a compact fourth order in space energy preserving method for riesz space fractional nonlinear wave equations in this work we investigate numerically a nonlinear hyperbolic partial differential equation with space fractional derivatives of the riesz type the model under consideration generalizes various nonlinear wave equations including the sine gordon and the nonlinear klein gordon models the system considered in this work is conservative when homogeneous dirichlet boundary conditions are imposed motivated by this fact we propose a finite difference method based on fractional centered differences that is capable of preserving the discrete energy of the system the method under consideration is a nonlinear implicit scheme which has various numerical properties among the most interesting numerical features we show that the methodology is consistent of second order in time and fourth order in space moreover we show that the technique is stable and convergent some numerical simulations show that the method is capable of preserving the energy of the discrete system this characteristic of the technique is in obvious agreement with the properties of its continuous counterpart

pade numerical schemes for the sine gordon equation abstract the sine gordon equation turn up in several problems in science and engineering although it is integrable in practical applications its numerical solution is powerful and versatile four novel implicit finite difference methods based on q s pade approximations with q s th order in space have been developed and analyzed for this equation all share the same treatment for the nonlinearity and integration in time concretely 0 4 2 2 2 4 and 4 4 pade methods additionally the energy conserving strauss vazquez scheme has been considered in a 0 2 pade implementation these methods have been compared among them for both the kink antikink and breather solutions in terms of global error computational cost and energy conservation the 0 4 and 2 4 pade methods are the most cost effective ones for small and large global error respectively our results indicate that spatial order of accuracy is more relevant to effectiveness of a method than energy conservation even in very long time integrations

a structure preserving method for the distribution of the first hitting time to a moving boundary for some gaussian processes abstract in this work we consider a model for the first hitting time of a moving boundary problem associated to some stochastic processes in addition to a gaussian component the model investigated in this manuscript includes a general deterministic source in either case the coefficients of the deterministic and the stochastic terms are general functions with suitable analytical properties that guarantee that the process under investigation possesses continuous paths as the cornerstone of this manuscript we establish that the cumulative distribution of probability of the first hitting time is governed by a deterministic advection diffusion partial differential equation subject to initial boundary data for which the exact solution is known only in certain specific scenarios motivated by these limitations we propose a crank nicolson discretization of the deterministic model which is capable of preserving the main structural features of probability distributions namely the non negativity the boundedness from above by 1 and the monotonicity to guarantee the preservation of those properties relatively flexible conditions on the parameters need to be imposed additionally we also prove that our scheme is a consistent and unconditionally stable and convergent technique which has second order of convergence some illustrative simulations demonstrate that the order of convergence is indeed quadratic and the comparisons against the known exact solutions establish that the method preserves the same structural properties of the relevant solutions

positivity preserving nonstandard finite difference schemes for cross diffusion equations in biosciences we design nonstandard finite difference nsfd schemes which are unconditionally dynamically consistent with respect to the positivity property of solutions of cross diffusion equations in biosciences this settles a problem that was open for quite some time the study is done in the setting of three concrete and highly relevant cross diffusion systems regarding tumor growth convective predator prey pursuit and evasion model and reaction diffusion chemotaxis model it is shown that nsfd schemes used for classical reaction diffusion equations such as the fisher equation for which the solutions enjoy the positivity property are not appropriate for cross diffusion systems the reliable nsfd schemes are therefore obtained by considering a suitable implementation on the cross diffusive term of mickens rule of nonlocal approximation of nonlinear terms apart from his rule of complex denominator function of discrete derivatives we provide numerical experiments that support the theory as well as the power of the nsfd schemes over the standard ones in the case of the cancer growth model we demonstrate computationally that our nsfd schemes replicate the property of traveling wave solutions of developing shocks observed in marchant et al 2000

new conservative schemes with discrete variational derivatives for nonlinear wave equations new conservative finite difference schemes for certain classes of nonlinear wave equations are proposed the key tool there is discrete variational derivative by which discrete conservation property is realized a similar approach for the target equations was recently proposed by furihata but in this paper a different approach is explored where the target equations are first transformed to the equivalent system representations which are more natural forms to see conservation properties applications for the nonlinear klein gordon equation and the so called good boussinesq equation are presented numerical examples reveal the good performance of the new schemes

analysis of four numerical schemes for a nonlinear klein gordon equation we compare the properties of four explicit finite difference schemes used to integrate the nonlinear klein gordon equation f t t f x x f f 0 it turns out that the energy conserving scheme is the most suitable to study the long time behavior of the solutions the same result is found for the special case of no spatial dependence

numerical solution of a nonlinear wave equation in polar coordinates we study a finite element scheme and a difference scheme for the radial solutions of a nonlinear klein gordon equation

two energy conserving numerical schemes for the sine gordon equation two explicit conservative numerical schemes for the sine gordon equation are proposed their stability and convergence are proved numerical simulation of a sine gordon soliton shows that the new schemes are very accurate and fast

a filter bank for the directional decomposition of images theory and design the authors introduce a directionally oriented 2 d filter bank with the property that the individual channels may be critically sampled without loss of information the passband regions of the component filters are wedge shaped and thus provide directional information it is shown that these filter bank outputs may be maximally decimated to achieve a minimum sample representation in a way that permits the original signal to be exactly reconstructed the authors discuss the theory for directional decomposition and reconstruction in addition implementation issues are addressed where realizations based on both recursive and nonrecursive filters are considered

variational integrators and the finite element method based on the finite element method discretizations of lagrangians in multisymplectic field theory are presented in this paper in particular we obtain discrete lagrangians of high order the corresponding variational integrators are constructed the convergence of the variational integrators is discussed numerical experiments are also reported

general tensor discriminant analysis and gabor features for gait recognition traditional image representations are not suited to conventional classification methods such as the linear discriminant analysis lda because of the undersample problem usp the dimensionality of the feature space is much higher than the number of training samples motivated by the successes of the two dimensional lda 2dlda for face recognition we develop a general tensor discriminant analysis gtda as a preprocessing step for lda the benefits of gtda compared with existing preprocessing methods such as the principal components analysis pca and 2dlda include the following 1 the usp is reduced in subsequent classification by for example lda 2 the discriminative information in the training tensors is preserved and 3 gtda provides stable recognition rates because the alternating projection optimization algorithm to obtain a solution of gtda converges whereas that of 2dlda does not we use human gait recognition to validate the proposed gtda the averaged gait images are utilized for gait representation given the popularity of gabor function based image decompositions for image understanding and object recognition we develop three different gabor function based image representations 1 gabord is the sum of gabor filter responses over directions 2 gabors is the sum of gabor filter responses over scales and 3 gaborsd is the sum of gabor filter responses over scales and directions the gabord gabors and gaborsd representations are applied to the problem of recognizing people from their averaged gait images a large number of experiments were carried out to evaluate the effectiveness recognition rate of gait recognition based on first obtaining a gabor gabord gabors or gaborsd image representation then using gdta to extract features and finally using lda for classification the proposed methods achieved good performance for gait recognition based on image sequences from the university of south florida usf humanid database experimental comparisons are made with nine state of the art classification methods in gait recognition

