the schur algorithm applied to the one dimensional continuous inverse scattering problem the one dimensional continuous inverse scattering problem can be solved by the schur algorithm in the discrete time domain using sampled scattering data the sampling rate of the scattering data should be increased to reduce the discretization error but the complexity of the schur algorithm is proportional to the square of the sampling rate to improve this tradeoff between the complexity and the accuracy we propose a schur algorithm with the richardson extrapolation sare the asymptotic expansion of the schur algorithm necessary for the richardson extrapolation is derived in powers of the discretization step which shows that the accuracy order with respect to the discretization step of the schur algorithm is 1 the accuracy order of the sare with the n step richardson extrapolation is increased to n 1 with comparable complexity to the schur algorithm therefore the discretization error of the schur algorithm can be decreased in a computationally efficient manner by the sare

exact and operator rational approximate solutions of the helmholtz weyl composition equation in underwater acoustics the quadratic profile the application of phase space and path integral methods to both mathematical and computational direct and inverse wave propagation modeling at the level of the scalar one way helmholtz equation is briefly reviewed the role of operator symbols is stressed and their properties briefly discussed the construction of the operator symbol requires the exact or approximate solution of the helmholtz weyl composition equation in the weyl pseudodifferential operator calculus the exact symbols for several quadratic profiles are presented and briefly analyzed the symbols exactly corresponding to a family of operator rational approximations are also presented for the quadratic case these results are used to illustrate several points pertinent to wide angle propagation modeling and the refractive index profile reconstruction problem in underwater acoustics

differential and integral methods for multidimensional inverse scattering problems a layer stripping procedure for solving three dimensional schrodinger equation inverse scattering problems is developed this procedure operates by recursively reconstructing the radon transform of the potential from the jump in the radon transform of the scattered field at the wave front this reconstructed potential is then used to propagate the wave front and scattered field differentially further into the support of the potential the connections between this differential procedure and integral equation procedures are then illustrated by the derivations of two well known exact integral equation procedures using the radon transform and a generalized radon transform these procedures as well as the layer stripping procedure are then reduced to the familiar born approximation result for this problem by neglecting multiple scattering events this illustrates the central role of the radon transform in both exact and approximate inversion procedures

direct and inverse scattering in the time domain via invariant imbedding equations this paper examines the implementation of a new approach to direct and inverse scattering problems in the time domain which is applied here to the case of a one dimensional lossless medium the method is based on an integro differential equation which is satisfied by the reflection kernel and has been derived elsewhere using invariant imbedding techniques an example of an exact solution to this equation is given numerical schemes for solving the direct and inverse problems are derived by discretizing this equation the behavior of the resulting algorithms is then tested on several examples the results suggest that the inversion method is stable in the presence of additive noise

generalized schur parameters and the effects of perturbations abstract let r be a matrix of the form r uu t vv t where u and v are real lower triangular toeplitz matrices and the main diagonal of v consists of zeros lozenge algorithms relating u v and schur parameters for r are presented using two known descriptions of the cholesky factors of r an explicit formula for the schur parameters generalizing the levinson durbin formula is proved statistical estimates of the effects of variations in u and v on the schur parameters are derived

a feature point matching based on spatial order constraints bilateral neighbor vote feature point matching is a fundamental and challenging problem in many computer vision applications in this paper a robust feature point matching algorithm named spatial order constraints bilateral neighbor vote socbv is proposed to remove outliers for a set of matches including outliers between two images a directed k nearest neighbor knn graph of match sets is generated and the problem of feature point matching is formulated as a binary discrimination problem in the discrimination process the class labeled matrix is built via the spatial order constraints defined on the edges that connect a point to its knn then the posterior inlier class probability of each match is estimated with the knn density estimation and spatial order constraints the vote of each match is determined by averaging all posterior class probabilities that originate from its associative inliers set and is used for removing outliers the algorithm iteratively removes outliers from the directed graph and recomputes the votes until the stopping condition is satisfied compared with other popular algorithms such as ransac rsoc gtm soc and wgtm experiments under various testing data sets demonstrate strong robustness for the proposed algorithm

