analytic smoothing effect for a system of schrodinger equations with three wave interaction we consider the global cauchy problem for a system of schrodinger equations with quadratic interaction two types of analytic smoothing effect for the solutions are formulated in the small data setting under the mass resonance condition one is the usual analytic smoothing effect in space variables in terms of the generator of galilei transforms we prove the existence and uniqueness of global solutions which are analytic with respect to galilei generators for sufficiently small data with exponential decay at infinity in space n with n 3 the other is analytic smoothing effect in space time variables in terms of generator of pseudo conformal and galilei transforms we prove the existence and uniqueness of global solutions which are analytic with respect to pseudo conformal and galilei generators for sufficiently small data with exponential decay in 4 we also discuss the associated lagrange structure

application of the karhunen loeve procedure for the characterization of human faces the use of natural symmetries mirror images in a well defined family of patterns human faces is discussed within the framework of the karhunen loeve expansion this results in an extension of the data and imposes even and odd symmetry on the eigenfunctions of the covariance matrix without increasing the complexity of the calculation the resulting approximation of faces projected from outside of the data set onto this optimal basis is improved on average

analytic smoothing effect for nonlinear schrodinger equation with quintic nonlinearity abstract we prove the global existence of analytic solutions to nonlinear schrodinger equation with quintic nonlinearity in n space dimensions for sufficiently small cauchy data with exponential decay the smallness assumption on the data is imposed in terms of the critical sobolev space h n 2 1 2 moreover a characterization of some class of analytic functions is given

deformable contours modeling and extraction this paper considers the problem of modeling and extracting arbitrary deformable contours from noisy images we propose a global contour model based on a stable and regenerative shape matrix which is invariant and unique under rigid motions combined with markov random field to model local deformations this yields prior distribution that exerts influence over a global model while allowing for deformations we then cast the problem of extraction into posterior estimation and show its equivalence to energy minimization of a generalized active contour model we discuss pertinent issues in shape training energy minimization line search strategies minimax regularization and initialization by generalized hough transform finally we present experimental results and compare its performance to rigid template matching

probabilistic visual learning for object representation we present an unsupervised technique for visual learning which is based on density estimation in high dimensional spaces using an eigenspace decomposition two types of density estimates are derived for modeling the training data a multivariate gaussian for unimodal distributions and a mixture of gaussians model for multimodal distributions those probability densities are then used to formulate a maximum likelihood estimation framework for visual search and target detection for automatic object recognition and coding our learning technique is applied to the probabilistic visual modeling detection recognition and coding of human faces and nonrigid objects such as hands

advances in the adomian decomposition method for solving two point nonlinear boundary value problems with neumann boundary conditions a new straightforward approach for solving ordinary and partial second order boundary value problems with neumann boundary conditions is introduced in this research this approach depends mainly on the adomian decomposition method with a new definition of the differential operator and its inverse which has been modified for neumann boundary conditions the effectiveness of the proposed approach is verified by several linear and nonlinear examples

analyticity in time and smoothing effect of solutions to nonlinear schrodinger equations in this paper we consider analyticity in time and smoothing effect of solutions to nonlinear schrodinger equations where we prove that if satisfies then there exists a unique solution of 1 and positive constants t c 0 c 1 such that is analytic in time and space variables for and and has an analytic continuation on and in the case the condition 2 can be relaxed as follows where m 0 if n 1 p 1 m 1 if n 2 and m 1 if n 3 p 1

adomian decomposition method for a reliable treatment of the bratu type equations in this paper we present a framework to determine exact solutions of bratu type equations the algorithm rests mainly on the adomian decomposition method the proposed scheme is illustrated by studying two boundary value problems and an initial value problem of bratu type the first type gives a solution that blows up at the middle of the domain whereas the other equations give bounded solutions

mixture densities maximum likelihood and the em algorithm the problem of estimating the parameters which determine a mixture density has been the subject of a large diverse body of literature spanning nearly ninety years during the last two decades the

explicit solutions of nonlinear partial differential equations explicit solutions are calculated by the decomposition method for burger s equation for comparison with other existing procedures such as similarity reduction etc

