on the large time galerkin approximation of the navier stokes equations in this article we are interested in the difficult problem of relating the large time behaviour of the navier stokes equations to the large time behaviour of their galerkin approximation we restrict ourselves to the simplest situation dealing with stationary solutions and the question is the following one if the computed approximation of the time dependent equations seems to converge to some limit as t to infty is the same true for the exact problem and are the limits related we give here some sufficient conditions reasonably easy to verify which guarantee a positive answer to this question

gaussian beams and legendre polynomials as invariants of the time reversal operator for a large rigid cylinder the dort method french acronym for decomposition of the time reversal operator is an active remote sensing technique using an array of antennas for the detection and localization of scatterers this method is based on the singular value decomposition of the interelement response matrix in this paper an analytical expression of the singular vectors due to the reflection from a large rigid cylinder is provided depending on the array aperture two asymptotic regimes are described it is shown that the singular vectors correspond to hermite gaussian modes for large apertures and legendre polynomials for small ones using perturbation theory the corresponding singular values are deduced theoretical predictions are in good agreement with experimental results

rst invariant image watermarking algorithm with mathematical modeling and analysis of the watermarking processes in this paper a new rotation and scaling invariant image watermarking scheme is proposed based on rotation invariant feature and image normalization a mathematical model is established to approximate the image based on the mixture generalized gaussian distribution which can facilitate the analysis of the watermarking processes using maximum a posteriori probability based image segmentation the cover image is segmented into several homogeneous areas each region can be represented by a generalized gaussian distribution which is critical for the analysis of the watermarking processes mathematically the rotation invariant features are extracted from the segmented areas and are selected as reference points subregions centered at the feature points are used for watermark embedding and extraction image normalization is applied to the subregions to achieve scaling invariance meanwhile the watermark embedding and extraction schemes are analyzed mathematically based on the established mathematical model the watermark embedding strength is adjusted adaptively using the noise visibility function and the probability of error is analyzed mathematically the mathematical relationship between fidelity and robustness is established the experimental results show the effectiveness and accuracy of the proposed scheme

image watermarking based on invariant regions of scale space representation this paper proposes a novel content based image watermarking method based on invariant regions of an image the invariant regions are self adaptive image patches that deform with geometric transformations three different invariant region detection methods based on the scale space representation of an image were considered for watermarking at each invariant region the watermark is embedded after geometric normalization according to the shape of the region by binding watermarking with invariant regions resilience against geometric transformations can be readily obtained experimental results show that the proposed method is robust against various image processing steps including geometric transformations cropping filtering and jpeg compression

invariant grids for reaction kinetics abstract in this paper we construct low dimensional manifolds of reduced description for equations of chemical kinetics from the standpoint of the method of invariant manifold mim mim is based on a formulation of the condition of invariance as an equation and its solution by newton iterations a grid based version of mim is developed the method of invariant grids we describe the newton method and the relaxation method for the invariant grids construction the problem of the grid correction is fully decomposed into the problems of the grid s nodes correction the edges between the nodes appear only in the calculation of the tangent spaces this fact determines high computational efficiency of the method of invariant grids the method is illustrated by two examples the simplest catalytic reaction michaelis menten mechanism and the hydrogen oxidation the algorithm of analytical continuation of the approximate invariant manifold from the discrete grid is proposed generalizations to open systems are suggested the set of methods covered makes it possible to effectively reduce description in chemical kinetics

moment based image normalization with high noise tolerance in this paper the effects of noise with nonzero mean on existing moment based image normalization methods are studied several modifications to reduce noise sensitivity are presented and tested they involve nonlinear mapping and fractional and negative order moments

inertial manifolds the non self adjoint case abstract in contrast with the existing theories of inertial manifolds which are based on the self adjoint assumption of the principal differential operator in this paper we show that for general dissipative evolutionary systems described by semilinear parabolic equations with principal differential operator being sectorial and having compact resolvent there exists an inertial manifold provided that certain gap conditions hold we also show that by using an elliptic regularization this theory can be extended to a class of kdv equations where the principal differential operator is not sectorial

