wavelet like bases for the fast solutions of second kind integral equations a class of vector space bases is introduced for the sparse representation of discretizations of integral operators an operator with a smooth nonoscillatory kernel possessing a finite number of singularities in each row or column is represented in these bases as a sparse matrix to high precision a method is presented that employs these bases for the numerical solution of second kind integral equations in time bounded by o n log 2 n where n is the number of points in the discretization numerical results are given which demonstrate the effectiveness of the approach and several generalizations and applications of the method are discussed

the numerical range theory and boundedness of solutions of the complementarity problem abstract using the numerical range theory of an operator defined on a hilbert space we study the boundedness of the solution set for the complementarity problem defined in a hilbert space

identification of a crack in a beam based on the finite element method of a b spline wavelet on the interval the model based forward and inverse problems in the diagnosis of structural crack location and size by using the finite element method of a b spline wavelet on the interval fem bswi were studied first the crack and uncracked elements of bswi were built to solve the forward problem the first three frequencies influencing functions of normalized crack location and size are approximated by means of surface fitting techniques then the first three measured natural frequencies are employed as inputs of the functions the intersection of the three frequencies contour lines predicted the normalized crack location and size both the numerical and experimental studies verified the validity of the bswi elements in solving crack singular problems with high performance

on the use of coifman intervallic wavelets in the method of moments for fast construction of wavelet sparsified matrices orthonormal wavelets have been successfully used as basis and testing functions for the integral equations and extremely sparse impedance matrices have been obtained however in many practical problems the solution domain is confined in a bounded interval while the wavelets are originally defined on the entire real line to overcome this problem periodic wavelets have been described in the literature nonetheless the unknown functions must take on equal values at the endpoints of the bounded interval in order to apply periodic wavelets as the basis functions we present the intervallic coifman wavelets coiflets for the method of moments mom the intervallic wavelets release the endpoints restrictions imposed on the periodic wavelets the intervallic wavelets form an orthonormal basis and preserve the same multiresolution analysis mra of other usual unbounded wavelets the coiflets possesses a special property that their scaling functions have many vanishing moments as a result the zero entries of the matrices are identified directly without using a truncation scheme with an artificially established threshold further the majority of matrix elements are evaluated directly without performing numerical integration procedures such as gaussian quadrature for an n spl times n matrix the number of actual numerical integrations is reduced from n sup 2 to the order of 3n 2l 1 when the coiflets of order l is employed the construction of intervallic wavelets is presented numerical examples of scattering problems are discussed and the relative error of this method is studied analytically

existence of solutions for a class of hemivariational inequality problems in this paper we are concerned with the existence of solutions for a class of hartman stampacchia type hemivariational inequalities by using the clarke generalized directional derivative and the galerkin approximation method two existence results of solutions for the generalized pseudomonotone mapping hemivariational inequality and elliptic hemivariational inequality are obtained

adaptive multiscale moment method ammm for analysis of scattering from perfectly conducting plates adaptive multiscale moment method ammm is presented for the analysis of scattering from a thin perfectly conducting plate this algorithm employs the conventional moment method and a special matrix transformation which is derived from the tensor products of the two one dimensional 1 d multiscale triangular basis functions that are used for expansion and testing functions in the conventional moment method the special feature of these new basis functions introduced through this transformation is that they are orthogonal at the same scale except at the initial scale and not between scales from one scale to another scale the initial estimate for the solution can be predicted using this multiscale technique hence the compression is applied directly to the solution and the size of the linear equations to be solved is reduced thereby improving the efficiency of the conventional moment method the basic difference between this methodology and the other techniques that have been presented so far is that we apply the compression not to the impedance matrix but to the solution itself directly using an iterative solution methodology the extrapolated results at the higher scale thus provide a good initial guess for the iterative method typically when the number of unknowns exceeds a few thousand unknowns the matrix solution time exceeds generally the matrix fill time hence the goal of this method is directed in solving electrically larger problems where the matrix solution time is of concern two numerical results are presented which demonstrate that the ammm is a useful method to analyze scattering from perfectly conducting plates

