uniform decay for the unilateral problem associated to the kirchhoff type wave equations with nonlinear boundary damping in this article we study the existence of solutions and the uniform decay rate of the energy for nonlinear unilateral problem associated to the kirchhoff type wave equations with nonlinear boundary damping to obtain the existence of solutions we make use of faedo galerkin s approximation and also to show the uniform stabilization we use the perturbed energy method

energy decay rates for the semilinear wave equation with memory boundary condition and acoustic boundary conditions in this paper we consider the energy decay rates for the semilinear wave equation with memory boundary condition and acoustic boundary conditions motivated by results of gerbi and said houari 2011 2008 li and zhao 2011 liu and chen 2016 wu etal 2010 and lu etal 2011 we intend to study the energy decay rates for problem 1 1 1 6 by using the perturbed energy method and riemannian geometry method we obtained general energy decay rates

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

asymptotic behavior of a nonlinear kirchhoff type equation with spring boundary conditions in this paper we consider the initial boundary value problem for a nonlinear kirchhoff type equation with the damping term and spring boundary conditions we establish the global existence and uniqueness of solutions to this problem in time and give an example and simulation to illustrate our results for the proof we use the faedo galerkin approximate method finally we study the asymptotic behavior of solutions and some of its simulation results results of this paper are able to apply industrial parts such as a typical model widely used to represent threads wires magnetic tapes belts band saws and so on

on uniform decay of the solution for a damped nonlinear coupled system of wave equations with nonlinear boundary damping and memory term in this paper we are concerned with the existence and energy decay of the solution to the initial boundary value problem for the nonlinear coupled wave equations with nonlinear boundary damping and memory term

a restricted second order logic for finite structures we introduce a restricted version of second order logic so in which the second order quantifiers range over relations that are closed under the equivalence relation k of k variable equivalence for some k this restricted second order logic is an effective fragment of the infinitary logic l which differs from other such fragments in that it is not based on a fixpoint logic we explore the relationship of so with fixpoint logics showing that its inclusion relations with these logics are equivalent to problems in complexity theory we also look at the expressibility of np complete problems in this logic

abstract cauchy problems for quasi linear evolution equations in the sense of hadamard this paper is devoted to the well posedness of abstract cauchy problems for quasi linear evolution equations the notion of hadamard well posedness is considered and a new type of stability condition is introduced from the viewpoint of the theory of finite difference approximations the result obtained here generalizes not only some results on abstract cauchy problems closely related with the theory of integrated semigroups or regularized semigroups but also the kato theorem on quasi linear evolution equations an application to some quasi linear partial differential equation of weakly hyperbolic type is also given

dynamic affine invariant shape appearance handshape features and classification in sign language videos we propose the novel approach of dynamic affine invariant shape appearance model aff sam and employ it for handshape classification and sign recognition in sign language sl videos aff sam offers a compact and descriptive representation of hand configurations as well as regularized model fitting assisting hand tracking and extracting handshape features we construct sa images representing the hand s shape and appearance without landmark points we model the variation of the images by linear combinations of eigenimages followed by affine transformations accounting for 3d hand pose changes and improving model s compactness we also incorporate static and dynamic handshape priors offering robustness in occlusions which occur often in signing the approach includes an affine signer adaptation component at the visual level without requiring training from scratch a new singer specific model we rather employ a short development data set to adapt the models for a new signer experiments on the boston university 400 continuous sl corpus demonstrate improvements on handshape classification when compared to other feature extraction approaches supplementary evaluations of sign recognition experiments are conducted on a multi signer 100 sign data set from the greek sign language lemmas corpus these explore the fusion with movement cues as well as signer adaptation of aff sam to multiple signers providing promising results

inductive definitions over finite structures inductive definitions have played a central role in the foundations of mathematics for over a century they were used in the 1970s as the backbone of one major generalization of recursive function theory moschovakis 1974 aczel 1977 in recent years the relevance of inductive definitions in particular over finite structures to database theory to descriptive computational complexity and to logics of programs has been recognized a seminal paper on inductive definitions in database theory is chandra and hare1 1982 where they define a hierarchy of queries over finite structures within which minor steps successor ordinals correspond to first order quantifier alternations and major steps limit ordinals correspond to uses of lixpoints they left open the question of whether the hierarchy remains strict above the first major step level w this problem was answered in the negative by immerman 1986 since the collection of first order lixpoint queries over finite structures is closed under composition and first order operations other than negation moschovakis 1974 the main component of immerman s solution was