an lp theory of invariant manifolds for parabolic partial differential equations on rd abstract we study the problem about the existence of finite dimensional invariant manifolds for nonlinear heat equations of the form u u f u u on r d 1 we show that in spite of the fact that the linearized equation has continuous spectrum extending from negative infinity to zero there exist finite dimensional invariant manifolds which control the long time asymptotics of solutions we consider the problem for these equations in the framework of weighted sobolev spaces of l p type the l p theory of this problem gives the l estimate of the long time asymptotics of solutions under natural assumptions on the nonlinear term f and their initial data

characterization of subwavelength elastic cylinders with the decomposition of the time reversal operator theory and experiment the decomposition of the time reversal operator provides information on the scattering medium it has been shown chambers and gautesen j acoust soc am 109 2616 2624 2001 that a small spherical scatterer is in general associated with four eigenvalues and eigenvectors of the time reversal operator in this paper the 2d problem of scattering by an elastic cylinder imbedded in water measured by a linear array of transducers is considered in this case the array response matrix has three nonzero singular values experimental results are obtained with linear arrays of transducers and for wires of different diameters smaller that the wavelength it is shown how the singular value distribution and the singular vectors depend on the elastic velocities cl ct the density of each wire and on the density 0 and velocity c0 of the surrounding fluid these results offer a new perspective towards solution of the inverse problem by determining more than scattering contrast using conventional array proce

bifurcation computations on an approximate inertial manifold for the 2d navier stokes equations abstract we compare the minimum number of modes needed to capture certain bifurcations of the 2d navier stokes equations by a certain nonlinear galerkin method and by the traditional galerkin method the boundary conditions are periodic and the forcing is in a single mode two different choices of the forcing mode are tested we introduce and implement a homotopy which allows continuation between approximations of different size

inertial manifolds for nonlinear evolutionary equations abstract in this paper we introduce the concept of an inertial manifold for nonlinear evolutionary equations in particular for ordinary and partial differential equations these manifolds which are finite dimensional invariant lipschitz manifolds seem to be an appropriate tool for the study of questions related to the long time behavior of solutions of the evolutionary equations the inertial manifolds contain the global attractor they attract exponentially all solutions and they are stable with respect to perturbations furthermore in the infinite dimensional case they allow for the reduction of the dynamics to a finite dimensional ordinary differential equation

on the selection of optimal feature region set for robust digital image watermarking a novel feature region selection method for robust digital image watermarking is proposed in this paper this method aims to select a nonoverlapping feature region set which has the greatest robustness against various attacks and can preserve image quality as much as possible after watermarked it first performs a simulated attacking procedure using some predefined attacks to evaluate the robustness of every candidate feature region according to the evaluation results it then adopts a track with pruning procedure to search a minimal primary feature set which can resist the most predefined attacks in order to enhance its resistance to undefined attacks under the constraint of preserving image quality the primary feature set is then extended by adding into some auxiliary feature regions this work is formulated as a multidimensional knapsack problem and solved by a genetic algorithm based approach the experimental results for stirmark attacks on some benchmark images support our expectation that the primary feature set can resist all the predefined attacks and its extension can enhance the robustness against undefined attacks comparing with some well known feature based methods the proposed method exhibits better performance in robust digital watermarking

approximate inertial manifolds for the kuramoto sivashinsky equation analysis and computations abstract we evaluate several alternative methods for the approximation of inertial manifolds for the one dimensional kuramoto sivashinsky equation kse a method motivated by the dynamics originally developed for the navier stokes equation is adapted for the kse rigorous error estimates are obtained and compared to those of other methods introduced in the literature formal relationships between these other methods and the one introduced here are established numerical bifurcation diagrams of the various approximate inertial forms for the kse are presented we discuss the correspondence between the rigorous error estimates and the accuracy of the computational results these methods can be adapted to other dissipative partial differential equations