efficient implementation of a wavelet based galerkin scheme wavelets can substantially accelerate the computation of planar circuits in method of moments mom schemes this contribution deals with the prediction of the significant system matrix entries a key to numerical efficiency further optimized grids for improved performance are defined the implementation of the method is addressed relevant practical examples such as a coupled antenna array serve to demonstrate the advantages of the proposed approach and to illustrate some of its limits

a practical determination strategy of optimal threshold parameter for matrix compression in wavelet bem a practical strategy is developed to determine the optimal threshold parameter for wavelet based boundary element be analysis the optimal parameter is determined so that the amount of storage and computational work is minimized without reducing the accuracy of the be solution in the present study the beylkin type truncation scheme is used in the matrix assembly to avoid unnecessary integration concerning the truncated entries of a coefficient matrix a priori estimation of the matrix entries is introduced and thus the truncated entries are determined twice before and after matrix assembly the optimal threshold parameter is set based on the equilibrium of the truncation and discretization errors these errors are estimated in the residual sense for laplace problems the discretization error is in particular indicated with the potential s contribution c to the residual norm r used in error estimation for mesh adaptation since the normalized residual norm c u u the potential components of be solution cannot be computed without main be analysis the discretization error is estimated by the approximate expression constructed through subsidiary be calculation with smaller degree of freedom dof the matrix compression using the proposed optimal threshold parameter enables us to generate a sparse matrix with o n 1 7 0 1 non zero entries although the quasi optimal memory requirements and complexity are not attained the compression rate of a few per cent can be achieved for n 1000

a force identification method using cubic b spline scaling functions for force identification the solution may differ from the desired force seriously due to the unknown noise included in the measured data as well as the ill posedness of inverse problem in this paper an efficient basis function expansion method based on wavelet multi resolution analysis using cubic b spline scaling functions as basis functions is proposed for identifying force history with high accuracy which can overcome the deficiency of the ill posed problem the unknown force is approximated by a set of translated cubic b spline scaling functions at a certain level and thereby the original governing equation of force identification is reformulated to find the coefficients of scaling functions which yields a well posed problem the proposed method based on wavelet multi resolution analysis has inherent numerical regularization for inverse problem by changing the level of scaling functions the number of basis functions employed to approximate the identified force depends on the level of scaling functions a regularization method for selecting the optimal level of cubic b spline scaling functions by virtue of condition number of matrix is proposed in this paper the validity and applicability of the proposed method are illustrated by two typical examples of volterra fredholm integral equations that are both typical ill posed problems force identification experiments including impact and harmonic forces are conducted on a cantilever beam to compare the accuracy and efficiency of the proposed method with that of the truncated singular value decomposition tsvd technique

nonlinear complementarity problem and galerkin method etude du probleme de complementarite non lineaire dans des espaces de dimensions infinies en utilisant l approximation de galerkin et une generalisation de l hypothese de karamardian on obtient plusieurs resultats d existence pour une forme speciale du probleme ou f x x l x t x l etant un operateur lineaire et t un operateur non lineaire

variational inequalities and fixed point theorems for pm maps abstract we study mapstfor whichj tis pseudo monotone we call suchta pm map this includes compact maps in suitable spaces and pseudo contractive maps in hilbert spaces we study variational inequalities in a situation which was previously done only whentis compact we show that our variational inequalities are well suited to treating existence of fixed points for generalized inward in particular weakly inward pm maps in hilbert spaces our new results on existence of fixed points generalizes many earlier results obtained by using other methods an application to homogeneous integral equations is provided