a deterministic model for the distribution of the stopping time in a stochastic equation and its numerical solution in this work we consider a stochastic differential equation that generalizes the well known paris equation from fracture of materials the model describes the propagation of cracks on solids and it includes a deterministic summand and a stochastic component in terms of a brownian motion the use of ito s stochastic integral gives an equivalent stochastic integral equation that is further generalized here we note that the probability distribution of the stopping time of the general model satisfies a deterministic diffusion advection partial differential equation for which the solution is known only in a reduced number of particular cases motivated by these analytical results we develop a fast finite difference method to approximate the distribution of the stopping time the method is an explicit exponential like technique that preserves the main features of a probability distribution namely the non negativity the boundedness from above by 1 as well as the spatial monotonicity moreover the method is a monotone technique that is also capable of preserving the temporal monotonicity of the approximations these properties of the proposed methodology are thoroughly established in the present manuscript a continuity condition of the numerical solutions in terms of the initial conditions and the temporal computational parameter is established also together with a limiting property of the methodology when the free parameter tends to infinity for comparison purposes we are providing an implicit and stable discretization of the mathematical model which has a second order of convergence but for which conditions that guarantee the positivity the boundedness and the monotonicity of approximations are not available the numerical simulations obtained with implementations of our techniques show that the explicit method is an efficient scheme that preserves the characteristics of interest non negativity boundedness from above by 1 and monotonicity and that the numerical approximations are in good agreement with the known exact solutions

the tangent approximation to one sided brownian exit densities let p t be the density of the first exit time of a brownian motion over a one sided moving boundary and let p1 t be the density at t of the first exit time over the tangent to the boundary at t when is p1 t a good approximation to p t we investigate this question by means of a new integral equation for p t which makes possible explicit estimates for the error of the approximation

numerical solution for series sine gordon equations using variational method and finite element approximation this paper investigates numerical solutions for several kinds of sine gordon equations using variational method and finite element approximation for the case of one dimension and continuous time a semi discrete algorithm is proposed using gauss legendre quadrature and runge kutta method furthermore the convergence of the algorithm is proved finally several numerical examples are implemented and some simulation results are presented to show the efficiency of the scheme

tension spline method for solution of non linear fisher equation tension spline method is proposed for the non linear fisher equation with initial boundary values the three time level implicit method based on the non polynomial cubic tension spline is developed for the solution of the non linear reaction diffusion equation the method involves the parameters and its order can be increased from o k 2 k 2 h 2 h 2 to o k 2 k 2 h 2 h 4 by an appropriate choice of the parameters the stability of proposed method is analyzed finally numerical results are presented to demonstrate the accuracy and efficiency of this method

the contourlet transform an efficient directional multiresolution image representation the limitations of commonly used separable extensions of one dimensional transforms such as the fourier and wavelet transforms in capturing the geometry of image edges are well known in this paper we pursue a true two dimensional transform that can capture the intrinsic geometrical structure that is key in visual information the main challenge in exploring geometry in images comes from the discrete nature of the data thus unlike other approaches such as curvelets that first develop a transform in the continuous domain and then discretize for sampled data our approach starts with a discrete domain construction and then studies its convergence to an expansion in the continuous domain specifically we construct a discrete domain multiresolution and multidirection expansion using nonseparable filter banks in much the same way that wavelets were derived from filter banks this construction results in a flexible multiresolution local and directional image expansion using contour segments and thus it is named the contourlet transform the discrete contourlet transform has a fast iterated filter bank algorithm that requires an order n operations for n pixel images furthermore we establish a precise link between the developed filter bank and the associated continuous domain contourlet expansion via a directional multiresolution analysis framework we show that with parabolic scaling and sufficient directional vanishing moments contourlets achieve the optimal approximation rate for piecewise smooth functions with discontinuities along twice continuously differentiable curves finally we show some numerical experiments demonstrating the potential of contourlets in several image processing applications

the solution of the two dimensional sine gordon equation using the method of lines the method of lines is used to transform the initial boundary value problem associated with the two dimensional sine gordon equation in two space variables into a second order initial value problem the finite difference methods are developed by replacing the matrix exponential term in a recurrence relation with rational approximants the resulting finite difference methods are analyzed for local truncation error stability and convergence to avoid solving the nonlinear system a predictor corrector scheme using the explicit method as predictor and the implicit as corrector is applied numerical solutions for cases involving the most known from the bibliography line and ring solitons are given

dual geometric neighbor embedding for image super resolution with sparse tensor neighbors embedding ne technology has proved its efficiency in single image super resolution sisr however image patches do not strictly follow the similar structure in the low resolution and high resolution spaces consequently leading to a bias to the image restoration in this paper considering that patches are a set of data with multiview characteristics and spatial organization we advance a dual geometric neighbor embedding dgne approach for sisr in dgne multiview features and local spatial neighbors of patches are explored to find a feature spatial manifold embedding for images we adopt a geometrically motivated assumption that for each patch there exists a small neighborhood in which only the patches that come from the same feature spatial manifold will lie approximately in a low dimensional affine subspace formulated by sparse neighbors in order to find the sparse neighbors a tensor simultaneous orthogonal matching pursuit algorithm is advanced to realize a joint sparse coding of feature spatial image tensors some experiments are performed on realizing a 3x amplification of natural images and the recovered results prove its efficiency and superiority to its counterparts

collective coordinates and length scale competition in spatially inhomogeneous soliton bearing equations perturbed one dimensional integrable i e soliton bearing equations arise in many applied contexts when trying to improve the usually highly idealized description of problems of interest in terms of the purely integrable equations in particular when the assumption of perfect homogeneity is dropped to account for unavoidable impurities or defects perturbations depending on the spatial coordinate must be added to the original equation in this review we use the one dimensional sine gordon sg equation perturbed by a spatially periodic term as a generic paradigm to discuss the main perturbative techniques available for the study of this class of problems to place the work in context we summarize the approaches developed to date and focus on the collective coordinate approach as one of the most useful tools we introduce several versions of this perturbative method and relate them to more involved procedures we analyze in detail the application to the sg equation but the procedure is very general to illustrate this other examples of the application of collective coordinates are briefly revisited in our case study this approach helps us identify perturbative and nonperturbative regimes yielding a very simple picture of the former beyond perturbative calculations the same example of the inhomogeneous sg equation allows us to introduce a phenomenon termed length scale competition which we show to be a rather general mechanism for the appearance of complex spatiotemporal behavior in perturbed integrable systems as other instances discussed in the review show such nonperturbative results are obtained by means of numerical simulations of the full perturbed problem numerical linear stability analysis is also used to clarify the origins of the instability originated by this competition to complement our description of the techniques employed in these studies computational details of our numerical simulations are also included finally the paper closes with a discussion of the above ideas and a speculative outlook on general questions concerning the interplay of nonlinearity with disorder