closed form solutions for physically based shape modeling and recognition the authors present a closed form physically based solution for recovering a three dimensional 3 d solid model from collections of 3 d surface measurements given a sufficient number of independent measurements the solution is overconstrained and unique except for rotational symmetries the proposed approach is based on the finite element method fem and parametric solid modeling using implicit functions this approach provides both the convenience of parametric modeling and the expressiveness of the physically based mesh formulation and in addition can provide great accuracy at physical simulation a physically based object recognition method that allows simple closed form comparisons of recovered 3 d solid models is presented the performance of these methods is evaluated using both synthetic range data with various signal to noise ratios and using laser rangefinder data

modal matching for correspondence and recognition modal matching is a new method for establishing correspondences and computing canonical descriptions the method is based on the idea of describing objects in terms of generalized symmetries as defined by each object s eigenmodes the resulting modal description is used for object recognition and categorization where shape similarities are expressed as the amounts of modal deformation energy needed to align the two objects in general modes provide a global to local ordering of shape deformation and thus allow for selecting which types of deformations are used in object alignment and comparison in contrast to previous techniques which required correspondence to be computed with an initial or prototype shape modal matching utilizes a new type of finite element formulation that allows for an object s eigenmodes to be computed directly from available image information this improved formulation provides greater generality and accuracy and is applicable to data of any dimensionality correspondence results with 2d contour and point feature data are shown and recognition experiments with 2d images of hand tools and airplanes are described

analytic smoothing effect for the schrodinger equation with long range perturbation we study microlocal analytic singularity of solutions to schr odinger equation with analytic coefficients using microlocal weight estimate developped for estimating the phase space tunneling we prove microlocal smoothing estimates that generalize results by l robbiano and c zuily we suppose the schr odinger operator is a long range type perturbation of the laplacian and we employ positive commutator type estimates to prove the smoothing property

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

a new approach to the solution of the prey and predator problem and comparison of the results with the adomian method in this article the problem of prey and predator is presented and the power series method is employed to compute an approximation to the solution of the system of nonlinear volterra differential equations governing the problem the results are compared with the results using the adomian decomposition method some plots are presented to show the populations of the prey and the predator versus time for illustrating the reliability and simplicity of the method

singularities of solutions to the schrodinger equation on scattering manifold in this paper we study microlocal singularities of solutions to schr odinger equations on scattering manifolds i e noncompact riemannian manifolds with asymptotically conic ends we characterize the wave front set of the solutions in terms of the initial condition and the classical scattering maps under the nontrapping condition our result is closely related to a recent work by hassell and wunsch though our model is more general and the method which relies heavily on scattering theoretical ideas is simple and quite different in particular we use an egorov type argument in the standard pseudodifferential symbol classes and avoid using legendre distributions in the proof we employ a microlocal smoothing property in terms of the it radially homogenous wave front set which is more precise than the preceding results

analytic wave front set for solutions to schrodinger equations this paper is a continuation of a martinez s nakamura v sordoni analytic smoothing effect for the schrodinger equation with long range perturbation comm pure appl math lix 2006 1330 1351 where an analytic smoothing effect was proved for long range type perturbations of the laplacian h0 on rn in this paper we consider short range type perturbations h of the laplacian on rn and we characterize the analytic wave front set of the solution to the schrodinger equation e ithf in terms of that of the free solution e ith0f for t 0 in the backward non trapping region this result is an analytic analogue of results by hassel and wunsch a hassel j wunsch the schrodinger propagator for scattering metrics ann of math 162 2005 487 523 and nakamura s nakamura wave front set for solutions to schrodinger equations j funct anal 256 2009 1299 1309

the comparison of the stability of adomian decomposition method with numerical methods of equation solution the purpose of this article is to study adomian decomposition method as well as its stability and also to comparatively investigate it with other methods

analytic solution of nonlinear boundary value problems in several dimensions by decomposition abstract nonlinear partial differential equations are systematically solved by the decomposition method of g adomian for general boundary conditions described by boundary operator equations linear partial differential equations and linear or nonlinear ordinary differential equations become special cases all dealt with by a single procedure

on the analytic smoothing effect for the hartree equation with a short range interaction potential abstract we consider the cauchy problem for the hartree equation in space dimension d 2 we assume that the interaction potential v x is short range more precisely we consider the case where v belongs to the weak l d space with 1 d we prove that if 2 d resp 1 2 the initial data is small in the sense of the homogeneous sobolev space h 2 1 resp the homogeneous weighted sobolev space f h 1 2 and the fourier transform f satisfies a real analytic condition then the corresponding solution u t is also real analytic for any t 0 we remark that no h 2 1 resp f h 1 2 smallness condition is imposed on first and higher order partial derivatives of f when 2 d resp 1 2