fast integral wavelet transform on a dense set of the time scale domain the objective of this paper is to introduce a fast algorithm for computing the integral wavelet transform iwt on a dense set of points in the time scale domain by applying the duality principle and using a compactly supported spline wavelet as the analyzing wavelet this fast integral wavelet transform fiwt is realized by applying only fir moving average operations and can be implemented in parallel since this computational procedure is based on a local optimal order spline interpolation scheme and the fir filters are exact the iwt values so obtained are guaranteed to have zero moments up to the order of the cardinal spline functions the semi orthogonal s o spline wavelets used here cannot be replaced by any other biorthogonal wavelet spline or otherwise which is not s o since the duality principle must be applied to some subspace of the multiresolution analysis under consideration in contrast with the existing procedures based on direct numerical integration or an fft based multi voice per octave scheme the computational complexity of our fiwt algorithm does not increase with the increasing number of values of the scale parameter

variational inequalities with generalized monotone operators we investigate the variational inequality with pseudomonotone operators in the sense of karamardian in banach spaces new existence results which extend many known results in infinite dimensional spaces are derived under rather weak assumptions new uniqueness results which also seem to be new even in finite dimensional spaces are also derived in particular new existence and uniqueness results for the complementarity problem with pseudomonotone operators in banach spaces are obtained also existence and uniqueness results for minimization problems with pseudoconvex functions in banach spaces are obtained

asymptotic behavior of matrix coefficients of admissible representations introduction 869 1 generalities on reductive groups 873 2 the infinitesimal cartan decomposition 876 3 the t radial components 880 4 differential equations satisfied by sphereical functions 885 5 asymptotic behavior of spherical functions on a 888 6 asymptotic behavior of spherical functions along the walls of a 892 7 leading characters and growth estimates on the group 898 8 admissible representations and their matrix coefficients 906 appendix 917

exceptional family of elements and solvability of variational inequalities for mappings defined only on closed convex cones in banach spaces abstract in this paper we generalize the concept of exceptional family of elements for a completely continuous field from hilbert spaces to banach spaces and we study the solvability of the variational inequalities with respect to a mapping f that is from a closed convex cone of a banach space b to the dual space b by applying the generalized projection operator k and by using the leray schauder type alternative

smooth local cosine based galerkin method for scattering problems the smooth local trigonometric slt functions are employed as the basis and testing functions in the galerkin based method of moments mom and sparse impedance matrices are obtained the basic idea of slt is to use smooth cutoff functions to split the function and to fold overlapping parts back into the intervals so that the orthogonality of the system is preserved moreover by choosing the correct trigonometric basis rapid convergence in the case of smooth functions is ensured the slt system is particularly suitable to handle electrically large scatterers where the integral kernel behaves in a highly oscillatory manner numerical examples demonstrate the scattering of electromagnetic waves from two dimensional objects with smooth contours as well as with sharp edges a comparison of the new approach versus the traditional mom and wavelet methods is provided

efficient linear system solution in moment methods using wavelet expansions an efficient strategy is proposed to solve linear systems encountered when method of moments mom and wavelet expansions are used it exploits a high performance matrix bandwidth reduction algorithm so that it can be taken advantage of direct banded solvers which have a more favorable computational complexity with respect to the typically used iterative sparse methods speedups of up to seven have been experienced with respect to standard iterative sparse solvers

numerical solutions for the system of fredholm integral equations of second kind by a new approach involving semiorthogonal b spline wavelet collocation method in this paper a new approach based on linear b spline wavelet method has been developed to approximate the solutions of system of linear fredholm integral equations of second kind compactly supported linear semi orthogonal b spline scaling functions and wavelet functions together with their dual functions are applied to approximate the solutions of linear fredholm integral equations system of second kind this method reduces the system of integral equations to a linear system of algebraic equations that can be solved easily with any of the usual methods the numerical results obtained by the present method have been compared with those obtained by adaptive method based on trapezoidal rule numerical examples are presented to illustrate the accuracy of the method

