high quality image resizing using oblique projection operators the standard interpolation approach to image resizing is to fit the original picture with a continuous model and resample the function at the desired rate however one can obtain more accurate results if one applies a filter prior to sampling a fact well known from sampling theory the optimal solution corresponds to an orthogonal projection onto the underlying continuous signal space unfortunately the optimal projection prefilter is difficult to implement when sine or high order spline functions are used we propose to resize the image using an oblique rather than an orthogonal projection operator in order to make use of faster simpler and more general algorithms we show that we can achieve almost the same result as with the orthogonal projection provided that we use the same approximation space the main advantage is that it becomes perfectly feasible to use higher order models e g splines of degree n spl ges 3 we develop the theoretical background and present a simple and practical implementation procedure using b splines our experiments show that the proposed algorithm consistently outperforms the standard interpolation methods and that it provides essentially the same performance as the optimal procedure least squares solution with considerably fewer computations the method works for arbitrary scaling factors and is applicable to both image enlargement and reduction

sensor location for discrete mode observability of switching linear systems with unknown inputs this paper deals with the problem of additional sensor placement in order to recover the discrete mode observability of switching structured linear systems with unknown inputs such a property is quite important for designing control laws observers fault detection and isolation schemes when the fault occurrence implies a commutation between two modes and so on the proposed method based on a graph theoretic approach assumes only the knowledge of the system s structure we express in graphical terms new necessary and sufficient conditions for discrete mode generic observability when these conditions are not satisfied we propose a sensor placement procedure which allows us to recover the mode observability our approach can be implemented by classical and quite simple graph theory algorithms

on the wave equation with hyperbolic dynamical boundary conditions interior and boundary damping and supercritical sources abstract the aim of this paper is to study the problem u t t u p x u t f x u in 0 u 0 on 0 0 u t t u u q x u t g x u on 0 1 u 0 x u 0 x u t 0 x u 1 x in where is a bounded open subset of r n with c 1 boundary n 2 1 is relatively open on denotes the laplace beltrami operator on is the outward normal to and the terms p and q represent nonlinear damping terms while f and g are nonlinear perturbations in the paper we establish local and global existence uniqueness and hadamard well posedness results when source terms can be supercritical or super supercritical

general decay of solutions of a viscoelastic equation abstract in this paper we consider the following viscoelastic equation u t t u 0 t g t u d 0 in a bounded domain and establish a general decay result which is not necessarily of exponential or polynomial type this work generalizes and improves earlier results in the literature

the error amended sharp edge ease scheme for image zooming this paper proposes a new interpolation method called the error amended sharp edge ease scheme which is a modified bilinear method in order to remove reduce interpolation artifacts such as image blur and the checkerboard effect ringing ease tries to amend the interpolation error by employing the classical interpolation error theorem in an edge adaptive fashion ease is applied for image zooming by both integer and noninteger magnification factors the new interpolation scheme has proved to result in high resolution images having clearer and sharper edges than linear interpolation methods for all synthetic and natural images we have tested ease can be implemented with ease it turns out to be similarly efficient as cubic interpolation schemes

uniform stabilization of wave equation with localized damping and acoustic boundary condition abstract in this paper we deal with stability of the nonlinear wave equation with acoustic boundary conditions to non locally reacting boundary

uniform decay in viscoelasticity for kernels with small non decreasingness zones abstract we consider a viscoelastic problem with a relaxation function which may be strictly increasing in some sub intervals that is we go beyond the zero which was a bound for the derivative of the kernel in the previous works it is proved that we have different types of decay rates including the exponential one provided that the rate and or the non decreasingness zone including the flat zone is small enough in a certain sense

existence of a solution of the wave equation with nonlinear damping and source terms abstract we study the nonlinear wave equation involving the nonlinear damping term u t u t m 1 and a source term of type u u p 1 for 1 p m we prove a global existence theorem with large initial data for 1 m p a blow up result is established for sufficiently large initial data

shift variance and nonstationarity of linear periodically shift variant systems and applications to generalized sampling reconstruction processes we present a systematic analysis on shift variance of linear t periodically shift variant t lpsv systems with continuous time input and output we first determine how far a t lpsv system h is away from being shift invariant in terms of two measures namely the distance and the angle between h and the subspace of linear shift invariant systems we then consider the level and the index of shift variance svi of h via commutator of h and the shift operator and examine the amount of shift variance of h under particular input all these quantities are characterized in terms of the so called shift variant part and the shift variance kernel of h moreover we study nonstationarity of wide sense cyclostationary random processes possibly induced by t lpsv systems we define and calculate a measure of nonstationarity nst of the output as the svi of the autocorrelation operator the nst can be used to characterize performance loss when the output is treated with a wss approach the expected shift variance of h subject to particular wss random process is also calculated we apply the above results to generalized sampling reconstruction processes gsrps in addition we consider the approximation error of the gsrp and relate it to the shift variance measures three sampling schemes namely the orthogonal the consistent and the minimax regret sampling are examined in detail we show that for both deterministic and wss random inputs the minimax regret gsrp always introduces less shift variance than the consistent counterparts numerical results for the gsrps of b splines of various orders are provided

a graph theoretical approach to the parameters identifiability characterisation this paper is devoted to the generic parameters identifiability analysis for structured linear systems with unknown inputs the proposed method is based on a graph theoretic approach and assumes only the knowledge of the system s structure necessary and sufficient conditions are expressed in graphical terms which ensure that a given set of unknown parameters characterising the model of the system are structurally identifiable using the available measurements assuming that the inputs and initial conditions are quite informative even if we are not interested in proposing identification schemes these given conditions are necessary and sufficient to the parameter identification whatever the used algorithms to determine numerically the parameters values finally note that the given conditions are quite easy to check because they are based on searching and comparing some specific paths and cycles in a digraph this makes our approach well suited to study large scale systems