maximum likelihood estimation with side information of a 1 d discrete layered medium from its noisy impulse reflection response we consider the problem of computing the maximum likelihood estimates of the reflection coefficients of a discrete 1 d layered medium from noisy observations of its impulse reflection response we have side information in that a known subset of the reflection coefficients are known to be zero this knowledge could come from either a priori knowledge of a homogeneous subregion inside the scattering medium or from a thresholding operation in which noisy reconstructed reflection coefficients with absolute values below a threshold are known to be zero our procedure converges in one or two iterations each of which requires only setting up and solving a small system of linear equations and running the levinson algorithm numerical examples are provided that demonstrate not only the operation of the algorithm but also that the side information improves the reconstruction of unconstrained reflection coefficients as well as constrained ones due to the nonlinearity of the inverse scattering problem

a layer stripping solution of the inverse problem for a one dimensional elastic medium a fast algorithm for recovering profiles of density and lame parameters as functions of depth for the inverse seismic problem in an elastic medium is obtained the medium is probed with planar impulsive p and sv waves at oblique incidence and the medium velocity components are measured at the surface the interconversion of p and sv waves defines reflection coefficients from which the medium parameter profiles are obtained recursively the algorithm works on a layer stripping principle and it is specified in both differential and recursive forms a physical interpretation of this procedure is given in terms of a lattice filter where the first reflections of the downgoing waves in each layer yield the various reflection coefficients for that layer a computer run of the algorithm on the synthetic impulsive plane wave responses of a twenty layer medium shows that the algorithm works satisfactorily

a kalman filter solution of the inverse scattering problem with a rational reflection coefficient abstract this paper presents a new inverse scattering method for reconstructing the reflectivity function of symmetric two component wave equations or the potential of a schrodinger equation when the reflection coefficient is rational this method relies on the so called chandrasekhar equations which implement the kalman filter associated to a stationary state space model these equations are derived by using first a general layer stripping principle to obtain some differential equations for reconstructing a general scattering medium and by specializing these recursions to the case when the probing waves have a state space model

differential methods in inverse scattering this paper discusses a new set of differential methods for solving the inverse scattering problem associated to the propagation of waves in an inhomogeneous medium by writing the medium equations in the form of a two component system describing the interaction of rightward and leftward propagating waves the causality of the propagation phenomena is exploited in order to identify the medium layer by layer the recursive procedure that we obtain constitutes a continuous version of an algorithm first derived by schur in order to test for the boundedness of functions analytic inside the unit circle it recovers the local reflectivity function of the medium using similar ideas some other differential methods can also be derived to reconstruct alternative parametrizations of the layered medium in terms of the local impedance or of the potential function the differential inverse scattering methods turn out to be very efficient since in some sense they let the medium perform the inversion by itself and thus

application of the schur algorithm to the inverse problem for a layered acoustic medium the schur algorithm is a signal processing algorithm which works on a layer stripping principle its time domain version the fast cholesky recursion is a fast and efficient algorithm well suited for high speed data processing in this paper these algorithms are applied to the inverse problem for a continuous layered acoustic medium three different excitations of the medium are considered impulsive plane waves at normal incidence impulsive plane waves at oblique incidence and spherical waves emanating from an impulsive point source the fast algorithms obtained for each of these problems seem to be computationally superior to past work done on these problems that employed gelfand levitan theory to reconstruct the potential of a schrodinger equation

estimation of acoustic macro models using a genetic full waveform inversion applications to the marmousi model abstractwe have developed a stochastic full waveform inversion that uses genetic algorithms ga fwi to estimate acoustic macro models of the p wave velocity field stochastic methods such as ga severely suffer the curse of dimensionality meaning that they require unaffordable computer resources for inverse problems with many unknowns and expensive forward modeling to mitigate this issue we have proposed a two grid technique with a coarse grid to represent the subsurface for the ga inversion and a finer grid for the forward modeling we have applied this procedure to invert synthetic acoustic data of the marmousi model and we have developed three different tests the first two tests use a velocity model derived from standard stacking velocity analysis as prior information and differ only for the parameterization of the coarse grid their comparison indicates that a smart parameterization of the coarse grid may significantly improve the final result the third test uses a linearly increasing 1d velocit