on solving first kind integral equations using wavelets on a bounded interval the conventional method of moments mom when applied directly to integral equations leads to a dense matrix which often becomes computationally intractable to overcome the difficulties wavelet bases have been used previously which lead to a sparse matrix the authors refer to mom with wavelet bases as wavelet mom there have been three different ways of applying the wavelet techniques to boundary integral equations 1 wavelets on the entire real line which requires the boundary conditions to be enforced explicitly 2 wavelet bases for the bounded interval obtained by periodizing the wavelets on the real line and 3 wavelet like basis functions furthermore only orthonormal on bases have been considered the present authors propose the use of compactly supported semi orthogonal so spline wavelets specially constructed for the bounded interval in solving first kind integral equations they apply this technique to analyze a problem involving 2d em scattering from metallic cylinders it is shown that the number of unknowns in the case of wavelet mom increases by m 1 as compared to conventional mom where m is the order of the spline function results for linear m 2 and cubic m 4 splines are presented along with their comparisons to conventional mom results it is observed that the use of cubic spline wavelets almost diagonalizes the matrix while maintaining less than 1 5 of relative normed error the authors also present the explicit closed form polynomial representation of the scaling functions and wavelets

on the solution of a nonlinear integral equation on the basis of a fixed point technique and cubic b spline scaling functions in this paper we apply the fixed point method to solve some nonlinear functional volterra integral equations which appear in many physical chemical and biological problems in each iteration of this method cubic semi orthogonal compactly supported b spline wavelets are used as basis functions to approximate the solution also the convergence of this numerical method is investigated and some examples are presented to show the accuracy and convergence of the method

periodic solutions for second order systems with not uniformly coercive potential abstract the existence and multiplicity of periodic solutions are obtained for the nonautonomous second order systems with locally coercive potential that is f t x as x for a e t in some positive measure subset of 0 t by using an analogy of egorov s theorem the properties of subadditive functions the least action principle and a three critical point theorem proposed by brezis and nirenberg

existence of a nontrivial solution for a class of hemivariational inequality problems at double resonance abstract in this paper we discuss a class of semilinear elliptic hemivariational inequality problems by using the nonsmooth minimax principle for locally lipschitz functions we establish the existence of a nontrivial solution for the semilinear elliptic hemivariational inequality problem where incomplete double resonance occurs at infinity between two distinct consecutive eigenvalues

existence of solutions for dirichlet elliptic problems with discontinuous nonlinearity abstract in this paper we concern with definite sign and sign changing solutions of a class of discontinuous problems by using the dual method we overcome the difficulty of non differentiability and obtain the existence results of definite sign solution and a sign changing solutions on the nehari manifold for the discontinuous problems some continuous results are extended to the discontinuous cases

generalized linear complementarity problems it has been shown by lemke that if a matrix is copositive plus on n then feasibility of the corresponding linear complementarity problem implies solvability in this article we show under suitable conditions that feasibility of ageneralized linear complementarity problem i e defined over a more general closed convex cone in a real hilbert space implies solvability whenever the operator is copositive plus on that cone we show that among all closed convex cones in a finite dimensional real hilbert space polyhedral cones are theonly ones with the property that every copositive plus feasible glcp is solvable we also prove a perturbation result for generalized linear complementarity problems

wave motion analysis in arch structures via wavelet finite element method abstract the application of b spline wavelet on interval bswi finite element method for wave motion analysis in arch structures is presented in this paper instead of traditional polynomial interpolation scaling functions at certain scales have been adopted to form the shape functions and construct wavelet based elements different from other wavelet numerical methods adding wavelets directly the element displacement field represented by the coefficients of wavelets expansions is transformed from wavelet space to physical space via the corresponding transformation matrix the energy functional of the arch is obtained by the generalized shell theory and the finite element model for wave motion analysis is constructed according to hamilton s principle and the central difference method in time domain taking the practical application into account damaged arch waveguides are also investigated proper analysis of the responses from structure damages allows one to indicate the location very precisely this paper mainly focuses on the crack in structures based on castigliano s theorem and the pairs equation the local flexibility of crack is formulated for bswi element numerical experiments are performed to study the effect of wave propagations in arch waveguides that is frequency dispersion and mode spilt in the arch the responses of the arch with cracks are simulated under the broad band narrow band and chirp excitations in order to estimate the spatial time and frequency concentrations of responses the reciprocal length time frequency transform and correlation coefficient are introduced in this investigation

