time fractional telegraph equations and telegraph processes with brownian time we study the fundamental solutions to time fractional telegraph equations of order 2 we are able to obtain the fourier transform of the solutions for any and to give a representation of their inverse in terms of stable densities for the special case 1 2 we can show that the fundamental solution is the distribution of a telegraph process with brownian time in a special case this becomes the density of the iterated brownian motion which is therefore the fundamental solution to a fractional diffusion equation of order 1 2 with respect to time

an energy conservative difference scheme for the nonlinear fractional schrodinger equations abstract in this paper an energy conservative crank nicolson difference scheme for nonlinear riesz space fractional schrodinger equations is studied we give a rigorous analysis of the conservation properties including mass conservation and energy conservation in the discrete sense based on brouwer fixed point theorem the existence of the difference solution is proved by virtue of the energy method the difference solution is shown to be unique and convergent at the order of o 2 h 2 in the l 2 norm with time step and mesh size h finally a linearized iterative algorithm is presented and numerical experiments are given to confirm the theoretical results

collocation method for fractional quantum mechanics we show that it is possible to obtain numerical solutions to quantum mechanical problems involving a fractional laplacian using a collocation approach based on little sinc functions which discretizes the schrodinger equation on a uniform grid the different boundary conditions are naturally implemented using sets of functions with the appropriate behavior good convergence properties are observed a comparison with results based on a wentzel kramers brillouin analysis is performed

invariant image recognition by zernike moments the problem of rotation scale and translation invariant recognition of images is discussed a set of rotation invariant features are introduced they are the magnitudes of a set of orthogonal complex moments of the image known as zernike moments scale and translation invariance are obtained by first normalizing the image with respect to these parameters using its regular geometrical moments a systematic reconstruction based method for deciding the highest order zernike moments required in a classification problem is developed the quality of the reconstructed image is examined through its comparison to the original one the orthogonality property of the zernike moments which simplifies the process of image reconstruction make the suggest feature selection approach practical features of each order can also be weighted according to their contribution to the reconstruction process the superiority of zernike moment features over regular moments and moment invariants was experimentally verified

some solutions to the space fractional schrodinger equation using momentum representation method the space fractional schrodinger equation with linear potential delta function potential and coulomb potential is studied under momentum representation using fourier transformation by use of mellin transform and its inverse transform we obtain the energy levels and wave functions expressed in h function for a particle in linear potential field the wave function expressed also by the h function and the unique energy level of the bound state for the particle of even parity state in delta function potential well which is proved to have no action on the particle of odd parity state is also obtained the integral form of the wave functions for a particle in coulomb potential field is shown and the corresponding energy levels which have been discussed in laskin s paper phys rev e 66 056108 2002 are proved to satisfy an equality of infinite limit of the h function all of these results contain the ones of the standard quantum mechanics as their special cases

3d model retrieval and classification by semi supervised learning with content based similarity the rapid development of 3d digital technology has led to an increasing volume of 3d model data in addressing the management of such large scale data effective content based 3d model retrieval and recognition methods are highly desirable in 3d model retrieval and recognition tasks the distance measure between two 3d models plays an important role in this paper we propose a novel 3d model retrieval and recognition method that employs both a distance histogram and 3d moment invariants as features that are invariant to 3d object scaling translation and rotation disjoint information is used to measure the distance between the feature histograms and the euclidean distance is applied in calculating the distance between two moment features these measures are then combined as the 3d model distance using this distance measure the relationships between all 3d models in the dataset are formulated as a graph structure a semi supervised learning process is then conducted to estimate the relevance among the 3d models and this is employed for 3d model retrieval and classification to evaluate the effectiveness of the proposed method we conduct experiments on two datasets experimental results and a comparison with state of the art methods demonstrate that the proposed method achieves improved performance for 3d model retrieval and recognition tasks

sign changing bubble towers for asymptotically critical elliptic equations on riemannian manifolds given a smooth compact riemannian n manifold m g we consider the equation gu hu u 2 2 eu where h is a c1 function on m the exponent 2 2n n 2 is the critical sobolev exponent and e is a small positive real parameter such that e 0 we prove the existence of blowing up families of sign changing solutions which develop bubble towers at some point where the function h is greater than the yamabe potential n 24 n 1 scalg

graph based characteristic view set extraction and matching for 3d model retrieval in recent times multi view representation of the 3d model has led to extensive research in view based methods for 3d model retrieval however most approaches focus on feature extraction from 2d images while ignoring the spatial information of the 3d model in order to improve the effectiveness of view based methods on 3d model retrieval this paper proposes a novel method for characteristic view extraction and similarity measurement first the graph clustering method is used for view grouping and the random walk algorithm is applied to adaptively update the weight of each view the spatial information of the 3d object is utilized to construct a view graph model thus enabling each characteristic view to represent the discriminative visual feature in terms of specific spatial context next by considering the view set as a graph model the similarity measurement of two models can be converted into a graph matching problem this problem is solved by mathematically formulating it as a rayleigh quotient maximization with affinity constraints for similarity measurement extensive comparison experiments were conducted on the popular eth ntu psb and mv red 3d model datasets the results demonstrate the superiority of the proposed method

the fractional schrodinger equation with hardy type potentials and sign changing nonlinearities abstract we look for solutions to a fractional schrodinger equation of the following form 2 u v x x u f x u k x u q 2 u o n r n 0 where v is bounded and close to periodic potential and x is a hardy type potential we assume that v is positive and f has the subcritical growth but not higher than u q 2 u if is positive and small enough we find a ground state solution i e a critical point of the energy being minimizer on the nehari manifold if is negative we show that there is no ground state solutions we are also interested in an asymptotic behaviour of solutions as 0 and k 0