on approximate inertial manifolds to the navier stokes equations abstract recently the theory of inertial manifolds has shown that the long time behavior the dynamics of certain dissipative partial differential equations can be fully discribed by that of a finite ordinary differential system although we are still unable to prove existence of inertial manifolds to the navier stokes equations we present here a nonlinear finite dimensional analytic manifold that approximates closely the global attractor in the two dimensional case and certain bounded invariant sets in the three dimensional case this approximate manifold and others allow us to introduce modified galerkin approximations

a novel image watermarking scheme based on amplitude attack this paper presents a novel image watermark scheme based on the characteristics of amplitude attacks first of all the analysis of amplitude attacks is performed then the amplitude attacks are categorized into three types positive attack negative attack and random attack finally based on these attack types we design three corresponding detectors the detectors remove the unreliable discrete cosine transform dct coefficients in the attacked image so that only reliable coefficients are used for the extraction of the watermark embedded the experimental results indicate that the proposed technique improves robustness significantly without sacrificing the false alarm rate

a feature based robust digital image watermarking scheme a robust digital image watermarking scheme that combines image feature extraction and image normalization is proposed the goal is to resist both geometric distortion and signal processing attacks we adopt a feature extraction method called mexican hat wavelet scale interaction the extracted feature points can survive a variety of attacks and be used as reference points for both watermark embedding and detection the normalized image of an image object is nearly invariant with respect to rotations as a result the watermark detection task can be much simplified when it is applied to the normalized image however because image normalization is sensitive to image local variation we apply image normalization to nonoverlapped image disks separately the disks are centered at the extracted feature points several copies of a 16 bit watermark sequence are embedded in the original image to improve the robustness of watermarks simulation results show that our scheme can survive low quality jpeg compression color reduction sharpening gaussian filtering median filtering row or column removal shearing rotation local warping cropping and linear geometric transformations

c1approximations of inertial manifolds for dissipative nonlinear equations abstract in this paper we study a class of nonlinear dissipative partial differential equations that have inertial manifolds this means that the long time behavior is equivalent to a certain finite system of ordinary differential equations we investigate ways in which these finite systems can be approximated in thec1sense geometrically this may be interpreted as constructing manifolds in phase space that arec1close to the inertial manifold of the partial differential equation under such approximations the invariant hyperbolic sets of the global attractor persist

rotation invariant watermark embedding based on scale adapted characteristic regions rotation invariance is one of the most challenging issues in robust image watermarking this paper presents two rotation invariant watermark embedding schemes in the non subsampled contourlet transform nsct domain based on the scale adapted local regions watermark synchronization is achieved using the scale space feature point based local characteristic regions the first method embeds a binary watermark sequence by partitioning the local regions in a rotation invariant pattern the second method embeds a binary watermark image in a content based manner and the watermark signal is adaptive to the orientation of the image both methods achieve rotation invariant embedding by only using the rotation normalizing angle thus no interpolation operation is performed extensive simulation results and comparisons show that the proposed schemes can efficiently resist both signal processing attacks and geometric attacks

attractive invariant manifolds under approximation inertial manifolds a class of nonlinear dissipative partial differential equations that possess finite dimensional attractive invariant manifolds is considered an existence and perturbation theory is developed which unifies the cases of unstable manifolds and inertial manifolds into a single framework it is shown that certain approximations of these equations such as those arising from spectral or finite element methods in space one step time discretization or a combination of both also have attractive invariant manifolds convergence of the approximate manifolds to the true manifolds is established as the approximation is refined in this part of the paper applications to the behavior of inertial manifolds under approximation are considered from this analysis deductions about the structure of the attractor and the flow on the attractor under discretization can be made