on a large class of kernels yielding exponential stability in viscoelasticity in this paper we prove exponential decay of solutions for a problem which appears in viscoelasticity the conditions on the admissible kernels are relaxed so as to allow for more kernels to be treated namely the smallness of the kernels is replaced by the smallness of the set where the kernel is flat this work extends previous works and improves in particular a recent result by pata 16 this is established by introducing two lemmas an idea due to pata and using the energy method

on decay and blow up of the solution for a viscoelastic wave equation with boundary damping and source terms abstract in this paper we consider the decay and blow up properties of a viscoelastic wave equation with boundary damping and source terms we first extend the decay result for the case of linear damping obtained by lu et al on a viscoelastic equation with nonlinear boundary damping and source terms global existence and decay of the solution nonlinear analysis real world applications 12 1 2011 295 303 to the nonlinear damping case under weaker assumption on the relaxation function g t then we give an exponential decay result without the relation between g t and g t for the linear damping case provided that g l 1 0 is small enough finally we establish two blow up results one is for certain solutions with nonpositive initial energy as well as positive initial energy for both the linear and nonlinear damping cases the other is for certain solutions with arbitrarily positive initial energy for the linear damping case

linear interpolation revitalized we present a simple original method to improve piecewise linear interpolation with uniform knots we shift the sampling knots by a fixed amount while enforcing the interpolation property we determine the theoretical optimal shift that maximizes the quality of our shifted linear interpolation surprisingly enough this optimal value is nonzero and close to 1 5 we confirm our theoretical findings by performing several experiments a cumulative rotation experiment and a zoom experiment both show a significant increase of the quality of the shifted method with respect to the standard one we also observe that in these results we get a quality that is similar to that of the computationally more costly high quality cubic convolution

blow up and critical exponents for nonlinear hyperbolic equations we prove nonexistence results for the cauchy problem for the abstract hyperbolic equation in a banach space x utt f u t 0 u 0 u0 ut 0 u1 where f x r is a c1 function several applications to the second and higher order hyperbolic equations with local and nonlocal nonlinearities are presented we also describe an approach to kato s and john s critical exponents for the semilinear equations ut u b x t u p p 1 which are responsible for phenomena of stability unstability blow up and asymptotic behaviour

stabilization of hyperbolic and parabolic systems with nonlinearly perturbed boundary conditions abstract sufficient conditions for the local exponential stabilizability of abstract systems described by an arbitrary co semigroup with nonlinear unbounded perturbations are formulated applications to parabolic and in particular hyperbolic problems with nonlinearity appearing in the boundary conditions are given

global existence and asymptotic behavior for a coupled hyperbolic system with localized damping abstract in this paper we investigate the global existence and energy decay rate for the solution of a coupled hyperbolic system the semi explicit energy decay rate is established by using piecewise multiplier techniques and weighted integral inequality we extend the energy decay result in alabau boussouira f alabau boussouira convexity and weighted integral inequalities for energy decay rates of nonlinear dissipative hyperbolic systems appl math optim 51 2005 61 105 for a single equation to the coupled hyperbolic system

on the wave equation with semilinear porous acoustic boundary conditions the goal of this work is to study a model of the wave equation with semilinear porous acoustic boundary conditions with nonlinear boundary interior sources and a nonlinear boundary interior damping first applying the nonlinear semigroup theory we show the existence and uniqueness of local in time solutions the main difficulty in proving the local existence result is that the neumann boundary conditions experience loss of regularity due to boundary sources using an approximation method involving truncated sources and adapting the ideas in lasiecka and tataru 1993 28 we show that the existence of solutions can still be obtained second we prove that under some restrictions on the source terms then the local solution can be extended to be global in time in addition it has been shown that the decay rates of the solution are given implicitly as solutions to a first order ode and depends on the behavior of the damping terms in several situations the obtained ode can be easily solved and the decay rates can be given explicitly third we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping then the solution ceases to exists and blows up in finite time moreover in either the absence of the interior source or the boundary source then we prove that the solution is unbounded and grows as an exponential function

blow up of a hyperbolic equation of viscoelasticity with supercritical nonlinearities abstract we investigate a hyperbolic pde modeling wave propagation in viscoelastic media under the influence of a linear memory term of boltzmann type and a nonlinear damping modeling friction as well as an energy amplifying supercritical nonlinear source u t t k 0 u 0 k s u t s d s u t m 1 u t u p 1 u in 0 t u x t u 0 x t in 0 where is a bounded domain in r 3 with a dirichlet boundary condition the relaxation kernel k is monotone decreasing and k 1 we study blow up of solutions when the source is stronger than dissipations i e p max m k 0 under two different scenarios first the total energy is negative and the second the total energy is positive with sufficiently large quadratic energy this manuscript is a follow up work of the paper 30 in which hadamard well posedness of this equation has been established in the finite energy space the model under consideration features a supercritical source and a linear memory that accounts for the full past history as time goes to which is distinct from other relevant models studied in the literature which usually involve subcritical sources and a finite time memory

observability and controllability of piecewise affine and hybrid systems we prove in a constructive way the equivalence between piecewise affine systems and a broad class of hybrid systems described by interacting linear dynamics automata and propositional logic by focusing our investigation on the former class we show through counterexamples that observability and controllability properties cannot be easily deduced from those of the component linear subsystems instead we propose practical numerical tests based on mixed integer linear programming