variational iteration method for solving nonlinear boundary value problems abstract in this paper he s variational iteration method is implemented to give approximate and analytical solutions for a class of boundary value problems the variational iteration method which produces the solutions in terms of convergent series requiring no linearization or small perturbation numerical examples are given and comparisons are made with the adomian decomposition method the fact that this method solves nonlinear equations without using adomian polynomials can be considered as an advantage of this method over adomian decomposition method

bayesian shape model for facial feature extraction and recognition abstract a facial feature extraction algorithm using the bayesian shape model bsm is proposed in this paper a full face model consisting of the contour points and the control points is designed to describe the face patch using which the warping normalization of the extracted face patch can be performed efficiently first the bsm is utilized to match and extract the contour points of a face in bsm the prototype of the face contour can be adjusted adaptively according to its prior distribution moreover an affine invariant internal energy term is introduced to describe the local shape deformations between the prototype contour in the shape domain and the deformable contour in the image domain thus both global and local shape deformations can be tolerated then the control points are estimated from the matching result of the contour points based on the statistics of the full face model finally the face patch is extracted and normalized using the piece wise affine triangle warping algorithm experimental results based on real facial feature extraction demonstrate that the proposed bsm facial feature extraction algorithm is more accurate and effective as compared to that of the active shape model asm

analytic smoothing effect for global solutions to nonlinear schrodinger equations abstract we prove the global existence of analytic solutions to the cauchy problem for the cubic schrodinger equation in space dimension n 3 for sufficiently small data with exponential decay at infinity minimal regularity assumption regarding scaling invariance is imposed on the cauchy data

wave front set for solutions to schrodinger equations abstract we consider solutions to schrodinger equation on r d with variable coefficients let h be the schrodinger operator and let u t e i t h u 0 be the solution to the schrodinger equation with the initial condition u 0 l 2 r d we show that the wave front set of u t in the nontrapping region can be characterized by the wave front set of e i t h 0 u 0 where h 0 is the free schrodinger operator the characterization of the wave front set is given by the wave operator for the corresponding classical mechanical scattering or equivalently by the asymptotics of the geodesic flow

adomian decomposition method with green s function for sixth order boundary value problems in this paper the adomian decomposition method with green s function is applied to solve linear and nonlinear sixth order boundary value problems the numerical results obtained with a small amount of computation are compared with the exact solutions to show the efficiency of the method the results show that the decomposition method is of high accuracy more convenient and efficient for solving high order boundary value problems

active appearance models we describe a new method of matching statistical models of appearance to images a set of model parameters control modes of shape and gray level variation learned from a training set we construct an efficient iterative matching algorithm by learning the relationship between perturbations in the model parameters and the induced image errors

local smoothing property and strichartz inequality for schrodinger equations with potentials superquadratic at infinity abstract we study smoothing properties for time dependent schrodinger equations i u t 1 2 u v x u u 0 l 2 r n with potentials which satisfy v x o x m at infinity m 2 we show that the solution u t x is 1 m times differentiable with respect to x at almost all t r and explain that this is the result of the fact that the sojourn time of classical particles with energy in arbitrary compact set is less than ct 1 m during 0 t when is very large we also show strichartz s inequality with derivative loss for such potentials and give its application to nonlinear schrodinger equations

gain of analyticity for semilinear schrodinger equations abstract we discuss gain of analyticity phenomenon of solutions to the initial value problem for semilinear schrodinger equations with gauge invariant nonlinearity we prove that if the initial data decays exponentially then the solution becomes real analytic in the space variable and a gevrey function of order 2 in the time variable except in the initial plane our proof is based on the energy estimates developed in our previous work and on fine summation formulae concerned with a matrix norm

bayesian constrained local models revisited this paper presents a novel bayesian formulation for aligning faces in unseen images our approach revisits the constrained local models clm formulation where an ensemble of local feature detectors are constrained to lie within the subspace spanned by a point distribution model pdm fitting such a model to an image typically involves two main steps a local search using a detector obtaining response maps for each landmark likelihood term and a global optimization that finds the pdm parameters that jointly maximize all the detections at once the so called global optimization can be posed as a bayesian inference problem where the posterior distribution of the shape and pose parameters can be inferred in a maximum a posteriori map sense this work introduces an extended bayesian global optimization strategy that includes two novel additions 1 to perform second order updates of the pdm parameters accounting for their covariance and 2 to model the underlying dynamics of the shape variations encoded in the prior term by using recursive bayesian estimation extensive evaluations were performed against state of the art methods on several standard datasets imm bioid xm2vts lfw and fgnet talking face results show that the proposed approach significantly increases the fitting performance