a fast linearized conservative finite element method for the strongly coupled nonlinear fractional schrodinger equations abstract in this paper a fast linearized conservative finite element method is studied for solving the strongly coupled nonlinear fractional schrodinger equations we prove that the scheme preserves both the mass and energy which are defined by virtue of some recursion relationships using the sobolev inequalities and then employing the mathematical induction the discrete scheme is proved to be unconditionally convergent in the sense of l 2 norm and h 2 norm which means that there are no any constraints on the grid ratios then the prior bound of the discrete solution in l 2 norm and l norm are also obtained moreover we propose an iterative algorithm by which the coefficient matrix is independent of the time level and thus it leads to toeplitz like linear systems that can be efficiently solved by krylov subspace solvers with circulant preconditioners this method can reduce the memory requirement of the proposed linearized finite element scheme from o m 2 to o m and the computational complexity from o m 3 to o m log m in each iterative step where m is the number of grid nodes finally numerical results are carried out to verify the correction of the theoretical analysis simulate the collision of two solitary waves and show the utility of the fast numerical solution techniques

an algorithm for weighted sub graph matching based on gradient flows an algorithm for matching the weighted sub graphs based on gradient flows is proposed in this paper first the smaller and larger graphs for matching are represented by means of their weighted adjacency matrices then an objective function is introduced to measure the differences between two weighted adjacency matrices because the permutation matrix for graph matching is usually relaxed to an orthogonal matrix with non negative elements an optimization based approach is adopted to navigate the solution toward an appropriate permutation matrix to accomplish this goal two gradient flows in the space of orthogonal matrices are defined in such a way that they minimize the objective functions one minimizes the objective function in the space of orthogonal matrices and the other minimizes the distance of an orthogonal matrix from the set of permutations in addition two cost functions are introduced to force satisfaction approximately of the constraint that a translation matrix must have integer entries of different values the experimental results show that the proposed sub graph matching is feasible

the global solution for a class of systems of fractional nonlinear schrodinger equations with periodic boundary condition in this paper we consider a class of systems of fractional nonlinear schrodinger equations we prove the existence and uniqueness of the global solution to the periodic boundary value problem by using the faedo galerkin method

existence and stability of standing waves for nonlinear fractional schrodinger equations in this paper we consider the nonlinear fractional schrodinger equations by studying constrained minimization problems and applying the method of concentration compactness and commutator estimates we obtain the existence of standing waves for nonlinear fractional schrodinger equations under some assumptions moreover we prove that the set of minimizers is a stable set for the initial value problem of the equations in the sense that a solution which starts near the set will remain near it for all time

analysis of the damped nonlinear space fractional schrodinger equation abstract in this paper we verify the unique existence of the global smooth solution of the damped nonlinear space fractional schrodinger dnfs equation and show it follows a conformal mass conservation law we propose a conformal mass preserving linearized scheme it is rigorously proved that this scheme preserves the discrete conformal mass furthermore we prove that the proposed scheme admits a unique solution and is of second order convergence in space and first order convergence in time some numerical experiments are carried out to validate the theoretical analysis

on mittag leffler type functions in fractional evolution processes abstract we review a variety of fractional evolution processes so defined being governed by equations of fractional order whose solutions turn out to be related to mittag leffler type functions the chosen equations are the simplest of the fractional calculus and include the abel integral equations of the second kind which are relevant in typical inverse problems and the fractional differential equations which govern generalized relaxation and oscillation phenomena

on the nonlocality of the fractional schrodinger equation a number of papers over the past eight years have claimed to solve the fractional schrodinger equation for systems ranging from the one dimensional infinite square well to the coulomb potential to one dimensional scattering with a rectangular barrier however some of the claimed solutions ignore the fact that the fractional diffusion operator is inherently nonlocal preventing the fractional schrodinger equation from being solved in the usual piecewise fashion we focus on the one dimensional infinite square well and show that the purported ground state which is based on a piecewise approach is definitely not a solution of the fractional schrodinger equation for the general fractional parameter on a more positive note we present a solution to the fractional schrodinger equation for the one dimensional harmonic oscillator with 1

bubble tower radial solutions in the slightly supercritical brezis nirenberg problem abstract in this paper we consider the brezis nirenberg problem in dimension n 4 in the supercritical case we prove that if the exponent gets close to n 2 n 2 and if simultaneously the bifurcation parameter tends to zero at the appropriate rate then there are radial solutions which behave like a superposition of bubbles namely solutions of the form j 1 k 1 1 m j 4 n 2 y 2 n 2 2 m j 1 o 1 n n 2 n 2 4 where mj and mj o mj 1 for all j these solutions lie close to turning points to the right of the associated bifurcation diagram

multidimensional solutions of space fractional diffusion equations green s functions and propagators for the multidimensional anisotropic spacetime fractional diffusion equation are obtained in integral form uniqueness of the solutions is studied in the framework

quasi periodic solutions of a fractional nonlinear schrodinger equation in the present paper it is proved that there are many quasi periodic solutions of a class of space fractional nonlinear schrodinger equations with the riesz fractional derivative by means of kam kolmogorov arnold moser theorem in the present paper it is proved that there are many quasi periodic solutions of a class of space fractional nonlinear schrodinger equations with the riesz fractional derivative by means of kam kolmogorov arnold moser theorem