computation of eigenvalues in proportionally damped viscoelastic structures based on the fixed point iteration abstract linear viscoelastic structures are characterized by dissipative forces that depend on the history of the velocity response via hereditary damping functions the free motion equation leads to a nonlinear eigenvalue problem characterized by a frequency dependent damping matrix in the present paper a novel and efficient numerical method for the computation of the eigenvalues of linear and proportional or lightly non proportional viscoelastic structures is developed the central idea is the construction of two complex valued functions of a complex variable whose fixed points are precisely the eigenvalues this important property allows the use of these functions in a fixed point iterative scheme with help of some results in fixed point theory necessary conditions for global and local convergence are provided it is demonstrated that the speed of convergence is linear and directly depends on the level of induced damping in addition under certain conditions the recursive method can also be used for the calculation of non viscous real eigenvalues in order to validate the mathematical results two numerical examples are analyzed one for single degree of freedom systems and another for multiple ones

global existence and uniform stabilization of a generalized dissipative klein gordon equation type with boundary damping in this paper we prove the existence uniqueness and uniform stability of strong and weak solutions of the nonlinear generalized klein gordon equation 1 1 1 see sec i in bounded domains with nonlinear damped boundary conditions given by 1 1 3 see sec i with some restrictions on function f u h u g ut and b x we prove the existence and uniqueness by means of nonlinear semigroup method and obtain the uniform stabilization by using the multiplier technique

stabilization of wave and plate like equations with nonlinear dissipation on the boundary abstract in this paper we consider second order in time equations of petrovsky type wave and plate like with nonlinear dissipative boundary conditions under certain geometric conditions imposed on the domain the results on asymptotic behavior of the solutions are established

survey generic properties and control of linear structured systems a survey in this survey paper we consider linear structured systems in state space form where a linear system is structured when each entry of its matrices like a b c and d is either a fixed zero or a free parameter the location of the fixed zeros in these matrices constitutes the structure of the system indeed a lot of man made physical systems which admit a linear model are structured a structured system is representative of a class of linear systems in the usual sense it is of interest to investigate properties of structured systems which are true for almost any value of the free parameters therefore also called generic properties interestingly a lot of classical properties of linear systems can be studied in terms of genericity moreover these generic properties can in general be checked by means of directed graphs that can be associated to a structured system in a natural way we review here a number of results concerning generic properties of structured systems expressed in graph theoretic terms by properties we mean here system specific properties like controllability the finite and infinite zero structure and so on as well as solvability issues of certain classical control problems like disturbance rejection input output decoupling and so on in this paper we do not try to be exhaustive but instead by a selection of results we would like to motivate the reader to appreciate what we consider as a wonderful modelling and analysis tool we emphasize the fact that this modelling technique allows us to get a number of important results based on poor information on the system only moreover the graph theoretic conditions are intuitive and are easy to check by hand for small systems and by means of well known polynomially bounded combinatorial techniques for larger systems

least squares image resizing using finite differences we present an optimal spline based algorithm for the enlargement or reduction of digital images with arbitrary noninteger scaling factors this projection based approach can be realized thanks to a new finite difference method that allows the computation of inner products with analysis functions that are b splines of any degree n a noteworthy property of the algorithm is that the computational complexity per pixel does not depend on the scaling factor a for a given choice of basis functions the results of our method are consistently better than those of the standard interpolation procedure the present scheme achieves a reduction of artifacts such as aliasing and blocking and a significant improvement of the signal to noise ratio the method can be generalized to include other classes of piecewise polynomial functions expressed as linear combinations of b splines and their derivatives

local hadamard well posedness for nonlinear wave equations with supercritical sources and damping abstract we consider the wave equation with supercritical interior and boundary sources and damping terms the main result of the paper is local hadamard well posedness of finite energy weak solutions the results obtained 1 extend the existence results previously obtained in the literature by allowing more singular sources 2 show that the corresponding solutions satisfy hadamard well posedness conditions during the time of existence this result provides a positive answer to an open question in the area and it allows for the construction of a strongly continuous semigroup representing the dynamics governed by the wave equation with supercritical sources and damping

global solutions to a structure acoustic interaction model with nonlinear sources abstract this article focuses on a structural acoustic interaction system consisting of a semilinear wave equation defined on a smooth bounded domain r 3 which is strongly coupled with a berger plate equation acting only on a flat part of the boundary of in particular the source terms acting on the wave and plate equations are allowed to have arbitrary growth order we employ a standard galerkin approximation scheme to establish a rigorous proof of the existence of local weak solutions in addition under some conditions on the parameters in the system we prove such solutions exist globally in time and depend continuously on the initial data

the generic number of invariant zeros of a structured linear system in this paper we consider a structured linear system represented by means of a directed graph we present a graph theoretic method to compute the generic number of invariant zeros of the corresponding rosenbrock matrix the method is based on a fundamental decomposition of the directed graph representing the structured system the generic number of invariant zeros is important in generic versions of problems involving controllability and pole placement

arbitrary decays in linear viscoelasticity it is by now well known that a necessary condition for the exponential polynomial decay of the energy of a problem arising in viscoelasticity is that the kernel which appears in the memory term itself be of exponential polynomial type by a kernel of exponential polynomial type we mean that the product of this kernel with an exponential polynomial function is summable some researchers have started from this condition to seek other sufficient conditions ensuring exponential or polynomial decay of the energy in this work we generalize these works to an arbitrary decay not necessarily of an exponential or polynomial rate