comparison of the solutions obtained by adomian decomposition and wavelet galerkin methods of boundary value problems abstract in this paper we will compare the performance of adomian decomposition method and the wavelet galerkin method applied to the solution of boundary value problems involving non homogeneous heat and wave equations it is shown that the adomian decomposition method in many instances gives better results in the wavelet galerkin solutions daubechies six wavelets are used because they give better results than those of lower degree wavelets the results are then compared with those obtained using the adomian decomposition method although the adomian decomposition solution required slightly more computational effort than the wavelet galerkin solution it resulted in more accurate results than the wavelet galerkin method

equality of partial solutions in the decomposition method for linear or nonlinear partial differential equations abstract we consider the solution of partial differential equations for initial boundary conditions using the decomposition method the partial solutions obtained from the seperate equations for the highest ordered linear operator terms are shown to be identical when the boundary conditions are general and asymptotically equal when the boundary conditions in one independent variable are independet of other variables

a reliable algorithm for obtaining positive solutions for nonlinear boundary value problems abstract in this paper we propose an algorithm for solving the nonlinear two point boundary value problem that has at least one positive solution 1 6 for in a compatible interval our method stems mainly from combining the decomposition series solution obtained by adomian decomposition method with pade approximates the validity of the approach is verified through illustrative numerical examples

approximate solutions to the nonlinear vibrations of multiwalled carbon nanotubes using adomian decomposition method abstract this paper applies the adomian decomposition method adm to the search for the approximate solutions to the problem of the nonlinear vibrations of multiwalled carbon nanotubes embedded in an elastic medium a multiple beam model is utilized in which the governing equations of each layer are coupled with those of its adjacent ones via the van der waals inter layer forces the amplitude frequency curves for large amplitude vibrations of single walled double walled and triple walled carbon nanotubes are obtained the influence of changes in material constants of the surrounding elastic medium and the effect of changes in nanotube geometrical parameters on the vibration characteristics are studied by comparing the results with those from the open literature this method needs less work in comparison with the traditional methods and decreases considerable volume of calculation and it s powerful mathematical tool for solving wide class of nonlinear differential equations special attention is given to prove the convergence of the method some examples are given to illustrate the determination approximate solutions of the proposed problem

application of the adomian decomposition method for two dimensional parabolic equation subject to nonstandard boundary specifications in this work we are concerned with the solution of a nonlocal boundary value problem an approach is presented for solving the two dimensional parabolic partial differential equation subject to integral boundary specifications the main objective is to propose an alternative method of solution one not based on finite difference methods or finite element schemes or spectral techniques the aim of the present paper is to investigate the application of the adomian decomposition method for solving the two dimensional linear parabolic partial differential equation with nonlocal boundary specifications replacing the classical boundary conditions the adomian decomposition method is used by many researchers to investigate several scientific applications and requires less work if compare with the traditional techniques the introduction of this idea as will be discussed not only provides the solution in a series form but it also guarantees considerable saving of the calculations volume the solutions will be handle more easily quickly and elegantly without linearizing the problem by implementing the decomposition method rather than the standard methods for the exact solutions in this approach the solution is found in the form of a convergent power series with easily computed components the adomian decomposition scheme is easy to program in applied problems and provides immediate and convergent solutions without any need for linearization or discretization to give a clear overview of the methodology we have selected illustrative example

commutator algebra and abstract smoothing effect abstract we consider a dispersive evolution equation in a hilbert space and prove abstract smoothing effects in an incoming region under a mourre type condition near infinity for this purpose we introduce commutator algebras acting on weighted sobolev spaces associated with two self adjoint operators and construct various time dependent nonnegative observables with nonpositive heisenberg derivative our approach is applicable to schrodinger evolution equations on complete riemannian manifolds with suitable strictly convex functions near infinity i asymptotically euclidean metric with long range metric perturbation ii conformally compact metric iii generalized scattering metric iv metric of separation of variables near infinity etc

the adomian decomposition method in turning point problems in this paper the decomposition method is applied to boundary value problems of ordinary differential equations with a parameter exhibiting turning points