levinson like and schur like fast algorithms for solving block slanted toeplitz systems of equations arising in wavelet based solution of integral equations the wiener hopf integral equation of linear least squares estimation of a wide sense stationary random process and the krein integral equation of one dimensional 1 d inverse scattering are fredholm equations with symmetric toeplitz kernels they are transformed using a wavelet based galerkin method into a symmetric block slanted toeplitz bst system of equations levinson like and schur like fast algorithms are developed for solving the symmetric bst system of equations the significance of these algorithms is as follows if the kernel of the integral equation is not a calderon zygmund operator the wavelet transform may not sparsify it the kernel of the krein and wiener hopf integral equations does not in general satisfy the calderon zygmund conditions as a result application of the wavelet transform to the integral equation does not yield a sparse system matrix there is therefore a need for fast algorithms that directly exploit the symmetric block slanted toeplitz structure of the system matrix and do not rely on sparsity the first such o n sup 2 algorithms viz a levinson like algorithm and a schur 1917 like algorithm are presented these algorithms are also applied to the factorization of the bst system matrix the levinson like algorithm also yields a test for positive definiteness of the bst system matrix the results obtained are directly applicable to the problem of constrained deconvolution of a nonstationary signal where the locations of the smooth regions of the signal being deconvolved are known a priori

the one dimensional inverse problem of reflection seismology an impulsive normal traction is applied uniformly over the surface of a perfectly stratified plane layered earth the ensuing particle velocity at the surface is assumed to be measured the problem of calculating the subsurface characteristic impedance from knowledge of the input pulse and the measured data is the one dimensional inverse problem of reflection seismology the problem is set up mathematically as an inverse problem for a first order 2 times 2 hyperbolic system the role of propagation of singularities is explained and the relation between the solution of the inverse problem and the cholesky factorization of certain matrices constructed from the data is elaborated for both the continuum problem and the related discrete problem it is found that recursive numerical techniques such as the levinson algorithm and certain other fast methods for cholesky factorization are intimately related to explicit finite difference schemes for solving hyperbolic systems the order of approximation between the

inverse scattering for a layered acoustic medium using the first order equations of motion the inverse scattering problem for a layered acoustic medium is considered from the first order differential equations of motion resulting in a vector formulation of the problem and using a vector form of the schrodinger inverse scattering methods the result is a vector marchenko equation the differentiability constraints on the acoustic impedance are somewhat relaxed compared to the more standard approach of beginning with the wave equation the solution for plane waves at normal incidence is given along with a good approximate solution which is easily obtainable and takes into account transmission losses not included in the normal wkbj born approximation a new solution for extracting separately the velocity and density of the medium using the reflection response for two different angles of incidence is given which involves a nonlinear integral equation to relate the apparent traveltimes to depth

completion problems and scattering problems for dirac type differential equations with singularities abstract a completion problem to recover a rational matrix function which is j unitary on the line is treated a dirac type system with singularities on the semi axis is recovered explicitly from its left reflection coefficient the close relation between these two problems is discussed

a numerical solution to the zakharov shabat inverse scattering problem a novel numerical method to solve the inverse scattering problem associated with the zakharov shabat coupled mode equations is developed in this problem the coupling coefficient for two propagating modes is determined from reflection data both codirectional and contradirectional coupling can be accommodated as well as the presence of bound states analytical results based on an independent analytical method are derived in order to demonstrate the accuracy of the proposed method which is applicable to a broad class of reflection data

high frequency perturbational analysis of the surface point source response of a layered fluid abstract we linearize the relation between the parameters density and velocity profiles of a layered fluid subject to a specified surface point traction and the precitically reflected part of its surface motion we decompose the resulting linear map into a high frequency leading term and a lower order smoother remainder and show that the spectral analysis of the leading term may be described in terms of ray geometry the leading term is generally well conditioned but may become poorly conditioned in low velocity zones these results imply stability estimates for the linearized acoustic reflection inversion problem as well as for the nonlinear problem and yield insight into the behavior of numerical algorithms for the determination of the density and velocity of a layered fluid from its surface response

analysis of dynamic nonlinear thermoviscoelastic beam problems abstract in this paper we study a dynamic contact problem between a nonlinear viscoelastic beam and two rigid obstacles thermal effects are also taken into account and the contact is modeled using the classical signorini condition the existence of solutions is proved by considering approximate problems from a penalization procedure proving some a priori estimates and passing to the limit an exponential decay property is also obtained then fully discrete approximations of the approximate problem are provided using the finite element method for the spatial approximation and the implicit euler scheme for the discretization of the time derivatives a stability property is obtained and a priori error estimates are proved from which under some additional regularity conditions the linear convergence of the algorithm is deduced fully discrete approximations of the signorini problem are then introduced proceeding in a similar way for which a stability property is obtained finally some numerical simulations are performed to demonstrate the accuracy of the approximation and the behavior of the solution