on the ground states and dynamics of space fractional nonlinear schrodinger gross pitaevskii equations with rotation term and nonlocal nonlinear interactions in this paper we propose some efficient and robust numerical methods to compute the ground states and dynamics of fractional schrodinger equation fse with a rotation term and nonlocal nonlinear interactions in particular a newly developed gaussian sum gausum solver is used for the nonlocal interaction evaluation 31 to compute the ground states we integrate the preconditioned krylov subspace pseudo spectral method 4 and the gausum solver for the dynamics simulation using the rotating lagrangian coordinates transform 14 we first reformulate the fse into a new equation without rotation then a time splitting pseudo spectral scheme incorporated with the gausum solver is proposed to simulate the new fse in parallel to the numerical schemes we also prove some existence and nonexistence results for the ground states dynamical laws of some standard quantities including the mass energy angular momentum and the center of mass are stated the ground states properties with respect to the fractional order and or rotating frequencies dynamics involving decoherence and turbulence together with some interesting phenomena are reported

the role of the green s function in a non linear elliptic equation involving the critical sobolev exponent this paper is concerned with non linear elliptic problems of the type pe u u n 2 n 2 eu u 0 on u 0 on where is a smooth and bounded domain in rn n 4 and e 0 we show that if the ue are solutions of pe which concentrate around a point as e 0 then this point cannot be on the boundary of and is a critical point of the regular part of the green s function conversely we show that for n 5 and any non degenerate critical point x0 of the regular part of the green s function there exist solutions of pe concentrating around x0 as e 0

analysis of time fractional and space nonlocal stochastic nonlinear schrodinger equation driven by multiplicative white noise abstract in this paper we establish the existence and uniqueness of the mild solution and the holder continuity for the time fractional and space nonlocal stochastic nonlinear schrodinger equation driven by multiplicative white noise a full discrete scheme with spectral galerkin method in space and exponential method in time is proposed it is rigorously proved that the numerical scheme admits an unique solution finally we present the optimal error estimates of the proposed scheme based on the regularity analysis

differentiation to fractional orders and the fractional telegraph equation using methods of differential and integral calculus we present and discuss the calculation of a fractional green function associated with the one dimensional case of the so called general fractional telegraph equation with one space variable this is a fractional partial differential equation with constant coefficients the equation is solved by means of juxtaposition of transforms i e we introduce the laplace transform in the time variable and the fourier transform in the space variable several particular cases are discussed in terms of the parameters some known results are recovered as a by product of our main result we obtain two new relations involving the two parameter mittag leffler function

crank nicolson difference scheme for the coupled nonlinear schrodinger equations with the riesz space fractional derivative in this paper the crank nicolson cn difference scheme for the coupled nonlinear schrodinger equations with the riesz space fractional derivative is studied the existence of this difference solution is proved by the brouwer fixed point theorem the stability and convergence of the cn scheme are discussed in the l 2 norm when the fractional order is two all those results are in accord with the difference scheme developed for the classical non fractional coupled nonlinear schrodinger equations some numerical examples are also presented

applications of continuity and discontinuity of a fractional derivative of the wave functions to fractional quantum mechanics the space fractional schrodinger equation with a finite square potential periodic potential and delta function potential is studied in this paper we find that the continuity or discontinuity condition of a fractional derivative of the wave functions should be considered to solve the fractional schrodinger equation in fractional quantum mechanics more parity states than those given by standard quantum mechanics for the finite square potential well are obtained the corresponding energy equations are derived and then solved by graphical methods we show the validity of bloch s theorem and reveal the energy band structure for the periodic potential the jump discontinuity condition for the fractional derivative of the wave function of the delta function potential is given with the help of the jump condition we study some delta function potential fields for the delta function potential well an alternate expression of the wave function the h function form of it was given by dong and xu j math phy

parameter estimation for the fractional schrodinger equation using bayesian method in this paper the fractional schrodinger equation is studied the bayesian method is put forward to estimate some relevant parameters of the equation results show that the estimated values can fit well with the exact solution the varying initial values and maximum iterations have little effect on the estimated results it indicates that the bayesian method is efficient for the multi parameter estimation for the fractional schrodinger equation this method can also be used to estimate parameters for the fractional schrodinger equation in other potential field

linearized crank nicolson scheme for the nonlinear time space fractional schrodinger equations abstract in this paper a crank nicolson difference scheme is first derived for solving the nonlinear time space fractional schrodinger equations the truncation error and stability of the scheme are discussed in detail the existence of the numerical solution is shown by the brouwer fixed point theorem for improving the calculating efficiency a three level linearized difference scheme is also proposed and analyzed both schemes are subsequently extended to the nonlinear coupled equations and some similar results are given and proved several numerical experiments are included to verify the accuracy and efficiency of the two types of schemes and comparison with the related work is presented

time fractional schrodinger equation the schrodinger equation is considered with the first order time derivative changed to a caputo fractional derivative the time fractional schrodinger equation the resulting hamiltonian is found to be non hermitian and nonlocal in time the resulting wave functions are thus not invariant under time reversal the time fractional schrodinger equation is solved for a free particle and for a potential well probability and the resulting energy levels are found to increase over time to a limiting value depending on the order of the time derivative new identities for the mittag leffler function are also found and presented in an appendix

fractional schrodinger equation some properties of the fractional schrodinger equation are studied we prove the hermiticity of the fractional hamilton operator and establish the parity conservation law for fractional quantum mechanics as physical applications of the fractional schrodinger equation we find the energy spectra of a hydrogenlike atom fractional bohr atom and of a fractional oscillator in the semiclassical approximation an equation for the fractional probability current density is developed and discussed we also discuss the relationships between the fractional and standard schrodinger equations

bubble towers for supercritical semilinear elliptic equations we construct positive solutions of the semilinear elliptic problem u u up 0 with dirichet boundary conditions in a bounded smooth domain rn n 4 when the exponent p is supercritical and close enough to n 2n 2 and the parameter r is small enough as p n 2n 2 the solutions have multiple blow up at finitely many points which are the critical points of a function whose definition involves green s function our result extends the result of del pino et al j differential equations 193 2 2003 280 when is a ball and the solutions are radially symmetric