reduced order based feedback control of the kuramoto sivashinsky equation in this paper we consider the kuramoto sivashinsky equation kse which describes the long wave motions of a thin film over a vertical plane solution procedures for the kse often yield a large or infinite dimensional nonlinear system we first discuss two reduced order methods the approximate inertial manifold and the proper orthogonal decomposition and show that these methods can be used to obtain a reduced order system that can accurately describe the dynamics of the kse moreover from this resulting reduced order system the feedback controller can readily be designed and synthesized for our control techniques we use the linear and nonlinear quadratic regulator methods which are the first and second order approximated solutions of the hamilton jacobi bellman equation respectively numerical simulations comparing the performance of the reduced order based linear and nonlinear controllers are presented

fusion of color edge detection and color quantization for color image watermarking using principal axes analysis in the past few years many gray level image watermarking schemes have been proposed although the extension to the color case is rare and regularly accomplished by marking the image luminance or by processing each color channel separately this paper presents a new color image watermarking scheme that combines color edge detection and color quantization using principal axes analysis in three dimensional color space the watermark is hidden within the data by modifying a subset of carefully selected edge points to resist both geometric distortion and signal processing attacks experimental results show the robustness of the proposed scheme to resist common attacks

the prolate spheroidal wave functions as invariants of the time reversal operator for an extended scatterer in the fraunhofer approximation the decomposition of the time reversal operator known by the french acronym dort is widely used to detect locate and focus on scatterers in various domains such as underwater acoustics medical ultrasound and nondestructive evaluation in the case of point scatterers the theory is well understood the number of nonzero eigenvalues is equal to the number of scatterers and the eigenvectors correspond to the scatterers green s function in the case of extended objects however the formalism is not as simple it is shown here that in the fraunhofer approximation analytical solutions can be found and that the solutions are functions called prolate spheroidal wave functions these functions have been studied in information theory as a basis of band limited and time limited signals they also arise in optics the theoretical solutions are compared to simulation results most importantly the intuition that for an extended objects the number of nonzero eigenvalues is proportional to the number of resol

perturbations of attractors of differential equations abstract in this paper we study small c 1 perturbations of a differential equation that has a hyperbolic attractor k we show that if k has a suitable lipschitz property and if the perturbation is small enough then there is a homeomorphism h k k y where k y is a hyperbolic attractor for the perturbed equation examples are included

high order symmetrical hyperbolic wavelets this paper studies high order wavelets of the first order hyperbolic choi williams cw and nth order hyperbolic kernels for analyses of digital time series by using their second and higher order derivatives for time domain investigations normalisation constants of the second fourth sixth eighth and tenth order hyperbolic and cw wavelets are numerically given for frequency domain investigations wavelet parameters including band peak frequencies minimum numbers of sampling points scale limits scale resolutions and total number of scales are explicitly given and numerically estimated for the fourth order hyperbolic and cw wavelets parameter comparisons among the morlet wavelet hyperbolic and cw second and fourth order wavelets are also given detection of periodicity and chaos in the duffing oscillator is discussed

localized image watermarking based on feature points of scale space representation this paper proposes a novel method for content based watermarking based on feature points of an image at each feature point the watermark is embedded after scale normalization according to the local characteristic scale characteristic scale is the maximum scale of the scale space representation of an image at the feature point by binding watermarking with the local characteristics of an image resilience against affine transformations can be obtained easily experimental results show that the proposed method is robust against various image processing steps including affine transformations cropping filtering and jpeg compression

explicit construction of an inertial manifold for a reaction diffusion equation abstract an inertial manifold is constructed for the scalar reaction diffusion equation u t vu xx u with a cubic nonlinearity uniform bounds are obtained for the number of zeros along solutions to the variational equations satisfied by the difference of two elements on the unstable manifolds of equilibria this uniformity leads to the global parameterization of the attractor as a function defined in the linear unstable manifold of the least stable equilibrium by the introduction of local techniques near each equilibrium we succeed in constructing an inertial manifold of lowest possible dimension