b spline signal processing ii efficiency design and applications for pt i see ibid vol 41 no 2 p 821 33 1993 a class of recursive filtering algorithms for the efficient implementation of b spline interpolation and approximation techniques is described in terms of simplicity of realization and reduction of computational complexity these algorithms compare favorably with conventional matrix approaches a filtering interpretation low pass filter followed by an exact polynomial spline interpolator of smoothing spline and least squares approximation methods is proposed these techniques are applied to the design of digital filters for cubic spline signal processing an efficient implementation of a smoothing spline edge detector is proposed it is also shown how to construct a cubic spline image pyramid that minimizes the loss of information in passage from one resolution level to the next in terms of common measures of fidelity this data structure appears to be superior to the gaussian laplacian pyramid

stability analysis of the anti stable heat equation with uncertain disturbance on the boundary abstract in this paper we study the stability of the anti stable 1 d heat equation with uncertain disturbance on the boundary we first estimate the disturbance in terms of the output then we design some control strategy to stabilize the anti stable system

discrete mode observability of structured switching descriptor linear systems a graph theoretic approach abstract the main result of the paper consists in necessary and sufficient graphical conditions which ensure the generic discrete mode observability of structured switching descriptor systems the methods used in the previous studies on the observability of switching linear systems on standard form are not applicable to switching descriptor systems so we develop a new approach starting from bipartite representations of these systems and then building a new kind of digraph dedicated to the discrete mode observability study the proposed method assumes only the knowledge of the system s structure and is applicable to a large class of descriptor systems including regular and non regular systems even if they are square or under determined the provided conditions can be implemented by the classical graph theory algorithms

on existence and asymptotic stability of solutions of the degenerate wave equation with nonlinear boundary conditions abstract we study the global existence of solutions of the nonlinear degenerate wave equation 0 x y y 0 in 0 y 0 on 1 0 y y f y g y 0 on 0 0 y x 0 y 0 y x 0 y 1 x in where y denotes the derivative of y with respect to parameter t f s c0 s s and g is a nondecreasing c1 function such that k1 s 2 g s s k2 s 2 for some k1 k2 0 with 0 0 if n 1 2 the existence of solutions is proved by means of the faedo galerkin method furthermore when 0 the uniform decay is obtained by making use of the perturbed energy method

existence and decay rate estimates for the wave equation with nonlinear boundary damping and source term the wave equation with a source term is considered utt u u uin 0 we prove the existence and uniform decay rates of the energy by assuming a nonlinear feedback ut acting on the boundary provided that has necessarily not a polynomial growth near the origin to obtain the existence of global solutions we make use of the potential well method combined with the faedo galerkin procedure and constructing a special basis furthermore we prove that the energy of the system decays uniformly to zero and we obtain an explicit decay rate estimate adapting the ideas of lasiecka and tataru differential integral equations 6 3 1993 507 and patrick martinez esain control optimisation calc var 4 1999 419 the resulting problem generalizes martinez results and complements the works of lasiecka and tataru 1993 and vitillaro glasgow math j 44 2002 375

on a mixed problem with a nonlinear acoustic boundary condition for a non locally reacting boundaries abstract we discuss global solvability to the mixed problem for a nonlinear wave equation in domains with non locally reacting boundaries and nonlinear acoustic boundary condition we prove the existence and uniqueness of solution additionally using the method of nakao we demonstrate the decay of the associated energy stability

decay of energy for second order boundary hemivariational inequalities with coercive damping abstract in this article we consider the asymptotic behavior of solutions to second order evolution inclusions with the boundary multivalued term u t a t u t b u t j t u t 0 and u t a t u t b u t j t u t 0 where a is a possibly nonlinear coercive and pseudomonotone operator b is linear continuous symmetric and coercive is the trace operator and j is a locally lipschitz integral functional with denoting the clarke generalized gradient taken with respect to the second variable for both cases we provide conditions under which the appropriately defined energy decays exponentially to zero as time tends to infinity we discuss assumptions and provide examples of multivalued laws that satisfy them

existence and asymptotic stability for the semilinear wave equation with boundary damping and source term in this paper we consider the semilinear wave equation with boundary conditions this work is devoted to prove the existence of solutions and uniform decay rates of the wave equation with boundary damping and source term

energy decay rate for a coupled hyperbolic system with nonlinear damping abstract in this paper we investigate the energy decay rate for the solution of a coupled hyperbolic system the explicit energy decay rate is established by using multiplier techniques and constructing a suitable energy functional

uniform decay of solutions for a quasilinear system of viscoelastic equations abstract in this paper we consider a system of two coupled quasilinear viscoelastic equations in canonical form with dirichlet boundary condition we use the perturbed energy method to show that the dissipations given by the viscoelastic terms are strong enough to ensure uniform decay with exponential and polynomial rates of the solutions energy which extends some existing results for a single equation to the case of a coupled system

energy decay rates for von karman system with memory and boundary feedback abstract in this paper we study the von karman plate model with long range memory and boundary nonlinear feedback we establish an explicit and general decay rate result using some properties of the convex functions our result is obtained without imposing any restrictive growth assumption on the damping term and strongly weakening the usual assumptions on the relaxation function

observability of the discrete state for dynamical piecewise hybrid systems abstract in this paper we deal with the observability of piecewise affine hybrid systems our aim is to give sufficient conditions to observe the discrete and continuous states in terms of algebraic and geometrical conditions firstly we will give the algebraic conditions to observe the discrete state based on the switch function reconstruction for linear hybrid systems secondly we will give a geometrical condition based on the transversality concept for nonlinear hybrid systems throughout this paper we illustrate our propositions with examples and simulations