comparison of the adomian decomposition method and the variational iteration method in solving the moving boundary problem in this paper a comparison between two methods the adomian decomposition method and the variational iteration method used for solving the moving boundary problem is presented both of the methods consist in constructing the appropriate iterative or recurrence formulas on the basis of the equation considered and additional conditions enabling one to determine the successive elements of a series or sequence approximating the function sought the precision and speed of convergence of the procedures compared are verified with an example

microlocal dispersive smoothing for the schrodinger equation this paper establishes a connection between the microlocal smoothness of solutions of the initial value problem for schrodinger s equation and the global behavior of bicharacteristics of the principal symbol in particular localized initial data gives rise to solutions which are microlocally smooth at all points which are not trapped backwards by the bicharacteristic flow the origin of the phenomenon is in the dispersive nature of the equation the results imply microlocal regularity properties of the fundamental solution 1995 john wiley sons inc

adomian decomposition method for solving bvps for fourth order integro differential equations the adomian decomposition method adm is applied to solve both linear and nonlinear boundary value problems bvps for fourth order integro differential equations the numerical results obtained with minimum amount of computation or mathematics compare reasonably well with exact solutions

the numerical solution of fifth order boundary value problemsby the decomposition method in this paper we present a fast and accurate numerical scheme for the solution of fifth order boundary value problems with two point boundary conditions the adomian decomposition method and a modified form of this method are applied to construct the numerical solution the new approach provides the solution in the form of a rapidly convergent series and not at grid points two numerical illustrations are given to show the pertinent features of technique

remarks on analytic smoothing effect for the schrodinger equation we study analytic smoothing effect of solutions to the schrodinger equation with cauchy data decaying exponentially at infinity the domain of analyticity in the space variables of solutions is described under weight conditions on the data in terms of the corresponding supporting function the domain of analyticity in the time variable is characterized by means of weight conditions of gaussian type on the data a generalization of various isometrical identities related to the analytic smoothing effect is introduced

small analytic solutions to the hartree equation we consider the cauchy problem for the hartree equation in space dimension d 3 we assume that the interaction potential v belongs to the weak ld 2 space we prove that if the initial data is sufficiently small in the l2 sense and either or its fourier transform f satisfies a real analytic condition then the solution u t is also real analytic for any t 0 we also prove that if and v satisfy some strong condition then u t can be extended to an entire function on cd for any t 0 a part of our method is applicable to the final value problem we remark that no l2 smallness condition is imposed on first and higher order partial derivatives of and f

analytic approximate solution for a nonlinear oscillator equation abstract analytical approximate oscillatory solutions for the differential equation u 2u um with the boundary conditions u 0 0 u 1 are derived using the adomian decomposition method the parameters and are positive real numbers and m is a positive integer the solutions are given in the form of series with easily computable terms and are valid for all including the critical frequencies the validity of the solutions is verified through some numerical examples

detection and segmentation of generic shapes based on affine modeling of energy in eigenspace this paper presents a novel approach for detection and segmentation of man made generic shapes in cluttered images the set of shapes to be detected are members of affine transformed versions of basic geometric shapes such as rectangles circles etc the shape set is represented by its vectorial edge map transformed over a wide range of affine parameters we use vectorial boundary instead of regular boundary to improve the robustness to noise background clutter and partial occlusion our approach consists of a detection stage and a verification stage in the detection stage we first derive the energy from the principal eigenvectors of the set next an a posteriori probability map of energy distribution is computed from the projection of the edge map representation in a vectorial eigen space local peaks of the posterior probability map are located and indicate candidate detections we use energy probability based detection since we find that the underlying distribution is not gaussian and resembles a hypertoroid in the verification stage each candidate is verified using a fast search algorithm based on a novel representation in angle space and the corresponding pose information of the detected shape is obtained the angular representation used in the verification stage yields better results than a euclidean distance representation experiments are performed in various interfering distortions and robust detection and segmentation are achieved

boundary finding with parametrically deformable models segmentation using boundary finding is enhanced both by considering the boundary as a whole and by using model based global shape information the authors apply flexible constraints in the form of a probabilistic deformable model to the problem of segmenting natural 2 d objects whose diversity and irregularity of shape make them poorly represented in terms of fixed features or form the parametric model is based on the elliptic fourier decomposition of the boundary probability distributions on the parameters of the representation bias the model to a particular overall shape while allowing for deformations boundary finding is formulated as an optimization problem using a maximum a posteriori objective function results of the method applied to real and synthetic images are presented including an evaluation of the dependence of the method on prior information and image quality