multiple scattering by multiple spheres a new proof of the lloyd berry formula for the effective wavenumber we provide the first classical derivation of the lloyd berry formula for the effective wavenumber of an acoustic medium filled with a sparse random array of identical small scatterers our approach clarifies the assumptions under which the lloyd berry formula is valid more precisely we derive an expression for the effective wavenumber which assumes the validity of lax s quasi crystalline approximation but makes no further assumptions about scatterer size and then we show that the lloyd berry formula is obtained in the limit as the scatterer size tends to zero

uniqueness of thermodynamic projector and kinetic basis of molecular individualism three results are presented first we solve the problem of persistence of dissipation for reduction of kinetic models kinetic equations with thermodynamic lyapunov functions are studied uniqueness of the thermodynamic projector is proven there exists only one projector which transforms any vector field equipped with the given lyapunov function into a vector field with the same lyapunov function for a given anzatz manifold which is not tangent to the lyapunov function levels second we use the thermodynamic projector for developing the short memory approximation and coarse graining for general nonlinear dynamic systems we prove that in this approximation the entropy production increases the theorem about entropy overproduction in example we apply the thermodynamic projector to derive the equations of reduced kinetics for the fokker planck equation a new class of closures is developed the kinetic multipeak polyhedra distributions of this type are expected in kinetic models with multidimensional instability as universally as the gaussian distribution appears for stable systems the number of possible relatively stable states of a nonequilibrium system grows as 2m and the number of macroscopic parameters is in order mn where n is the dimension of configuration space and m is the number of independent unstable directions in this space the elaborated class of closures and equations pretends to describe the effects of molecular individualism this is the third result

smoothness of inertial manifolds the theory of invariant manifolds plays an important role in the study of dynamics of nonlinear systems in finite dimensional or infinite dimensional spaces such invariant manifolds include stable manifolds unstable manifolds and center manifolds see pliss 36 for example recently the theory of inertial manifolds has been developed for some dissipative evolution equations the inertial manifold introduced by foias sell and ttmam 141 is a finite dimensional lipschitz invariant manifold attracting solutions exponentially one of the important properties of inertial manifolds is that they contain the global attractors thus the study of dynamics of infinite dimensional nonlinear systems can be reduced to the study of dynamics of flows on the inertial manifold which in turn is described by the dynamics of an ordinary differential equation there are extensive works on this subject see for example constantin 3 constantin foias nicolaenko

affine legendre moment invariants for image watermarking robust to geometric distortions geometric distortions are generally simple and effective attacks for many watermarking methods they can make detection and extraction of the embedded watermark difficult or even impossible by destroying the synchronization between the watermark reader and the embedded watermark in this paper we propose a new watermarking approach which allows watermark detection and extraction under affine transformation attacks the novelty of our approach stands on a set of affine invariants we derived from legendre moments watermark embedding and detection are directly performed on this set of invariants we also show how these moments can be exploited for estimating the geometric distortion parameters in order to permit watermark extraction experimental results show that the proposed watermarking scheme is robust to a wide range of attacks geometric distortion filtering compression and additive noise

quasi equilibrium closure hierarchies for the boltzmann equation abstract after boltzmann and gibbs the notion of disorder in statistical physics relates to ensembles not to individual states this disorder is measured by the logarithm of ensemble volume the entropy but recent results about measure concentration effects in analysis and geometry allow us to return from the ensemble based point of view to a state based one at least partially in this paper the order disorder problem is represented as a problem of relation between distance and measure the effect of strong order disorder separation for multiparticle systems is described the phase space could be divided into two subsets one of them set of disordered states has almost zero diameter the second one has almost zero measure the symmetry with respect to permutations of particles is responsible for this type of concentration dynamics of systems with strong order disorder separation has high average acceleration squared which can be interpreted as evolution through a series of collisions acceleration dominated dynamics the time arrow direction from order to disorder follows from the strong order disorder separation but inverse for systems in space of symmetric configurations with sticky boundaries the way back from disorder to order is typical natural selection recommendations for mining of molecular dynamics results are also presented