simultaneous state and input estimation of hybrid systems with unknown inputs this paper addresses the problem of the simultaneous state and input estimation for hybrid systems when subject to input disturbances the proposed algorithm is based on the moving horizon estimation mhe method and uses mixed logical dynamical mld systems as equivalent representations of piecewise affine pwa systems so far the mhe method has been successfully applied for the state estimation of linear hybrid and nonlinear systems the proposed extension of the mhe algorithm enables the estimation of unknown inputs or disturbances acting on the hybrid system the new algorithm is shown to improve the convergence characteristics of the mhe method by reducing the delay of convergent estimates while assuring convergence for every possible sequence of input disturbances to ensure convergence the system is required to be incrementally input observable which is an extension to the classical incremental observability property

global nonexistence for a semilinear wave equation with nonlinear boundary dissipation in this paper we consider the following problem ytt yxx yt y p 1y x t 0 l 0 t y 0 t 0 t 0 t yx l t y l t yt l t m 1yt l t 0 t 0 t y x 0 y0 x yt x 0 y1 x x 0 l where 0 l is a bounded open interval in r p 1 and m 1 we are interested in the interaction between the boundary damping yt l t m 1yt l t and the interior source y t p 1y t under some appropriate assumptions on the initial data two blow up results with positive initial energy are established furthermore we obtain that the solutions blow up if p or y0 l is sufficiently large

shifting interpolation kernel toward orthogonal projection orthogonal projection offers the optimal solution for many sampling reconstruction problems in terms of the least square error in the standard interpolation setting where the sampling is assumed to be ideal however the projection is impossible unless the interpolation kernel is related to the sinc function and the input is bandlimited in this paper we propose a notion of shifting kernel toward the orthogonal projection for a given interpolation kernel we formulate optimization problems whose solutions lead to shifted interpolations that while still being interpolatory are closest to the orthogonal projection in the sense of the minimax regret the quality of interpolation is evaluated in terms of the average approximation error over input shift for the standard linear interpolation we obtain several values of optimal shift dependent on a priori information on input signals for evaluation we apply the new shifted linear interpolations to a gaussian signal an ecg signal a speech signal a two dimensional signal and three natural images significant improvements are observed over the standard and the 0 21 shifted linear interpolation proposed early

well posedness and optimal decay rates for the wave equation with nonlinear boundary damping source interaction we establish subject to some natural additional assumptions imposed on the relation between the source and the damping both well posedness and effective optimal decay rates for the solutions of a semilinear model of the wave equation the theory presented allows to consider both superlinear and sublinear behaviours of the dissipation in the presence of unstructured sources

interpolation revisited medical images application based on the theory of approximation this paper presents a unified analysis of interpolation and resampling techniques an important issue is the choice of adequate basis functions the authors show that contrary to the common belief those that perform best are not interpolating by opposition to traditional interpolation the authors call their use generalized interpolation they involve a prefiltering step when correctly applied the authors explain why the approximation order inherent in any basis function is important to limit interpolation artifacts the decomposition theorem states that any basis function endowed with approximation order ran be expressed as the convolution of a b spline of the same order with another function that has none this motivates the use of splines and spline based functions as a tunable way to keep artifacts in check without any significant cost penalty the authors discuss implementation and performance issues and they provide experimental evidence to support their claims

asymptotic behavior for a viscoelastic problem with not necessarily decreasing kernel in this paper we consider a problem which arises in viscoelasticity we prove an exponential decay of solutions under weaker assumptions than the ones frequently used in the literature in particular the kernels we are considering are not necessarily exponentially decaying to zero as was assumed before the present results improve also a previous work of the authors

global existence for the wave equation with nonlinear boundary damping and source terms abstract the paper deals with local and global existence for the solutions of the wave equation in bounded domains with nonlinear boundary damping and source terms the typical problem studied is u tt u 0 in 0 u 0 on 0 0 u u t m 2 u t u p 2 u on 0 1 u 0 x u 0 x u t 0 x u 1 x on where r n n 1 is a regular and bounded domain 0 1 m 1 2 p r where r 2 n 1 n 2 when n 3 r when n 1 2 and the initial data are in the energy space we prove local existence of the solutions in the energy space when m r r 1 p or n 1 2 and global existence when p m or the initial data are inside the potential well associated to the stationary problem

general decay rate estimates for viscoelastic dissipative systems abstract the linear viscoelastic equation is considered we prove uniform decay rates of the energy by assuming a nonlinear feedback acting on the boundary without imposing any restrictive growth assumption on the damping term and strongly weakening the usual assumptions on the relaxation function our estimate depends both on the behavior of the damping term near zero and on the behavior of the relaxation function at infinity the proofs are based on the multiplier method and on a general lemma about convergent and divergent series for obtaining the uniform decay rates

uniform boundedness and stability for a viscoelastic problem in this paper we consider the following integro differential problem which appears in viscoelasticityu t ru t email protected du t email protected email protected du t email protected email protected t 0on a bounded domain w with dirichlet boundary condition and initial values we prove an exponential decay result under different sufficient conditions on the relaxation function than the standard ones

minimax approximation of representation coefficients from generalized samples many sources of information are of analog or continuous time nature however digital signal processing applications rely on discrete data we consider the problem of approximating l2 inner products i e representation coefficients of a continuous time signal from its generalized samples adopting a robust approach we process these generalized samples in a minimax optimal sense specifically we minimize the worst approximation error of the desired representation coefficients by proper processing of the given sample sequence we then extend our results to criteria which incorporate smoothness constraints on the unknown function finally we compare our methods with the piecewise constant approximation technique commonly used for this problem and discuss the possible improvements by the suggested schemes