conservative numerical methods for x f x abstract two distinctly different numerical methods are developed for solving the conservative initial value problem x f x x o dot x o both methods conserve exactly the same total energy as does the given differential equation computer examples are described and

a structure preserving method for a class of nonlinear dissipative wave equations with riesz space fractional derivatives abstract in this manuscript we consider an initial boundary value problem governed by a 1 1 dimensional hyperbolic partial differential equation with constant damping that generalizes many nonlinear wave equations from mathematical physics the model considers the presence of a spatial laplacian of fractional order which is defined in terms of riesz fractional derivatives as well as the inclusion of a generic continuously differentiable potential it is known that the undamped regime has an associated positive energy functional and we show here that it is preserved throughout time under suitable boundary conditions to approximate the solutions of this model we propose a finite difference discretization based on fractional centered differences some discrete quantities are proposed in this work to estimate the energy functional and we show that the numerical method is capable of conserving the discrete energy under the same boundary conditions for which the continuous model is conservative moreover we establish suitable computational constraints under which the discrete energy of the system is positive the method is consistent of second order and is both stable and convergent the numerical simulations shown here illustrate the most important features of our numerical methodology

biorthogonal bases of compactly supported wavelets orthonormal bases of compactly supported wavelet bases correspond to subband coding schemes with exact reconstruction in which the analysis and synthesis filters coincide we show here that under fairly general conditions exact reconstruction schemes with synthesis filters different from the analysis filters give rise to two dual riesz bases of compactly supported wavelets we give necessary and sufficient conditions for biorthogonality of the corresponding scaling functions and we present a sufficient condition for the decay of their fourier transforms we study the regularity of these biorthogonal bases we provide several families of examples all symmetric corresponding to linear phase filters in particular we can construct symmetric biorthogonal wavelet bases with arbitrarily high preassigned regularity we also show how to construct symmetric biorthogonal wavelet bases close to a nonsymmetric orthonormal basis

multisymplectic geometry variational integrators and nonlinear pdes this paper presents a geometric variational approach to continuous and discrete mechanics and field theories using multisymplectic geometry we show that the existence of the fundamental geometric structures as well as their preservation along solutions can be obtained directly from the variational principle in particular we prove that a unique multisymplectic structure is obtained by taking the derivative of an action function and use this structure to prove covariant generalizations of conservation of symplecticity and noether s theorem natural discretization schemes for pdes which have these important preservation properties then follow by choosing a discrete action functional in the case of mechanics we recover the variational symplectic integrators of veselov type while for pdes we obtain covariant spacetime integrators which conserve the corresponding discrete multisymplectic form as well as the discrete momentum mappings corresponding to symmetries we show that the usual notion of symplecticity along an infinite dimensional space of fields can be naturally obtained by making a spacetime split all of the aspects of our method are demonstrated with a nonlinear sine gordon equation including computational results and a comparison with other discretization schemes

numerical simulation of nonlinear schro dinger systems a new conservative scheme we present a new numerical scheme for nonlinear schrodinger type equations the scheme conserves the energy and charge of the systems and it is linearly implicit numerical experiments for several physical problems show that our scheme is stable accurate and efficient

design and analysis of a dissipative scheme to solve a generalized multi dimensional higgs boson equation in the de sitter space time abstract in this work we design a numerically efficient finite difference technique for the solution of a fractional extension of the higgs boson equation in the de sitter space time the model under investigation is a multidimensional equation with riesz fractional derivatives of orders in 0 1 1 2 which considers a generalized potential and a time dependent diffusion factor an energy integral for the mathematical model is readily available and we propose an explicit and consistent numerical technique based on fractional order centered differences with similar hamiltonian properties as the continuous model a fractional energy approach is used then to prove the properties of stability and convergence of the technique for simulation purposes we consider both the classical and the fractional higgs real valued scalar fields in the 3 1 dimensional de sitter space time and find results qualitatively similar to those available in the literature the present work is the first paper to report on a hamiltonian discretization of the higgs boson equation both fractional and non fractional in the de sitter space time and its numerical analysis more precisely the present manuscript is the first paper of the literature in which a dissipation preserving scheme to solve the multi dimensional fractional higgs boson equation in the de sitter space time is proposed and thoroughly analyzed indeed it is worth pointing out that previous efforts used techniques based on the runge kutta method or discretizations that did not preserve the dissipation nor were rigorously analyzed

on spectral geometry of minimal surfaces in ⁿ by employing the standard isometric imbedding of cpn into the euclidean space a classification theorem for full minimal 2 type surfaces in cpn that are not holomorphic is given all such compact minimal surfaces are either totally real minimal surfaces in cp2 or totally real superminimal surfaces in cp3 and cp4 in the latter case they are locally unique moreover some eigenvalue inequalities for compact minimal surfaces of cpn with constant kaehler angle are shown

a numerically efficient hamiltonian method for fractional wave equations abstract in this work we consider a partial differential equation that extends the well known wave equation the model under consideration is a multidimensional equation which includes the presence of both a damping term and a fractional laplacian of the riesz type homogeneous dirichlet boundary conditions on a closed and bounded spatial interval are considered in this work the mathematical model has a fractional hamiltonian which is conserved when the damping coefficient is equal to zero and dissipated otherwise motivated by these facts we propose a finite difference method to approximate the solutions of the continuous model the method is an implicit scheme which is based on the use of fractional centered differences to approximate the spatial fractional derivatives of the model a discretized form of the hamiltoninan is also proposed in this work and we prove analytically that the method is capable of preserving dissipating the discrete energy when the continuous model preserves dissipates the energy we establish rigorously the properties of consistency stability and convergence of the method and provide some a priori bounds for the numerical solutions moreover we prove the existence and the uniqueness of the numerical solutions as well as the unconditional stability of the method in the linear regime some computer simulations that assess the capability of the method to preserve dissipate the energy are carried out for illustration purposes

implementation of meshless lbie method to the 2d non linear sg problem in this paper the meshless local boundary integral equation lbie method for numerically solving the non linear two dimensional sine gordon sg equation is developed the method is based on the lbie with moving least squares mls approximation for the mls nodal points spread over the analyzed domain are utilized to approximate the interior and boundary variables the approximation functions are constructed entirely using a set of scattered nodes and no element or connectivity of the nodes is needed for either the interpolation or the integration purposes a time stepping method is employed to deal with the time derivative and a simple predictor corrector scheme is performed to eliminate the non linearity a brief discussion is outlined for numerical integrations in the proposed algorithm some examples involving line and ring solitons are demonstrated and the conservation of energy in undamped sg equation is investigated the final numerical results confirm the ability of method to deal with the unsteady non linear problems in large domains copyright 2009 john wiley sons ltd

