resonances for microstrip transmission lines in this paper we rigorously derive asymptotic formulae for resonances associated with a microstrip transmission line mounted on a planar waveguide with variable electromagnetic characteristics when the width of the line goes to zero

degree of mapping for nonlinear mappings of monotone type abstract a classical degree function is constructed for pseudomonotone mappings from a reflexive banach space to its dual using galerkin approximations this generalizes the leray schauder degree when the banach space is a hilbert space and yields a flexible analytical tool for the study of nonlinear elliptic problems of higher order in divergence form

a multiplicity theorem for problems with the p laplacian abstract we consider nonlinear elliptic equations driven by the p laplacian differential operator using degree theoretic arguments based on the degree map for operators of type s we prove the existence of two nontrivial smooth solutions one of which is of constant sign

boundary layer techniques for solving the helmholtz equation in the presence of small inhomogeneities we consider solutions to the helmholtz equation in two and three dimensions based on layer potential techniques we provide for such solutions a rigorous systematic derivation of complete asymptotic expansions of perturbations resulting from the presence of diametrically small inhomogeneities with constitutive parameters different from those of the background medium it is expected that our results will find important applications for developing effective algorithms for reconstructing small dielectric inhomogeneities from boundary measurements

a variational inequality theory in reflexive smooth banach spaces and applications to p laplacian elliptic inequalities abstract we develop a theory of variational inequality for demicontinuous s contractive maps in reflexive smooth banach spaces variational inequality theorems are proved and applied to study existence of nonzero positive weak solutions for p laplacian elliptic inequalities and a population model of one species arising in mathematical biology

focusing and imaging using eigenfunctions of the scattering operator an inverse scattering method that uses eigenfunctions of the scattering operator is presented this approach provides a unified framework that encompasses eigenfunction methods of focusing and quantitative image reconstruction in arbitrary media scattered acoustic fields are described using a compact normal operator the eigenfunctions of this operator are shown to correspond to the far field patterns of source distributions that are directly proportional to the position dependent contrast of a scattering object conversely the eigenfunctions of the scattering operator specify incident wave patterns that focus on these effective source distributions these focusing properties are employed in a new inverse scattering method that represents unknown scattering media using products of numerically calculated fields of eigenfunctions a regularized solution to the nonlinear inverse scattering problem is shown to result from combinations of these products so that the products comprise a natural basis for efficient and accurate reconstructions of unknown inhomogeneities the corresponding linearized problem is solved analytically resulting in a simple formula for the low pass filtered scattering potential the linear formula is analytically equivalent to known filtered backpropagation formulas for born inversion and at least in the case of small scattering objects has advantages of computational simplicity and efficiency a similarly efficient and simple formula is derived for the nonlinear problem in which the total acoustic pressure can be determined based on an estimate of the medium computational results illustrate focusing of eigenfunctions on discrete and distributed scattering media quantitative imaging of inhomogeneous media using products of retransmitted eigenfunctions inverse scattering in an inhomogeneous background medium and reconstructions for data corrupted by noise

two numerical methods for recovering small inclusions from the scattering amplitude at a fixed frequency in this paper two noniterative algorithms for locating small electromagnetic inclusions from the scattering amplitude at a fixed frequency are developed in particular a variety of numerical results is presented to highlight their potential and their limitations

on the semi monotone operator theory and applications abstract in this paper eis a real banach space a e e e is a semi monotone operator we first study the variational inequality problem findu k such that a u u v u 0 wherek e is a closed convex subset then the operator equationa u u p and we also construct a degree theory for demi continuous semi monotone operators in reflexive banach spaces

the iterative time reversal process analysis of the convergence the efficiency of a time reversal acoustic mirror to focus on a reflective target through an inhomogeneous media has been demonstrated in a multitarget media the ability of such a mirror to work in an iterative mode in order to focus selectively on the strongest target was shown c prada f wu and m fink j acoust soc am 90 1119 1991 the theory of how the iterative time reversal process is built is based on a matrix formalism and treats the array of l transducers in a given medium as a linear system of l inputs l outputs the system is characterized at each frequency by its transfer matrix k and the time reversal iterative process is then described by a time reversal operator k k because of the reciprocity principle this operator is hermitian the following result is shown if the scattering medium is a set of well resolved targets of different reflectivities then each eigenvector of the operator k k with nonzero eigenvalue corresponds to one of the targets in the set and provides the opt

positive weak solutions of semilinear second order elliptic inequalities via variational inequalities existence uniqueness and convergence of approximants of positive weak solutions for semilinear second order elliptic inequalities are obtained the nonlinearities involved in these inequalities satisfy suitable upper or lower bound conditions or monotonicity conditions the lower bound conditions are allowed to contain the critical sobolev exponents the methodology is to establish variational inequality principles for demicontinuous pseudo contractive maps in hilbert spaces by considering convergence of approximants and apply them to the corresponding variational inequalities arising from the semilinear second order elliptic inequalities examples on the existence uniqueness and convergence of approximants of positive weak solutions of the semilinear second order elliptic inequalities are given