the algebraic approximation of attractors the finite dimensional case abstract in this article we present a constructive method for approximating attractors the approximate sets are parts of algebraic sets i e the zeros of high degree polynomial functions and they can approximate the attractor at an arbitrary high level of accuracy

a class of numerical algorithms for large time integration the nonlinear galerkin methods the nonlinear galerkin methods are numerical schemes well adapted to the long term integration of evolution partial differential equations they consist of looking for approximate solutions lying in nonlinear manifolds that are close in some sense to the attractor the aim of this paper is to extend these schemes to a large class of manifolds convergence results are derived for the schemes introduced

on the rate of convergence of the nonlinear galerkin methods in this paper we provide estimates to the rate of convergence of the nonlinear galerkin approximation method in particular and by means of an illustrative example we show that the nonlinear galerkin method converges faster than the usual galerkin method

multiple scattering by cylinders immersed in fluid high order approximations for the effective wavenumbers acoustic wave propagation in a fluid with a random assortment of identical cylindrical scatterers is considered while the leading order correction to the effective wavenumber of the coherent wave is well established at dilute areal density n0 of scatterers in this paper the higher order dependence of the coherent wavenumber on n0 is developed in several directions starting from the quasi crystalline approximation qca a consistent method is described for continuing the linton and martin formula which is second order in n0 to higher orders explicit formulas are provided for corrections to the effective wavenumber up to o n04 then using the qca theory as a basis generalized self consistent schemes are developed and compared with self consistent schemes using other dynamic effective medium theories it is shown that the linton and martin formula provides a closed self consistent scheme unlike other approaches

construction of inertial manifolds by elliptic regularization abstract in many cases an inertial manifold 2 m for an infinite dimensional dissipative dynamical system can be represented as the graph of a smooth function from a finite dimensional hilbert space hp to another hilbert space hq the invariance property of m means that can be written as the solution of a first order partial differential equation d p g1 p p a p g2 p p 0 over hp where g1 and g2 are nonlinear functions which depend on the original dynamical system and a is a suitably stable linear operator in this paper we use a method introduced by sacker r j sacker a new approach to the perturbation theory of invariant surface comm pure appl math 18 1965 717 732 for the study of finite dimensional dynamical systems to find inertial manifolds in the infinite dimensional setting this method involves replacing the first order equation for by the regularized elliptic equation e d p g1 p p a p g2 p p with suitable boundary conditions it is shown that if a satisfies a spectral gap condition then the solutions e of the elliptic equation converge to a weak solution of 0 as e 0 furthermore m graph is an invariant manifold for the given dynamical system

attractors and inertial manifolds for finite difference approximations of the complex ginzburg landau equation a semidiscrete spatial finite difference approximation and two fully discrete finite difference approximations to the complex ginzburg landau equation are considered in this paper the existence of an inertial manifold is proved inside a discrete h1 absorbing ball for the semi discrete approximation by showing that certain spectral properties hold for the linear operator and certain lipschitz properties hold for the nonlinear term convergence of the true and discrete inertial manifolds is then shown by considering the contraction mappings used to construct the inertial manifolds a fully implicit scheme is shown to form a continuous semigroup in a discrete l2 space and absorbing balls of radii independent of the spatial and temporal mesh sizes in discrete l2 and h1 spaces are constructed existence of a global attractor follows furthermore the existence of an inertial manifold is proved by showing that certain spectral and lipschitz properties hold for a semi implicit scheme existence of absorbing balls in the discrete space l2 of radii independent of the spatial and temporal mesh is proved existence of a global attractor follows

on a criterion for locating stable stationary solutions to the navier stokes equations on donne une estimation superieure uniforme explicite a la borne de constantin foias ternam et on donne une forme applicable explicite aux conditions suffisantes on considere seulement le cas a 2 dimensions