adaptive image data hiding in edges using patched reference table and pair wise embedding technique reference table rt based embedding method embeds secret digits into pixel pairs under the guidance of a reference table most of the existing rt based methods either require elaborate conversions among different bases or have limited embedding capacity in this paper we use a patched reference table prt as a guide and propose a prt method to provide a better image quality and extendable embedding capacity we also exploit the concept of pixel value differencing pvd and propose another method prt pvd in the traditional pvd based methods the shape of the difference histograms of the stego images is significantly altered and thus vulnerable to some steganalyzers prt pvd adopts the prt method and uses a specially designed embedding sequence to preserve the difference histogram shape experimental results reveal that the proposed prt and prt pvd methods not only have better embedding efficiency over the existing methods but also are robust to detection by modern steganalysis tools

numerical solution of one dimensional sine gordon equation using high accuracy multiquadric quasi interpolation abstract in this paper we propose a numerical scheme to solve one dimensional sine gordon equation related to many scientific research topics by using high accuracy multiquadric quasi interpolation we use the derivatives of a multiquadric quasi interpolant to approximate the spatial derivatives and a finite difference to approximate the temporal derivative the advantages of the scheme are that it is meshfree and in each time step only a multiquadric quasi interpolant is employed so that the algorithm is very easy to implement the accuracy of our scheme is demonstrated by some test problems

comparisons between sine gordon and perturbed nonlinear schrodinger equations for modeling light bullets beyond critical collapse abstract the sine gordon sg equation and perturbed nonlinear schrodinger nls equations are studied numerically for modeling the propagation of two space dimensional 2d localized pulses the so called light bullets in nonlinear dispersive optical media we begin with the 2 1 sg equation obtained as an asymptotic reduction in the two level dissipationless maxwell bloch system followed by the review on the perturbed nls equation in 2d for sg pulse envelopes which is globally well posed and has all the relevant higher order terms to regularize the collapse of standard critical cubic focusing nls the perturbed nls is approximated by truncating the nonlinearity into finite higher order terms undergoing focusing defocusing cycles efficient semi implicit sine pseudospectral discretizations for sg and perturbed nls are proposed with rigorous error estimates numerical comparison results between light bullet solutions of sg and perturbed nls as well as critical nls are reported which validate that the solution of the perturbed nls as well as its finite term truncations are in qualitative and quantitative agreement with the solution of sg for the light bullets propagation even after the critical collapse of cubic focusing nls in contrast standard critical nls is in qualitative agreement with sg only before its collapse as a benefit of such observations pulse propagations are studied via solving the perturbed nls truncated by reasonably many nonlinear terms which is a much cheaper task than solving sg equation directly

discrete singular convolution for the prediction of high frequency vibration of plates theoretical analysis of high frequency vibrations is indispensable in a variety of engineering designs much effort has been made on this subject in the past few decades however there is no single technique which can be applied with confidence to various engineering structures for high frequency predictions at present this paper introduces a novel computational approach the discrete singular convolution dsc algorithm for high frequency vibration analysis of plate structures square plates with six distinct boundary conditions are considered to validate the proposed method a completely independent approach the levy method is employed to provide exact solutions for a comparison the proposed method is also validated by convergence studies we demonstrate the ability of the dsc algorithm for high frequency vibration analysis by providing extremely accurate frequency parameters for plates vibrating in the first 5000 modes

discrete time orthogonal spline collocation methods for the nonlinear schrodinger equation with wave operator in this paper discrete time orthogonal spline collocation schemes are proposed for the nonlinear schrodinger equation with wave operator these schemes are constructed by using orthogonal spline collocation approaches combined with finite difference methods the conservative property the convergence and the stability of these methods are theoretically analyzed and also verified by extensive numerical experiments in addition some interesting phenomena which require further theoretical analysis are discussed numerically

fractal analysis for reduced reference image quality assessment in this paper multifractal analysis is adapted to reduced reference image quality assessment rr iqa a novel rr qa approach is proposed which measures the difference of spatial arrangement between the reference image and the distorted image in terms of spatial regularity measured by fractal dimension an image is first expressed in log gabor domain then fractal dimensions are computed on each log gabor subband and concatenated as a feature vector finally the extracted features are pooled as the quality score of the distorted image using ell 1 distance compared with existing approaches the proposed method measures image quality from the perspective of the spatial distribution of image patterns the proposed method was evaluated on seven public benchmark data sets experimental results have demonstrated the excellent performance of the proposed method in comparison with state of the art approaches

finite difference schemes for nonlinear wave equation that inherit energy conservation property abstract we propose two general finite difference schemes that inherit energy conservation property from nonlinear wave equations such as the nonlinear klein gordon equation nlkge one of proposed schemes is implicit and another is explicit many studies exist on fdss that inherit energy conservation property from nlkge and we can derive all of their schemes from the proposed general schemes in this paper the most important feature of our procedure is a rigorous discretization of variational derivatives using summation by parts which implies that the inherited properties are satisfied exactly because of this the derived schemes are expected to be numerically stable and yield solutions converging to pde solutions we make new fdss for fermi pasta ulam equation string vibration equation shimoji kawai equation ske and ebihara equation and verify numerically the inheritance of the energy conservation property for nlkge and ske

analysis of some new conservative schemes for nonlinear schrodinger equation with wave operator abstract some new conservative finite difference schemes are presented for an initial boundary value problem of schrodinger equation with wave operator they have the advantages that there are some discrete energies which are conserved respectively the existence of the solution of the finite difference schemes are proved by leray schauder fixed point theorem and the uniqueness stability and convergence of difference solutions with order o h2 2 are proved in the energy norm results of numerical experiment demonstrate the efficiency of the new scheme

multilevel augmentation methods for solving the sine gordon equation in this paper we develop the multilevel augmentation method for solving nonlinear operator equations of the second kind and apply it to solving the one dimensional sine gordon equation we first give a general setting of the multilevel augmentation method for solving the second kind nonlinear operator equations and prove that the multilevel augmentation method preserves the optimal convergence order of the projection method while reducing computational cost significantly then we describe the semi discrete scheme and the fully discrete scheme based on multiscale methods for solving the sine gordon equation and apply the multilevel augmentation method to solving the discrete equation a complete analysis for convergence order is proposed finally numerical experiments are presented to confirm the theoretical results and illustrate the efficiency of the method

a new conservative finite difference scheme for the rosenau equation a conservative difference scheme is given for the kdv like rosenau equation the unique solvability of numerical solutions is shown a priori bound convergence and stability of the difference scheme are proved

dsc analysis of rectangular plates with non uniform boundary conditions this paper introduces the discrete singular convolution dsc for the vibration analysis of rectangular plates with non uniform and combined boundary conditions a systematic scheme is proposed for the treatment of boundary conditions required in the proposed approach the validity of the dsc approach for plate vibration is tested by using a large number of numerical examples that have a combination of simply supported clamped and transversely supported with non uniform elastic rotational restraint edges the present results are in excellent agreement with those in the literature