attributed string matching with merging for shape recognition a new structural approach to shape recognition using attributed string matching with merging is proposed after illustrating the disadvantages of conventional symbolic string matching using changes deletions and insertions attributed strings are suggested for matching each attributed string is an ordered sequence of shape boundary primitives each representing a basic boundary structural unit line segment with two types of numerical attributes length and direction a new type of primitive edit operation called merge is then introduced which can be used to combine and then match any number of consecutive boundary primitives in one shape with those in another the resulting attributed string matching with merging approach is shown useful for recognizing distorted shapes experimental results prove the feasibility of the proposed approach for general shape recognition some possible extensions of the approach are also included

two dimensional object recognition through two stage string matching a two stage string matching method for the recognition of two dimensional 2 d objects is proposed in this work the first stage is a global cyclic string matching the second stage is a local matching with local dissimilarity measure computing the dissimilarity measure function of the input shape and the reference shape are obtained by combining the global matching cost and the local dissimilarity measure the proposed method has the advantage that there is no need to set any parameter in the recognition process experimental results indicate that the hostage string matching approach significantly improves the recognition rates compared to the one stage string matching method

fast algorithms for estimation and signal processing an inverse scattering framework the inverse scattering problem for a lossless transmission line has been used as a framework for deriving the levinson and schur fast algorithms for toeplitz matrices here the same framework is used to derive and attach novel simple scattering interpretations to the lattice algorithm and the split algorithms this demonstrates that the scattering and interpretation is more fundamental to fast signal processing algorithms than previously noted

acoustic impulse responses for nonuniform media abstract the acoustic impulse responses of a family of nonuniform lossless one dimensional media are determined the nonuniform portions of the media are confined to layers of either finite or infinite thicknesses the acoustic impedances of the nonuniform layers as functions of travel time are assumed known the impulse responses are determined by evaluating the fourier transforms of their reflection coefficients using infinite series expansions and contour integrations

inverse scattering for discrete transmission line models this paper presents several methods for the identification of the impedance and reflection coefficient profile of a nonuniform discrete transmission line from its response to a given forcing function this problem is the prototype for a wealth of one dimensional inverse scattering problems arising in various fields a unified straightforward approach is presented providing all known inversion procedures and some novel ones the derivations readily follow from causality of signal propagation on the transmission line it is shown that a direct exploitation of the signal propagation model leads to recursive computationally efficient and reliable inversion algorithms in particular the relationships between layer peeling schur type difference equation and layer adjoining levinson type integral equation algorithms are clearly displayed

layer stripping solutions of multidimensional inverse scattering problems a layer stripping procedure for solving three dimensional schrodinger equation inverse scattering problems is developed this method operates by recursively reconstructing the potential from the jump in the scattered field at the wave front and then using the reconstructed potential to propagate the wave front and the scattered field further into the inhomogeneous region it is thus a generalization of algorithms that have been developed for one dimensional inverse scattering problems although the procedure has not yet been numerically tested the corresponding one dimensional algorithms have performed well on synthetic data the procedure is applied to a two dimensional inverse seismic problem connections between simplifications of this method and born approximation inverse scattering methods are also noted

robust symbolic representation for shape recognition and retrieval a new method for shape recognition and retrieval is proposed here the suggested algorithm is based on several steps the algorithm analyzes the contour of pairs of shapes their contours are recovered and represented by a pair of n points obtained by linear interpolation given two points p i and q j from the two shapes the cost of their matching is evaluated by using the shape context and by using dynamic programming the best matching between the point sets is obtained dynamic programming not only recovers the best matching but also identifies occlusions i e points in the two shapes which cannot be properly matched given the correspondence between the two point sets the two contours are aligned using procrustes analysis after alignment each contour is transformed into a string of symbols and a modified version of edit distance is used to compute the similarity between strings of symbols finally recognition and retrieval are obtained by a simple nearest neighbor procedure the algorithm has been tested on a large set of shape databases kimia mpeg 7 natural silhouette database gesture database marine database swedish leaf database diatom database eth 80 3d object database providing performances for both in recognition and in retrieval superior to most of previously proposed approaches