analytic and approximate solutions of the space and time fractional telegraph equations the adomian decomposition method is used to obtain analytic and approximate solutions of the space and time fractional telegraph equations the space and time fractional derivatives are considered in the caputo sense the analytic solutions are calculated in the form of series with easily computable terms some examples are given the results reveal that the adomian method is very effective and convenient

generalized lippmann schwinger equation in the fractional quantum mechanics from the three dimensional space fractional schrodinger equation a generalized lippmann schwinger equation for the fractional quantum mechanics is obtained for both scattering and bound states we apply the generalized integral equation to study the fractional quantum scattering problem and give the approximate scattering wavefunction of first order and higher orders

some physical applications of fractional schrodinger equation the fractional schrodinger equation is solved for a free particle and for an infinite square potential well the fundamental solution of the cauchy problem for a free particle the energy levels and the normalized wave functions of a particle in a potential well are obtained in the barrier penetration problem the reflection coefficient and transmission coefficient of a particle from a rectangular potential wall is determined in the quantum scattering problem according to the fractional schrodinger equation the green s function of the lippmann schwinger integral equation is given

bound state for the fractional schrodinger equation with unbounded potential this paper considers the fractional schrodinger equation with unbounded potential we prove the existence of ground state by lagrange multiplier method the standing wave with prescribed frequency is also obtained by nehari s manifold approach in the last part we obtain that the standing wave is bound state

preconditioned modified hermitian and skew hermitian splitting iteration methods for fractional nonlinear schrodinger equations abstract a variant of preconditioned modified hermitian and skew hermitian splitting pmhss iteration method is proposed for a class of toeplitz like complex linear equations arising from the space fractional coupled nonlinear schrodinger equations theoretical analysis show that the new method is convergent unconditionally moreover the choice of the theoretical optimal parameter is further studied in detail which minimize the upper bound of the spectral radius and relate to the extreme eigenvalues of the toeplitz matrix and the extreme absolute values of the diagonal matrix in addition the splitting can be used as a preconditioner for krylov subspaces method numerical experiments show that the proposed method is efficient and the optimal parameter is independent of the mesh size which is very useful in large sparse practical problem

on a generalization of mittag leffler function and its properties abstract let s and z be complex variables s the gamma function and s s s for any complex the generalized pochhammer symbol the principal aim of the paper is to investigate the function e q z n 0 q n n z n n where c re 0 re 0 re 0 and q 0 1 n this is a generalization of the exponential function exp z the confluent hypergeometric function z the mittag leffler function e z the wiman s function e z and the function e z defined by prabhakar for the function e q z its various properties including usual differentiation and integration laplace transforms euler beta transforms mellin transforms whittaker transforms generalised hypergeometric series form mellin barnes integral representation with their several special cases are obtained and its relationship with laguerre polynomials fox h function and wright hypergeometric function is also established

radial solutions for the brezis nirenberg problem involving large nonlinearities abstract let us consider the problem 0 1 u a x u u p in b 1 u 0 in b 1 u 0 on b 1 where b 1 is the unit ball in r n n 3 and a x 0 is a smooth radial function under some suitable assumptions on the regular part of the green function of the operator u n 1 r u a r u we prove the existence of a radial solution to 0 1 for p large enough

neumann problem for nonlinear schrodinger equation with the riesz fractional derivative operator abstract we consider the initial boundary value problem for the fractional schrodinger equation posed on positive half line x 0 u t i u x x i u 2 u x 1 2 u 0 t 0 x 0 u x 0 u 0 x x 0 u x 0 t h t t 0 where x 1 2 is the fractional derivative operator defined by the riesz potential x 1 2 1 2 0 sign x y x y u y y d y we study the global existence in time and asymptotics of solutions to the initial boundary value problem

constant scalar curvature metrics with isolated singularities we extend the results and methods of 6 to prove the existence of constant positive scalar curvature metrics g which are complete and conformal to the standard metric on s where is a disjoint union of submanifolds of dimensions between 0 and n 2 2 the existence of solutions with isolated singularities occupies the majority of the paper their existence was previously established by schoen 12 but the proof we give here based on the techniques of 6 is more direct and provides more information about their geometry when is discrete we also establish that these solutions are smooth points in the moduli spaces of all such solutions introduced and studied in 7 and 8

multi modal clique graph matching for view based 3d model retrieval multi view matching is an important but a challenging task in view based 3d model retrieval to address this challenge we propose an original multi modal clique graph mcg matching method in this paper we systematically present a method for mcg generation that is composed of cliques which consist of neighbor nodes in multi modal feature space and hyper edges that link pairwise cliques moreover we propose an image set based clique edgewise similarity measure to address the issue of the set to set distance measure which is the core problem in mcg matching the proposed mcg provides the following benefits 1 preserves the local and global attributes of a graph with the designed structure 2 eliminates redundant and noisy information by strengthening inliers while suppressing outliers and 3 avoids the difficulty of defining high order attributes and solving hyper graph matching we validate the mcg based 3d model retrieval using three popular single modal data sets and one novel multi modal data set extensive experiments show the superiority of the proposed method through comparisons moreover we contribute a novel real world 3d object data set the multi view rgb d object data set to the best of our knowledge it is the largest real world 3d object data set containing multi modal and multi view information

type ii ancient compact solutions to the yamabe flow nsf 0604657 1266172 0905749 1056387 fondo basal cmm millenium nucleus capde nc130017 fondecyt 1150066

generalized mittag leffler functions in the theory of finite size scaling for systems with strong anisotropy and or long range interaction the difficulties arising in the investigation of finite size scaling in d dimensional o n systems with strong anisotropy and or long range interaction decaying with the interparticle distance r as r d 0 2 are discussed some integral representations aiming at the simplification of the investigations are presented for the classical and quantum lattice sums that take place in the theory special attention is paid to a more general form allowing to treat both cases on an equal footing and in addition cases with strong anisotropic interactions and different geometries the analysis is simplified further by expressing this general form in terms of a generalization of the mittag leffler special functions this turned out to be very useful for the extraction of asymptotic finite size behaviours of the thermodynamic functions

time fractional schrodinger equation fox s h functions and the effective potential after introducing the formalism of the general space and time fractional schrodinger equation we concentrate on the time fractional schrodinger equation and present new results via the elegant language of fox s h functions we show that the general time dependent part of the wave function for the separable solutions of the time fractional schrodinger equation is the mittag leffler function with an imaginary argument by two different methods after separating the mittag leffler function into its real and imaginary parts in contrast to existing works we show that the total probability is 1 and decays with time introducing the effective potential approach we also write the mittag leffler function with an imaginary argument as the product of its purely decaying and purely oscillating parts in the light of these we reconsider the simple box problem

fractional telegraph equations we investigate several aspects of the fractional telegraph equations in an effort to better understand the anomalous diffusion processes observed in blood flow experiments in the earlier work eckstein et al electron j differential equations conf 03 1999 39 50 the telegraph equation d 2 u 2adu au 0 was used where d d dt a nd it was shown that as t tends to infinity u is approximated by v w here 2adv av 0 here a d 2 dx 2 on l 2 r o ra can be a more general nonnegative selfadjoint operator in this paper the concern is with the fractional telegraph equation e 2 u 2aeu au 0 where e d and 0 1 after solving this equation it is shown that u is approximated

kullback leibler upper confidence bounds for optimal sequential allocation we consider optimal sequential allocation in the context of the so called stochastic multi armed bandit model we describe a generic index policy in the sense of gittins 1979 based on upper confidence bounds of the arm payoffs computed using the kullback leibler divergence we consider two classes of distributions for which instances of this general idea are analyzed the kl ucb algorithm is designed for one parameter exponential families and the empirical kl ucb algorithm for bounded and finitely supported distributions our main contribution is a unified finite time analysis of the regret of these algorithms that asymptotically matches the lower bounds of lai and robbins 1985 and burnetas and katehakis 1996 respectively we also investigate the behavior of these algorithms when used with general bounded rewards showing in particular that they provide significant improvements over the state of the art

green s function for the time dependent scattering problem in the fractional quantum mechanics we study the green s function of the time dependent 3d space fractional schrodinger equation for the scattering problem in the fractional quantum mechanics the green s function is expressed in terms of fox s h function and in a computable series form we get the asymptotic formula of the green s function and apply it to obtain the approximate wave function for the fractional quantum scattering problem

fox function representation of non debye relaxation processes applying the liouville riemann fractional calculus we derive and solve a fractional operator relaxation equation we demonstrate how the exponent of the asymptotic power law decay t relates to the order of the fractional operatordv dtv 0 1 continuous time random walk ctrw models offer a physical interpretation of fractional order equations and thus we point out a connection between a special type of ctrw and our fractional relaxation model exact analytical solutions of the fractional relaxation equation are obtained in terms of fox functions by using laplace and mellin transforms apart from fractional relaxation fox functions are further used to calculate fourier integrals of kohlrausch williams watts type relaxation functions because of its close connection to integral transforms the rich class of fox functions forms a suitable framework for discussing slow relaxation phenomena

dynamics of the 3 d fractional complex ginzburg landau equation abstract we study the initial boundary value problem of the fractional complex ginzburg landau equation in three spatial dimensions with the dissipative effect given by a fractional laplacian a priori estimates are derived when the nonlinearity satisfies certain growth conditions using galerkin s method the existence of a global smooth solution is established uniqueness is also proved furthermore the existence of a global attractor is proved and estimates of the hausdorff and fractal dimensions for the global attractor are obtained

highly accurate numerical schemes for multi dimensional space variable order fractional schrdinger equations as a natural generalization of the fractional schrdinger equation the variable order fractional schrdinger equation has been exploited to study fractional quantum phenomena in this paper we develop an exponentially accurate jacobigausslobatto collocation jgl c method to solve the variable order fractional schrdinger equations in one dimension 1d and two dimensions 2d in this method the aforementioned problem is reduced to a system of ordinary differential equations odes in the time variable as a result we propose two efficient schemes for dealing with the numerical solutions of initial value problems for nonlinear system of ordinary differential equations one based on the implicit rungekutta irk method of fourth order and the other based on jacobigaussradau collocation jgr c method the validity and effectiveness of the two methods are demonstrated by solving three numerical examples in 1d and 2d the convergence of the methods is graphically analyzed the results demonstrate that the proposed methods are powerful algorithms with high accuracy for solving the variable order nonlinear partial differential equations

the fractional schrodinger equation for delta potentials the fractional schrodinger equation is solved for the delta potential and the double delta potential for all energies the solutions are given in terms of fox s h function

on the cost of fast controls for some families of dispersive or parabolic equations in one space dimension in this paper we consider the cost of fast controls for a large class of linear equations of parabolic or dispersive type in one space dimension in small time by extending the work of tenenbaum and tucsnak j differential equations 243 2007 pp 70 100 we are able to give precise upper bounds on the time dependance of the cost of fast controls when the time of control t tends to 0 we also give a lower bound of the cost of fast controls for the same class of equations which proves the optimality of the power of t involved in the cost of the control these general results are then applied to treat notably the case of linear kdv equations and fractional heat or schrodinger equations

factorized graph matching graph matching gm is a fundamental problem in computer science and it plays a central role to solve correspondence problems in computer vision gm problems that incorporate pairwise constraints can be formulated as a quadratic assignment problem qap although widely used solving the correspondence problem through gm has two main limitations 1 the qap is np hard and difficult to approximate 2 gm algorithms do not incorporate geometric constraints between nodes that are natural in computer vision problems to address aforementioned problems this paper proposes factorized graph matching fgm fgm factorizes the large pairwise affinity matrix into smaller matrices that encode the local structure of each graph and the pairwise affinity between edges four are the benefits that follow from this factorization 1 there is no need to compute the costly in space and time pairwise affinity matrix 2 the factorization allows the use of a path following optimization algorithm that leads to improved optimization strategies and matching performance 3 given the factorization it becomes straight forward to incorporate geometric transformations rigid and non rigid to the gm problem 4 using a matrix formulation for the gm problem and the factorization it is easy to reveal commonalities and differences between different gm methods the factorization also provides a clean connection with other matching algorithms such as iterative closest point experimental results on synthetic and real databases illustrate how fgm outperforms state of the art algorithms for gm the code is available at http humansensing cs cmu edu fgm

levy path integrals of particle on circle and some applications fractional quantum mechanics in the non relativistic case is described by the space fractional schrodinger equation containing the fractional riesz operator which is a non local operator the non locality makes it difficult to solve the fractional schrodinger equation in the local potentials in this paper we study the solution of the fractional schrodinger equation of a free particle moving on a circle by use of the levy path integrals approach we present the levy path integrals propagator of a particle on circle and then use it to get the wave functions and energy eigenvalues of the free particle case in addition the laplace transform energy time transform and momentum representation of the free particle kernel are also obtained the results of this paper contain the ones in standard quantum mechanics as special cases the problem of a particle on circle is a fundamental problem of path integrals with topological constraints in quantum systems and the method of levy path integrals can be generalized to study more complex local potentials

lipschitz stability criteria for functional differential systems of fractional order in this paper a class of fractional functional differential equations is investigated using differential inequalities and lyapunov like functions lipschitz stability uniform lipschitz stability and global uniform lipschitz stability criteria are proved since the problem of lipschitz stability of dynamic systems is relevant in various contexts including many inverse and control problem our results can be applied in the qualitative investigations of many practical problems of diverse interest

solution of the fractional langevin equation and the mittag leffler functions we introduce the fractional generalized langevin equation in the absence of a deterministic field with two deterministic conditions for a particle with unitary mass i e an initial condition and an initial velocity are considered for a particular correlation function that characterizes the physical process and using the methodology of the laplace transform we obtain the solution in terms of the three parameter mittag leffler function as particular cases some recent results are also presented

generalized fractional schrodinger equation with space time fractional derivatives in this paper the generalized fractional schrodinger equation with space and time fractional derivatives is constructed the equation is solved for free particle and for a square potential well by the method of integral transforms fourier transform and laplace transform and the solution can be expressed in terms of mittag leffler function the green function for free particle is also presented in this paper finally we discuss the relationship between the cases of the generalized fractional schrodinger equation and the ones in standard quantum

a new approach to the maximum flow problem all previously known efficient maximum flow algorithms work by finding augmenting paths either one path at a time as in the original ford and fulkerson algorithm or all shortest length augmenting paths at once using the layered network approach of dinic an alternative method based on the preflow concept of karzanov is introduced a preflow is like a flow except that the total amount flowing into a vertex is allowed to exceed the total amount flowing out the method maintains a preflow in the original network and pushes local flow excess toward the sink along what are estimated to be shortest paths the algorithm and its analysis are simple and intuitive yet the algorithm runs as fast as any other known method on dense graphs achieving an o n 3 time bound on an n vertex graph by incorporating the dynamic tree data structure of sleator and tarjan we obtain a version of the algorithm running in o nm log n 2 m time on an n vertex m edge graph this is as fast as any known method for any graph density and faster on graphs of moderate density the algorithm also admits efficient distributed and parallel implementations a parallel implementation running in o n 2 log n time using n processors and o m space is obtained this time bound matches that of the shiloach vishkin algorithm which also uses n processors but requires o n 2 space

the global analysis on the spectral collocation method for time fractional schrodinger equation abstract in this paper a spectral collocation method is proposed and analyzed for solving the time fractional schrodinger equation the space derivative is discretized using the collocation method and the time fractional derivative using grunwald letnikov formulation the stability and convergence of the full discretization scheme are analyzed based on the z transform the global behavior of the finite difference spectral collocation method is derived numerical examples show a good agreement with the theoretical analysis

transmission through locally periodic potentials in space fractional quantum mechanics abstract we study transmission through locally periodic potentials in the framework of space fractional quantum mechanics sfqm in particular we calculate the transmission probabilities t n for a particle in a chain of n dirac barriers and for the other case a chain of n square barriers we use a transfer matrix m matrix approach in the context of sfqm to obtain equations for t n for both systems bandlike structures emerge even for a small number of barriers of as low as n 4 and are more apparent for lower values of levy index considered

a novel local surface feature for 3d object recognition under clutter and occlusion this paper presents a highly distinctive local surface feature called the trisi feature for recognizing 3d objects in the presence of clutter and occlusion for a feature point we first construct a unique and repeatable local reference frame lrf using the implicit geometrical information of neighboring triangular faces we then generate three signatures from the three orthogonal coordinate axes of the lrf these signatures are concatenated and then compressed into a trisi feature finally we propose an effective 3d object recognition algorithm based on hierarchical feature matching we tested our trisi feature on two popular datasets rigorous experimental results show that the trisi feature was highly descriptive and outperformed existing algorithms under all levels of gaussian noise laplacian noise shot noise varying mesh resolutions occlusion and clutter moreover we tested our trisi based 3d object recognition algorithm on four standard datasets the experimental results show that our algorithm achieved the best overall recognition results on these datasets

multi peak solutions for super critical elliptic problems in domains with small holes abstract this paper deals with the slightly super critical elliptic problem u u n 2 n 2 e in u 0 in u 0 on 1 where e 0 is a small parameter and r n is a bounded domain with smooth boundary assuming that the domain exhibits k sufficiently small holes multiple solutions are constructed by gluing double spike patterns located near each of the holes

3 d symmetry detection and analysis using the pseudo polar fourier transform symmetry detection and analysis in 3d images is a fundamental task in a gamut of scientific fields such as computer vision medical imaging and pattern recognition to name a few in this work we present a computational approach to 3d symmetry detection and analysis our analysis is conducted in the fourier domain using the pseudo polar fourier transform the pseudo polar representation enables to efficiently and accurately analyze angular volumetric properties such as rotational symmetries our algorithm is based on the analysis of the angular correspondence rate of the given volume and its rotated and rotated inverted replicas in their pseudo polar representations we also derive a novel rigorous analysis of the inherent constraints of 3d symmetries via groups theory based analysis thus our algorithm starts by detecting the rotational symmetry group of a given volume and the rigorous analysis results pave the way to detect the rest of the symmetries the complexity of the algorithm is o n 3log n where n n n is the volumetric size in each direction this complexity is independent of the number of the detected symmetries we experimentally verified our approach by applying it to synthetic as well as real 3d objects

distributed order reaction diffusion systems associated with caputo derivatives this paper deals with the investigation of the solution of an unified fractional reaction diffusion equation of distributed order associated with the caputo derivatives as the time derivative and riesz feller fractional derivative as the space derivative the solution is derived by the application of the joint laplace and fourier transforms in compact and closed form in terms of the h function the results derived are of general nature and include the results investigated earlier by other authors notably by mainardi et al the fundamental solution of the space time fractional diffusion equation fractional calculus appl anal 4 153 202 2001 mainardi et al fox h functions in fractional diffusion j comput appl math 178 321 331 2005 for the fundamental solution of the space time fractional equation including haubold et al solutions of reaction diffusion equations in terms of the h function bull astron soc india 35 681 689 2007 and saxena et al fractional reaction diffusio

fractional schrodinger operator with delta potential localized on circle we consider a system governed by the fractional schodinger operator with a delta potential supported by a circle in r2 we find out the function counting the number of bound states in particular we give the necessary and sufficient conditions for the absence of bound state in our system furthermore we reproduce the form of eigenfunctions and analyze the asymptotic behavior of eigenvalues for the strong coupling constant case

a linearly implicit conservative difference scheme for the space fractional coupled nonlinear schrodinger equations abstract in this paper a linearly implicit conservative difference scheme for the coupled nonlinear schrodinger equations with space fractional derivative is proposed this scheme conserves the mass and energy in the discrete level and only needs to solve a linear system at each step the existence and uniqueness of the difference solution are proved the stability and convergence of the scheme are discussed and it is shown to be convergent of order o 2 h 2 in the discrete l 2 norm with the time step and mesh size h when the fractional order is two all those results are in accord with the difference scheme proposed for the classical non fractional coupled nonlinear schrodinger equations some numerical examples are also reported

on some fractional green s functions in this paper we discuss some fractional green s functions associated with the fractional differential equations which appear in several fields of science more precisely the so called wave reaction diffusion equation and some of its particular cases the methodology presented is the juxtaposition of integral transforms in particular the laplace and the fourier integral transforms some recent results involving the reaction diffusion equation are pointed out

boundary towers of layers for some supercritical problems we consider the supercritical problem u u p 1uin d u 0on d where d is a bounded smooth domain in rn and p is smaller than the th critical sobolev exponent 2n n 2n 2 with 1 n 3 we show that in some suitable torus like domains d there exists an arbitrary large number of sign changing solutions with alternate positive and negative layers which concentrate at different rates along a dimensional submanifold of d as p approaches 2n from below

space time fractional schrodinger equation with time independent potentials abstract we develop a space time fractional schrodinger equation containing caputo fractional derivative and the quantum riesz fractional operator from a space fractional schrodinger equation in this paper by use of the new equation we study the time evolution behaviors of the space time fractional quantum system in the time independent potential fields and two cases that the order of the time fractional derivative is between zero and one and between one and two are discussed respectively the space time fractional schrodinger equation with time independent potentials is divided into a space equation and a time one a general solution which is composed of oscillatory terms and decay ones is obtained we investigate the time limits of the total probability and the energy levels of particles when time goes to infinity and find that the limit values not only depend on the order of the time derivative but also on the sign positive or negative of the eigenvalues of the space equation we also find that the limit value of the total probability can be greater or less than one which means the space time fractional schrodinger equation describes the quantum system where the probability is not conservative and particles may be extracted from or absorbed by the potentials additionally the non markovian time evolution laws of the space time fractional quantum system are discussed the formula of the time evolution of the mechanical quantities is derived and we prove that there is no conservative quantities in the space time fractional quantum system we also get a mittag leffler type of time evolution operator of wave functions and then establish a heisenberg equation containing fractional operators

fractional difference finite element approximations for the time space fractional telegraph equation abstract in this paper we study the numerical solution of the time space fractional order fractional for simplicity telegraph equation which can be used in signal analysis for transmission and propagation of electrical signals also the modeling of the reaction diffusion and the random walk of suspension flows and so on the semi discrete and fully discrete numerical approximations are both analyzed where the galerkin finite element method for the spatial riemann liouville fractional derivative with order 1 1 2 and the finite difference schemes for the temporal caputo derivatives with orders 1 2 1 and 2 are analyzed respectively results on the existence and uniqueness of the solution the numerical stability and the error estimates are displayed in details numerical examples are included to confirm the theoretical analysis

fast approximate energy minimization via graph cuts many tasks in computer vision involve assigning a label such as disparity to every pixel a common constraint is that the labels should vary smoothly almost everywhere while preserving sharp discontinuities that may exist e g at object boundaries these tasks are naturally stated in terms of energy minimization the authors consider a wide class of energies with various smoothness constraints global minimization of these energy functions is np hard even in the simplest discontinuity preserving case therefore our focus is on efficient approximation algorithms we present two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves namely expansion moves and swap moves these moves can simultaneously change the labels of arbitrarily large sets of pixels in contrast many standard algorithms including simulated annealing use small moves where only one pixel changes its label at a time our expansion algorithm finds a labeling within a known factor of the global minimum while our swap algorithm handles more general energy functions both of these algorithms allow important cases of discontinuity preserving energies we experimentally demonstrate the effectiveness of our approach for image restoration stereo and motion on real data with ground truth we achieve 98 percent accuracy

continuous time random walk as a guide to fractional schrodinger equation we argue that the continuous time random walk approach may be a useful guide to extend the schrodinger equation in order to incorporate nonlocal effects avoiding the inconsistencies raised by jeng et al j math phys 51 062102 2010 as an application we work out a free particle in a half space obtaining the time dependent solution by considering an arbitrary initial condition

a fast and robust local descriptor for 3d point cloud registration this paper proposes a novel local feature descriptor called a local feature statistics histogram lfsh for efficient 3d point cloud registration an lfsh forms a comprehensive description of local shape geometries by encoding their statistical properties on local depth point density and angles between normals the sub features in the lfsh descriptor are low dimensional and quite efficient to compute in addition an optimized sample consensus osac algorithm is developed to iteratively estimate the optimum transformation from point correspondences osac can handle the challenging cases of matching highly self similar models based on the proposed lfsh and osac a coarse to fine algorithm can be formed for 3d point cloud registration experiments and comparisons with the state of the art descriptors demonstrate that lfsh is highly discriminative robust and significantly faster than other descriptors meanwhile the proposed coarse to fine registration algorithm is demonstrated to be robust to common nuisances including noise and varying point cloud resolutions and can achieve high accuracy on both model data and scene data

lazer mckenna conjecture the critical case abstract we consider an elliptic problem of ambrosetti prodi type involving critical sobolev exponent on a bounded smooth domain of dimension six or higher by constructing solutions with many sharp peaks near the boundary of the domain but not on the boundary we prove that the number of solutions for this problem is unbounded as the parameter tends to infinity thereby proving the lazer mckenna conjecture in the critical case

bound states for multiple dirac δ wells in space fractional quantum mechanics using the momentum space approach we obtain bound states for multiple dirac wells in the framework of space fractional quantum mechanics introducing first an attractive dirac comb potential i e dirac comb with strength g g 0 in the space fractional schrodinger equation we show that the problem of obtaining eigenenergies of a system with n dirac wells can be reduced to a problem of obtaining the eigenvalues of an n n matrix as an illustration we use the present matrix formulation to derive expressions satisfied by the bound state energies of n 1 2 3 delta wells we also obtain the corresponding wave functions and express them in terms of fox s h function

a 3d shape retrieval framework supporting multimodal queries this paper presents a unified framework for 3d shape retrieval the method supports multimodal queries 2d images sketches 3d objects by introducing a novel view based approach able to handle the different types of multimedia data more specifically a set of 2d images multi views are automatically generated from a 3d object by taking views from uniformly distributed viewpoints for each image a set of 2d rotation invariant shape descriptors is produced the global shape similarity between two 3d models is achieved by applying a novel matching scheme which effectively combines the information extracted from the multi view representation the experimental results prove that the proposed method demonstrates superior performance over other well known state of the art approaches

explicit lower bounds for the cost of fast controls for some 1 d parabolic or dispersive equations and a new lower bound concerning the uniform controllability of the 1 d transport diffusion equation in this paper we prove explicit lower bounds for the cost of fast boundary controls for a class of linear equations of parabolic or dispersive type involving the spectral fractional laplace operator we notably deduce the following striking result in the case of the heat equation controlled on the boundary the miller s conjecture formulated in geometric bounds on the growth rate of null controllability cost for the heat equation in small time j differential equations 204 2004 pp 202 226 is not verified moreover we also give a new lower bound for the minimal time needed to ensure the uniform controllability of the one dimensional convection diffusion equation with negative speed controlled on the left boundary proving that the conjecture formulated in j m coron and s guerrero singular optimal control a linear 1 d parabolic hyperbolic example asymptot anal 44 2005 pp 237 257 concerning this problem is also not verified at least for negative speeds the proof is based on complex analysis and more precisely on a representation formula for entire functions of exponential type and is quite related to the moment method of fattorini and russell

split step alternating direction implicit difference scheme for the fractional schrodinger equation in two dimensions in this paper we propose a conservative and effective difference scheme for solving the two dimensional nonlinear space fractional schrodinger equation with the riesz fractional derivative the scheme is constructed by combining the split step method for handling the nonlinearity with the alternating direction implicit adi method for resolving the multi dimensions difficulty the riesz space fractional derivative is approximated by the second order accurate fractional centered difference based on matrix analysis we show that in the discrete sense the scheme conserves the mass and energy for linear problems and conserves the mass for nonlinear problems the unconditional convergence is proved rigorously in the linear case numerical tests are performed to support our theoretical results and show the efficiency of the proposed scheme

existence of the global smooth solution to the period boundary value problem of fractional nonlinear schrodinger equation in this paper we prove the existence and uniqueness of the global smooth solution to the period boundary value problem of fractional nonlinear schrodinger equation by using energy method