal matrix with eigenvalues 1 2 n and let denote the smallest disc containing these eigenvalues we give some inequalities relating the center and radius of to the entries in a when applied to hermitian matrices our results give lower bounds on the spread maxij i j of a when applied to positive definite hermitian matrices they give lower bounds on the kantorovich ratio maxij i j i j

new lower bounds for the randic spread abstract let g v g e g be an n m graph the randic spread of g s r g is defined as the maximum distance of its randic eigenvalues disregarding the randic spectral radius of g in this work we use numerical inequalities and bounds for the matricial spread to obtain relations between this spectral parameter and some structural and algebraic parameters of the underlying graph such as the sequence of vertex degrees the nullity randic index generalized randic indices and its independence number in the last section a comparison is presented for regular graphs

analysis of finite element approximation of evolution problems in mixed form this paper deals with the finite element approximation of evolution problems in mixed form following d boffi f brezzi and l gastaldi math comp 69 2000 pp 121 140 we handle separately two types of problems a model for the first case is the heat equation in mixed form while the time dependent stokes problem fits within the second one for either case we give sufficient conditions for a good approximation in the natural functional spaces the results are not obvious in the first situation in this case the well known conditions for the well posedness and convergence of the corresponding steady problem are not sufficient for the good approximation of the time dependent problem this issue is demonstrated with a numerical counter example and justified analytically

attack detection in sensor network target localization systems with quantized data we consider a sensor network focused on target localization where sensors measure the signal strength emitted from the target each measurement is quantized to one bit and sent to the fusion center a general attack is considered at some sensors that attempts to cause the fusion center to produce an inaccurate estimation of the target location the attack is a combination of man in the middle hacking and spoofing attacks that can effectively change both signals going into and coming out of the sensor nodes in a realistic manner we show that the essential effect of attacks is to alter the naive estimate of the distance between the target and each attacked sensor which ignores the existence of attacks to a different extent giving rise to a geometric inconsistency among the attacked and unattacked sensors with the help of two secure sensors a class of detectors are proposed to detect the attacked sensors by scrutinizing the existence of the geometric inconsistency we show that the false alarm and miss probabilities of the proposed detectors decrease exponentially as the number of measurement samples increases which implies that with sufficient measurement samples the proposed detectors can identify the attacked and unattacked sensors with any required accuracy numerical results show that compared to the cases where all sensors are employed without detecting attacks or only the secure sensors are employed the localization performance can be significantly improved if we employ the secure sensors and the sensors which are declared as unattacked by the proposed detector

guaranteed and robust a posteriori bounds for laplace eigenvalues and eigenvectors a unified framework this paper develops a general framework for a posteriori error estimates in numerical approximations of the laplace eigenvalue problem applicable to all standard numerical methods guaranteed and computable upper and lower bounds on an arbitrary simple eigenvalue are given as well as on the energy error in the approximation of the associated eigenvector the bounds are valid under the sole condition that the approximate i th eigenvalue lies between the exact i 1 th and i 1 th eigenvalue where the relative gaps are sufficiently large we give a practical way how to check this the precision of the resulting estimates depends on these relative gaps our bounds feature no unknown solution regularity or polynomial degree dependent constant are optimally convergent efficient and polynomial degree robust under a further explicit a posteriori minimal resolution condition the multiplicative constant in our estimates can be reduced by a fixed factor moreover when an elliptic regularity assumption on the corresponding source problem is satisfied with known constants this multiplicative constant can be brought to the optimal value of 1 with mesh refinement applications of our framework to nonconforming discontinuous galerkin and mixed finite element approximations of arbitrary polynomial degree are provided along with numerical illustrations our key ingredient are equivalences between the i th eigenvalue error the associated eigenvector energy error and the dual norm of the residual we extend them in an appendix to the generic class of bounded below self adjoint operators with compact resolvent