a distortion measure for blocking artifacts in images based on human visual sensitivity a visual model that gives a distortion measure for blocking artifacts in images is presented given the original and reproduced image as inputs the model output is a numerical value that quantifies the visibility of blocking error in the reproduced image the model is derived based on the human visual sensitivity to horizontal and vertical edge artifacts that result from blocking psychovisual experiments have been carried out to measure the visual sensitivity to these artifacts in the experiments typical edge artifacts are shown to subjects and the sensitivity to them is measured with the variation of background luminance background activity edge length and edge amplitude synthetic test patterns are used as background images in the experiments the sensitivity measures thus obtained are used to estimate the model parameters the final model is tested on real images and the results show that the error visibility predicted by the model correlates well with the subjective ranking

on minimal surfaces in a kahler manifold of constant holomorphic sectional curvature this paper studies minimal surfaces in kshler manifolds of constant holomorphic sectional curvature using the technique of the moving frame in particular we provide a classification of the minimal two spheres in cpst complex projective sf space equipped with the fubini study metric this classification can be described as follows to each holomorphic curve in c pt1 classically there is associated a particular framing of c l l called the frenet frame each element of the frenet frame induces a minimal surface in cp the classification theorem states that all minimal surfaces of topological type of the two sphere occur in this manner the theorem is proved using holomorphic differentials that occur naturally on minimal surfaces in kshler manifolds of constant holomorphic sectional curvature together with the riemann roch theorem

derivation of the discrete conservation laws for a family of finite difference schemes abstract we present conservative schemes in finite differences applied to nonlinear odes and nonlinear klein gordon schrodinger and dirac field equations a systematic approach is used and an explicit derivation of the corresponding conservation laws is given

finite difference discretization of the extended fisher kolmogorov equation in two dimensions approximate solutions are considered for the extended fisher kolmogorov efk equation in two space dimension with dirichlet boundary conditions by a crank nicolson type finite difference scheme a priori bounds are proved using lyapunov functional further existence uniqueness and convergence of difference solutions with order o h 2 k 2 in the l norm are proved numerical results are also given in order to check the properties of analytical solutions

an implicit numerical method for the two dimensional fractional percolation equation in this paper an implicit numerical method for the two dimensional fractional percolation equation without the assumption of continued and rigid body motion is proposed consistency stability and convergence of the implicit finite difference method are established finally some numerical examples are given the numerical results demonstrate the effectiveness of the theoretical analysis

a compact finite difference scheme for the nonlinear schrodinger equation with wave operator abstract in this paper a compact finite difference scheme is presented for an periodic initial value problem of the nonlinear schrodinger nls equation with wave operator this is a scheme of three levels with a discrete conservation law the unconditional stability and convergence in maximum norm with order o h 4 2 are proved by the energy method a numerical experiment is presented to support our theoretical results

human visual weighted progressive image transmission a progressive image transmission scheme which combines transform coding with the human visual system hvs model is developed the adaptive transform coding of w h chen and c h smith 1977 is utilized to classify an image into four equally populated subblocks based on their ac energies the modulation transfer function mtf of the hvs model is obtained experimentally based on processing a number of test images a simplified technique for incorporating the mtf into the discrete cosine transform dct domain is utilized in the hierarchical image buildup the image is first reconstructed from the dc coefficients of all subblocks further transmission hierarchy of transform coefficients and consequent image buildup are dependent on their hvs weighted variances the hvs weighted reconstructed images are compared to the ones without any weighting at several stages the hvs weighted progressive image transmission results in perceptually higher quality images compared to the unweighted scheme

continuous finite element methods which preserve energy properties for nonlinear problems abstract continuous finite elements are used to develop numerical methods which preserve energy properties for nonlinear ordinary and partial differential equations schemes are constructed that give high orders of accuracy time discretization algorithms for the cahn hilliard klein gordon korteweg de vries and schrodinger equations are presented comparisons are made with existing schemes

reduced reference quality assessment based on the entropy of dwt coefficients of locally weighted gradient magnitudes perceptual image quality assessment iqa attempts to use computational models to estimate the image quality in accordance with subjective evaluations reduced reference iqa rriqa methods make use of partial information or features extracted from the reference image for estimating the quality of distorted images finding a balance between the number of rr features and accuracy of the estimated image quality is essential and important in iqa in this paper we propose a training free low cost rriqa method that requires a very small number of rr features six rr features the proposed rriqa algorithm is based on the discrete wavelet transform dwt of locally weighted gradient magnitudes we apply human visual system s contrast sensitivity and neighborhood gradient information to weight the gradient magnitudes in a locally adaptive manner the rr features are computed by measuring the entropy of each dwt subband for each scale and pooling the subband entropies along all orientations resulting in l rr features one average entropy per scale for an l level dwt extensive experiments performed on seven large scale benchmark databases demonstrate that the proposed rriqa method delivers highly competitive performance as compared with the state of the art rriqa models as well as full reference ones for both natural and texture images the matlab source code of redlog and the evaluation results are publicly available online at https http lab engineering asu edu ivulab software redlog

on the convergence of conservative difference schemes for the 2d generalized rosenau korteweg de vries equation abstract two conservative finite difference schemes for the rosenau kdv equation rkdv in 2d are proposed the first scheme is two level and nonlinear implicit the second scheme is three level and linear implicit existence of its difference solutions has been shown it is proved by the discrete energy method that the two schemes are uniquely solvable unconditionally stable and the convergence is of second order in the uniform norm numerical experiments demonstrate that the schemes are accurate and efficient

on the solution of a generalized higgs boson equation in the de sitter space time through an efficient and hamiltonian scheme abstract the present work is the first paper in the literature to report on a hamiltonian discretization of the fractional higgs boson equation in the de sitter space time and its theoretical analysis more precisely we design herein a numerically efficient finite difference hamiltonian technique for the solution of a fractional extension of the higgs boson equation in the de sitter space time the model under investigation is a multidimensional equation with generalized potential and riesz space fractional derivatives of orders in 1 2 an energy integral for the model is readily available and we propose a nonlinear implicit and consistent numerical technique based on fractional order centered differences with similar hamiltonian properties in the discrete scenario a fractional energy approach is used then to prove the properties of stability and convergence of the technique for simulation purposes we consider both the classical and the fractional higgs real valued scalar fields in the de sitter space time and find results qualitatively similar to those available in the literature for the sake of convenience we provide the matlab code of an alternative linear discretization of the method presented in this work this linear implicit approach is thoroughly analyzed also

weighted curvature preserving pde image filtering method the tensor driven curvature preserving partial differential equation is an outstanding anisotropic diffusion filtering model to effectively preserve image edge well a weighted curvature preserving pde based filtering method is proposed which employ local image directional information to design weight coefficient for different vector fields experimental results indicate that new approach shows superior performance on preserving image edge and curvature geometric structure