on the feasibility of impulse reflection response data for the two dimensional inverse scattering problem layer stripping algorithms for inverse scattering problems are very fast but have the reputation of being numerically unstable especially when applied to noisy data the goal of this paper is to provide an explicitly discrete framework for layer stripping algorithms for the two dimensional 2 d schrodinger equation inverse scattering problem we determine when 2 d layer stripping algorithms are numerically stable explain why they are stable and specify exactly the discrete problem they solve when they are stable we reformulate the 2 d schrodinger equation as a multichannel two component wave system by fourier transforming the schrodinger equation in the lateral spatial variable discretization results in new 2 d layer stripping algorithms which incorporate multichannel transmission effects this leads to an important new feasibility condition on impulse reflection response data for stability of these algorithms a 2 d discrete schrodinger equation is defined and analogous results are obtained numerical examples illustrate the new results especially how rendering noisy data feasible stabilizes layer stripping algorithms

backscattering and inverse problem in random media with use of the invariant imbedding method and markov process approximation the statistical characteristics of the backscattering field from the impulse point source in a nonstationary multidimensional random medium are considered the equations for the characteristic function and the density of the probability in the functional space of the backscattering are obtained the equations for the statistical moments of the field are yielded and then solutions are presented in the matrix form the additional averaging of the fast field variations is used for the simplification of the statistical equations the procedures for the investigation of the direct and inverse statistical problem are proposed the role of the phenomenological transfer theory is discussed from the statistical point of view

inverse scattering and minimal partial realizations we present an inverse scattering interpretation of the classical minimal partial realization problem posed in a slightly generalized context our approach starts by considering a canonical cascade form structure for the realization of arbitrary transfer functions where the cascade structure can be interpreted as the description of a layered wave scattering medium in this context the partial realization problem calls for a recursive process of layer identification from a given input response pair the scattering data the realization algorithm uses a causality principle to progressively determine the parameters of cascaded linear 2 ports that model the successive wave interaction layers this method for approaching the realization problem turns out to fit nicely into a framework that was also used to obtain fast structured linear estimation algorithms and cascade realizations for digital filters

inverse problem in nonstationary multidimensional medium the problem of a scalar wave propagation from the point impulsive source in the layer of a nonstationary multidimensional medium is considered the boundary problem for the wave equation is reformulated in the problem with the initial condition using the invariant imbedding method the integral differential inverse procedures of the various orders were obtained from the imbedding equations using the singularities method the order of inverse procedure is defined by the degree of a polynomial in the analytical representation of the medium characteristic near the layer boundary it was shown that the coefficients of the polynomial are calculated with the help of the differential characteristics of the point impulsive source in the inhomogeneous medium the cause and character of the multidimensional inverse problem overdefiniteness are considered the application of the proposed procedure for a statistical problem is discussed

global existence and exponential stability for a contact problem between two thermoelastic beams in this paper we analyze a dynamic unilateral contact problem between two thermoelastic beams we establish the existence of a weak global in time solution by a penalization method moreover we study the asymptotic behavior of such a solution proving that the energy associated to the system decays exponentially to zero as time goes to infinity

a recursive method for solving unconstrained tangential interpolation problems an efficient recursive solution is presented for the one sided unconstrained tangential interpolation problem the method relies on the triangular factorization of a certain structured matrix that is implicitly defined by the interpolation data the recursive procedure admits a physical interpretation in terms of discretized transmission lines in this framework the generating system is constructed as a cascade of first order sections singular steps occur only when the input data is contradictory i e only when the interpolation problem does not have a solution various pivoting schemes can be used to improve numerical accuracy or to impose additional constraints on the interpolants the algorithm also provides coprime factorizations for all rational interpolants and can be used to solve polynomial interpolation problems such as the general hermite matrix interpolation problem a recursive method is proposed to compute a column reduced generating system that can be used to solve the minimal tangential interpolation problem

on discrete schrodinger equations and their two component wave equation equivalents an approach to inverse scattering problems for discrete schrodinger equations which are discrete three term recursions is presented by systematically transforming them into discrete two component wave propagation equations the wave propagation equations permit the immediate application of certain computationally efficient and physically insightful layer peeling algorithms for inverse scattering the mapping of three term recursions to two component evolution equations is one to many because the relation between the potential sequence parametrizing schrodinger equations and the reflection coefficient sequence determining local wave interaction is a nonlinear difference equation this mapping is examined in some detail and it is used to study both direct and inverse scattering problems associated with discrete schrodinger equations

the thermoelastic and viscoelastic contact of two rods we consider the thermoelastic and viscoelastic contact problem of two rods and prove the existence of a weak solution using a penalization method and compensated compactness moreover for the thermoelastic contact we show that the weak solution converges to zero exponentially as time goes to infinity and for the viscoelastic contact we prove that the weak solution decays to zero with the same rates as the relaxation functions do

global existence and decay for the semilinear thermoelastic contact problem in this paper a class of semilinear thermoelastic contact problems is considered and the existence and exponential decay of the weak solutions are obtained

iterative trace deconvolution and noncausal transform for processing band limited data in 1983 carrion and patton showed that if recorded seismic data do not have low frequencies in their spectrum inversion for acoustic impedance is unstable this concept is commonly accepted here we infer acoustic impedance from band limited data without low frequencies using iterative trace deconvolution with the so called noncausal projection which moves initial data samples corresponding to small eigenvalues to negative times we show that this procedure can solve ill posed problems by migrating large residuals uncertainties in the trend of the recovered impedance to the bottom of the model an important property of the proposed method is that it converges to the true solution independently of the chosen initial model another advantage of the proposed algorithm is that unlike conventional dynamic deconvolution characteristic integration schemes it increases neither errors nor the condition number with depth the method is illustrated on synthetic and real data

multidimensional inverse scattering an orthogonalization formulation the three dimensional schrodinger equation inverse scattering problem is solved using an orthogonalization approach the plane waves propagating in free space are orthogonalized with respect to an inner product defined in terms of a jost operator the resulting integral equation is identical to the generalized gel fand levitan equation of newton although the present derivation is simpler and more physical than that of newton newton s generalized marchenko equation is derived from the defining integral equation for the jost operator these integral equations are shown to be solved by fast algorithms derived directly from the properties of their solutions this paper thus presents a simple interpretation of newton s two integral equations two fast algorithms for solving these integral equations and relations between the various approaches this is a generalization of previously obtained results which are also reviewed here for the one dimensional inverse scattering problem

inverse scattering in multimode structures we consider the inverse scattering problem associated with any number of interacting modes in one dimensional structures the coupling between the modes is contradirectional in addition to codirectional and may be distributed continuously or in discrete points the local coupling as a function of position is obtained from reflection data using a layer stripping type method and the separate identification of the contradirectional and codirectional coupling is obtained using matrix factorization ambiguities are discussed in detail and different a priori information that can resolve the ambiguities is suggested the method is exemplified by applications to multimode optical waveguides with quasi periodical perturbations

reconstruction of the velocity and density in a stratified acoustic half space using a short pulse point source the reconstruction of the velocity and density in a stratified half space using the reflection data generated by a short pulse point source is considered transverse spatial hankel transform is applied to the transient reflected and incident pressures on the surface the reflection kernel in the hankel transformed space is obtained through a deconvolution the time domain green function approach based on the wave splitting is then used to reconstruct the parameters this time domain approach to the inverse problem is exact and noniterative numerical results for some synthetical examples are presented to illustrate the hankel transform deconvolution and the reconstruction the finite difference time domain method is used to generate the transient reflection data in the physical space in a numerical simulation the reconstruction using obliquely incident plane waves is also considered in an appendix

numerical solutions to one dimensional problems of thermoelastic contact abstract a numerical method based on the crank nicolson discretisation is applied to one dimensional thermoelastic contact problems such problems can be reduced using an appropriate transformation to the heat equation with a nonlinear and nonlocal source term it is proved that the method converges a number of numerical experiments are presented to illustrate the method and the behavior of the solutions to the problem

polygonal shape recognition using string matching techniques in this paper we study several aspects of the use of string matching techniques as an approach to the problem of recognizing and classifying polygons several authors have already proposed methods for polygon recognition that are based on string matching in many cases however linear strings are used to represent polygons which makes it difficult to handle different orientations of an object efficiently we can however easily extend the linear string matching techniques to cyclic strings at some small computational cost we will propose a method to represent polygons as cyclic strings and we will show how cyclic string matching techniques can be used for rotation translation and scale independent polygonal shape recognition we will however also point out the limitations of such an approach

a quasistatic contact problem in thermoelasticity with a radiation condition for the temperature abstract an abstract existence theorem is proved for variational inequalities of monotone operators with a nonlinear perturbation it is used to prove the existence of a strong solution to the problem of quasistatic one dimensional contact in linearized thermoelasticity the problem after reformulation consists of the heat equation with a nonlocal and nonlinear term the uniqueness and stability of the solution are also established