a new topological degree theory for densely defined s l perturbations of multivalued maximal monotone operators in reflexive separable banach spaces abstract let x be a real reflexive separable locally uniformly convex banach space with locally uniformly convex dual space x let t x d t 2 x be maximal monotone with 0 d t and 0 t 0 and c x d c x assume that l d c is a dense linear subspace of x c is of class s l and c x x x x d c where r r is nondecreasing a new topological degree theory is developed for the sum t c the current approach utilizes the approximate degree d t t c g 0 t 0 t t t 1 t j 1 1 g x open and bounded of kartsatos and skrypnik for the single valued mapping t t c the subdifferential for belonging to a large class of proper convex lower semicontinuous functions gives rise to operators t to which this degree theory applies a theoretical application to an existence problem of nonlinear analysis is included

computable algebra and group embeddings this work grew out of our investigations of the infinitely generated subgroups of finitely presented groups a useful technique for embedding countable groups with sufficiently nice local properties into finitely presented groups was introduced in l this technique was then applied in 1 21 to prove that every countable locally polycyclic group and every countable metabelian group can be embedded in a finitely presented group it became apparent from 2 that effective methods in commutative algebra could be extended to group rings of polycyclic groups and then used to embed certain groups in finitely presented groups in this paper these extensions are carried out with the consequent application that every countable locally abelian by nilpotent group can be embedded in a finitely presented group much of the effective commutative algebra we require seems to be known see for instance 6 9 14 171 unfortunately a systematic account is not available in particular we need a proof of the hilbert basis theorem which

reconstruction of a small inclusion in a two dimensional open waveguide we consider wave propagation in a perturbed open waveguide we provide a new asymptotic expansion for the scattered wave when the inclusion is of small diameter we design a music multiple signal classification type of algorithm for locating the inclusion and illustrate its viability in numerical examples

a multilevel sampling method for detecting sources in a stratified ocean waveguide in the reconstruction process of sound waves in a 3d stratified waveguide a key technique is to effectively reduce the huge computational demand in this work we propose an efficient and simple multilevel reconstruction method to locate the accurate position of a point source in a stratified ocean the proposed method can be viewed as a direct sampling method since no solutions of optimizations or linear systems are involved the novel method exhibits several strengths fast convergence robustness against noise advantages in computational complexity and applicability for a very small number of receivers

fixed point theory and nonlinear problems introduction among the most original and far reaching of the contributions made by henri poincare to mathematics was his introduction of the use of topological or qualitative methods in the study of nonlinear problems in analysis his starting point was the study of the differential equations of celestial mechanics and in particular of their periodic solutions his work on this topic began with his thesis in 1879 and was developed in detail in his great three volume work methodes nouvelles de la mechanique celeste which appeared in the early 1890s and summarized his many memoirs of the intervening period it continued until his memoir shortly before his death in 1912 in which he put forward the unproved fixed point result usually referred to as poincare s last geometric theorem the ideas introduced by poincare include the use of fixed point theorems the continuation method and the general concept of global analysis the writer s acquaintance with poincare s influence came through contact with solomon lefschetz and marston morse both of whom were very explicit as to the role of poincare as an initiator in this direction of mathematical development in 1934 in the foreword to his colloquium volume on the calculus of variations in the large morse had put this forward very forcefully in the first paragraph

acoustic scattering by an inhomogeneous layer on a rigid plate the problem of scattering of time harmonic acoustic waves by an inhomogeneous fluid layer on a rigid plate in r 2 is considered the density is assumed to be unity in the media within the layer the sound speed is assumed to be an arbitrary bounded measurable function the problem is modelled by the reduced wave equation with variable wavenumber in the layer and a neumann condition on the plate to formulate the problem and prove uniqueness of solution a radiation condition appropriate for scattering by infinite rough surfaces is introduced a generalization of the rayleigh expansion condition for diffraction gratings with the help of the radiation condition the problem is reformulated as a system of two second kind integral equations over the layer and the plate under additional assumptions on the wavenumber in the layer uniqueness of solution is proved and the nonexistence of guided wave solutions of the homogeneous problem established general results on the solvability of systems of integral equations on unbounded domains are used to establish existence and continuous dependence in a weighted norm of the solution on the given data

on the existence of periodic solutions for nonlinear evolutions in hilbert spaces a periodic solutions for nonlinear evolution equations of the form du dt au t f t u t t r where f r h 2 is a set valued caratheodory function are considered when both f and a are set valued mappings and not necessarily linear

limit cycles of discontinuous piecewise polynomial vector fields abstract when the first average function is non zero we provide an upper bound for the maximum number of limit cycles bifurcating from the periodic solutions of the center x y x 2 y 2 2 m and y x x 2 y 2 2 m with m 1 when we perturb it inside a class of discontinuous piecewise polynomial vector fields of degree n with k pieces the positive integers m n and k are arbitrary the main tool used for proving our results is the averaging theory for discontinuous piecewise vector fields