exponential decay of solutions of damped nonlinear hyperbolic equations on considere le comportement asymptotique des solutions de certaines equations hyperboliques non lineaires a amortissement lineaire

fixpoint logics relational machines and computational complexity we establish a general connection between fixpoint logic and complexity on one side we have fixpoint logic parameterized by the choices of 1st order operators inflationary or noninflationary and iteration constructs deterministic nondeterministic or alternating on the other side we have the complexity classes between p and exptime our parameterized fixpoint logics capture the complexity classes p np pspace and exptime but equally is achieved only over ordered structures there is however an inherent mismatch between complexity and logic while computational devices work on encodings of problems logic is applied directly to the underlying mathematical structures to overcome this mismatch we use a theory of relational complexity which bridges the gap between standard complexity and fixpoint logic on one hand we show that questions about containments among standard complexity classes can be translated to questions about containments among relational complexity classes on the other hand the expressive power of fixpoint logic can be precisely characterized in terms of relational complexity classes this tight three way relationship among fixpoint logics relational complexity and standard complexity yields in a uniform way logical analogs to all containments among the complexity classes p np pspace and exptime the logical formulation shows that some of the most tantalizing questions in complexity theory boil down to a single question the relative power of inflationary vs noninflationary 1st order operators

on the global solvability of kirchhoff equation for non analytic initial data abstract we give sufficient conditions for the global solvability of kirchhoff equation in terms of the spectral resolutions of the initial data u 0 x u t 0 x we assume no smallness conditions and only sobolev type regularity

on coupled wave equation of kirchhoff type with nonlinear boundary damping and memory term in this paper we prove the existence of the solution to the mixed problem for coupled wave equation of kirchhoff type with nonlinear boundary damping and memory term moreover we discuss the uniform decay of the solution

asymptotic stability and energy decay rates for solutions of the wave equation with memory in a star shaped domain we study the asymptotic stability and give the energy decay rates for solutions of the wave equation with boundary dissipation of the memory type

hyperbolic parabolic singular perturbation for mildly degenerate kirchhoff equations time decay estimates we consider degenerate kirchhoff equations with a small parameter e in front of the second order time derivative it is well known that these equations admit global solutions when e is small enough and that these solutions decay as t with the same rate of solutions of the limit problem of parabolic type in this paper we prove decay error estimates for the difference between a solution of the hyperbolic problem and the solution of the corresponding parabolic problem these estimates show in the same time that the difference tends to zero both as e 0 and as t concerning the decay rates it turns out that the difference decays faster than the two terms separately as t proofs involve a nonlinear step where we separate fourier components with respect to the lowest frequency followed by a linear step where we exploit weighted versions of classical energies

local soltutions for a nonlinear degenerate hyperbolic equation on etudie l existence et l unicite des solutions locales pour le probleme mixte associe a l equation hyperbolique degenere du type 2 u 2 m u x t 2 dx u 0 ou est un ouvert borne de r n a frontiere lisse et x est un vecteur de r n

existence results for boundary value problems of second order impulsive differential equations abstract with the help of lower and upper solutions the extremal solutions of a second order impulsive differential equation are obtained as limits of monotone iterates several existence results for the second order impulsive differential equation subject to nonlinear boundary conditions which include the usual periodic and linear separated boundary conditions are also established

statistical shape analysis clustering learning and testing using a differential geometric treatment of planar shapes we present tools for 1 hierarchical clustering of imaged objects according to the shapes of their boundaries 2 learning of probability models for clusters of shapes and 3 testing of newly observed shapes under competing probability models clustering at any level of hierarchy is performed using a minimum variance type criterion and a markov process statistical means of clusters provide shapes to be clustered at the next higher level thus building a hierarchy of shapes using finite dimensional approximations of spaces tangent to the shape space at sample means we implicitly impose probability models on the shape space and results are illustrated via random sampling and classification hypothesis testing together hierarchical clustering and hypothesis testing provide an efficient framework for shape retrieval examples are presented using shapes and images from eth surrey and amcom databases