universal blind image quality assessment metrics via natural scene statistics and multiple kernel learning universal blind image quality assessment iqa metrics that can work for various distortions are of great importance for image processing systems because neither ground truths are available nor the distortion types are aware all the time in practice existing state of the art universal blind iqa algorithms are developed based on natural scene statistics nss although nss based metrics obtained promising performance they have some limitations 1 they use either the gaussian scale mixture model or generalized gaussian density to predict the nongaussian marginal distribution of wavelet gabor or discrete cosine transform coefficients the prediction error makes the extracted features unable to reflect the change in nongaussianity ng accurately the existing algorithms use the joint statistical model and structural similarity to model the local dependency ld although this ld essentially encodes the information redundancy in natural images these models do not use information divergence to measure the ld although the exponential decay characteristic edc represents the property of natural images that large small wavelet coefficient magnitudes tend to be persistent across scales which is highly correlated with image degradations it has not been applied to the universal blind iqa metrics and 2 all the universal blind iqa metrics use the same similarity measure for different features for learning the universal blind iqa metrics though these features have different properties to address the aforementioned problems we propose to construct new universal blind quality indicators using all the three types of nss i e the ng ld and edc and incorporating the heterogeneous property of multiple kernel learning mkl by analyzing how different distortions affect these statistical properties we present two universal blind quality assessment models nss global scheme and nss two step scheme in the proposed metrics 1 we exploit the ng of natural images using the original marginal distribution of wavelet coefficients 2 we measure correlations between wavelet coefficients using mutual information defined in information theory 3 we use features of edc in universal blind image quality prediction directly and 4 we introduce mkl to measure the similarity of different features using different kernels thorough experimental results on the laboratory for image and video engineering database ii and the tampere image database2008 demonstrate that both metrics are in remarkably high consistency with the human perception and overwhelm representative universal blind algorithms as well as some standard full reference quality indexes for various types of distortions

a fourth order avf method for the numerical integration of sine gordon equation abstract in this paper a new scheme which has energy preserving property is proposed for solving the sine gordon equation with periodic boundary conditions it is obtained by the fourier pseudo spectral method and the fourth order average vector field method in numerical experiments the new high order energy preserving scheme is compared with a number of existing numerical schemes for the one dimensional sine gordon equation the new high order energy preserving scheme for the two dimensional sine gordon equation is also investigated numerical results are addressed to further illustrate the conservation of energy and the evolutional behaviors of solitons

superconvergence of the local discontinuous galerkin method for the sine gordon equation in one space dimension abstract in this paper we present superconvergence results for the local discontinuous galerkin ldg method for the sine gordon nonlinear hyperbolic equation in one space dimension we identify a special numerical flux and a suitable projection of the initial conditions for the ldg scheme for which the l 2 norm of the ldg solution and its spatial derivative are of order p 1 when piecewise polynomials of degree at most p are used our numerical experiments demonstrate optimal order of convergence we further prove superconvergence toward particular projections of the exact solutions more precisely we prove that the ldg solution and its spatial derivative are o h p 3 2 super close to particular projections of the exact solutions while computational results show higher o h p 2 convergence rate our analysis is valid for arbitrary regular meshes and for p p polynomials with arbitrary p 1 numerical experiments validating these theoretical results are presented

finite difference method to solve maxwell s equations for soliton propagation we present a finite difference fd scheme for the nonlinear maxwell s equations describing one dimensional scalar optical soliton propagation in polarization preserving nonlinear dispersive media the existence of a discrete analog of the underlying continuous energy conservation law is shown to play a central role in the global accuracy of the scheme and a proof of its generalized nonlinear stability using energy methods is given numerical simulations of initial fundamental second and third order hyperbolic secant ultra short soliton pulses of full width at half peak intensity equal to 25 7 fs fwhm containing as few as four and eight optical carrier cycles confirm the stability accuracy and efficiency of the algorithm the decay of such solitons under the combined effects of higher order dispersion and self steepening is clearly evidenced

a linearly implicit energy preserving exponential integrator for the nonlinear klein gordon equation abstract in this paper we generalize the exponential energy preserving integrator proposed in the recent paper siam j sci comput 38 2016 a1876 a1895 for conservative systems which now becomes linearly implicit by further utilizing the idea of the scalar auxiliary variable approach comparing with the original exponential energy preserving integrator which usually leads to a nonlinear algebraic system our new method only involves a linear system with a constant coefficient matrix taking the nonlinear klein gordon equation and the nonlinear schrodinger equation for examples we derive the concrete energy preserving schemes and demonstrate their high efficiency through numerical experiments

the laplacian pyramid as a compact image code we describe a technique for image encoding in which local operators of many scales but identical shape serve as the basis functions the representation differs from established techniques in that the code elements are localized in spatial frequency as well as in space pixel to pixel correlations are first removed by subtracting a lowpass filtered copy of the image from the image itself the result is a net data compression since the difference or error image has low variance and entropy and the low pass filtered image may represented at reduced sample density further data compression is achieved by quantizing the difference image these steps are then repeated to compress the low pass image iteration of the process at appropriately expanded scales generates a pyramid data structure the encoding process is equivalent to sampling the image with laplacian operators of many scales thus the code tends to enhance salient image features a further advantage of the present code is that it is well suited for many image analysis tasks as well as for image compression fast algorithms are described for coding and decoding

on the solution of hyperbolic two dimensional fractional systems via discrete variational schemes of high order of accuracy abstract in this work we consider a general class of damped wave equations in two spatial dimensions the model considers the presence of weyl space fractional derivatives as well as a generic nonlinear potential the system has an associated positive energy functional when damping is not present in which case the model is capable of preserving the energy throughout time meanwhile the energy of the system is dissipated in the damped scenario in this work the weyl space fractional derivatives are approximated through second order accurate fractional centered differences a high order compact difference scheme with fourth order accuracy in space and second order in time is proposed some associated discrete quantities are introduced to estimate the energy functional we prove that the numerical method is capable of conserving the discrete variational structure under the same conditions for which the continuous model is conservative the positivity of the discrete energy of the system is also discussed the properties of consistency solvability stability and convergence of the proposed method are rigorously proved we provide some numerical simulations that illustrate the agreement between the physical properties of the continuous and the discrete models

a conservative numerical scheme for a class of nonlinear schrodinger equation with wave operator in this paper the initial boundary value problem of a class of nonlinear schrodinger equation with wave operator is considered an explicit and efficient finite difference scheme is presented this is a scheme of four levels with a discrete conservative law convergence and stability are proved

the numerical solution of a generalized burgers huxley equation through a conditionally bounded and symmetry preserving method in this article we propose a non standard finite difference scheme to approximate the solutions of a generalized burgers huxley equation from fluid dynamics our numerical method preserves the skew symmetry of the partial differential equation under study and under some analytical constraints of the model constants and the computational parameters involved it is capable of preserving the boundedness and the positivity of the solutions in the linear regime the scheme is consistent to first order in time due partially to the inclusion of a tuning parameter in the approximation of a temporal derivative and to second order in space we compare the results of our computational technique against the exact solutions of some particular initial boundary value problems our simulations indicate that the method presented in this work approximates well the theoretical solutions and moreover that the method preserves the boundedness of solutions within the analytical constraints derived here in the problem of approximating solitary wave solutions of the model under consideration we present numerical evidence on the existence of an optimum value of the tuning parameter of our technique for which a minimum relative error is achieved finally we linearly perturb a steady state solution of the partial differential equation under investigation and show that our simulations still converge to the same constant solution establishing thus robustness of our method in this sense