b spline signal processing i theory the use of continuous b spline representations for signal processing applications such as interpolation differentiation filtering noise reduction and data compressions is considered the b spline coefficients are obtained through a linear transformation which unlike other commonly used transforms is space invariant and can be implemented efficiently by linear filtering the same property also applies for the indirect b spline transform as well as for the evaluation of approximating representations using smoothing or least squares splines the filters associated with these operations are fully characterized by explicitly evaluating their transfer functions for b splines of any order applications to differentiation filtering smoothing and least squares approximation are examined the extension of such operators for higher dimensional signals such as digital images is considered

on nonlinear wave equations with degenerate damping and source terms in this article we focus on the global well posedness of the differential equation u tt u u k j u t u p 1 u in x 0 t where j is a sub differential of a continuous convex function j under some conditions on j and the parameters in the equations we obtain several results on the existence of global solutions uniqueness nonexistence and propagation of regularity under nominal assumptions on the parameters we establish the existence of global generalized solutions with further restrictions on the parameters we prove the existence and uniqueness of a global weak solution in addition we obtain a result on the nonexistence of global weak solutions to the equation whenever the exponent p is greater than the critical value k m and the initial energy is negative we also address the issue of propagation of regularity specifically under some restriction on the parameters we prove that solutions that correspond to any regular initial data such that u 0 h 2 h 1 0 u 1 h 1 0 are indeed strong solutions

brief paper state and input observability for structured linear systems a graph theoretic approach this paper deals with the state and input observability analysis for structured linear systems with unknown inputs the proposed method is based on a graph theoretic approach and assumes only the knowledge of the system s structure using a particular decomposition of the systems into two subsystems we express in simple graphic terms necessary and sufficient conditions for the generic state and input observability these conditions are easy to check because they are based on comparison of integers and on finding particular subgraphs in a digraph therefore our approach is suited to study large scale systems

a general sampling theory for nonideal acquisition devices the authors first describe the general class of approximation spaces generated by translation of a function spl psi x and provide a full characterization of their basis functions they then present a general sampling theorem for computing the approximation of signals in these subspaces based on a simple consistency principle the theory puts no restrictions on the system input which can be an arbitrary finite energy signal bandlimitedness is not required in contrast to previous approaches this formulation allows for an independent specification of the sampling analysis and approximation synthesis spaces in particular when both spaces are identical the theorem provides a simple procedure for obtaining the least squares approximation of a signal they discuss the properties of this new sampling procedure and present some examples of applications involving bandlimited and polynomial spline signal representations they also define a spectral coherence function that measures the similarity between the sampling and approximation spaces and derive a relative performance bound for the comparison with the least squares solution

shift variance analysis of generalized sampling processes this paper is concerned with quantifying shift variance of linear systems with continuous time input and discrete time output we first introduce a notion of shift invariance for the system it specifies how the system should respond when the input signal is shifted for generalized sampling processes the property is characterized by the sampling kernel and is shown to be equivalent to lack of aliasing and to shiftability we then define a shift variance level which describes how far the system can be possibly away from the set of systems that are shift invariant the level is defined to be the maximum of the induced norms of the commutators of the system and the shift operators both continuous time or discrete time are necessarily involved a shift variance measure is then defined to be the ratio of the shift variance level to the system norm further divided by two so that the measure is between zero and unity for generalized sampling we obtain analytical formulas for the shift variance level and the shift variance measure the results allow us to analyze the shift variance of among others the discrete time wavelet transform dwt and the short time fourier transform stft we obtain a simple relation between the shift variance levels at all scales of the dwt and show that the shift variance measures are identical at all scales we calculate the shift variance level and the shift variance measure of some typical dwts and the stfts

a new formula for bivariate hermite interpolation on variable step grids and its application to image interpolation in this paper we present a novel formula of the bivariate hermite interpolating bhi polynomial in the case of support points arranged on a grid with variable step this expression is applicable when interpolation of a bivariate function is required given its value and the values of its partial derivatives of arbitrarily high order at the support points the proposed formula is a generalization of an existing formula for the bivariate hermite polynomial it is also algebraically much simpler thus can be computed more efficiently in order to apply hermite interpolation to image interpolation we simplify the proposed bhi to handle support points on a regular unit step grid the values of image partial derivatives are arithmetically approximated using compact finite differences the proposed method is being assessed in a number of image interpolation experiments that include a synthetic image for which the values of the partial derivatives are computed analytically as well as a collection of images from different medical modalities the proposed bhi with up to second order image partial derivatives outperforms the convolution based interpolation methods as well as generalized interpolation methods with the same number of support points that was compared with in the majority of image interpolation experiments the computational load of the proposed bhi is calculated and its behaviour with respect to its controlling parameters is investigated

general decay rate estimate for a viscoelastic equation with weakly nonlinear time dependent dissipation and source terms a viscoelastic wave equation in canonical form with weakly nonlinear time dependent dissipation and source terms is investigated in this paper for a wider class of relaxation functions and without imposing any restrictive growth assumption on the damping term at the origin we establish an explicit and general energy decay rate result

energy decay for a nonlinear wave equation of variable coefficients with acoustic boundary conditions and a time varying delay in the boundary feedback abstract a variable coefficient wave equation with acoustic boundary conditions and a time varying delay in the boundary feedback is considered applying the riemannian geometry method we show that the decay rates of the nonlinear system with a time varying delay are described by solutions to a first order ode

