signal recovery with certain involved convex data fidelity constraints this paper proposes an optimization framework that can efficiently deal with convex data fidelity constraints onto which the metric projections are difficult to compute although such an involved data fidelity constraint is expected to play an important role in signal recovery under non gaussian noise contamination the said difficulty precludes existing algorithms from solving convex optimization problems with the constraint to resolve this dilemma we introduce a fixed point set characterization of involved data fidelity constraints based on a certain computable quasi nonexpansive mapping this characterization enables us to mobilize the hybrid steepest descent method to solve convex optimization problems with such a constraint the proposed framework can handle a variety of involved data fidelity constraints in a unified manner without geometric approximation to them in addition it requires no computationally expensive procedure such as operator inversion and inner loop as applications of the proposed framework we provide image restoration under several types of non gaussian noise contamination with illustrative examples

stability of two soliton collision for nonintegrable gkdv equations we continue our study of the collision of two solitons for the subcritical generalized kdv equations label kdvabs partial t u partial x partial x 2 u f u 0 quad quad 0 1 solitons are solutions of the type u t x q c 0 x x 0 c 0 t where c0 0 in 21 mainly devoted to the case f u u4 we have introduced a new framework to understand the collision of two solitons q c 1 q c 2 for 0 1 in the case c 2 ll c 1 or equivalently q c 2 h 1 ll q c 1 h 1 in this paper we consider the case of a general nonlinearity f u for which q c 1 q c 2 are nonlinearly stable in particular since f is general and c1 can be large the results are not perturbations of the ones for the power case in 21

a finite element method for equal width equation abstract a numerical solution of the equal width ew equation is obtained using space splitting technique and quadratic b spline galerkin finite element method solitary wave motion interaction of two solitary waves wave undulation and wave generation are studied using the proposed method comparisons are made with analytical solutions and with some spline finite element method calculations at selected times accuracy and efficiency are discussed by computing the numerical conserved laws and l 2 l error norms

a mesh free numerical method for solution of the family of kuramoto sivashinsky equations in this paper radial basis function rbfs based mesh free method is implemented to find numerical solution of the kuramoto sivashinsky equations this approach has an edge over traditional methods such as finite difference and finite element methods because it does not require a mesh to discretize the problem domain and a set of scattered nodes in the domain of influence provided by initial data is required for the realization of the method the accuracy of the method is assessed in terms of the error norms l 2 l number of nodes in the domain of influence free parameter dependent parameter rbfs and time step length numerical experiments demonstrate accuracy and robustness of the method for solving a class of nonlinear partial differential equations

interactions of two dimensionally localized pulses of the regularized long wave equation abstract interactions between positive and or negative cylindrical bell shaped pulses are investigated numerically for a two dimensional regularized long wave equation overtaking collisions of two same signed pulses are found to be fairly elastic head on collisions between positive and negative pulses are inelastic and their overall features are analogous to those in the one dimentional case some properties of collision processes are discussed in terms of the conversed quantities

stability and asymptotic stability in the energy space of the sum of n solitons for subcritical gkdv equations we prove in this paper the stability and asymptotic stability in h1 of a decoupled sum of n solitons for the subcritical generalized kdv equations the proof of the stability result is based on energy arguments and monotonicity of the local l2 norm note that the result is new even for p 2 the kdv equation the asymptotic stability result then follows directly from a rigidity theorem in 16

numerical simulation of equal width wave equation by means of the variational iteration method the solution of the equal width wave equation is numerically obtained and compared with that obtained by the adomian decomposition method numerical results show that the variational iteration method can readily be implemented with excellent accuracy to nonlinear equations

stability and instability of solitary waves of korteweg de vries type considered herein are the stability and instability properties of solitary wave solutions of a general class of equations that arise as mathematical models for the unidirectional propagation of weakly nonlinear dispersive long waves special cases for which our analysis is decisive include equations of the korteweg de vries and benjamin ono type necessary and sufficient conditions are formulated in terms of the linearized dispersion relation and the nonlinearity for the solitary waves to be stable