on the use of wavelet expansions in the method of moments em scattering an approach which incorporates the theory of wavelet transforms in method of moments solutions for electromagnetic wave interaction problems is presented the unknown field or response is expressed as a twofold summation of shifted and dilated forms of a properly chosen basis function which is often referred to as the mother wavelet the wavelet expansion can adaptively fit itself to the various length scales associated with the scatterer by distributing the localized functions near the discontinuities and the more spatially diffused ones over the smooth expanses of the scatterer the approach is thus best suited for the analysis of scatterers which contain a broad spectrum of length scales ranging from a subwavelength to several wavelengths using a galerkin method and subsequently applying a threshold procedure the moment method matrix is rendered sparsely populated the structure of the matrix reveals the localized scale fitting distribution long before the matrix equation is solved the performance of the proposed discretization scheme is illustrated by a numerical study of electromagnetic coupling through a double slot aperture

fast wavelet transforms and numerical algorithms i a class of algorithms is introduced for the rapid numerical application of a class of linear operators to arbitrary vectors previously published schemes of this type utilize detailed analytical information about the operators being applied and are specific to extremely narrow classes of matrices in contrast the methods presented here are based on the recently developed theory of wavelets and are applicable to all calderon zygmund and pseudo differential operators the algorithms of this paper require order o n or o n log n operations to apply an n n matrix to a vector depending on the particular operator and the version of the algorithm being used and our numerical experiments indicate that many previously intractable problems become manageable with the techniques presented here

a multiresolution curvilinear rao wilton glisson basis function for fast analysis of electromagnetic scattering a new set of multiresolution curvilinear rao wilton glisson mr crwg basis functions is proposed for the method of moments mom solution of integral equations for three dimensional 3 d electromagnetic em problems the mr crwg basis functions are constructed as linear combinations of curvilinear rao wilton glisson crwg basis functions which are defined over curvilinear triangular patches thus allowing direct application on the existing mom codes that using crwg basis the multiresolution property of the mr crwg basis can lead to the fast convergence of iterative solvers merely by a simple diagonal preconditioning to the corresponding mom matrices moreover the convergence of iterative solvers can be further improved by introducing a perturbation from the principle value term of the magnetic field integral equation mfie operator to construct diagonal preconditioners for efficient iterative solution of the electric field integral equation efie another important property of the mr crwg basis is that the mom matrices using the mr crwg basis can be highly sparsified without loss of accuracy the mr crwg basis has been applied to the 3 d electromagnetic scattering problems and the numerical results indicate that the mr crwg basis performs much better than the crwg basis

penalty approximation method for a class of elliptic variational inequality problems in this paper two existence results of solutions for a class of elliptic variational inequalities are obtained by considering the approximations of the solutions to a class of penalized differential equations

uncertainty propagation using wiener linear b spline wavelet expansion abstract in this paper we have constructed a scheme combining generalized polynomial chaos gpc representation and b spline wavelets to begin with semi orthogonal compactly supported b spline wavelets are constructed for the bounded interval 0 1 which are used for pc expansion of possible stochastic processes to compute the deterministic coefficients of expansion we have applied galerkin projection on uncertain data and the solution variables then to ascertain the behavior of the random process the system of equations obtained from projection are integrated using fourth order runge kutta method to handle the nonlinearity we have compared galerkin projection with pseudo spectral projection the procedure is illustrated through three model problems of real life importance we conclude that galerkin approximation performs better in comparison to pseudo spectral approach which is numerically expected also it has been observed that the wavelet function based expansion shows superior results as compared to scaling function based expansion