bounded input bounded output stability of a damped nonlinear string in this paper we prove that the displacement of a damped nonlinear string under bounded distributed forces is bounded the proof is achieved by showing that an energy like lyapunov function corresponding to the string is bounded

on uniform decay of solutions for wave equation of kirchhoff type with nonlinear boundary damping and memory source term in this paper we prove the existence of solution to the mixed problem for wave equation of kirchhoff type with nonlinear boundary damping and memory term moreover we discuss the uniform decay of solution

linear recursive schemes and asymptotic expansion associated with the kirchoff carrier operator abstract in this paper we consider a nonlinear wave equation with the kirchoff carrier operator 1 u tt b 0 b u 2 u f x t u u x u t x 0 1 0 2 u 0 t u 1 t 0 3 u x 0 u 0 x u t x 0 u 1 x where b 0 0 is a given constant and b f are the given functions the above b u 2 depends on the integral u 2 u x t 2 dx in this paper we associate with the above problem a linear recursive scheme for which the existence of a local and unique solution is proved by using the standard compactness argument if b c 2 r b 1 c 1 r f c 2 formula 0 r 3 and f 1 c 1 formula 0 r 3 then an asymptotic expansion of order 2 in e is obtained with a right hand side of the form f x t u u x u t e f 1 x t u u x u t and b stands for b e b 1 for e sufficiently small

active appearance models revisited active appearance models aams and the closely related concepts of morphable models and active blobs are generative models of a certain visual phenomenon although linear in both shape and appearance overall aams are nonlinear parametric models in terms of the pixel intensities fitting an aam to an image consists of minimising the error between the input image and the closest model instances i e solving a nonlinear optimisation problem we propose an efficient fitting algorithm for aams based on the inverse compositional image alignment algorithm we show that the effects of appearance variation during fitting can be precomputed projected out using this algorithm and how it can be extended to include a global shape normalising warp typically a 2d similarity transformation we evaluate our algorithm to determine which of its novel aspects improve aam fitting performance

yosida approximation and nonlinear hyperbolic equation we are concerned with the initial value problem for nonlinear evolution equations of the form u t m a 1 2 u t 2 au t u t f t on 0 u 0 u o u o u 1 here a is a nonnegative selfadjoint operator in a real hilbert space h 0 is a constant and m is a c 1 class function satisfying m r m o 0 for r 0 with m o constant the equation has its motivation in the mathematical description of small amplitude vibrations of an elastic string

the existence and decay of solutions of a damped kirchhoff carrier equation in banach spaces abstract this paper is concerned with the study of the existence and decay of solutions of the following initial value problem b u t m u t w a u t 1 k t u t d s 2 a u t 0 t 0 u 0 u 0 u 0 u 1 where v is a hilbert space with dual v a and b symmetric linear operators from v into v with b v v 0 v 0 and a v v v v 2 0 s a restriction of the operator a w a banach space m the real function m m 0 m 1 with m 0 0 and m 1 0 real numbers k a positive function and real numbers with 0 and 1 the successive approximation method the characterization of the derivative of m u t w and the arzela ascoli theorem allow us to obtain a local solution of the global solution follows by the prolongation method of solutions the exponential decay of the solution is derived by the perturbed energy method

existence results for some kirchhoff carrier problems abstract analyzing the viscoelastic problem for small vibrations of elastic strings kirchhoff and carrier proposed two different models of nonlinear partial differential equations by combining these two models we deal here with some nonlocal hyperbolic problems that cover a large class of kirchhoff and carrier type problems the existence of local solutions of degenerate problems as well as local and nonlocal solutions of nondegenerate problems is established the proofs are based on the combination of the schauder fixed point theorem with some asymptotic method

global existence and stability for wave equation of kirchhoff type with memory condition at the boundary abstract we consider a nonlinear wave equation of kirchhoff type with memory condition at the boundary and we study the asymptotic behavior of the corresponding solutions we proved that the energy decay with the same rate of decay of the relaxation function that is the energy decays exponentially when the relaxation function decay exponentially and polynomially when the relaxation function decay polynomially