wavelet based color image compression exploiting the contrast sensitivity function the visual efficiency of an image compression technique depends directly on the amount of visually significant information it retains by visually significant we mean information to which a human observer is most sensitive the overall sensitivity depends on aspects such as contrast color spatial frequency and so forth one important aspect is the inverse relationship between contrast sensitivity and spatial frequency this is described by the contrast sensitivity function csf in compression algorithms the csf can be exploited to regulate the quantization step size to minimize the visibility of compression artifacts existing csf implementations for wavelet based image compression use the same quantization step size for a large range of spatial frequencies this is a coarse approximation of the csf this paper presents two new techniques that implement the csf at significantly higher precision adapting even to local variations of the spatial frequencies within a decomposition subband the approaches can be used for luminance as well as color images for color perception three different csfs describe the sensitivity the implementation technique is the same for each color band implemented into the jpeg2000 compression standard the new techniques are compared to conventional csf schemes the proposed techniques turn out to be visually more efficient than previously published methods however the emphasis of this paper is on how the csf can be implemented in a precise and locally adaptive way and not on the superior performance of these techniques

dual sparsity regularized sparse representation for single image super resolution row nonlocal similarity regularization term with l1 norm constraint is explored dual sparsity regularized sparse representation model is presented for sisr iterative shrinkage algorithm is extended to solve dual l1 norm constraints model recently by exploring the column nonlocal similarity prior among the sparse representation coefficients the column nonlocal similarity sparse representation models for solving the ill posed single image super resolution sisr problem are attracting more and more attention however these conventional models consider only the prior among nonlocal similar sparse representation coefficients and fail to consider the prior among all entries or rows of the sparse representation coefficient hence the modeling capability may be limited in fact if a cluster of similar representation coefficients is rearranged into a matrix in the sparse representation coefficient space the nonlocal similarity priors exist both among columns and rows using the row nonlocal similarity prior a row nonlocal similarity regularization term with l1 norm constraint is explored by introducing it to the conventional column nonlocal similarity sparse representation model we present a dual sparsity regularized sparse representation dsrsr model a surrogate function based iterative shrinkage algorithm is introduced to effectively solve the proposed model extensive experiments on sisr demonstrate that the presented model can effectively reconstruct the edge structures and suppress the noise achieving convincing improvement over many state of the art example based methods in terms of psnr ssim and visual quality

a novel approach for the analysis of high frequency vibrations abstract despite much effort in the past few decades the numerical prediction of high frequency vibrations remains a challenging task to the engineering and scientific communities due to the numerical instability of existing computational methods however such prediction is of crucial importance to certain problems of pressing practical concern as pointed out by langley and bardell 1998 the aeronautical journal102 287 297 this paper introduces the discrete singular convolution dsc algorithm for the prediction and analysis of high frequency vibration of structures both a beam and two span plates are employed as test examples to demonstrate the capability of the dsc algorithm for high frequency vibration analysis a completely independent approach the levy method is employed to provide exact solutions for a cross validation of the proposed method the reliability of the dsc results is also validated by convergence studies remarkably extremely accurate and stable results are obtained in this work e g the relative dsc errors for the first 7100 modes of the beam and the first 4500 modes of the two span plates are all

the sine gordon equation in the finite line a rather complete numerical study of the perturbed and nonperturbed sine gordon equation in one dimensional cartesian coordinates and finite domains is presented the numerical study is based on five three point linearly implicit finite difference methods of different spatial accuracy for the unperturbed sge the accuracy of these five methods is found to be very sensitive to the implicitness parameter less sensitive to the spatial order of accuracy and almost no sensitive to the time step for second order accurate temporal discretizations the largest errors of the five methods were found to occur at the front of the soliton solution of the unperturbed sge but the techniques were very accurate for long time computations of the unperturbed sge in both infinite domains and in finite domains upon many collisions of the kinks and antikinks with the boundaries despite the fact that they do not preserve a discrete energy it is shown that the largest values of the kinetic and total energies and the smallest values of the strain and potential energies occur when solitons and antisolitons strike on the boundaries subject to homogeneous neumann conditions and the four energies remain constant between collisions with the boundaries for the malomed s perturbation one of the fronts of the soliton soliton doublet and soliton antisoliton doublet is trapped at one boundary and the other one undergoes a change in amplitude and its front describes a curved trajectory the soliton antisoliton breather oscillates in a damped manner and slowly drifts towards one boundary the soliton antisoliton soliton soliton doublet and soliton antisoliton doublet of the unperturbed sge are robust under kivshar and malomed s perturbations whereas the soliton antisoliton breather loses its integrity becomes a kink antikink pair and then yields a chaotic behaviour in both space and time small amplifications proportional to the first order temporal derivative of the amplitude do not alter substantially the initial dynamics of the soliton antisoliton soliton soliton doublet and soliton antisoliton doublet but their amplitudes exhibit oscillatory behaviour of increasing amplitude at large times however small amplifications cause first a transition from the soliton antisoliton breather to the kink antikink solution a linearized stability analysis of the spatially homogeneous solutions of the unperturbed sge is performed and analytical solutions are obtained by means of the method of separation of variables for both homogeneous dirichlet and neumann boundary conditions and the results show that the solution corresponding to a zero amplitude is oscillatory in both space and time whereas that corresponding to an amplitude equal to p may exhibit exponential or linear growth depending on the length of the domain if either of these growths is present it is shown that the evolution of small initial perturbations may result in homoclinic crossings and chaotic behaviour in both space and time in the absence of perturbations in the sge and the existence of an attractor when perturbations of the malomed s type are present in either case the solution may exhibit certain spatial symmetries or antisymmetries at large times finally the results presented in this paper indicate that the accurate computation of homoclinic orbits of the sge is not only controlled by the spatial accuracy of the numerical method but also by its energy preserving characteristics and perhaps by the number of grid points used in the numerical technique

image quality assessment based on a degradation model we model a degraded image as an original image that has been subject to linear frequency distortion and additive noise injection since the psychovisual effects of frequency distortion and noise injection are independent we decouple these two sources of degradation and measure their effect on the human visual system we develop a distortion measure dm of the effect of frequency distortion and a noise quality measure nqm of the effect of additive noise the nqm which is based on peli s 1990 contrast pyramid takes into account the following 1 variation in contrast sensitivity with distance image dimensions and spatial frequency 2 variation in the local luminance mean 3 contrast interaction between spatial frequencies 4 contrast masking effects for additive noise we demonstrate that the nonlinear nqm is a better measure of visual quality than peak signal to noise ratio psnr and linear quality measures we compute the dm in three steps first we find the frequency distortion in the degraded image second we compute the deviation of this frequency distortion from an allpass response of unity gain no distortion finally we weight the deviation by a model of the frequency response of the human visual system and integrate over the visible frequencies we demonstrate how to decouple distortion and additive noise degradation in a practical image restoration system