analysis of wave motion in one dimensional structures through fast fourier transform based wavelet finite element method abstract this paper presents a hybrid method that combines the b spline wavelet on the interval bswi finite element method and spectral analysis based on fast fourier transform fft to study wave propagation in one dimensional 1d structures bswi scaling functions are utilized to approximate the theoretical wave solution in the spatial domain and construct a high accuracy dynamic stiffness matrix dynamic reduction on element level is applied to eliminate the interior degrees of freedom of bswi elements and substantially reduce the size of the system matrix the dynamic equations of the system are then transformed and solved in the frequency domain through fft based spectral analysis which is especially suitable for parallel computation a comparative analysis of four different finite element methods is conducted to demonstrate the validity and efficiency of the proposed method when utilized in high frequency wave problems other numerical examples are utilized to simulate the influence of crack and delamination on wave propagation in 1d rods and beams finally the errors caused by fft and their corresponding solutions are presented

optimal a priori clipping estimation for wavelet based method of moments matrices wavelet bases are mainly used in the methods of moments mom to render the system matrix sparse clipping entries below a given threshold is an essential operation to obtain the desired sparse matrix in this paper we present a novel a priori way to estimate the clipping threshold that can be used if one wants an error on the solution below a desired accuracy the procedure has a very low computational complexity typically of o n

application of discrete periodic wavelets to measured equation of invariance recently the wavelet expansions have been applied in field computations in the frequency domain the application is focused on the thinning of matrices arising from the method of moment mom the thinning of matrices can best be done by the measured equation of invariance mei which provides sparsity almost without sacrificing accuracy in that the boundary equation it entails is convertible to that of the mom the real power of the wavelet expansions is to give high resolution in convolution integrals high resolution is also needed in the process of finding the mei coefficients which are obtained via an integration process almost identical to that of the mom in this paper it is shown that when the fast discrete periodic wavelets fdpw are used as metron currents in the mei method the resolutions of the mei coefficients are improved at high frequency computations or at geometric extremities the level of sparsity of the mei is much more favorable than that achievable by the thinning of mom matrix using the wavelet expansions the role of fdpw in the mei happens to be more fitting than its place in the mom

solution of large dense complex matrix equations utilizing wavelet like transforms this paper presents the wavelet like transforms which are quite different from the wavelet transform for the solution of large dense complex matrix equations from a purely numerical standpoint these wavelet like transforms are not true orthogonal transforms as the condition number of the resulting matrix changes after the thresholding these effects are illustrated through examples

on the differential equations satisfied by weighted orbital integrals weighted orbital integrals are distributions on reductive groups over local fields appearing both in the local and global trace formulas there are associated invariant distributions which play the same role in the invariant trace formulas in the case of real groups the fourier transforms of these distributions satisfy a system of differential equations as a step towards determining those fourier transforms we show that this system is holonomic and has a simple singularity at infinity we deduce that any solution has a series expansion and is a linear combination of certain canonical solutions for some groups of small rank we solve the recursion formula for the coefficients explicitly

wavelets and dilation equations a brief introduction wavelets are new families of basis functions that yield the representation f x sum b jk w 2 j x k their construction begins with the solution phi x to a dilation equation with coefficients c k then w comes from phi and the basis comes by translation and dilation of w it is shown in part 1 how conditions on the c k lead to approximation properties and orthogonality properties of the wavelets part 2 describes the recursive algorithms also based on the c k that decompose and reconstruct f the object of wavelets is to localize as far as possible in both time and frequency with efficient algorithms

adaptive multiscale moment method ammm for analysis of scattering from three dimensional perfectly conducting structures the adaptive multiscale moment method ammm is presented for the analysis of scattering from three dimensional 3d perfectly conducting bodies this algorithm employs the conventional moment method mm using the subsectional triangular patch basis functions and a special matrix transformation which is derived from solving the fredholm equation of the first kind by the multiscale technique this methodology is more suitable for problems where the matrix solution time is much greater than the matrix fill time the widely used triangular patch vector basis functions developed by rao et al 1982 are used for expansion and testing functions in the conventional mm the objective here is to compress the unknowns in existing mm codes which solves for the currents crossing the edges of the triangular patch basis functions by use of a matrix transformation the currents source terms and impedance matrix can be arranged in the form of different scales from one scale to another scale the initial guess for the solution can be predicted according to the properties of the multiscale technique ammm can reduce automatically the size of the linear equations so as to improve the efficiency of the conventional mm the basic difference between this methodology and the other wavelet based techniques that have been presented so far is that we apply the compression not to the impedance matrix but to the solution itself directly in an iterative fashion even though it is an unknown two numerical results are presented which demonstrate that the ammm is a useful method for analysis of electromagnetic scattering from arbitrary shaped 3d perfectly conducting bodies

numerical solution for the weakly singular fredholm integro differential equations using legendre multiwavelets an effective method based upon legendre multiwavelets is proposed for the solution of fredholm weakly singular integro differential equations the properties of legendre multiwavelets are first given and their operational matrices of integral are constructed these wavelets are utilized to reduce the solution of the given integro differential equation to the solution of a sparse linear system of algebraic equations in order to save memory requirement and computational time a threshold procedure is applied to obtain the solution to this system of algebraic equations through numerical examples performance of the present method is investigated concerning the convergence and the sparseness of the resulted matrix equation

application of wavelets on the interval to numerical analysis of integral equations in electromagnetic scattering problems the wavelet expansions on the interval are employed for solving the problems of the electromagnetic em scattering from two dimensional 2 d conducting objects the arbitrary configurations of scatterers are modeled using the boundary element method bem by using the wavelets on the interval as basis and test functions a sparse matrix equation is generated from the integral equation under study the resulted sparse matrix equation allows the use of sparse matrix solvers or multi level iterations for rapid solution the utilization of wavelets on the interval circumvents the difficulties in the application of the wavelets on the real line to finite interval problems and has no periodicity constraint to the unknown function that is usually imposed by periodic wavelets numerical examples are provided and compared with the previously published data or other methods 1997 by john wiley sons ltd

finite dimensional approximation for a class of elliptic obstacle problems in this paper we study the finite dimensional approximation for a class of elliptic obstacle problems involving unbounded domains by using the galerkin method the convergence of the approximation is deduced

a multiresolution method of moments for triangular meshes this paper presents the construction use and properties of a multiresolution wavelet basis for the method of moments mom analysis of metal antennas scatterers and microwave circuits discretized by triangular meshes several application examples show fast convergence of iterative solvers and accurate solutions with highly sparse mom matrices the proposed basis is organized in hierarchical levels and keeps the different scales of the problem directly into the basis functions representation the current is divided into a solenoidal and a quasi irrotational part which allows mapping these two vector parts onto fully scalar quantities where the wavelets are defined as a byproduct this paper also presents a way to construct hierarchical sets of rao wilton glisson rwg functions on a family of meshes obtained by subsequent refinement i e with the rwg of coarser meshes expressed as linear combinations of those of finer meshes

existence results for the nonlinear complementarity problem and applications to nonlinear analysis abstract we produce an existence result for the nonlinear complementarity problem associated to a weakly locally compact convex cone k in a banach space e and to the difference j f of two nonlinear operators we specialize our result to the case where k is a so called galerkin cone j is the duality mapping and f satisfies a suitable growth condition applications to the fixed point theory and to eigenvalue problems conclude the paper

semi orthogonal versus orthogonal wavelet basis sets for solving integral equations the two categories of wavelets orthogonal and semi orthogonal are compared and it is shown that the semi orthogonal wavelet is best suited for integral equation applications the battle lemarie orthogonal wavelet and the spline generated semi orthogonal wavelet are each used to solve for the current distribution on an infinite strip illuminated by a transverse magnetic tm plane wave and a straight thin wire illuminated by a normally incident plane wave the grounds for comparison are accuracy in characterizing the current matrix sparsity computation time and singularity extraction capability the limitations and advantages of solving integral equations with each of the two wavelet categories are discussed

existence and multiplicity of solutions for semilinear hemivariational inequalities at resonance abstract in this paper we study semilinear hemivariational inequalities at resonance assuming a partially anticoercive nonsmooth potential we prove an existence and a multiplicity theorem the method of the proof is variational and in the multiplicity result we employ the nonsmooth local linking theorem