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

closed form solutions for a generalized benjamin bona mahony burgers equation with higher order nonlinearity we obtain closed form solutions for a generalized benjamin bona mahony burgers gbbmb equation with higher order nonlinearity which belong to a class of so called nonlinear pseudo parabolic or type sobolev equations the generalized tanh coth method is used here with the aid of mathematica periodic and soliton solutions are formally derived finally some conclusions are given

application of galerkin s method to equal width wave equation the non linear equal width equation is solved by galerkin s method using linear finite elements a linear recurrence relationship for the numerical solution of the resulting system of ordinary differential equations is found employing the crank nicolson approach including a product approximation the three invariants of the motion are calculated to determine the conservation properties of the system l 2 and l error norms are used to measure differences between the exact and numerical solutions the simulations of solitary wave motion are used to determine the properties of the algorithm finally the development of an undular bore is studied

a spectral method for the equal width equation a spectral discretization of the equal width equation ewe is presented the method is shown to be convergent and nonlinearly stable time stepping is performed with high order adams methods the spectral accuracy of the scheme reveals some features of the ewe that the methods previously used could not bare out properly for instance we may now study the changes in amplitude and velocity of solitary waves after collisions

imposing various boundary conditions on positive definite kernels abstract this work is motivated by the frequent occurrence of boundary value problems with various boundary conditions in the modeling of some problems in engineering and physical science here we propose a new technique to force the positive definite kernels such as some radial basis functions to satisfy the boundary conditions exactly it can improve the applications of existing methods based on positive definite kernels and radial basis functions especially the kernel based pseudospectral method for handling the differential equations with more complicated boundary conditions in the proposed technique some new kernels are constructed using the positive definite kernels in a manner that they satisfy the required conditions in addition we prove the positive definiteness of the newly constructed kernel and also the non singularity of the collocation matrix is proved under some conditions the proposed method is verified through the numerical solution of some benchmark problems such as a singularly perturbed steady state convection diffusion problem two and three dimensional poissons equations with various boundary conditions

asymptotic stability of solitary waves for the regularized long wave equation we show that a family of solitary waves for the regularized long wave rlw equation is asymptotically stable the large time dynamics of a solution near a solitary wave are studied by decomposing the solution into a modulating solitary wave with speed and phase shift that are functions of t plus a perturbation the strategy of proof follows that used by pego and weinstein 24 who considered the asymptotic stability of solitary waves of korteweg devries kdv type equations for rlw it is necessary to modify the basic ansatz to incorporate a new time scale which must be determined by the scheme different techniques are also required to analyze the spectral theory of the differential operator that arises in the linearized equation for a solitary wave perturbation in particular we use a result of pruss 27 to show that the linearized operator generates a semigroup with exponentially decaying norm on a certain weighted function space and we exploit the formal convergence of rlw to kdv under a certain scaling kdv scaling in order to rule out the existence of nonzero eigenvalues of the linearized operator 1996 john wiley sons inc

numerical solution of complex modified korteweg de vries equation by mesh free collocation method a mesh free method based on radial basis functions rbfs is proposed for the solution of complex modified korteweg de vries cmkdv equation the mesh free algorithm is based on scattered data interpolation along with approximating functions known as radial basis functions rbfs a set of scattered nodes provided by initial data is used for solution of the problem computational experiments examine the accuracy of the method in terms of error norms l 2 l and the three invariants i 1 i 2 and i 3 the results obtained by the method are in good agreement with exact solutions and the earlier work

convergence of unsymmetric kernel based meshless collocation methods this paper proves convergence of variations of the unsymmetric kernel based collocation method introduced by kansa in 1986 since then this method has been very successfully used in many applications though it may theoretically fail in special situations and though it had no error bound or convergence proof up to now thus it is necessary to add assumptions or to make modifications our modifications prevent numerical failure by dropping strict collocation and allow a rigorous mathematical analysis proving error bounds and convergence rates these rates improve with the smoothness of the solution the domain and the kernel providing the trial spaces but they are currently not yet optimal and deserve refinement they are based on rates of approximation to the residuals by nonstationary meshless kernel based trial spaces and they are independent of the type of differential operator the results are applicable to large classes of linear problems in strong form provided that there is a smooth solution and the test and trial discretizations are chosen with some care our analysis does not require assumptions like ellipticity and it can be extended to ill posed problems