boundary element method for a free boundary problem modeling three dimensional tumor growth abstract in the mathematical model of tumor growth the initial boundary surface of the three dimensional tumor domain is known but the tumor domain and its boundary surface change over time in a way that is unknown in advance people are concerned whether the tumor is likely to spread or shrink and how the tumor will change in this article by the boundary element method the free boundary problem in the three dimensional tumor domain will be solved via the integration on a two dimensional boundary surfaces at the expense of singularity in the green s functions we will numerically compute and graphically show the changing boundary surfaces of the three dimensional tumor domain over time we will numerically analyze the trend of tumor growth with varying proliferation rate our numerical approach professor bei hu proposed is new and our numerical experiments contribute to the prediction of tumor growth in clinical medicine

image quality assessment based on multiscale geometric analysis reduced reference rr image quality assessment iqa has been recognized as an effective and efficient way to predict the visual quality of distorted images the current standard is the wavelet domain natural image statistics model wnism which applies the kullback leibler divergence between the marginal distributions of wavelet coefficients of the reference and distorted images to measure the image distortion however wnism fails to consider the statistical correlations of wavelet coefficients in different subbands and the visual response characteristics of the mammalian cortical simple cells in addition wavelet transforms are optimal greedy approximations to extract singularity structures so they fail to explicitly extract the image geometric information e g lines and curves finally wavelet coefficients are dense for smooth image edge contours in this paper to target the aforementioned problems in iqa we develop a novel framework for iqa to mimic the human visual system hvs by incorporating the merits from multiscale geometric analysis mga contrast sensitivity function csf and the weber s law of just noticeable difference jnd in the proposed framework mga is utilized to decompose images and then extract features to mimic the multichannel structure of hvs additionally mga offers a series of transforms including wavelet curvelet bandelet contourlet wavelet based contourlet transform wbct and hybrid wavelets and directional filter banks hwd and different transforms capture different types of image geometric information csf is applied to weight coefficients obtained by mga to simulate the appearance of images to observers by taking into account many of the nonlinearities inherent in hvs jnd is finally introduced to produce a noticeable variation in sensory experience thorough empirical studies are carried out upon the live database against subjective mean opinion score mos and demonstrate that 1 the proposed framework has good consistency with subjective perception values and the objective assessment results can well reflect the visual quality of images 2 different transforms in mga under the new framework perform better than the standard wnism and some of them even perform better than the standard full reference iqa model i e the mean structural similarity index and 3 hwd performs best among all transforms in mga under the framework

two structure preserving doubling like algorithms for obtaining the positive definite solution to a class of nonlinear matrix equation in this paper we present two structure preserving doubling like algorithms for obtaining the positive definite solution of the nonlinear matrix equation x a h x 1 a q where x c n i n is an unknown matrix and q c n i n is a hermitian positive definite matrix we prove that the sequences generated by the algorithms converge to the positive definite solution of the considered matrix equation r quadratically in addition we also present some numerical results to illustrate the behavior of the considered algorithm

the dual reciprocity boundary element method drbem for two dimensional sine gordon equation this paper presents the dual reciprocity boundary element method drbem for solving two dimensional sine gordon sg equation the integral equation formulation employs the fundamental solution of the laplace equation and hence a domain integral arises in the boundary integral equation furthermore the time derivatives are approximated by the time stepping method and the domain integral also appears from these approximations the domain integral is transformed into boundary integral by using the dual reciprocity method drm the linear radial basis function rbf is employed for drm the dynamics of line solitons and ring solitons of circular and elliptic shapes are studied numerical results are presented for some problems involving line and ring solitons to demonstrate the usefulness and accuracy of this approach

mammographic mass segmentation embedding multiple features in vector valued level set in ambiguous regions mammographic mass segmentation plays an important role in computer aided diagnosis systems it is very challenging because masses are always of low contrast with ambiguous margins connected with the normal tissues and of various scales and complex shapes to effectively detect true boundaries of mass regions we propose a feature embedded vector valued contour based level set method with relaxed shape constraint in particular we initially use the contour based level set method to obtain the initial boundaries on the smoothed mammogram as the shape constraint to prevent the contour leaking and meanwhile preserve the radiative characteristics of specific malignant masses afterward we relax the obtained shape constraint by analyzing possible valid regions around the initial boundaries the relaxed shape constraint is then used to design a novel stopping function for subsequent vector valued level set method since texture maps gradient maps and the original intensity map can reflect different characteristics of the mammogram we integrate them together to obtain more accurate segmentation by incorporating the new stopping function into the newly proposed feature embedded vector valued contour based level set method the experimental results suggest that the proposed feature embedded vector valued contour based level set method with relaxed shape constraint can effectively find ambiguous margins of the mass regions comparing against existing active contours methods the new scheme is more effective and robust in detecting complex masses

numerical solution of the sine gordon equation two new difference schemes are proposed for the sine gordon equation they have the advantage that there is a discrete energy which is conserved their stability and convergence is proved also we show some numerical computations using one of these schemes

two classes of finite difference methods for generalized sine gordon equations abstract in this paper we shall study two classes of finite difference methods for the generalized sine gordon equations the convergence and the stability will be studied in detail

nonconforming quadrilateral finite element method for a class of nonlinear sine gordon equations nonconforming quadrilateral finite element method fem of the two dimensional nonlinear sine gordon equation is studied for semi discrete and crank nicolson fully discrete schemes respectively firstly we prove a special feature of a new arbitrary quadrilateral element named modified quasi wilson element i e the consistency error is of order o h 2 h denotes the mesh size in h 1 norm which leads to optimal order error estimate and superclose result with order o h 2 for the semi discrete scheme through a different approach from the existing literature secondly because the consistency error estimate of the new modified quasi wilson element can reach a staggering o h 3 order two orders higher than that of interpolation error the optimal order error estimates of crank nicolson fully discrete scheme are obtained on arbitrary quadrilateral meshes with ritz projection moreover a superclose result in h 1 norm is presented on generalized rectangular meshes by a new technique thirdly the global superconvergence results of h 1 norm for both semi discrete and fully discrete schemes are derived on rectangular meshes with interpolated postprocessing technique finally a numerical test is carried out to verify the theoretical analysis

meshless local petrov galerkin mlpg approximation to the two dimensional sine gordon equation during the past few years the idea of using meshless methods for numerical solution of partial differential equations pdes has received much attention throughout the scientific community and remarkable progress has been achieved on meshless methods the meshless local petrov galerkin mlpg method is one of the truly meshless methods since it does not require any background integration cells the integrations are carried out locally over small sub domains of regular shapes such as circles or squares in two dimensions and spheres or cubes in three dimensions in this paper the mlpg method for numerically solving the non linear two dimensional sine gordon sg equation is developed a time stepping method is employed to deal with the time derivative and a simple predictor corrector scheme is performed to eliminate the non linearity a brief discussion is outlined for numerical integrations in the proposed algorithm some examples involving line and ring solitons are demonstrated and the conservation of energy in undamped sg equation is investigated the final numerical results confirm the ability of proposed method to deal with the unsteady non linear problems in large domains

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed