multiple existence of sign changing solutions for coupled nonlinear schrodinger equations abstract in this paper we consider the multiple existence of sign changing solutions of coupled nonlinear schrodinger equations p u 1 u 1 u 3 v 2 u in r 3 v 2 v 2 v 3 u 2 v in r 3 where 1 2 1 2 are positive and 0

an adaptive order statistic noise filter for gamma corrected image sequences original video signals are often corrupted by a certain amount of noise originating from the camera electronics as a result of the gamma correction in cameras the observed noise is signal dependent we present a spatio temporal order statistic os noise filter that takes into account the gamma correction in the camera the calculation of the filter coefficients requires higher order order statistics hoos of the noise process we make use of a range test rt to determine locally from which neighboring signal values an estimate should be formed the noise filter that we arrive at is adaptive and computationally efficient

optimal liouville type theorems for noncooperative elliptic schrodinger systems and applications we study multi component elliptic schrodinger systems arising in nonlinear optics and bose einstein condensation phenomena we prove new liouville type nonexistence theorems as well as a priori bounds decay and singularity estimates this is shown under an optimal sobolev growth restriction on the nonlinearities thus improving on recent results of dancer et al and of tavares et al these systems are of non cooperative form and hence cannot be tackled by maximum principle methods such as moving planes instead we rely on a delicate combination of rellich pohozaev type identities sobolev and interpolation inequalities on sn 1 and feedback and measure arguments we also extend our results to a rather general class of gradient type systems

infinitely many sign changing solutions for system of p laplace equations in rn abstract in this paper we consider the system of p laplacian equations in r n p u j j x u j p 2 u j i 1 k i j u i q u j q 2 u j in r n u j x 0 as x j 1 k where 1 p n max 2 p 2 q p n p n p i j are constants i j 1 k j j 0 j 1 2 k i j 0 i j i j 1 k j j 1 k are the potential functions and satisfy suitable decay assumptions the existence of infinitely many sign changing solutions is proved by the truncation method and by the concentration compactness analysis on the approximating solutions

blind inverse gamma correction the luminance nonlinearity introduced by many imaging devices can often be described by a simple point wise operation gamma correction this paper presents a technique for blindly estimating the amount of gamma correction in the absence of any calibration information or knowledge of the imaging device the basic approach exploits the fact that gamma correction introduces specific higher order correlations in the frequency domain these correlations can be detected using tools from polyspectral analysis the amount of gamma correction is then estimated by minimizing these correlations

self similarity and asymptotic stability for coupled nonlinear schrodinger equations in high dimensions abstract this paper is concerned with systems of coupled schrodinger equations with polynomial nonlinearities and dimension n 1 we show the existence of global self similar solutions and prove that they are asymptotically stable in a framework based on weak l p spaces whose elements have local finite l 2 mass the radial symmetry of the solutions is also addressed

radial solutions and phase separation in a system of two coupled schrodinger equations we consider the nonlinear elliptic system left begin aligned delta u u u 3 beta v 2u 0 quad rm in mathbb b delta v v v 3 beta u 2v 0 quad rm in mathbb b u v 0 quad rm in mathbb b quad u v 0 quad rm on partial mathbb b end aligned right where n leqq 3 and mathbb b subset mathbb r n is the unit ball we show that for every beta leqq 1 and k in mathbb n the above problem admits a radially symmetric solution u v such that u v changes sign precisely k times in the radial variable furthermore as beta to infty after passing to a subsequence u w and v w uniformly in mathbb b where w w w has precisely k nodal domains and is a radially symmetric solution of the scalar equation w w w3 0 in mathbb b w 0 on partial mathbb b within a hartree fock approximation the result provides a theoretical indication of phase separation into many nodal domains for bose einstein double condensates with strong repulsion

infinitely many solutions to a linearly coupled schrodinger system with non symmetric potentials we study a linearly coupled schrodinger system in n n 3 assume that the potentials in the system are continuous functions satisfying suitable decay assumptions but without any symmetry properties and the parameters in the system satisfy some suitable restrictions using the liapunov schmidt reduction methods two times and combining localized energy method we prove that the problem has infinitely many positive synchronized solutions which extends result theorem 1 2 about nonlinearly coupled schrodinger equations in ao and wei calculus var partial differ equations 51 761 798 2014 to our linearly coupled problem

diffeomorphisms groups and pattern matching in image analysis in a previous paper it was proposed to see the deformations of a common pattern as the action of an infinite dimensional group we show in this paper that this approac h can be applied numerically for pattern matching in image analysis of digital images using lie group ideas we construct a distance between deformations defined through a metric given the cost of infinitesimal deformations then we propose a numerical scheme to solve a variational problem involving this distance and leading to a sub optimal gradient pattern matching its links with fluid models are established

multiple existence of solutions for coupled nonlinear schrodinger equations abstract in this paper we consider the multiple existence of solutions of the coupled nonlinear schrodinger equations p u 1 u u 3 v 2 u in r 3 v 2 v v 3 u 2 v in r 3 where 1 2 and 0

a nonconservative lagrangian framework for statistical fluid registration safira in this paper we used a nonconservative lagrangian mechanics approach to formulate a new statistical algorithm for fluid registration of 3 d brain images this algorithm is named safira acronym for statistically assisted fluid image registration algorithm a nonstatistical version of this algorithm was implemented where the deformation was regularized by penalizing deviations from a zero rate of strain in the terms regularizing the deformation included the covariance of the deformation matrices and the vector fields q here we used a lagrangian framework to reformulate this algorithm showing that the regularizing terms essentially allow nonconservative work to occur during the flow given 3 d brain images from a group of subjects vector fields and their corresponding deformation matrices are computed in a first round of registrations using the nonstatistical implementation covariance matrices for both the deformation matrices and the vector fields are then obtained and incorporated separately or jointly in the nonconservative terms creating four versions of safira we evaluated and compared our algorithms performance on 92 3 d brain scans from healthy monozygotic and dizygotic twins 2 d validations are also shown for corpus callosum shapes delineated at midline in the same subjects after preliminary tests to demonstrate each method we compared their detection power using tensor based morphometry tbm a technique to analyze local volumetric differences in brain structure we compared the accuracy of each algorithm variant using various statistical metrics derived from the images and deformation fields all these tests were also run with a traditional fluid method which has been quite widely used in tbm studies the versions incorporating vector based empirical statistics on brain variation were consistently more accurate than their counterparts when used for automated volumetric quantification in new brain images this suggests the advantages of this approach for large scale neuroimaging studies

dynamic programming generation of curves on brain surfaces dynamic programming algorithms are presented for automated generation of length minimizing geodesics and curves of extremal curvature on the neocortex of the macaque and the visible human probabilistic models of curve variation are constructed in terms of the variability in speed curvature and torsion in the frenet representation

nonlinear camera response functions and image deblurring theoretical analysis and practice this paper investigates the role that nonlinear camera response functions crfs have on image deblurring we present a comprehensive study to analyze the effects of crfs on motion deblurring in particular we show how nonlinear crfs can cause a spatially invariant blur to behave as a spatially varying blur we prove that such nonlinearity can cause large errors around edges when directly applying deconvolution to a motion blurred image without crf correction these errors are inevitable even with a known point spread function psf and with state of the art regularization based deconvolution algorithms in addition we show how crfs can adversely affect psf estimation algorithms in the case of blind deconvolution to help counter these effects we introduce two methods to estimate the crf directly from one or more blurred images when the psf is known or unknown our experimental results on synthetic and real images validate our analysis and demonstrate the robustness and accuracy of our approaches

bifurcation diagrams of coupled schrodinger equations radially symmetric solutions of many important systems of partial differential equations can be reduced to systems of special ordinary differential equations a numerical solver for initial value problems for such systems is developed based on matlab and numerical bifurcation diagrams are obtained according to the behavior of the solutions various bifurcation diagrams of coupled schrodinger equations from nonlinear physics are obtained which suggests the uniqueness of the ground state solution

existence of multiple solutions to a class of nonlinear schrodinger system with external sources terms abstract we study a class of nonlinear schrodinger system with external sources terms as perturbations in order to obtain existence of multiple solutions this system arises from bose einstein condensates etc as these external sources terms are positive functions and small in some sense we use nehari manifold to get the existence of a positive ground state solution and a positive bound state solution

a bayesian hierarchical nonoverlapping random disc growth model a methodology is proposed to efficiently model a random set via a multistage hierarchical bayesian model we define a nonoverlapping random disk model nordm which is similar in spirit to the well known poisson boolean model this model is formulated in a conditional setting that facilitates bayesian sampling of important parameters in the model this framework can accommodate any object not just those with disk shapes although the model can be easily extended to include any known compact convex set instead of the disc e g polygons or ellipses we further propose a growth model that is conceptually simple and allows straightforward estimation of parameters without the need for tedious calculations of hitting or inclusion probabilities the model is applied to severe storm cell development as obtained from weather radar

solutions with a prescribed number of zeros for nonlinear schrodinger systems abstract we find an interval of some parameters where there exists a sign changing solution of nonlinear schrodinger systems having a prescribed number of zeros

multi bump bound states for a system of nonlinear schrodinger equations abstract motivated by problems arising in nonlinear optics and bose einstein condensates we consider in r n with n 3 the following system of coupled schrodinger equations u i v i x u i u i j 1 d i j u j 2 u i 0 lim x u i x 0 i 1 d where 0 is a parameter i j j i are positive constants and v i non negative given potentials we assume that the interior of i 1 d v i 1 0 admits m connected components 1 m which are of class c 1 and isolated in each v i 1 0 for each non empty j 1 m we prove that the system admits for any large a multi bump solution u r n r d which is small in r n j j j and on each j j j close in h 1 norm to a least energy solution of the limit problem u i u i j 1 d i j u j 2 i 1 d subjected to homogeneous dirichlet boundary condition an explicit condition on the matrix i j is given to ensure our solutions have at least two positive components

a minimal energy tracking method for non radially symmetric solutions of coupled nonlinear schrodinger equations we aim at developing methods to track minimal energy solutions of time independent m component coupled discrete nonlinear schrodinger dnls equations we first propose a method to find energy minimizers of the 1 component dnls equation and use it as the initial point of the m component dnls equations in a continuation scheme we then show that the change of local optimality occurs only at the bifurcation points the fact leads to a minimal energy tracking method that guides the choice of bifurcation branch corresponding to the minimal energy solution curve by combining all these techniques with a parameter switching scheme we successfully compute a non radially symmetric energy minimizer that can not be computed by existing numerical schemes straightforwardly

nonlinear and nonideal sampling theory and methods we study a sampling setup where a continuous time signal is mapped by a memoryless invertible and nonlinear transformation and then sampled in a nonideal manner such scenarios appear for example in acquisition systems where a sensor introduces static nonlinearity before the signal is sampled by a practical analog to digital converter we develop the theory and a concrete algorithm to perfectly recover a signal within a subspace from its nonlinear and nonideal samples three alternative formulations of the algorithm are described that provide different insights into the structure of the solution a series of oblique projections approximated projections onto convex sets and quasi newton iterations using classical analysis techniques of descent based methods and recent results on frame perturbation theory we prove convergence of our algorithm to the true input signal we demonstrate our method by simulations and explain the applicability of our theory to wiener hammerstein analog to digital hybrid systems

a sharp threshold of blow up for coupled nonlinear schrodinger equations this paper is concerned with the coupled supercritical nonlinear schrodinger equations which have applications in many physical problems especially in nonlinear optics two types of new invariant evolution flows are established a sharp threshold of blow up and global existence of solutions for the equations is derived it is shown that the main result obtained includes parts of those presented by fanelli and montefusco 2007 j phys a math theor 40 14139 50x

existence and asymptotic behavior of vector solutions for coupled nonlinear kirchhoff type systems abstract this paper deals with the following linearly coupled nonlinear kirchhoff type system a 1 b 1 r 3 u 2 d x u 1 u f u v in r 3 a 2 b 2 r 3 v 2 d x v 2 v g v u in r 3 u v h 1 r 3 where a i 0 b i 0 i 0 are constants for i 1 2 0 is a parameter and f g c r r under the general berestycki lions type assumptions on f and g we establish the existence of positive vector solutions and positive vector ground state solutions respectively by using variational methods we also study the asymptotic behavior of these solutions as 0

positive solutions for a weakly coupled nonlinear schrodinger system abstract existence of a nontrivial solution is established via variational methods for a system of weakly coupled nonlinear schrodinger equations the main goal is to obtain a positive solution of minimal action if possible with all vector components not identically zero generalizations for nonautonomous systems are considered

on the classification of standing wave solutions to a coupled schrodinger system in this paper we consider a nonlinear elliptic system which is an extension of the single equation derived by investigating the stationary states of the nonlinear schrodinger equation we establish the existence and uniqueness of solutions to the dirichlet problem on the ball and entire space as the parameters within certain regions in addition a complete structure of different types of solutions for the radial case is also provided

special set and solutions of coupled nonlinear schrodinger equations a special set of n coupled nonlinear schrodinger equations which consists of 2n interaction types each of which is characterized by a specific array of interaction parameters is presented it is shown that every lame function of order n n is a solution for one or more components for one or more interaction types of this special set simple rules that relate interaction and solution types and interesting features of these relationships are presented

least energy solitary waves for a system of nonlinear schrodinger equations in mathbb r n in this paper we consider systems of coupled schrodinger equations which appear in nonlinear optics the problem has been considered mostly in the one dimensional case here we make a rigorous study of the existence of least energy standing waves solitons in higher dimensions we give conditions on the parameters of the system under which it possesses a solution with least energy among all multi component solutions conditions under which the system does not have positive solutions and the associated energy functional cannot be minimized on the natural set where the solutions lie

stationary solitons of a three wave model generated by type ii second harmonic generation in quadratic media abstract in this paper we prove the uniqueness of stationary standing wave solutions of an optical model generated by type ii second harmonic generation shg with behaviors tending to zero at infinity under certain conditions on parameters in addition we provide the same issues for the dirichlet boundary value problems on the ball centered at the origin a classification of solutions for radial case is also established

multiple positive solutions for linearly coupled nonlinear elliptic systems with critical exponent abstract this paper deals with the following system linearly coupled by nonlinear elliptic equations u 1 u u 2 2 u v x v 2 v v 2 2 v u x u v 0 on here is a smooth bounded domain in r n n 3 1 2 1 are constants 1 is the first eigenvalue of h 0 1 2 2 n n 2 is the sobolev critical exponent and r is a coupling parameter by variational method we prove that this system has a positive ground state solution for some 0 via a perturbation argument we show that this system also admits a positive higher energy solution when is small moreover the asymptotic behaviors of the positive ground state and higher energy solutions as 0 are analyzed

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

existence and symmetry of positive ground states for a doubly critical schrodinger system n n 2 and 1 1 satisfying 2 this problem is related to coupled nonlinear schrodinger equations with critical exponent for bose einstein condensate for different ranges of n and 0 we obtain positive ground state solutions via some quite different methods which are all radially symmetric it turns out that the least energy level depends heavily on the relations among and 2 besides for sufficiently small 0 positive solutions are also obtained via a variational perturbation approach note that the palais smale condition can not hold for any positive energy level which makes the study via variational methods rather complicated

a liouville s theorem for a fractional elliptic system with indefinite nonlinearities abstract in this paper we consider a fractional elliptic system with indefinite nonlinearities we prove that every positive bounded solution of the system is monotone increasing along x 1 direction by using the direct method of moving planes based on this monotonicity we obtain the nonexistence of positive solutions and a liouville type results for the fractional elliptic system as an application we get the liouville type results for the fractional elliptic system with cubic nonlinearities

standing waves of a weakly coupled schrodinger system with distinct potential functions abstract the standing wave solutions of a weakly coupled nonlinear schrodinger system with distinct trapping potential functions in r n 1 n 3 are considered this type of system arises from models in bose einstein condensates theory and nonlinear optics the existence of a positive ground state solution is shown when the coupling constant is larger than a sharp threshold value which is explicitly defined in terms of potential functions and system parameters it is also shown that such solutions concentrate near the minimum points of potential functions and multiple positive concentration solutions exist when the topological structure of the set of minimum points satisfies certain condition variational approach is used for the existence and concentration of positive solutions

estimating planar surface orientation using bispectral analysis in this correspondence we propose a direct method for estimating the orientation of a plane from a single view under perspective projection assuming that the underlying planar texture has random phase we show that the nonlinearities introduced by perspective projection lead to higher order correlations in the frequency domain we also empirically show that these correlations are proportional to the orientation of the plane minimization of these correlations using tools from polyspectral analysis yields the orientation of the plane we show the efficacy of this technique on synthetic and natural images

spike layer solutions to singularly perturbed semilinear systems of coupled schrodinger equations abstract let be a bounded domain in r n n 3 we are concerned with the interaction and the configuration of spikes in a double condensate by analyzing the least energy solutions of the following two couple schrodinger equations in se e 2 u u 1 u 3 u v 2 e 2 v v 2 v 3 u 2 v u 0 v 0 where 1 2 are positive constants we prove that under neumann or dirichlet boundary conditions for any e 0 when min 1 2 or max 1 2 system se has a least energy solution u e v e and when min 1 2 max 1 2 system se has no solution suppose p e q e are the local maximum points of u e v e respectively then under neumann boundary conditions as e small enough both of p e q e locate on the boundary of furthermore when 0 p e q e e 0 as e 0 and for n 2 and n 3 p e q e converge to the same point on the boundary which is the maximum point of mean curvature of the boundary however when 0 p e q e e as e 0 and suppose p e p and q e q then for n 2 and n 3 p q must be the maximum points of the mean curvature on the boundary and p q might be a same point if the mean curvature of the boundary has only one maximum point under dirichlet boundary conditions we can prove that as long as the least energy solution se exists the same asymptotic behavior of the least energy solution u e v e holds as described in lin and wei 2005 10 for 0 or for 0 thus our results are an extension of the results in lin and wei 2005 10

new existence and symmetry results for least energy positive solutions of schrodinger systems with mixed competition and cooperation terms abstract in this paper we focus on existence and symmetry properties of solutions to the cubic schrodinger system u i i u i j 1 d i j u j 2 u i in r n i 1 d where d 2 i i i 0 i j j i r for j i n 2 3 the underlying domain is either bounded or the whole space and u i h 0 1 or u i h rad 1 r n respectively we establish new existence and symmetry results for least energy positive solutions in the case of mixed cooperation and competition coefficients as well as in the purely cooperative case

statistics of natural images scaling in the woods we study the statistics of an ensemble of images taken in the woods distributions of local quantities such as contrast are scale invariant and have nearly exponential tails power spectra exhibit scaling with a nontrivial exponent these data limit the information content of natural images and point to the importance of gain control strategies in visual processing

sign changing solutions for coupled nonlinear schrodinger equations with critical growth abstract we consider the following nonlinear schrodinger system with critical growth u j j u j i 1 k i j u i 2 2 u j 2 2 2 u j in u j 0 on j 1 k where is a bounded smooth domain in r n 2 2 n n 2 0 j 1 j 1 k 1 is the first eigenvalue of with zero dirichlet boundary condition we consider the repulsive case namely j j 0 j 1 k i j j i 0 i j i j 1 k the existence of infinitely many sign changing solutions as bound states is proved provided n 7 by approximations of systems with subcritical growth and by the concentration analysis on approximating solutions

positive solutions to some systems of coupled nonlinear schrodinger equations abstract we study the existence of nontrivial bound state solutions to the following system of coupled nonlinear time independent schrodinger equations u j j u j j u j 3 k 1 k j n j k u j u k 2 u j w 1 2 r n j 1 n where n 1 2 3 j j 0 for j 1 n the coupling parameters j k k j r for j k 1 n j k precisely we prove the existence of nonnegative bound state solutions for suitable conditions on the coupling factors additionally with more restrictive conditions on the coupled parameters we show that the bound states founded are positive

sharp thresholds of blow up and global existence for the coupled nonlinear schrodinger system in this paper we establish two new types of invariant sets for the coupled nonlinear schrodinger system in the euclidean n space rn and derive two sharp thresholds of blow up and global existence for its solutions some analogous results for the nonlinear schrodinger system posed on the hyperbolic space hn and on the standard 2 sphere s2 are also presented our arguments and constructions are improvements of some previous works on this direction at the end we give some heuristic analysis about the strong instability of the solitary waves the relation between the two types of thresholds is a very interesting problem and we leave it as an open problem for further study

radiometric calibration by rank minimization we present a robust radiometric calibration framework that capitalizes on the transform invariant low rank structure in the various types of observations such as sensor irradiances recorded from a static scene with different exposure times or linear structure of irradiance color mixtures around edges we show that various radiometric calibration problems can be treated in a principled framework that uses a rank minimization approach this framework provides a principled way of solving radiometric calibration problems in various settings the proposed approach is evaluated using both simulation and real world datasets and shows superior performance to previous approaches

group actions homeomorphisms and matching a general framework this paper constructs metrics on the space of images cal i defined as orbits under group actions cal g the groups studied include the finite dimensional matrix groups and their products as well as the infinite dimensional diffeomorphisms examined in trouve 1999 quaterly of applied math and dupuis et al 1998 quaterly of applied math left invariant metrics are defined on the product cal g times cal i thus allowing the generation of transformations of the background geometry as well as the image values examples of the application of such metrics are presented for rigid object matching with and without signature variation curves and volume matching and structural generation in which image values are changed supporting notions such as tissue creation in carrying one image to another

existence and nonexistence of bound state solutions for schrodinger systems with linear and nonlinear couplings abstract we study the schrodinger systems with linear and nonlinear coupling terms doubly coupled nonlinear schrodinger system for short which arise naturally in nonlinear optics and in the hartree fock theory for bose einstein condensates among other physical problems first for small linear coupling constant we get existence of a nontrivial bound state solution to the system via perturbation method furthermore we prove each component of the bound state solution is nonnegative by energy estimate second we establish a version of pohozaev nehari identity and prove a nonexistence result for the more general system when the spatial dimension n 4

positive ground state solutions and multiple nontrivial solutions for coupled critical elliptic systems in this study we consider the following coupled elliptic system with a sobolev critical exponent p u1 1u1 1u1p1 1 1u12 1 u12 2 1u22 2 x u2 2u2 2u2p2 1 2u22 1 u12 2u22 2 1 x u1 u2 0in u1 u2 0on where rn is a bounded smooth domain n 5 2 0 for j 1 2 and 1 is the first eigenvalue of with the dirichlet boundary condition we demonstrate the existence of a positive ground state solution for problem p when the coupling parameter 1 2 under some other conditions we show the nonexistence of positive solutions for p when n 3 we also construct multiple nontrivial solutions and sign changing solutions for the following system u1 1u1 1u13 u22u1 x u2 2u2 2u23 u12u2 x u1 u2 0on where rn is a bounded smooth domain and n 4

two component bose einstein condensates abstract recently coupled systems of nonlinear schrodinger equations have been used extensively to describe bose einstein condensates in this paper we study the structure of vortices of the coupled nonlinear equations for two component bose einstein condensates bec in a three dimensional space we show that vortices is 1 rectifiable set and give its mean curvature in particular we show that large interspecies scattering length causes vortices for two component bec

uniform holder bounds for nonlinear schrodinger systems with strong competition for the positive solutions of the gross pitaevskii system u u 1 u 3 u v 2 v v 2 v 3 u 2 v we prove that l boundedness implies c 0 boundedness for every 0 1 uniformly as moreover we prove that the limiting profile as is lipschitz continuous the proof relies upon the blowup technique and the monotonicity formulae by almgren and alt caffarelli and friedman this system arises in the hartree fock approximation theory for binary mixtures of bose einstein condensates in different hyperfine states extensions to systems with k 2 densities are given

ground state of n coupled nonlinear schrodinger equations in mathbb r n n leq 3 we establish some general theorems for the existence and nonexistence of ground state solutions of steady state n coupled nonlinear schrodinger equations the sign of coupling constants ij s is crucial for the existence of ground state solutions when all ij s are positive and the matrix is positively definite there exists a ground state solution which is radially symmetric however if all ij s are negative or one of ij s is negative and the matrix is positively definite there is no ground state solution furthermore we find a bound state solution which is non radially symmetric when n 3

blowup and solitary wave solutions with ring profiles of two component nonlinear schrodinger systems abstract blowup ring profiles have been investigated by finding non vortex blowup solutions of nonlinear schrodinger equations nlses cf fibich et al 2005 7 and fibich et al 2007 8 however those solutions have infinite l 2 norm so one may not maintain the ring profile all the way up to the singularity to find h 1 non vortex blowup solutions with ring profiles we study the blowup solutions of two component systems of nlses with nonlinear coefficients and j j 1 2 when 0 and 1 2 0 the two component system can be transformed into a multi scale system with fast and slow variables which may produce h 1 blowup solutions with non vortex ring profiles we use the localized energy method with symmetry reduction to construct these solutions rigorously on the other hand these solutions may describe steady non vortex bright ring solitons various types of ring profiles including m ring and ring ring profiles are presented by numerical solutions

solitary and self similar solutions of two component system of nonlinear schrodinger equations conventionally to learn wave collapse and optical turbulence one must study finite time blow up solutions of one component self focusing nonlinear schrodinger equations nlse here we consider simultaneous blow up solutions of two component systems of self focusing nlse by studying the associated self similar solutions we prove two components of solutions blow up at the same time these self similar solutions may come from solitary wave solutions with multi bumps forming abundant geometric patterns which cannot be found in one component self focusing nlse our results may provide the first step to investigate optical turbulence in two component systems of nlse

semitrivial vs fully nontrivial ground states in cooperative cubic schrodinger systems with d 3 equations abstract in this work we consider the weakly coupled schrodinger cubic system u i i u i i u i 3 u i j i b i j u j 2 u i h 1 r n r i 1 d where 1 n 3 i i 0 and b i j b j i 0 for i j this system admits semitrivial solutions that is solutions u u 1 u d with null components we provide optimal qualitative conditions on the parameters i i and b i j under which the ground state solutions have all components nontrivial or conversely are semitrivial this question had been clarified only in the d 2 equations case for d 3 equations prior to the present paper only very restrictive results were known namely when the above system was a small perturbation of the super symmetrical case i and b i j b we treat the general case uncovering in particular a much more complex and richer structure with respect to the d 2 case

symmetry properties in systems of semilinear elliptic equations abstract we investigate symmetry properties of solutions of systems of semilinear elliptic equations the two main tools we use consist of the maximum principle and the device of moving parallel planes to a critical position and then showing that the solution is symmetric about the limiting plane an application to the belousov zhabotinskii chemical reaction is given

a pattern theoretic characterization of biological growth mathematical and statistical modeling of biological growth is an important problem in medical diagnostics here we seek tools to analyze changes in anatomical parts using images collected over time we introduce a structured model called growth by random iterated diffeomorphisms grid that treats a cumulative growth deformation as a composition of several elementary deformations each elementary deformation applies to a small region by capturing deformation local to that region and is characterized by a seed and a radial deformation pattern around that seed these grid variables seed locations and radial deformation patterns are estimated from observed images in two steps 1 estimate a cumulative deformation over an observation interval 2 estimate grid variables using maximum likelihood criterion from this estimated cumulative deformation we demonstrate this framework using an mri image data of a rat s brain growth for future statistical analysis we propose a time varying poisson process for the seed placements and a random drawing from a predetermined catalog of deformations for the radial deformation patterns

sparse adaptive parameterization of variability in image ensembles this paper introduces a new parameterization of diffeomorphic deformations for the characterization of the variability in image ensembles dense diffeomorphic deformations are built by interpolating the motion of a finite set of control points that forms a hamiltonian flow of self interacting particles the proposed approach estimates a template image representative of a given image set an optimal set of control points that focuses on the most variable parts of the image and template to image registrations that quantify the variability within the image set the method automatically selects the most relevant control points for the characterization of the image variability and estimates their optimal positions in the template domain the optimization in position is done during the estimation of the deformations without adding any computational cost at each step of the gradient descent the selection of the control points is done by adding a l 1 prior to the objective function which is optimized using the fista algorithm

segregated and synchronized vector solutions for nonlinear schrodinger systems we consider the following nonlinear schrodinger system in mathbb r 3 left begin array ll delta u p x u mu u 2 u beta v 2u quad x in mathbb r 3 delta v q x v nu v 2 v beta u 2v quad x in mathbb r 3 end array right where p r and q r are positive radial potentials mu 0 nu 0 and beta in mathbb r is a coupling constant this type of system arises in particular in models in bose einstein condensates theory

symmetric ground state solutions of m coupled nonlinear schrodinger equations abstract we prove the existence of radial and radially decreasing ground states of an m coupled nonlinear schrodinger equation with a general nonlinearity

toward a comprehensive framework for the spatiotemporal statistical analysis of longitudinal shape data this paper proposes an original approach for the statistical analysis of longitudinal shape data the proposed method allows the characterization of typical growth patterns and subject specific shape changes in repeated time series observations of several subjects this can be seen as the extension of usual longitudinal statistics of scalar measurements to high dimensional shape or image data the method is based on the estimation of continuous subject specific growth trajectories and the comparison of such temporal shape changes across subjects differences between growth trajectories are decomposed into morphological deformations which account for shape changes independent of the time and time warps which account for different rates of shape changes over time given a longitudinal shape data set we estimate a mean growth scenario representative of the population and the variations of this scenario both in terms of shape changes and in terms of change in growth speed then intrinsic statistics are derived in the space of spatiotemporal deformations which characterize the typical variations in shape and in growth speed within the studied population they can be used to detect systematic developmental delays across subjects in the context of neuroscience we apply this method to analyze the differences in the growth of the hippocampus in children diagnosed with autism developmental delays and in controls result suggest that group differences may be better characterized by a different speed of maturation rather than shape differences at a given age in the context of anthropology we assess the differences in the typical growth of the endocranium between chimpanzees and bonobos we take advantage of this study to show the robustness of the method with respect to change of parameters and perturbation of the age estimates

filters random fields and maximum entropy frame towards a unified theory for texture modeling this article presents a statistical theory for texture modeling this theory combines filtering theory and markov random field modeling through the maximum entropy principle and interprets and clarifies many previous concepts and methods for texture analysis and synthesis from a unified point of view our theory characterizes the ensemble of images i with the same texture appearance by a probability distribution f i on a random field and the objective of texture modeling is to make inference about f i given a set of observed texture examples in our theory texture modeling consists of two steps 1 a set of filters is selected from a general filter bank to capture features of the texture these filters are applied to observed texture images and the histograms of the filtered images are extracted these histograms are estimates of the marginal distributions of f i this step is called feature extraction 2 the maximum entropy principle is employed to derive a distribution p i which is restricted to have the same marginal distributions as those in 1 this p i is considered as an estimate of f i this step is called feature fusion a stepwise algorithm is proposed to choose filters from a general filter bank the resulting model called frame filters random fields and maximum entropy is a markov random field mrf model but with a much enriched vocabulary and hence much stronger descriptive ability than the previous mrf models used for texture modeling gibbs sampler is adopted to synthesize texture images by drawing typical samples from p i thus the model is verified by seeing whether the synthesized texture images have similar visual appearances to the texture images being modeled experiments on a variety of 1d and 2d textures are described to illustrate our theory and to show the performance of our algorithms these experiments demonstrate that many textures which are previously considered as from different categories can be modeled and synthesized in a common framework

on strongly indefinite systems involving the fractional laplacian abstract this paper is devoted to study strongly indefinite systems involving the fractional laplacian on bounded domains explicitly we obtain existence and non existence results a p r i o r i estimates of gidas spruck type and a symmetry result in addition we give a different proof for the a p r i o r i estimate for nonlinear elliptic problems with the fractional laplacian obtained in cabre and tan 2010 and tan 2013

multi peak solutions to coupled schrodinger systems with neumann boundary conditions abstract in this paper we are concerned with the following two coupled schrodinger systems in a bounded domain r n n 2 3 with neumann boundary conditions e 2 u u 1 u 3 u v 2 e 2 v v 2 v 3 u 2 v u 0 v 0 u n 0 v n 0 on suppose the mean curvature h p of the boundary has several local minimums or local maximums we obtain the existence of solutions with multi peaks to the system with all peaks being on the boundary and all peaks locate either near the local maxima or near the local minima of the mean curvature at the boundary of the domain

blow up behavior of ground states for a nonlinear schrodinger system with attractive and repulsive interactions abstract we consider a nonlinear schrodinger system arising in a two component bose einstein condensate bec with attractive intraspecies interactions and repulsive interspecies interactions in r 2 we get ground states of this system by solving a constrained minimization problem for some kinds of trapping potentials we prove that the minimization problem has a minimizer if and only if the attractive interaction strength a i i 1 2 of each component of the bec system is strictly less than a threshold a furthermore as a 1 a 2 a a the asymptotical behavior for the minimizers of the minimization problem is discussed our results show that each component of the bec system concentrates at a global minimum of the associated trapping potential

multiplicity of localized solutions of nonlinear schrodinger systems for infinite attractive case abstract in this paper we consider the following nonlinear schrodinger system 2 u v 1 x u u v 2 in r n u h 1 r n 2 v v 2 x v u 2 v in r n v h 1 r n where n 3 0 1 v i c 1 r n r 0 inf x r n v i x sup x r n v i x i 1 2 and there exists a bounded open set r n with smooth boundary such that inf x min v 1 x v 2 x 0 we prove the existence of a given number of semi positive solutions localized in here we say u v is semi positive if either u 0 or v 0

note on ground states of a nonlinear schrodinger system abstract we give a sufficient condition for the existence of positive radial ground states of the time independent schrodinger system u 1 u 1 1 u 1 3 12 u 2 2 u 1 13 u 3 2 u 1 in r n u 2 u 2 12 u 1 2 u 2 2 u 2 3 23 u 3 2 u 2 in r n u 3 u 3 13 u 1 2 u 3 23 u 2 2 u 3 3 u 3 3 in r n u 1 x 0 u 2 x 0 u 3 x 0 as x where n 1 2 3 0 j 0 and i j 0 i j for i j 1 2 3 and in some special cases our conditions are also necessary