a petrov galerkin method for solving the generalized equal width gew equation the generalized equal width gew equation is solved numerically by the petrov galerkin method using a linear hat function as the test function and a quadratic b spline function as the trial function product approximation has been used in this method a linear stability analysis of the scheme shows it to be conditionally stable test problems including the single soliton and the interaction of solitons are used to validate the suggested method which is found to be accurate and efficient finally the maxwellian initial condition pulse is studied

total variation projection with first order schemes this article proposes a new algorithm to compute the projection on the set of images whose total variation is bounded by a constant the projection is computed through a dual formulation that is solved by first order non smooth optimization methods this yields an iterative algorithm that applies iterative soft thresholding to the dual vector field and for which we establish convergence rate on the primal iterates this projection algorithm can then be used as a building block in a variety of applications such as solving inverse problems under a total variation constraint or for texture synthesis numerical results are reported to illustrate the usefulness and potential applicability of our tv projection algorithm on various examples including denoising texture synthesis inpainting deconvolution and tomography problems we also show that our projection algorithm competes favorably with state of the art tv projection methods in terms of convergence speed

the classification of the single traveling wave solutions to the generalized equal width equation abstract the complete discrimination system for polynomial is applied to the generalized equal width ew equation to obtain the classifications of single traveling wave solutions in particular we construct the corresponding solutions for the concrete parameters to show that each solution in the classification can be realized

hermite infinite elements and graded quadratic b spline finite elements quadratic b spline finite elements are defined for a graded mesh hermite infinite elements are proposed to extend the applicability of these finite elements to unbounded regions test problems used to compare this technique with published procedures show that the quadratic b spline finite element solution has as expected lower error bounds than a linear element solution these experiments also demonstrate that the hermite infinite elements used to close the b spline finite element arrays lead to error norms comparable in size with other infinite element formulations the generation of solitary waves in a semi infinite shallow channel by boundary forcing is modelled by the korteweg de vries equation using an array of graded elements closed by a zero pole infinite element the resulting simulation of solitary wave motion across a non uniform mesh confirms existing work and illustrates the effectiveness of the present formulation

unsymmetric meshless methods for operator equations a general framework for proving error bounds and convergence of a large class of unsymmetric meshless numerical methods for solving well posed linear operator equations is presented the results provide optimal convergence rates if the test and trial spaces satisfy a stability condition operators need not be elliptic and the problems can be posed in weak or strong form without changing the theory non stationary kernel based trial and test spaces are shown to fit into the framework disregarding the operator equation as a special case unsymmetric meshless kernel based methods solving weakly posed problems with distributional data are treated in some detail this provides a foundation of certain variations of the meshless local petrov galerkin technique of s n atluri and collaborators

an interval for the shape parameter in radial basis function approximation the radial basis functions rbfs depend on an auxiliary parameter called the shape parameter great theoretical and numerical efforts have been made to find the relationship between the accuracy of the rbf approximations and the value of the shape parameter in many cases the numerical approaches are based on minimization of an estimation of the error function such as rippa s approach and its modifications these approaches determine a value for the shape parameter in this paper we propose a practical approach to determine an interval instead of a value without any minimization and estimation of error function the idea is based on adding a loop on the shape parameter but not to minimize an error norm suitable values of the shape parameter are determined by take into account the practical convergence behavior of the problem the proposed method is applied to some illustrative examples including one and two dimensional interpolation and partial differential equations the results of the method are compared with those of some other approaches to confirm the reliability of the method furthermore numerical stability of the method of line respect to the shape parameter is considered for time dependent pdes the results show that the proposed method can be used as an independent method to find a shape parameter and also as an alternative for investigating the validity of the values of the other methods

ordered directional monotonicity in the construction of edge detectors abstract in this paper we provide a specific construction method of ordered directionally monotone functions we show that the functions obtained with this construction method can be used to build edge detectors for grayscale images we compare the results of these detectors to those obtained with some other ones that are widely used in the literature finally we show how a consensus edge detector can be built improving the results obtained both by our proposal and by those in the literature when applied individually

rbf ps scheme for solving the equal width equation the equal width equation is solved by a rbf ps scheme this technique is meshless and there is no need to linearize the nonlinear terms the radial kernels are used to transform the pde into a system of odes a higher order ode solver is used to solve the ode system the method is tested for single solitary wave interaction of two and three solitary waves the development of an undular bore and the interaction of two solitary waves the results are compared with earlier work and other methods