spectral approximations by the hdg method we consider the numerical approximation of the spectrum of a secondorder elliptic eigenvalue problem by the hybridizable discontinuous galerkin hdg method we show for problems with smooth eigenfunctions that the approximate eigenvalues and eigenfunctions converge at the rate 2k 1 and k 1 respectively here k is the degree of the polynomials used to approximate the solution its flux and the numerical traces our numerical studies show that a rayleigh quotient like formula applied to certain locally postprocessed approximations can yield eigenvalues that converge faster at the rate 2k 2 for the hdg method as well as for the brezzidouglas marini bdm method we also derive and study a condensed nonlinear eigenproblem for the numerical traces obtained by eliminating all the other variables

spectral approximation of variationally posed eigenvalue problems by nonconforming methods this paper deals with the nonconforming spectral approximation of variationally posed eigenvalue problems it is an extension to more general situations of known previous results about nonconforming methods as an application of the present theory convergence and optimal order error estimates are proved for the lowest order crouzeix raviart approximation of the eigenpairs of two representative second order elliptical operators

linearization techniques for band structure calculations in absorbing photonic crystals band structure calculations for photonic crystals require the numerical solution of eigenvalue problems in this paper we consider crystals composed of lossy materials with frequency dependent per

discontinuous galerkin computation of the maxwell eigenvalues on simplicial meshes this paper is concerned with the discontinuous galerkin approximation of the maxwell eigenproblem after reviewing the theory developed in a buffa i perugia discontinuous galerkin approximation of the maxwell eigenproblem technical report 24 pv imati cnr pavia italy 2005 we present a set of numerical experiments which both validate the theory and provide further insight regarding the practical performance of discontinuous galerkin methods particularly in the case when non conforming meshes characterized by the presence of hanging nodes are employed

rational eigenvalue problems and applications to photonic crystals we establish new analytic results for a general class of rational spectral problems they arise e g in modelling photonic crystals whose capability to control the flow of light depends on specific

a schwarz generalized eigen oscillation spectral element method gesem for 2 d high frequency electromagnetic scattering in dispersive inhomogeneous media in this paper we propose a parallel schwarz generalized eigen oscillation spectral element method gesem for 2 d complex helmholtz equations in high frequency wave scattering in dispersive inhomogeneous media this method is based on the spectral expansion of complex generalized eigen oscillations for the electromagnetic fields and the schwarz non overlapping domain decomposition iteration method the gesem takes advantages of a special real orthogonality property of the complex eigen oscillations and a new radiation interface condition for the system of equations for the spectral expansion coefficients numerical results validate the high resolution and the flexibility of the method for various materials

attacks on sensor network parameter estimation with quantization performance and asymptotically optimum processing byzantine attacks on sensor systems estimating the value of an unknown deterministic parameter based on quantized observations are studied initially asymptotically optimum processing is investigated for the family of attacks that would pass bad data detectors at the sensors bad data detectors check that the sensor data fits the models employed by the estimation approach when it assumes no attack is present it is then shown that it is possible to identify the attacked sensors under stated assumptions with perfect accuracy as the number of observations k from each sensor tends to infinity if the number of sensors tends to infinity while having a finite k it is shown that the attacked sensors can be identified with a given accuracy that can be set by k allowing considerable design flexibility next the performance of any estimation approach employed by the sensor system under any general attack is described for cases where any number of observations and sensors are employed a classification for these general attacks which categorizes them according to the information available to the attacking entity is introduced solving optimization problems over these attack classes leads to expressions which describe the performance of any specific estimation algorithm under the most devastating attacks with full information and the generally less effective information free attacks constraints are considered to account for some attack detection performed by the sensor system

finite element spectral analysis for the mixed formulation of the elasticity equations the aim of this paper is to analyze the linear elasticity eigenvalue problem formulated in terms of the stress tensor and the rotation this is achieved by considering a mixed variational formulation in which the symmetry of the stress tensor is imposed weakly we show that a discretization of the mixed eigenvalue elasticity problem with reduced symmetry based on the lowest order arnold falk winther element provides a correct approximation of the spectrum we also prove quasi optimal error estimates finally we report some numerical experiments