survey interpolation methods in medical image processing image interpolation techniques often are required in medical imaging for image generation e g discrete back projection for inverse radon transform and processing such as compression or resampling since the ideal interpolation function spatially is unlimited several interpolation kernels of finite size have been introduced this paper compares 1 truncated and windowed sine 2 nearest neighbor 3 linear 4 quadratic 5 cubic b spline 6 cubic g lagrange and 7 gaussian interpolation and approximation techniques with kernel sizes from 1 spl times 1 up to 8 spl times 8 the comparison is done by 1 spatial and fourier analyses 2 computational complexity as well as runtime evaluations and 3 qualitative and quantitative interpolation error determinations for particular interpolation tasks which were taken from common situations in medical image processing for local and fourier analyses a standardized notation is introduced and fundamental properties of interpolators are derived successful methods should be direct current dc constant and interpolators rather than dc inconstant or approximators each method s parameters are tuned with respect to those properties this results in three novel kernels which are introduced in this paper and proven to be within the best choices for medical image interpolation the 6 spl times 6 blackman harris windowed sinc interpolator and the c2 continuous cubic kernels with n 6 and n 8 supporting points for quantitative error evaluations a set of 50 direct digital x rays was used they have been selected arbitrarily from clinical routine in general large kernel sizes were found to be superior to small interpolation masks except for truncated sine interpolators all kernels with n 6 or larger sizes perform significantly better than n 2 or n 3 point methods p spl lt 0 005 however the differences within the group of large sized kernels were not significant summarizing the results the cubic 6 spl times 6 interpolator with continuous second derivatives as defined in 24 can be recommended for most common interpolation tasks it appears to be the fastest six point kernel to implement computationally it provides eminent local and fourier properties is easy to implement and has only small errors the same characteristics apply to b spline interpolation but the 6 spl times 6 cubic avoids the intrinsic border effects produced by the b spline technique however the goal of this study was not to determine an overall best method but to present a comprehensive catalogue of methods in a uniform terminology to define general properties and requirements of local techniques and to enable the reader to select that method which is optimal for his specific application in medical imaging

a minimum squared error framework for generalized sampling we treat the problem of reconstructing a signal from its nonideal samples where the sampling and reconstruction spaces as well as the class of input signals can be arbitrary subspaces of a hilbert space our formulation is general and includes as special cases reconstruction from finitely many samples as well as uniform sampling of continuous time signals which are not necessarily bandlimited to obtain a good approximation of the signal in the reconstruction space from its samples we suggest two design strategies that attempt to minimize the squared norm error between the signal and its reconstruction the approaches we propose differ in their assumptions on the input signal if the signal is known to lie in an appropriately chosen subspace then we propose a method that achieves the minimal squared error on the other hand when the signal is not restricted we show that the minimal norm reconstruction cannot generally be obtained instead we suggest minimizing the worst case squared error between the reconstructed signal and the best possible but usually unattainable approximation of the signal within the reconstruction space we demonstrate both theoretically and through simulations that the suggested methods can outperform the consistent reconstruction approach previously proposed for this problem

exponential and polynomial decay for a quasilinear viscoelastic equation abstract we consider the following nonlinear viscoelastic equation u t u t t u u t t 0 t g t s u s d s 0 in a bounded domain for 0 we show that the dissipation induced by the integral term is strong enough to stabilize the solution this result improves an earlier one given by cavalcanti et al in m m cavalcanti v n d cavalcanti j ferreira existence and uniform decay for nonlinear viscoelastic equation with strong damping math methods appl sci 24 2001 1043 1053

quantitative fourier analysis of approximation techniques i interpolators and projectors we present a general fourier based method that provides an accurate prediction of the approximation error as a function of the sampling step t our formalism applies to an extended class of convolution based signal approximation techniques which includes interpolation generalized sampling with prefiltering and the projectors encountered in wavelet theory we claim that we can predict the l sup 2 approximation error by integrating the spectrum of the function to approximate not necessarily bandlimited against a frequency kernel e spl omega that characterizes the approximation operator this prediction is easier yet more precise than was previously available our approach has the remarkable property of providing a global error estimate that is the average of the true approximation error over all possible shifts of the input function our error prediction is exact for stationary processes as well as for bandlimited signals we apply this method to the comparison of standard interpolation and approximation techniques our method has interesting implications for approximation theory in particular we use our results to obtain some new asymptotic expansions of the error as t spl rarr 0 as well as to derive improved upper bounds of the kind found in the strang fix 1971 theory we finally show how we can design quasi interpolators that are near optimal in the least squares sense

some well posedness and general stability results in timoshenko systems with infinite memory and distributed time delay in this paper we consider a timoshenko system in one dimensional bounded domain with infinite memory and distributed time delay both acting on the equation of the rotation angle without any restriction on the speeds of wave propagation and under appropriate assumptions on the infinite memory and distributed time delay convolution kernels we prove first the well posedness and second the stability of the system where we present some decay estimates depending on the equal speed propagation case and the opposite one the obtained decay rates depend on the growths of the memory and delay kernels at infinity in the nonequal speed case the decay rate depends also on the regularity of initial data our stability results show that the only dissipation resulting from the infinite memory guarantees the asymptotic stability of the system regardless to the speeds of wave propagation and in spite of the presence of a distributed time delay applications of our approach to specific coupled timoshenko heat and timoshenko wave systems as well as the discrete time delay case are also presented