solitary waves of the regularized long wave equation abstract a finite element solution of the regularised long wave equation based on galerkin s method using cubic splines as element shape functions is set up a linear stability analysis shows the scheme to be unconditionally stable test problems including the migration and interaction of solitary waves are used to validate the method which is found to be accurate and efficient the three invariants of the motion are evaluated to determine the conservation properties of the algorithm the temporal evolution of a maxwellian initial pulse is then studied

scattering for the quartic generalised korteweg de vries equation abstract we show that the quartic generalised kdv equation u t u x x x u 4 x 0 is globally well posed for data in the critical scale invariant space h x 1 6 r with small norm and locally well posed for large norm improving a result of grunrock a grunrock a bilinear airy estimate with application to gkdv 3 differential integral equations 18 12 2005 1333 1339 as an application we obtain scattering results in h x 1 r h x 1 6 r for the radiation component of a perturbed soliton for this equation improving the asymptotic stability results of martel and merle y martel f merle asymptotic stability of solitons for subcritical generalized kdv equations arch ration mech anal 157 3 2001 219 254

on semi competing risks data summary we consider a variation of the competing risks problem in which a terminal event censors a non terminal event but not vice versa the joint distribution of the events is formulated via a gamma frailty model in the upper wedge where data are observable day et al 1997 with the marginal distributions unspecified an estimator for the association parameter is obtained from a concordance estimating function a novel plug in estimator for the marginal distribution of the non terminal event is shown to be uniformly consistent and to converge weakly to a gaussian process the assumptions on the joint distribution outside the upper wedge are weaker than those usually made in competing risks analyses simulations demonstrate that the methods work well with practical sample sizes the proposals are illustrated with data on morbidity and mortality in leukaemia patients

stable and convergent unsymmetric meshless collocation methods in the theoretical part of this paper we introduce a simplified proof technique for error bounds and convergence of a variation of kansa s well known unsymmetric meshless collocation method for a numerical implementation of the convergent variation a previously proposed greedy technique is coupled with linear optimization this algorithm allows a fully adaptive on the fly data dependent meshless selection of test and trial spaces the new method satisfies the assumptions of the background theory and numerical experiments demonstrate its stability

an efficient numerical scheme for burgers equation this paper applies the multiquadric mq as a spatial approximation scheme for solving the nonlinear burgers equation for comparison purposes a low order explicit finite difference approximation of the time derivative is employed by decreasing the time step of the computation it is shown that the major numerical error is from the time integration instead of the mq spatial approximation the numerical results indicate that this mq offers an excellent approximation for all possible values of reynolds number an adaptive algorithm is also developed to adjust the mq interpolation points to the peak of the shock wave which is shown to provide an improved numerical result numerical comparisons are made with most of the existing numerical schemes for solving the burgers equation

the meshless kernel based method of lines for solving the equal width equation the equal width equation governs nonlinear wave phenomena like waves in shallow water here it is solved numerically by the method of lines using a somewhat unusual setup there is no linearization of the nonlinear terms no error in handling the starting approximation and there are boundary conditions only at infinity to achieve a space discretization of high accuracy with only few trial functions meshless translates of radial kernels are used in the numerical examples the motion of solitary waves the interaction of two and three solitary waves the generation of wave undulation the maxwell initial condition and the clash of two colliding solitary waves are simulated our numerical results compare favourably with results of earlier papers using other techniques

solitary waves of the equal width wave equation a numerical solution of the equal width wave equation based on galerkin s method using cubic b spline finite elements is used to simulate the migration and interaction of solitary waves the interaction of two solitary waves is seen to cause the creation of a source for solitary waves usually these are of small magnitude but when the amplitudes of the two interacting waves are equal and opposite the source produces trains of solitary waves whose amplitudes are of the same order as those of the initiating waves the three invariants of the motion are evaluated to determine the conservation properties of the system finally the temporal evolution of a maxwellian initial pulse is studied for small ut uux uxxt 0 only positive waves are formed and the behaviour mimics that of the kdv and filw equations for larger values of d both positive and negative solitary waves are generated