postprocessing the galerkin method a novel approach to approximate inertial manifolds a postprocess of the standard galerkin method for the discretization of dissipative equations is presented the postprocessed galerkin method uses the same approximate inertial manifold phi app to approximate the high wave number modes of the solution as in the nonlinear galerkin nlg method however in this postprocessed galerkin method the value of phi app is calculated only once after the time integration of the standard galerkin method is completed contrary to the nlg in which phi app evolves with time and affects the time evolution of the lower wave number modes the postprocessed galerkin method which is much cheaper to implement computationally than the nlg is shown in the case of fourier modes to possess the same rate of convergence accuracy as the simplest version of the nlg which is based on either the foias manley temam approximate inertial manifold or the euler galerkin approximate inertial manifold this is proved for some problems in one and two spatial dimensions including the navier stokes equations under periodic boundary conditions the advantages of postprocessing that we present here apply not only to the standard galerkin method but also to the computationally more efficient pseudospectral method

on approximate inertial manifolds for two and three dimensional turbulent flows abstract in this paper we present some results concerning finite dimensional analytic manifolds that approximate the global attractor and the structure of the small eddies for the navier stokes equations under periodic boundary conditions we show that the smoother the external force the better the approximation

an approximate inertial manifolds approach to postprocessing the galerkin method for the navier stokes equation in a recent paper we have introduced a postprocessing procedure for the galerkin method for dissipative evolution partial differential equations with periodic boundary conditions the postprocessing technique uses approximate inertial manifolds to approximate the high modes the small scale components in the exact solutions in terms of the galerkin approximations which in this case play the role of the lower modes large scale components this procedure can be seen as a defect correction technique but contrary to standard procedures the correction is computed only when the time evolution is completed here we extend these results to more realistic boundary conditions specifically we study in detail the two dimensional navier stokes equations subject to homogeneous nonslip dirichlet boundary conditions we also discuss other equations such as reaction diffusion systems and the cahn hilliard equations

analysis of the time reversal operator for scatterers of finite size recently it was shown that the time reversal operator for a single small spherical scatterer could have up to four distinguishable eigenstates chambers and gautesen j acoust soc am 109 2616 2624 2001 in this paper that analysis is generalized for scatterers of arbitrary shape and larger size it is shown that the time reversal operator may have an indefinitely large number of distinguishable eigenstates with the exact number depending on the nature of the scatterer and the geometry of the time reversal mirror in addition the case of a multiple number of well separated scatterers is investigated with the result that the total spectrum is the direct combination of the eigenstates associated with each scatterer as an example the singular value spectrum of the time reversal operator for a linear array is calculated explicitly for bubbles and hard rubber spheres of finite size both resonance peaks and apparent crossing points can be observed in the spectrum as the size of the scatterer increases

decomposition of the time reversal operator detection and selective focusing on two scatterers the decomposition of the time reversal operator dort method is a selective detection and focusing technique using an array of transmit receive transducers it relies on the theory of iterative time reversal mirrors which was presented by prada et al c prada j l thomas and m fink j acoust soc am 97 62 71 1995 the time reversal operator was defined as k k where is the frequency means complex conjugate and k is the transfer matrix of the array of l transducers insonifying a time invariant scattering medium it was shown that this time reversal operator can be diagonalized and that for ideally resolved scatterers of different reflectivities each of its eigenvectors of nonzero eigenvalue provides the phase law to be applied to the transducers in order to focus on one of the scatterers the dort method consists in determining these eigenvectors and using them for the selective focusing this paper presents a complete analysis of this method in the case of two scatterers the

feature based watermarking using watermark template match this paper presents a robust digital image watermarking scheme using feature point detection and watermark template match a scale interactive model based filter is used to extract the feature points of original image based on which a watermark template is constructed and embedded adaptively into the local region of these points watermark decision is made by computing the statistical correlation between the watermark and the embedded region because the proposed feature detection is robust against jpeg compression filtering noise addition and geometric distortions the proposed watermarking scheme can achieve good performance against these attacks and experimental results also demonstrate the superiority

robust watermarking against geometric attacks using partial calculation of radial moments and interval phase modulation this paper presents a new image watermarking scheme which is blind and robust against geometric attacks the proposed algorithm is based on the features of radial moments in this algorithm the radial moments were first computed and then the watermark was embedded into the differential phase of various blocks of the original image using a special type of psk modulation called interval phase modulation ipm in order to embed the watermark into the phase of moments a particular method namely the partial calculation of moments was utilized for computation the implementation results show the improvement in the robustness and quality of the watermarked images in comparison with other methods

persistence of invariant sets for dissipative evolution equations we show that results concerning the persistence of invariant sets of ordinary differential equations under perturbation may be applied directly to a certain class of partial differential equations our framework is particularly well suited to encompass numerical approximations of these partial differential equations specifically we show that for a class of pdes with ac 1 inertial form certain natural numerical approximations possess an inertial form close to that of the underlying pde in thec 1 norm

multiple scattering between two elastic cylinders and invariants of the time reversal operator theory and experiment the decomposition of the time reversal operator method is an ultrasonic method based on the analysis of the array response matrix used for detection and characterization the eigenvalues and the eigenvectors of the time reversal operator equivalent to the singular values and the singular vectors of the array response matrix provide information on the localization and nature of scatterers in the insonified medium here the eigenmodes of the time reversal operator are studied for two elastic cylinders the effects of multiple scattering and anisotropic scattering are considered analytical expressions for the singular values are established within the isotropic scattering approximation then the comparison with a complete model is presented putting in evidence the importance of the anisotropy of the scattering experiments carried out at central frequency 1 5mhz on 0 25mm diameter nylon and copper cylinders embedded in water confirm the theory in particular the small cylinder limit and the effect o

estimating the number of asymptotic degrees of freedom for nonlinear dissipative systems we show that the long time behavior of the projection of the exact solutions to the navier stokes equations and other dissipative evolution equations on the finite dimensional space of interpolant polynomials determines the long time behavior of the solution itself provided that the spatial mesh is fine enough we also provide an explicit estimate on the size of the mesh moreover we show that if the evolution equation has an inertial manifold then the dynamics of the evolution equation is equivalent to the dynamics of the projection of the solutions on the finite dimensional space spanned by the approximating polynomials our results suggest that certain numerical schemes may capture the essential dynamics of the underlying evolution equation

quickly tracing detection for spread spectrum watermark based on effect estimation of the affine transform recently watermarking synchronization and spread spectrum watermarking schemes have become two interesting new focuses of study in this paper we propose a method based on the synchronization pre estimation in order to resist geometric attacks first we utilize the global features by testing them against translation rotation and scaling and present a simple method to estimate the geometric transform kernel of the two dimensional gray image maps applying some correlative barycenters to the original are produced that can accurately reflect the affine transform feature of the image furthermore unknown variables existing in the kernel of the transform are calculated secondly the watermark is directly embedded in the spatial domain watermarking tracing is well performed on the watermarked image instead of performing an inverse geometrical transform on it experimental results show that the proposed scheme can work well under several kinds of geometrical attacks

nonlinear galerkin methods this article presents a new method of integrating evolution differential equations the non linear galerkin method that is well adapted to the long term integration of such equations while the usual galerkin method can be interpreted as a projection of the considered equation on a linear space the methods considered here are related to the projection of the equation on a nonlinear manifold from the practical point of view some terms have been identified as small and sometimes but not always disregarded

a phase and space coherent direct imaging method a direct imaging algorithm for point and extended targets is presented the algorithm is based on a physical factorization of the response matrix of a transducer array the factorization is used to transform a passive target problem to an active source problem and to extract principal components tones in a phase consistent way the multitone imaging function can superpose multiple tones spatial diversity aperture of the array and frequencies bandwidth of the probing signal based on phase coherence the method is a direct imaging algorithm that is simple and efficient since no forward solver or iteration is needed robustness of the algorithm with respect to noise is demonstrated via numerical examples