local convergence and speed estimates for semilinear wave systems damped by boundary friction abstract we study the local convergence to equilibria as time goes to infinity of trajectories of semilinear wave systems with friction damping on the boundary and subject to nonlinear potential energy estimates for the speed of convergence are obtained in terms of the behavior of the nonlinear feedback close to the origin as an example of application we show that the trajectories of a sine gordon system with nonlinear boundary damping approach equilibria at least polynomially

asymptotic stability of the wave equation on compact manifolds and locally distributed damping a sharp result let m g be a n dimensional n geqq 2 compact riemannian manifold with boundary where g denotes a riemannian metric of class c this paper is concerned with the study of the wave equation on m g with locally distributed damping described by left begin array l u tt delta bf g u a x g u t 0 quad hbox on thinspace m times left 0 infty right u 0 hbox on partial m times left 0 infty right end array right where m represents the boundary of m and a x g ut is the damping term the main goal of the present manuscript is to generalize our previous result in cavalcanti et al trans ams 361 9 4561 4580 2009 treating the conjecture in a more general setting and extending the result for n dimensional compact riemannian manifolds m g with boundary in two ways i by reducing arbitrarily the region m ast subset m where the dissipative effect lies this gives us a totally sharp result with respect to the boundary measure and interior measure where the damping is effective ii by controlling the existence of subsets on the manifold that can be left without any dissipative mechanism namely a precise part of radially symmetric subsets an analogous result holds for compact riemannian manifolds without boundary

blow up for semilinear wave equation with boundary damping and source terms abstract in this paper we consider the semilinear wave equation with boundary damping and source terms this work is devoted to prove a finite time blow up result under suitable condition on the initial data and positive initial energy

global well posedness and stability of semilinear mindlin timoshenko system abstract we study long term behavior of reissner mindlin timoshenko rmt plate systems focusing on the interplay between nonlinear viscous damping and source terms the sources may represent restoring forces but may also be focusing thus potentially amplifying the total energy which is the primary scenario of interest this work complements 28 which established local well posedness of this problem global well posedness when damping dominates the sources in an appropriate sense and a blow up in the complementary scenario assuming negative total initial energy the current paper develops the potential well theory for the rmt system it proves global existence for potential well solutions without restricting the source exponents derives explicit energy decay rates dependent on the order of the damping exponents and verifies a blow up result for positive total initial energy

global existence and uniform decay for a nonlinear viscoelastic equation with damping abstract in this paper we investigate a nonlinear viscoelastic equation with linear damping global existence of weak solutions and the uniform decay estimates for the energy have been established

global existence and blow up of solutions for a system of nonlinear viscoelastic wave equations with damping and source abstract in this paper we investigate the global existence and finite time blow up of solutions to the system of nonlinear viscoelastic wave equations u t t u 0 t g 1 t u d u t m 1 u t f 1 u v v t t v 0 t g 2 t v d v t r 1 v t f 2 u v in 0 t with initial and dirichlet boundary conditions where is a bounded domain in r n n 1 2 3 under suitable assumptions on the functions g i f i i 1 2 the initial data and the parameters in the equations we establish several results concerning local existence global existence uniqueness and finite time blow up property

global existence uniform decay and blow up of solutions for a system of petrovsky equations abstract in this paper we investigate global existence uniform decay and blow up of solutions for the following petrovsky equations u t t 2 u u t p 1 u t f u u v x t 0 t v t t 2 v v t q 1 v t f v u v x t 0 t where is a bounded domain of r n n 1 2 3 having a smooth boundary and f is a c 1 function given by f u v u v r 1 2 u v r 1 2 r 3 1 0 for the case of p q 1 we obtain the blow up of solutions and the lifespan estimates for four different ranges of initial energy for the case of 1 p q r we show the blow up of solutions when the initial energy is negative or nonnegative at less than the mountain pass level value global existence of solutions is proved by the potential well theory and decay estimates of the energy function are established by using nakao s inequality

mixed finite elements for global tide models with nonlinear damping we study mixed finite element methods for the rotating shallow water equations with linearized momentum terms but nonlinear drag by means of an equivalent second order formulation we prove long time stability of the system without energy accumulation we also give rates of damping in unforced systems and various continuous dependence results on initial conditions and forcing terms a priori error estimates for the momentum and free surface elevation are given in l 2 as well as for the time derivative and divergence of the momentum numerical results confirm the theoretical results regarding both energy damping and convergence rates

general decay and blow up of solution for a quasilinear viscoelastic problem with nonlinear source abstract in this paper we consider a quasilinear viscoelastic wave equation in canonical form with the homogeneous dirichlet boundary condition we prove that for certain class of relaxation functions and certain initial data in the stable set the decay rate of the solution energy is similar to that of the relaxation function this result improves earlier ones obtained by messaoudi and tatar s a messaoudi n e tatar global existence and uniform stability of solutions for a quasilinear viscoelastic problem math methods appl sci 30 2007 665 680 in which only the exponential and polynomial decay rates are considered conversely for certain initial data in the unstable set there are solutions that blow up in finite time the last result is new since it allows a larger class of initial energy which may take positive values

brief paper observability of switching structured linear systems with unknown input a graph theoretic approach this paper deals with the observability of the discrete mode the internal state and the input of switching structured linear systems with unknown input the proposed method based on a graph theoretic approach assumes only the knowledge of the system s structure we express in graphical terms necessary and sufficient conditions for the generic observability of the discrete mode the continuous internal state and the input of a switching structured linear system these conditions can be implemented by classical graph theory algorithms based on finding particular paths and cycles in a digraph