a new topological degree theory for perturbations of the sum of two maximal monotone operators abstract let x be an infinite dimensional real reflexive banach space with dual space x and g x open and bounded assume that x and x are locally uniformly convex let t x d t 2 x be maximal monotone and strongly quasibounded s x d s x maximal monotone and c x d c x strongly quasibounded w r t s and such that it satisfies a generalized s condition w r t s assume that d s l d t d c where l is a dense subspace of x and 0 t 0 s 0 0 a new topological degree theory is introduced for the sum t s c with degree mapping d t s c g 0 the reason for this development is the creation of a useful tool for the study of a class of time dependent problems involving three operators this degree theory is based on a degree theory that was recently developed by kartsatos and skrypnik just for the single valued sum s c as above

source localization using recursively applied and projected rap music a new method for source localization is described that is based on a modification of the well known music algorithm in classical music the array manifold vector is projected onto an estimate of the signal subspace errors in the estimate of the signal subspace can make localization of multiple sources difficult recursively applied and projected rap music uses each successively located source to form an intermediate array gain matrix and projects both the array manifold and the signal subspace estimate into its orthogonal complement the music projection to find the next source is then performed in this reduced subspace special assumptions about the array manifold structure such as vandermonde or shift invariance are not required using the metric of principal angles we describe a general form of the rap music algorithm for the case of diversely polarized sources through a uniform linear array simulation with two highly correlated sources we demonstrate the improved monte carlo error performance of rap music relative to music and two other sequential subspace methods s and ies music we then demonstrate the more general utility of this algorithm for multidimensional array manifolds in a magnetoencephalography meg source localization simulation

generalizations of browder s degree theory the starting point of this paper is the recent important work of f e browder who extended degree theory to operators of monotone type the degree function of browder is generalized to maps of the form t f g where t is maximal monotone f is of class s bounded and g is an u s c compact multifunction it is also generalized to maps of the form f ng with f of class s and ng the nemitsky operator of a multifunction g x r satisfying various types of sign conditions some examples are also included to illustrate the abstract results

experimental subwavelength localization of scatterers by decomposition of the time reversal operator interpreted as a covariance matrix the d o r t method french acronym for decomposition of the time reversal operator is an active remote sensing technique using arrays of antennas for the detection and localization of scatterers prada et al j acoust soc am 99 2067 2076 1996 the analogy between the time reversal operator and the covariance matrix used for classical sources separation in passive remote sensing bienvenu et al ieee trans assp 31 1235 1247 1983 is established then an experiment of subwavelength detection and localization of point like scatterers with a linear array of transducers is presented using classical estimators in reception like maximum likelihood and multiple signal characterization music two point like scatterers separated by 3 and placed at 100 from the array of transducers are resolved in these experiments the role of multiple scattering and the existence of additional eigenvectors associated with dipolar and monopolar radiation of each scatterer is discussed

direct recovery of wave penetrable scatterers in a stratified ocean waveguide abstract we shall derive a direct sampling method for the recovery of wave penetrable inhomogeneous scatterers in a three dimensional stratified ocean waveguide the proposed method is simple straightforward and computationally efficient since no matrix inversions optimizations or solutions of ill posed linear systems are involved moreover it is highly tolerant to noise and is applicable with a few scattered fields corresponding to only two or four incidences in addition a priori knowledge of either the number of disconnected components or the physical features of the unknown obstacles is not required by the direct sampling method a mathematical derivation is provided for its validation and several extensive numerical experiments are shown to evaluate the effectiveness and feasibility of the newly proposed method

scattering of time harmonic electromagnetic waves by anisotropic inhomogeneous scatterers or impenetrable obstacles we investigate an overlapping solution technique to compute the scattering of time harmonic electromagnetic waves in two dimensions the technique can be used to compute waves scattered by penetrable anisotropic inhomogeneous scatterers or impenetrable obstacles the major focus is on implementing the method using finite elements we prove existence of a unique solution to the discretized problem and derive an optimal convergence rate for the scheme which is verified by numerical examples

the algorithmic theory of finitely generated metabelian groups algorithms are constructed which when an explicit presentation of a finitely generated metabelian group g in the variety x 2 is given produce finitary presentations for the derived subgroup g the centre z g the fitting subgroup fit g and the frattini subgroup 0 g additional algorithms of independent interest are developed for commutative algebra which construct the associated set of primes ass m of a finitely generated module m over a finitely generated commutative ring r and the intersection pr m of the maximal submodules of m

a simple method for detecting scatterers in a stratified ocean waveguide abstract in this paper we have designed a simple method for the inverse scattering problem of stratified ocean waveguide the simple approach applies the bisection technique in parallel to estimate the boundaries of inhomogeneous media from the received partial data in addition the algorithm only involves the matrix vector operations and possesses the optimal computation complexity in both two and three dimensions in practice it is easy to carry out robust against noise and capable of reconstructing the penetrable obstacles of different locations and shapes we can consider the simple method as a direct and straightforward process to supply satisfactory initial positions for the implementation of any existing more refined but computationally more demanding techniques to achieve accurate reconstructions of physical features of scatterers