on the win ratio statistic in clinical trials with multiple types of event pocock et al 2012 following finkelstein schoenfeld 1999 has popularized the win ratio for analysis of controlled clinical trials with multiple types of outcome event the approach uses pairwise comparisons between patients in the treatment and control groups using a primary outcome say the time to death with ties broken using a secondary outcome say the time to hospitalization in general the observed pairwise preferences and the weight they attach to the component rankings will depend on the distribution of potential follow up time we present expressions for the win and loss probabilities for general bivariate survival models when follow up of all patients is limited to a specified time horizon in the special case of a bivariate lehmann model we show that the win ratio does not depend on this horizon we show how the win ratio may be estimated nonparametrically or from a parametric model extensions to events of three or more types are described application of the method of marginal estimation due to wei et al 1989 to this problem is described

global convergence of splitting methods for nonconvex composite optimization we consider the problem of minimizing the sum of a smooth function h with a bounded hessian and a nonsmooth function we assume that the latter function is a composition of a proper closed function p and a surjective linear map mathcal m with the proximal mappings of tau p tau 0 simple to compute this problem is nonconvex in general and encompasses many important applications in engineering and machine learning in this paper we examined two types of splitting methods for solving this nonconvex optimization problem the alternating direction method of multipliers and the proximal gradient algorithm for the direct adaptation of the alternating direction method of multipliers we show that if the penalty parameter is chosen sufficiently large and the sequence generated has a cluster point then it gives a stationary point of the nonconvex problem we also establish convergence of the whole sequence under an additional assumption that the functions h and p are semialgebraic further

collocation method using quartic b spline for the equal width ew equation the equal width ew equation is solved numerically by giving a new algorithm based on collocation method using quartic b splines at the mid knots points as element shape also we use the fourth runge kutta method for solving the system of first order ordinary differential equations instead of finite difference method our test problems including the migration and interaction of solitary waves are used to validate the algorithm which is found to be accurate and efficient the three invariants of the motion are evaluated to determine the conservation properties of the algorithm the temporal evaluation of a maxwellian initial pulse is then studied

hierarchical convex optimization with primal dual splitting this paper addresses the selection of a desirable solution among all the solutions of a convex optimization problem referred to as the first stage problem mainly for inverse problems in signal processing this is realized in the framework of hierarchical convex optimization i e minimizing another convex function over the solution set of the first stage problem hierarchical convex optimization is an ideal strategy when the first stage problem has infinitely many solutions because of the non strict convexity of its objective function which could arise in various scenarios e g convex feasibility problems to this end first the fixed point set characterization behind a primal dual splitting type method is incorporated into the framework of hierarchical convex optimization which enables the framework to cover a broad class of first stage problem formulations then a pair of efficient algorithmic solutions to the hierarchical convex optimization problem as certain realizations of the hybrid steepest descent method are provided with guaranteed convergence we also present a specialized form of the proposed framework to focus on a typical scenario of inverse problems and show its application to signal interpolation

description of the inelastic collision of two solitary waves for the bbm equation we prove that the collision of two solitary waves of the bbm equation is inelastic but almost elastic in the case where one solitary wave is small in the energy space we show precise estimates of the nonzero residue due to the collision moreover we give a precise description of the collision phenomenon change of size of the solitary waves and shifts in their trajectories to prove these results we extend the method introduced in martel and merle description of two soliton collision for the quartic gkdv equation submitted preprint http arxiv org abs 0709 2672 commun math phys 286 39 79 2009 for the generalized kdv equation in particular in the quartic case the main argument is the construction of an explicit approximate solution in the collision region

l_ 0 gradient projection minimizing l 0 gradient the number of the non zero gradients of an image together with a quadratic data fidelity to an input image has been recognized as a powerful edge preserving filtering method however the l 0 gradient minimization has an inherent difficulty a user given parameter controlling the degree of flatness does not have a physical meaning since the parameter just balances the relative importance of the l 0 gradient term to the quadratic data fidelity term as a result the setting of the parameter is a troublesome work in the l 0 gradient minimization to circumvent the difficulty we propose a new edge preserving filtering method with a novel use of the l 0 gradient our method is formulated as the minimization of the quadratic data fidelity subject to the hard constraint that the l 0 gradient is less than a user given parameter alpha this strategy is much more intuitive than the l 0 gradient minimization because the parameter alpha has a clear meaning the l 0 gradient value of the output image itself so that one can directly impose a desired degree of flatness by alpha we also provide an efficient algorithm based on the so called alternating direction method of multipliers for computing an approximate solution of the nonconvex problem where we decompose it into two subproblems and derive closed form solutions to them the advantages of our method are demonstrated through extensive experiments