distributed recursive filtering for stochastic systems under uniform quantizations and deception attacks through sensor networks this paper is concerned with the distributed recursive filtering problem for a class of discrete time delayed stochastic systems subject to both uniform quantization and deception attack effects on the measurement outputs the target plant is disturbed by the multiplicative as well as additive white noises a novel distributed filter is designed where the available innovations are from not only the individual sensor but also its neighboring ones according to the given topology attention is focused on the design of a distributed recursive filter such that in the simultaneous presence of time delays deception attacks and uniform quantization effects an upper bound for the filtering error covariance is guaranteed and subsequently minimized by properly designing the filter parameters via a gradient based method at each sampling instant furthermore by utilizing the mathematical induction a sufficient condition is established to ensure the asymptotic boundedness of the sequence of the error covariance finally a simulation example is utilized to illustrate the usefulness of the proposed design scheme of distributed filters

discontinuous galerkin approximation of the laplace eigenproblem in this paper we analyse the problem of computing eigenvalues and eigenfunctions of the laplace operator by means of discontinuous galerkin dg methods it results that several dg methods actually provide a spectrally correct approximation of the laplace operator we present here the convergence theory which applies to a wide class of dg methods as well as numerical tests demonstrating the theoretical results

non conforming high order approximations of the elastodynamics equation in this paper we formulate and analyze two non conforming high order strategies for the approximation of elastic wave problems in heterogeneous media namely the mortar spectral element method and the discontinuous galerkin spectral element method starting from a common variational formulation we make a full comparison of the two techniques from the points of view of accuracy convergence grid dispersion and stability

laplacian spread of graphs lower bounds and relations with invariant parameters abstract the spread of an n n complex matrix b with eigenvalues 1 2 n is defined by s b max i j i j where the maximum is taken over all pairs of eigenvalues of b let g be a graph on n vertices the concept of laplacian spread of g is defined by the difference between the largest and the second smallest laplacian eigenvalue of g in this work by combining old techniques of interlacing eigenvalues and rank 1 perturbation matrices new lower bounds on the laplacian spread of graphs are deduced some of them involving invariant parameters of graphs as it is the case of the bandwidth independence number and vertex connectivity

a discontinuous hp finite element method for convection diffusion problems this paper presents a new method which exhibits the best features of both finite volume and finite element techniques special attention is given to the issues of conservation flexible accuracy and stability the method is elementwise conservative the order of polynomial approximation can be adjusted element by element and the stability is not based on the introduction of artificial diffusion but on the use of a very particular finite element formulation with discontinuous basis functions the method supports h p and hp approximations and can be applied to any type of meshes including non matching grids a priori error estimates and numerical experiments on representative model problems indicate that the method is robust and capable of delivering high accuracy

superconvergence of the local discontinuous galerkin method for elliptic problems on cartesian grids in this paper we present a superconvergence result for the local discontinuous galerkin ldg method for a model elliptic problem on cartesian grids we identify a special numerical flux for which the l2 norm of the gradient and the l2 norm of the potential are of orders k 1 2 and k 1 respectively when tensor product polynomials of degree at most k are used for arbitrary meshes this special ldg method gives only the orders of convergence of k and k 1 2 respectively we present a series of numerical examples which establish the sharpness of our theoretical results

some inequalities for positive linear maps it has long been known that an analogue of jensen s inequality holds for positive unital linear maps on matrix algebras provided that instead of ordinary convex functions one restricts to matrix convex functions we show that this restriction is not necessary in the case of 2 2 matrices a noncommutative analogue of the variance is studied and a basic inequality with several applications is established

hyperplane based vector quantization for distributed estimation in wireless sensor networks this paper considers distributed estimation of a vector parameter in the presence of zero mean additive multivariate gaussian noise in wireless sensor networks due to stringent power and bandwidth constraints vector quantization is performed at each sensor to convert its local noisy vector observation into one bit of information which is then forwarded to a fusion center where a final estimate of the vector parameter is obtained within such a context this paper focuses on a class of hyperplane based vector quantizers which linearly convert the observation vector into a scalar by using a compression vector and then carry out a scalar quantization it is shown that the key of the vector quantization design is to find a compression vector for each sensor under the framework of the cramer rao bound crb analysis the compression vector design problem is formulated as an optimization problem that minimizes the trace of the crb matrix such an optimization problem is extensively studied in particular an efficient iterative algorithm is developed for the general case along with optimal and near optimal solutions for some specific but important noise scenarios performance analysis and simulation results are carried out to illustrate the effectiveness of the proposed scheme

two families of mixed finite elements for second order elliptic problems two families of mixed finite elements one based on triangles and the other on rectangles are introduced as alternatives to the usual raviart thomas nedelec spaces error estimates inl 2 andh 5 are derived for these elements a hybrid version of the mixed method is also considered and some superconvergence phenomena are discussed

a stabilized finite element method for the two field and three field stokes eigenvalue problems in this paper the stabilized finite element approximation of the stokes eigenvalue problems is considered for both the two field displacement pressure and the three field stress displacement pressure formulations the method presented is based on a subgrid scale concept and depends on the approximation of the unresolvable scales of the continuous solution in general subgrid scale techniques consist in the addition of a residual based term to the basic galerkin formulation the application of a standard residual based stabilization method to a linear eigenvalue problem leads to a quadratic eigenvalue problem in discrete form which is physically inconvenient as a distinguished feature of the present study we take the space of the unresolved subscales orthogonal to the finite element space which promises a remedy to the above mentioned complication in essence we put forward that only if the orthogonal projection is used the residual is simplified and the use of term by term stabilization is allowed thus we do not need to put the whole residual in the formulation and the linear eigenproblem form is recovered properly we prove that the method applied is convergent and present the error estimates for the eigenvalues and the eigenfunctions we report several numerical tests in order to illustrate that the theoretical results are validated

on mass conservation in least squares methods we compare three least squares finite element reformulations of the stokes equations paying particular attention to mass conservation the first problem we approximate has a simple analytical solution over a convex region even for this simple problem without special treatment of the conservation of mass term very poor numerical solutions may result sufficiently weighting this term leads to a dramatic improvement in the results over a range of test problems

on the problem of spurious eigenvalues in the approximation of linear elliptic problems in mixed form in the approximation of linear elliptic operators in mixed form it is well known that the so called inf sup and ellipticity in the kernel properties are sufficient and in a sense to be made precise necessary in order to have good approximation properties and optimal error bounds one might think in the spirit of mercier osborn rappaz raviart and in consideration of the good behavior of commonly used mixed elements like raviart thomas or brezzi douglas marini elements that these conditions are also sufficient to ensure good convergence properties for eigenvalues in this paper we show that this is not the case in particular we present examples of mixed finite element approximations that satisfy the above properties but exhibit spurious eigenvalues such bad behavior is proved analytically and demonstrated in numerical experiments we also present additional assumptions fulfilled by the commonly used mixed methods already mentioned which guarantee optimal error bounds for eigenvalue approximations as well

mixed discontinuous galerkin approximation of the elasticity eigenproblem we introduce a discontinuous galerkin method for the mixed formulation of the elasticity eigenproblem with reduced symmetry the analysis of the resulting discrete eigenproblem does not fit in the standard spectral approximation framework since the underlying source operator is not compact and the scheme is nonconforming we show that the proposed scheme provides a correct approximation of the spectrum and prove asymptotic error estimates for the eigenvalues and the eigenfunctions finally we provide several numerical tests to illustrate the performance of the method and confirm the theoretical results

bandwidth constrained distributed estimation for wireless sensor networks part i gaussian case we study deterministic mean location parameter estimation when only quantized versions of the original observations are available due to bandwidth constraints when the dynamic range of the parameter is small or comparable with the noise variance we introduce a class of maximum likelihood estimators that require transmitting just one bit per sensor to achieve an estimation variance close to that of the clairvoyant sample mean estimator when the dynamic range is comparable or larger than the noise standard deviation we show that an optimum quantization step exists to achieve the best possible variance for a given bandwidth constraint we will also establish that in certain cases the sample mean estimator formed by quantized observations is preferable for complexity reasons we finally touch upon algorithm implementation issues and guarantee that all the numerical maximizations required by the proposed estimators are concave

an a posteriori estimator of eigenvalue eigenvector error for penalty type discontinuous galerkin methods we provide an abstract framework for analyzing discretization error for eigenvalue problems discretized by discontinuous galerkin methods such as the local discontinuous galerkin method and symmetric interior penalty discontinuous galerkin method the analysis applies to clusters of eigenvalues that may include degenerate eigenvalues we use asymptotic perturbation theory for linear operators to analyze the dependence of eigenvalues and eigenspaces on the penalty parameter we first formulate the dg method in the framework of quadratic forms and construct a companion infinite dimensional eigenvalue problem with the use of the companion problem the eigenvalue vector error is estimated as a sum of two components the first component can be viewed as a non conformity error that we argue can be neglected in practical estimates by properly choosing the penalty parameter the second component is estimated a posteriori using auxiliary subspace techniques and this constitutes the practical estimate

discontinuous galerkin methods of the non selfadjoint steklov eigenvalue problem in inverse scattering abstract in this paper we apply discontinuous galerkin methods to the non selfadjoint steklov eigenvalue problem arising in inverse scattering the variational formulation of the problem is non selfadjoint and does not satisfy h1 elliptic condition by using the spectral approximation theory of compact operators we prove the spectral approximation and optimal convergence order for the eigenvalues finally some numerical experiments are reported to show that the proposed numerical schemes are efficient for real and complex steklov eigenvalues

asymptotically optimum distributed estimation in the presence of attacks distributed estimation of a deterministic mean shift parameter in additive zero mean noise is studied when using quantized data in the presence of byzantine attacks several subsets of sensors are assumed to be tampered with by adversaries using different attacks such that the compromised sensors transmit fictitious data first we consider the task of identifying and categorizing the attacked sensors into different groups according to distinct types of attacks it is shown that increasing the number k of time samples at each sensor and enlarging the size n of the sensor network can both ameliorate the identification and categorization but to different extents as k rightarrow infty the attacked sensors can be perfectly identified and categorized while with finite but sufficiently large k as n rightarrow infty it can be shown that the fusion center can also ascertain the number of attacks and obtain an approximate categorization with a sufficiently small percentage of sensors that are misclassified next in order to improve the estimation performance by utilizing the attacked observations we consider joint estimation of the statistical description of the attacks and the parameter to be estimated after the sensors have been well categorized when using the same quantization approach successfully employed without attacks it can be shown that the corresponding fisher information matrix fim is singular to overcome this a time variant quantization approach is proposed which will provide a nonsingular fim provided that k geq 2 furthermore the fim is employed to provide necessary and sufficient conditions under which utilizing the compromised sensors in the proposed fashion will lead to better estimation performance when compared to approaches where the compromised sensors are ignored

a fundamental limitation on maximum parameter dimension for accurate estimation with quantized data it is revealed that there is a link between the quantization approach employed and the dimension of the vector parameter which can be accurately estimated by a quantized estimation system a critical quantity called inestimable dimension for quantized data idqd is introduced which does not depend on the quantization regions and the statistical models of the observations but instead depends only on the number of sensors and on the precision of the vector quantizers employed by the system it is shown that the idqd describes a quantization induced fundamental limitation on the estimation capabilities of the system to be specific if the dimension of the desired vector parameter is larger than the idqd of the quantized estimation system then the fisher information matrix for estimating the desired vector parameter is singular and moreover there exist infinitely many nonidentifiable vector parameter points in the vector parameter space furthermore it is shown that under some common assumptions on the statistical models of the observations and the quantization system a smaller idqd can be obtained which can specify an even more limiting quantization induced fundamental limitation on the estimation capabilities of the system

functional forms of optimum spoofing attacks for vector parameter estimation in quantized sensor networks estimation of an unknown deterministic vector from quantized sensor data is considered in the presence of spoofing attacks which alter the data presented to several sensors contrary to the previous work a generalized attack model is employed which manipulates the data using transformations with arbitrary functional forms determined by some attack parameters whose values are unknown to the attacked system for the first time necessary and sufficient conditions are provided under which the transformations provide a guaranteed attack performance in terms of cramer rao bound crb regardless of the processing the estimation system employs thus defining a highly desirable attack interestingly these conditions imply that for any such attack when the attacked sensors can be perfectly identified by the estimation system either the fisher information matrix fim for jointly estimating the desired and attack parameters is singular or that the attacked system is unable to improve the crb for the desired vector parameter through this joint estimation even though the joint fim is nonsingular it is shown that it is always possible to construct such a highly desirable attack by properly employing a sufficiently large dimension attack vector parameter relative to the number of quantization levels employed which was not observed previously to illustrate the theory in a concrete way we also provide some numerical results which corroborate that under the highly desirable attack attacked data are not useful in reducing the crb

mixed finite element methods in fluid structure systems the eigenvalue problem describing the frequencies of a fluid vibrating in a rigid cavity or within moving boundaries is considered based on the method of lagrange multipliers a three field mixed formulation is introduced in order to avoid the spurious circulating modes stability and optimal error bounds are proved for two choices of finite element spaces

stable and semistable low order finite elements for viscous flows it is shown that i the bilinear constant and linear constant box elements are not uniformly stable and ii certain element pairs derived from those above by restricting the pressure spaces are stable the notion of div semistability is developed to study the behavior of the bilinear constant and linear constant box elements in detail

universal decentralized estimation in a bandwidth constrained sensor network consider a situation where a set of distributed sensors and a fusion center wish to cooperate to estimate an unknown parameter over a bounded interval u u each sensor collects one noise corrupted sample performs a local estimation and transmits a message to the fusion center while the latter combines the received messages to produce a final estimate this correspondence investigates optimal local estimation and final fusion schemes under the constraint that the communication from each sensor to the fusion center must be a one bit message such a binary message constraint is well motivated by the bandwidth limitation of the communication links fusion center and by the limited power budget of local sensors in the absence of bandwidth constraint and assuming the noises are bounded to the interval u u additive independent but otherwise unknown the classical estimation theory suggests that a total of o u2 epsi2 sensors are necessary and sufficient in order for the sensors and the fusion center to jointly estimate the unknown parameter within epsi root mean squared error mse it is shown in this correspondence that the same remains true even with the binary message constraint furthermore the optimal decentralized estimation scheme suggests allocating 1 2 of the sensors to estimate the first bit of the unknown parameter 1 4 of the sensors to estimate the second bit and so on

mathematical analysis of a finite element method without spurious solutions for computation of dielectric waveguides in this paper we propose a finite element method to compute dielectric waveguides which does not present spurious solutions in addition to a theoretical analysis showing the good stability properties of this method we give numerical results for some classical test problems

immersed finite element method for eigenvalue problem abstract we consider the approximation of elliptic eigenvalue problem with an interface the main aim of this paper is to prove the stability and convergence of an immersed finite element method ifem for eigenvalues using crouzeix raviart p 1 nonconforming approximation we show that spectral analysis for the classical eigenvalue problem can be easily applied to our model problem we analyze the ifem for elliptic eigenvalue problems with an interface and derive the optimal convergence of eigenvalues numerical experiments demonstrate our theoretical results

the aα spread of a graph abstract let a g and d g be the adjacency matrix and the degree diagonal matrix of a graph g respectively for any real number 0 1 nikiforov defined the a matrix of a graph g as a g d g 1 a g the a spread of a graph is the difference between the largest eigenvalue and the smallest eigenvalue of the a matrix of the graph in this paper we obtain some new lower bounds on a spread and characterize the extremal graphs for certain cases which extend the results of a spread and q spread moreover some graph operations on a spread are presented

quadratic assignment problems abstract this paper surveys quadratic assignment problems qap at first several applications of this problem class are described and mathematical formulations of qaps are given then some exact solution methods and good heuristics are outlined their computational behaviour is illustrated by numerical results further recent results on the asymptotic probabilistic behaviour of qaps are outlined

lower bounds for the spread of a matrix a characterization of the spread of a normal matrix is used to derive several simple lower bounds for the spread comparisons are then made with several known bounds

lower bounds for the spread of a hermitian matrix abstract some simple lower bounds for the spread of a hermitian matrix are derived these bounds are explicit functions of the entries of the matrix one of which is sharper than a recent result due to e r barnes and a j hoffman comparisons are made with several known results

characterizations and lower bounds for the spread of a normal matrix abstract the spread of an n n matrix a with eigenvalues 1 n is defined by spr a max j k j k we prove that if a is normal then spr a max x ax y ay x y c n x y 1 max x ay y ax x y c n x y 1 re x y 0 max x ay y ax x y c n x y 1 x y 0 max spr z a z a 2 z c z 1 2 max x a 2 x x ax 2 x a ax x ax 2 1 2 x c n x 1 we also present several lower bounds for spr a given by these characterizations

new bounds for the signless laplacian spread abstract let g be an undirected simple graph the signless laplacian spread of g is defined as the maximum distance of pairs of its signless laplacian eigenvalues this paper establishes some new bounds both lower and upper for the signless laplacian spread several of these bounds depend on invariant parameters of the graph we also use a minmax principle to find several lower bounds for this spectral invariant

target location estimation in sensor networks with quantized data a signal intensity based maximum likelihood ml target location estimator that uses quantized data is proposed for wireless sensor networks wsns the signal intensity received at local sensors is assumed to be inversely proportional to the square of the distance from the target the ml estimator and its corresponding crameacuter rao lower bound crlb are derived simulation results show that this estimator is much more accurate than the heuristic weighted average methods and it can reach the crlb even with a relatively small amount of data in addition the optimal design method for quantization thresholds as well as two heuristic design methods are presented the heuristic design methods which require minimum prior information about the system prove to be very robust under various situations

bounds on the q spread of a graph the spread s m of an n n complex matrix m is s m maxij i j where the maximum is taken over all pairs of eigenvalues of m i 1 i n 9 and 11 based on this concept gregory et al 7 determined some bounds for the spread of the adjacency matrix a g of a simple graph g and made a conjecture regarding the graph on n vertices yielding the maximum value of the spread of the corresponding adjacency matrix the signless laplacian matrix of a graph g q g d g a g where d g is the diagonal matrix of degrees of g and a g is its adjacency matrix has been recently studied 4 5 the main goal of this paper is to determine some bounds on s q g we prove that for any graph on n 5 vertices 2 s q g 2n 4 and we characterize the equality cases in both bounds further we prove that for any connected graph g with n 5 vertices s q g 2n 4 we conjecture that for n 5 sq g 4n 2 20n 33 and that in this case the upper bound is attained if and only if g is a certain pathcomplete graph

super resolution delay doppler estimation for ofdm passive radar in this paper we consider the problem of joint delay doppler estimation of moving targets in a passive radar that makes use of orthogonal frequency division multiplexing communication signals a compressed sensing algorithm is proposed to achieve supper resolution and better accuracy using both the atomic norm and the ell 1 norm the atomic norm is used to manifest the signal sparsity in the continuous domain unlike previous works that assume the demodulation to be error free we explicitly introduce the demodulation error signal whose sparsity is imposed by the ell 1 norm on this basis the delays and doppler frequencies are estimated by solving a semidefinite program sdp which is convex we also develop an iterative method for solving this sdp via the alternating direction method of multipliers where each iteration involves closed form computation simulation results are presented to illustrate the high performance of the proposed algorithm

decentralized estimation with dependent gaussian observations this paper considers decentralized estimation with correlated noises under the bayesian framework for a tandem network with correlated additive gaussian noises we establish that threshold quantizers on local observations are optimal in the sense of maximizing fisher information at the fusion center this is true despite the fact that subsequent estimators may differ at the fusion center depending on the statistical distribution of the parameter to be estimated in addition it is always beneficial to have the better sensor i e the one with higher signal to noise ratio serve as the fusion center in a tandem network finally we identify different correlation regimes in terms of their impact on the estimation performance these include the well known case where negatively correlated noise benefits estimation performance as it facilitates noise cancellation as well as two distinct regimes with positively correlated noises

analysis of some mixed finite element methods related to reduced integration we prove error estimates for the following two mixed finite element methods related to reduced integration a method for stokes problem using rectangular elements with piecewise bilinear approximations for the velocities and piecewise constants for the pressure and one method for a plate problem using bilinear approximations for transversal displacement and rotations and piecewise constants for the shear stress the main idea of the proof in the case of stokes problem is to combine a weak babuska brezzi type stability estimate for the pressure with a superapproximability property for the velocities a similar technique is used in the case of the plate problem