on uniform decay of coupled wave equation of kirchhoff type subject to memory condition on the boundary abstract in this paper we prove the existence of solution and uniform decay of energy to the mixed problem for coupled wave equation of kirchhoff type subject to memory condition on the boundary

existence of global smooth solutions to the initial boundary value problem for the quasi linear wave equation with a degenerate dissipative term let c be a bounded domain with smooth boundary dq in the n dimen sional euclidean space rn and let us consider the initial boundary value problem for the classical quasi linear wave equation with a dissipation u v a lvul vu u x u o in qx o ce 4x 0 uo

nonlinear parabolic equations with nonlinear functionals abstract in this paper we study a class of nonlinear parabolic equations in which certain functionals of the solution are involved a priori estimates for the solutions are derived by the use of integral estimates and the existence and uniqueness of the solutions are demonstrated via a retarding argument

stabilization for the kirchhoff type equation from an axially moving heterogeneous string modeling with boundary feedback control abstract the first objective of this paper is to make the mathematical model for vibration suppression of an axially moving heterogeneous string in order to describe the geometrical nonlinearity due to finite transverse deformation the exact expression of the strain is used the mathematical modeling is derived first by using hamilton s principle and variational lemma and the derived nonlinear pde system is the kirchhoff type equation with boundary feedback control next we show the existence and uniqueness of strong solutions of the pde system via techniques of functional analysis mainly a theorem of compactness for the analysis of the approximation of the faedo galerkin method and estimate a decay rate for the energy the theoretical results are assured by numerical results of the solution s shape and asymptotic behavior for the system

kirchhoff type system with linear weak damping and logarithmic nonlinearities abstract for the nonlinear kirchhoff type wave system with logarithmic nonlinearities and weak dissipation the global well posedness of initial boundary value problem is analyzed focusing on the interplay between kirchhoff terms and logarithmic sources we investigate the kirchhoff system controlled by logarithmic forces thus amplifying the difficulties in blow up analysis which is the primary scenario of interest by employing potential well method and concavity method we obtain several results related to the sufficient conditions posed on subcritical initial energy and critical initial energy which is used to classify initial data for global existence and finite time blow up finally via careful analysis involving the unstable invariant set under supercritical initial energy we are able to show an affirmative result that the solution blows up in finite time when initial data satisfy some suitable assumptions

on local solutions of a mildly degenerate hyperbolic equation in this work we prove the existence of a unique nonlocal solution for the vibrations of a nonhomogeneous stretched string in sobolev spaces and without any smallness conditions on the size of the initial data

existence of local solutions of the kirchhoff carrier equation in banach spaces abstract this paper is concerned with the study of the existence of a local solution of the problem b u t m u t w a u t 0 in v t 0 u 0 u 0 u 0 u 1 u 0 0 where v is a hilbert space with dual v a and b symmetric linear operators from v into v with a v v 0 and b v v 0 v 0 w a banach space with v continuously embedding in w a real number with 1 and m a function with m 0 m u 0 w 0 and smooth in a neighborhood of u 0 w the characterization of the derivative of the nonlinear term of the equation of and the arzela ascoli theorem allow us to obtain a solution u of defined in 0 t 0 where t 0 depends on u 0 u 1 and m

existence uniqueness and uniform decay for the non linear degenerate equation with memory condition at the boundary this paper is concerned with the existence uniqueness and uniform decay for the solution to the non linear degenerate equation with memory condition at the boundary

vibrations of elastic string with nonhomogeneous material abstract in this paper we analyze from the mathematical point of view a model for small vertical vibrations of an elastic string with fixed ends and the density of the material being not constant we employ techniques of functional analysis mainly a theorem of compactness for the analysis of the approximation of faedo galerkin method we obtain strong global solutions with restrictions on the initial data u 0 and u 1 uniqueness of solutions and a rate decay estimate for the energy

some nonlinear degenerate wave equations on etudie la resolubilite locale du probleme aux valeurs limites et initiales suivant 2 u t 2 m gradu x t 2 dx u 0 dans 0 u 0 sur w 0 u 0 0 u t 0 dans ou m r est une fonction c 1 non negative sur 0 un domaine borne de r n a frontiere lisse w

on a quasilinear wave equation with memory equation 1 l with a 0 and n 1 has its roots in a model for the small amplitude vibrations of a string in which the dependence of the tension on the deformation cannot be ignored see for example bernstein 2 carrier 3 41 dickey s and nishida 13 when a 0 1 1 may be used to describe the dynamics of an extensible string with fading memory this equation states that the dynamic equilibrium of a body depends not only on the present state of deformation but also on the previous history of the deformation gradient since the publication of the aforementioned papers equation 1 1 with a 0 has been the subject of intense scrutiny see for example arosio and spagnolo 11 lions 9 medeiros lo menzala ll nishihara 14 151 pohoiaev 16 and yamada 17 181 to name but a few among the facts thus far proved pohoiaev s results and their extension to the degenerate case of arosio and spagnolo are of particular significance they show that if the data satisfy an analytic type condition then solutions are global in time in spite of the abundant literature on the memoryless form of equation l l to our best knowledge equation 1 1 with a f 0 appears to be untouched our main results theorem 5 1 theorem 5 2 and theorem 5 4 will show that under appropriate assumptions on the kernel

energy decay of solutions of a degenerate kirchhoff equation with a weak nonlinear dissipation abstract in this paper we study decay properties of the solutions to the degenerate kirchhoff equation with a weak nonlinear dissipative term

relational queries computable in polynomial time we characterize the polynomial time computable queries as those expressible in relational calculus plus a least fixed point operator and a total ordering on the universe we also show that even without the ordering one application of fixed point suffices to express any query expressible with several alternations of fixed point and negation this proves that the fixed point query hierarchy suggested by chandra and harel collapses at the first fixed point level it is also a general result showing that in finite model theory one application of fixed point suffices

lucas kanade 20 years on a unifying framework since the lucas kanade algorithm was proposed in 1981 image alignment has become one of the most widely used techniques in computer vision applications range from optical flow and tracking to layered motion mosaic construction and face coding numerous algorithms have been proposed and a wide variety of extensions have been made to the original formulation we present an overview of image alignment describing most of the algorithms and their extensions in a consistent framework we concentrate on the inverse compositional algorithm an efficient algorithm that we recently proposed we examine which of the extensions to lucas kanade can be used with the inverse compositional algorithm without any significant loss of efficiency and which cannot in this paper part 1 in a series of papers we cover the quantity approximated the warp update rule and the gradient descent approximation in future papers we will cover the choice of the error function how to allow linear appearance variation and how to impose priors on the parameters

monotone versus positive in connection with the least fixed point operator the following question was raised suppose that a first order formula p p is semantically monotone in a predicate symbol p on finite structures is p p necessarily equivalent on finite structures to a first order formula with only positive occurrences of p in this paper this question is answered negatively moreover the counterexample naturally gives a uniform sequence of constant depth polynomial size monotone boolean circuits that is not equivalent to any however nonuniform sequence of constant depth polynomial size positive boolean circuits

on graph rewritings abstract the purpose of the present paper is twofold firstly show that it is possible to rewrite graphs in a way equivalent to and in fact slightly more powerful than that of ehrig pfender and schneider 1973 which has since then been developed mainly by the berlin school our method consists in using a single push out of partial morphisms and is described in section 3 section 1 is devoted to the elementary definitions concerning graphs and related terms section 2 contains the set theoretic prerequisites for the sequel but the proofs have been moved into an appendix for easier reading secondly we indicate in section 4 why this method is not really fit for rewriting graphs that represent collapsed terms i e sharing common subterms and we introduce pushouts of total functions which are not morphisms everywhere on their domain this method is connected to the classical rewriting of the corresponding terms the adequacy of these new rewriting rules is then tested to prove a local confluence criterion a la knuth bendix 1970 in section 5 the proof of which turns out to be very short

on damped kirchhoff equation with variable coefficients in this work we are concerned with the existence and uniqueness of strong global solutions and exponential decay of the total energy for an initial boundary value problem associated with the kirchhoff equation with variable coefficients on the action of a nonlinear internal damping