an alternative approach to confidence interval estimation for the win ratio statistic summary pocock et al 2012 european heart journal 33 176 182 proposed a win ratio approach to analyzing composite endpoints comprised of outcomes with different clinical priorities in this article we establish a statistical framework for this approach we derive the null hypothesis and propose a closed form variance estimator for the win ratio statistic in all pairwise matching situation our simulation study shows that the proposed variance estimator performs well regardless of the magnitude of treatment effect size and the type of the joint distribution of the outcomes

solitary waves induced by the boundary forced ew equation the development of a train of ew solitary waves induced by boundary forcing is studied using a petrov galerkin finite element scheme with shape functions taken as quadratic b spline functions a linear recurrence relationship for the numerical scheme is obtained via a crank nicholson approach involving a product approximation results are compared with those for the rlw and kdv equations

a class of proportional win fractions regression models for composite outcomes the win ratio is gaining traction as a simple and intuitive approach to analysis of prioritized composite endpoints in clinical trials to extend it from two sample comparison to regression we propose a novel class of semiparametric models that includes as special cases both the two sample win ratio and the traditional cox proportional hazards model on time to the first event under the assumption that the covariate specific win and loss fractions are proportional over time the regression coefficient is unrelated to the censoring distribution and can be interpreted as the log win ratio resulting from one unit increase in the covariate u statistic estimating functions in the form of an arbitrary covariate specific weight process integrated by a pairwise residual process are constructed to obtain consistent estimators for the regression parameter the asymptotic properties of the estimators are derived using uniform weak convergence theory for u processes visual inspection of a score process provides useful clues as to the plausibility of the proportionality assumption extensive numerical studies using both simulated and real data from a major cardiovascular trial show that the regression methods provide valid inference on covariate effects and outperform the two sample win ratio in both efficiency and robustness the proposed methodology is implemented in the r package wr publicly available from the comprehensive r archive network cran

the boundary forced mkdv equation an unconditionally stable numerical algorithm for the modified korteweg de vries equation based on the b spline finite element method is described the algorithm is validated through a single soliton simulation in further numerical experiments forced boundary conditions u u0 are applied at the end x 0 and the generated states of solitary waves are studied by long impulse experiments these are shown to be generated periodically with period tb proportional to u 30 and to have a limiting amplitude proportional to u0 this limit is achieved by all waves after the first provided the experiment proceeds long enough the temporal development of the derivatives u 0 t u 0 t and u 0 t is also periodic with period tb the effect of negative forcing is to generate a train of negative waves the solitary wave states generated by applying a positive impulse followed immediately by an negative impulse of equal amplitude and duration is dependent on the period of forcing the solitary waves generated by these various forcing functions possess many of the attributes of free solitons

a petrov galerkin method for equal width equation abstract the equal width equation is solved numerically by petrov galerkin method using linear hat function and quadratic b spline function as trial and test functions respectively product approximation has been used in this method a linear stability analysis of the scheme is shown to be conditionally stable test problems including the single soliton and the interaction of solitons are used to validate the suggested method which is found to be accurate and efficient the maxwellian initial condition pulse and the development of an undular bore are also studied

on the alternative hypotheses for the win ratio we extend the results of luo et al 2015 biometrics 71 139 145 regarding the alternative hypotheses for the win ratio from hazard orders to the upper quadrant stochastic order on the plane this extension substantially widens the range of alternatives against which the win ratio is known to be consistent it incorporates alternatives induced by simple and popular copula models that are left out by the characterization of luo et al 2015 we also discuss how our results may be generalized to win ratios in multivariate and stratified settings

multilevel compact radial functions based computational schemes for some elliptic problems abstract compactly supported radial basis functions cs rbfs have been recently introduced in the context of the dual reciprocity method as a possible cure of dense matrices and ill conditioning problems when using the classical radial basis functions however the support scaling factor and slow convergence rate of the cs rbfs have also raised issues on the effectiveness of the cs rbfs in this paper two multilevel schemes have been proposed to alleviate these problems

stability theory of solitary waves in the presence of symmetry ii abstract consider an abstract hamiltonian system which is invariant under a group of operators we continue to study the effect of the group invariance on the stability of solitary waves applications are given to bound states and traveling wave solutions of nonlinear wave equations

unique continuation property and control for the benjamin bona mahony equation on a periodic domain abstract we consider the benjamin bona mahony bbm equation on the one dimensional torus t r 2 z we prove a unique continuation property ucp for small data in h 1 t with nonnegative zero means next we extend the ucp to certain bbm like equations including the equal width wave equation and the kdv bbm equation applications to the stabilization of the above equations are given in particular we show that when an internal control acting on a moving interval is applied in the bbm equation then a semiglobal exponential stabilization can be derived in h s t for any s 1 furthermore we prove that the bbm equation with a moving control is also locally exactly controllable in h s t for any s 0 and globally exactly controllable in h s t for any s 1 in a sufficiently large time depending on the h s norms of the initial and terminal states

a least squares finite element scheme for the ew equation abstract the equal width ew equation is solved by a least squares technique using linear space time finite elements in simulations of the migration of a single solitary wave this algorithm is shown to have good accuracy and conservation the development of solitary waves from an arbitrary initial condition within an ew environment is examined

b spline quasi interpolation based numerical methods for some sobolev type equations in this article we intend to use quadratic and cubic b spline quasi interpolants to develop higher order numerical methods for some sobolev type equations in one space dimension our aim is also to compare the performance of the proposed methods in terms of the accuracy and the rate of convergence we also discuss another approach to the cubic b spline quasi interpolation based method where we achieve fourth order of accuracy in space we theoretically establish the order of accuracy for the three proposed methods and also establish the l 2 stability in the linear case using von neumann analysis as a particular case of the sobolev type equations we take the equal width and the benjamin bona mahony burgers equations and perform several numerical experiments to support our theoretical results

scattering of regularized long wave solitary waves abstract the lagrangian density for the regularized long wave equation also known as the bbm equation is presented using the trial function technique ordinary differential equations that describe the time dependence of the position of the peaks amplitudes and widths for the collision of two solitary waves are obtained these equations are analyzed in the born and equal width approximations and compared with numerical results obtained by direct integration utilizing the split step fast fourier transform method the computations show that collisions are inelastic and that production of solitary waves may occur

computation of natural frequencies of shear deformable beams and plates by an rbf pseudospectral method a study of free vibration of timoshenko beams and mindlin plates is presented the analysis is based on a new numerical scheme where collocation by radial basis functions and pseudospectral methods are combined to produce highly accurate results numerical results are presented and discussed for various thickness to length ratios

convergence analysis of alternating direction method of multipliers for a family of nonconvex problems the alternating direction method of multipliers admm is widely used to solve large scale linearly constrained optimization problems convex or nonconvex in many engineering fields however there is a general lack of theoretical understanding of the algorithm when the objective function is nonconvex in this paper we analyze the convergence of the admm for solving certain nonconvex consensus and sharing problems we show that the classical admm converges to the set of stationary solutions provided that the penalty parameter in the augmented lagrangian is chosen to be sufficiently large for the sharing problems we show that the admm is convergent regardless of the number of variable blocks our analysis does not impose any assumptions on the iterates generated by the algorithm and is broadly applicable to many admm variants involving proximal update rules and various flexible block selection rules

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

stability of blow up profile and lower bounds for blow up rate for the critical generalized kdv equation the generalized korteweg de vries equations are a class of hamiltonian systems in infinite dimension derived from the kdv equation where the quadratic term is replaced by a higher order power term these equations have two conservation laws in the energy space h 1 l 2 norm and energy we consider in this paper the critical generalized kdv equation which corresponds to the smallest power of the nonlinearity such that the two conservation laws do not imply a bound in h 1 uniform in time for all h 1 solutions and thus global existence from 15 there do exist for this equation solutions u t such that u t h1 as t t where t we call them blow up solutions the question is to describe in a qualitative way how blow up occurs for solutions with l 2 mass close to the minimal mass allowing blow up and with decay in l 2 at the right we prove after rescaling and translation which leave invariant the l 2 norm that the solution converges to a universal profile locally in space at the blow up time t from the nature of this profile we improve the standard lower bound on the blow up rate for finite time blow up solutions

a numerical solution of the equal width wave equation by a lumped galerkin method in this paper the equal width wave ew equation is solved by a numerical technique based on a lumped galerkin method using quadratic b spline finite elements to investigate the motion of a single solitary wave development of two solitary waves interaction and an undular bore the obtained results are compared with published numerical solutions a linear stability analysis of the method is also investigated

asymptotic n soliton like solutions of the subcritical and critical generalized korteweg de vries equations we consider the generalized korteweg de vries equations ut uxx upx 0t x r inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i in the subcritical and critical cases p 2 3 4 or 5 let r j t x qc j x c j t x j where j 1 n be n soliton solutions of this equation with corresponding speeds 0 c 1 c 2 c n in this paper we construct a solution u t of the generalized korteweg de vries equation such that inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i this solution behaves asymptotically as t as the sum of n solitons without loss of mass by dispersion this is an exceptional behavior indeed being given the parameters c j 1 j n x j 1 j n we prove uniqueness of such a solution in the integrable cases p 2 and 3 such solutions are explicitly known and their properties were extensively studied in the literature they are called n soliton solutions therefore the existence result is new only for the nonintegrable cases the uniqueness result is new for all cases

painleve analysis and lie group symmetries of the regularized long wave equation the painleve formulation is given for the regularized long wave equation which has been used to describe shallow water waves and drift waves in a plasma the lie group symmetries of the equation is then studied and it is shown that the only symmetries are due to the three conserved quantities

guided image filtering in this paper we propose a novel explicit image filter called guided filter derived from a local linear model the guided filter computes the filtering output by considering the content of a guidance image which can be the input image itself or another different image the guided filter can be used as an edge preserving smoothing operator like the popular bilateral filter 1 but it has better behaviors near edges the guided filter is also a more generic concept beyond smoothing it can transfer the structures of the guidance image to the filtering output enabling new filtering applications like dehazing and guided feathering moreover the guided filter naturally has a fast and nonapproximate linear time algorithm regardless of the kernel size and the intensity range currently it is one of the fastest edge preserving filters experiments show that the guided filter is both effective and efficient in a great variety of computer vision and computer graphics applications including edge aware smoothing detail enhancement hdr compression image matting feathering dehazing joint upsampling etc

local radial basis function based differential quadrature method and its application to solve two dimensional incompressible navier stokes equations local radial basis function based differential quadrature method is presented in detail in this paper the method is a natural mesh free approach like the conventional differential quadrature dq method it discretizes any derivative at a knot by a weighted linear sum of functional values at its neighbouring knots which may be distributed randomly however different from the conventional dq method the weighting coefficients in present method are determined by taking the radial basis functions rbfs instead of high order polynomials as the test functions the method works in a similar fashion as conventional finite difference schemes but with truly mesh free property in this paper we mainly concentrate on the multiquadric rbfs since they have exponential convergence the effects of shape parameter c on the accuracy of numerical solution of linear and nonlinear partial differential equations are studied and how the value of optimal c varies with the number of local support knots is also numerically demonstrated the proposed method is validated by its application to the simulation of natural convection in a square cavity excellent numerical results are obtained on an irregular knot distribution

conservative scheme for a model of nonlinear dispersive waves and its solitary waves induced by boundary motion abstract a conservative difference scheme is given for a model of nonlinear dispersive waves convergence and stability of the scheme are proved by means of this scheme we explore numerically the relationship between the boundary data and the amplitudes and number of solitary waves it produces

asymptotic stability of solitary wave solutions to the regularized long wave equation abstract we study the asymptotic stability of solitary wave solutions to the regularized long wave equation rlw in h 1 r rlw is an equation which describes the long waves in water to prove the result we make use of the monotonicity of the local h1 norm and apply the liouville property of rlw as in merle and martel j math pures appl 79 2000 339 arch rational mech anal 157 2001 219