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

abstract functional differential equations and reaction diffusion systems functional differential equations and reaction diffusion systems r h martin jr and h l smith abstract several fundamental results on the existence and behavior of solutions to semilinear functional differential equations are developed in a banach space setting the ideas are applied to reaction diffusion systems that have time delays in the nonlinear reaction terms the techniques presented here include differential inequalities invariant sets and lyapunov functions and therefore they provide for a wide range of applicability the results on inequalities and especially strict inequalities are new even in the context of semilinear equations whose nonlinear terms do not contain delays several fundamental results on the existence and behavior of solutions to semilinear functional differential equations are developed in a banach space setting the ideas are applied to reaction diffusion systems that have time delays in the nonlinear reaction terms the techniques presented here include differential inequalities invariant sets and lyapunov functions and therefore they provide for a wide range of applicability the results on inequalities and especially strict inequalities are new even in the context of semilinear equations whose nonlinear terms do not contain delays suppose q is a bounded domain in rn with aq smooth and a is the laplacian operator on q also let m be a positive integer z a positive number and f fi m a continuous bounded function from 0 xc x q x c z 0 m into rm where c t 0 is the space of continuous functions from z 0 into r the purpose of this paper is to apply abstract results for semilinear functional differential equations in banach spaces to reactiondiffusion systems with time delays having the form a tu x t diau x t i t x ut x t a xeq i 1 m rdd ai x ui x t au i x t 81 x t t a x eaq u x a 0 x x 0 5 t 0 di 0 and ca q 0 o is c and i q x 0 oo r is c2 here an is the outward normal derivative on aq and if di 0 it is assumed that no boundary conditions are specified for this i also tu x t denotes the partial with respect to t whereas ut x denotes the member of c z 0 defined by 0 u x t 0 u x t 0 m our techniques provide basic existence criteria but the main point is that they can also be effectively applied to obtain estimates for solutions especially received by the editors october 7 1987 and in revised form october 7 1988 1980 mathematics subject classification 1985 revision primary 35r10 34k30

eigenfaces vs fisherfaces recognition using class specific linear projection we develop a face recognition algorithm which is insensitive to large variation in lighting direction and facial expression taking a pattern classification approach we consider each pixel in an image as a coordinate in a high dimensional space we take advantage of the observation that the images of a particular face under varying illumination but fixed pose lie in a 3d linear subspace of the high dimensional image space if the face is a lambertian surface without shadowing however since faces are not truly lambertian surfaces and do indeed produce self shadowing images will deviate from this linear subspace rather than explicitly modeling this deviation we linearly project the image into a subspace in a manner which discounts those regions of the face with large deviation our projection method is based on fisher s linear discriminant and produces well separated classes in a low dimensional subspace even under severe variation in lighting and facial expressions the eigenface technique another method based on linearly projecting the image space to a low dimensional subspace has similar computational requirements yet extensive experimental results demonstrate that the proposed fisherface method has error rates that are lower than those of the eigenface technique for tests on the harvard and yale face databases

constructing descriptive and discriminative nonlinear features rayleigh coefficients in kernel feature spaces we incorporate prior knowledge to construct nonlinear algorithms for invariant feature extraction and discrimination employing a unified framework in terms of a nonlinearized variant of the rayleigh coefficient we propose nonlinear generalizations of fisher s discriminant and oriented pca using support vector kernel functions extensive simulations show the utility of our approach

nonlocal problems involving spatial structure for coupled reaction diffusion systems the purpose of this work is to investigate the uniqueness and existence of solutions for a system of nonlinear parabolic equations weakly coupled with ordinary differential equations in bounded domains subject to nonlocal boundary conditions that involve values of the unknown functions inside of the spatial domain the solutions of such problems allow for considering not only physical chemical or biological properties but also spatial structure of the modelled system the uniqueness of classical solutions of the nonlocal boundary problems for coupled reaction diffusion systems is proved by means of comparison principles for differential inequalities the existence of the unique solution is obtained via a monotone iterative method applications are given to some model problems in epidemiology and ecology with the nonlocal boundary conditions based on the inverse distance weighting interpolation and cokriging

incremental learning of discriminant common vectors for feature extraction abstract discriminant common vectors dcv which can effectively extract the features of face images is a recently proposed algorithm to overcome the small sample size sss problem encountered by linear discriminant analysis lda its numerical accuracy is high and computational complexity is low however the dcv algorithm is not suitable for online training problems in order to address this problem an incremental dcv idcv method is developed in this paper the idcv algorithm can incrementally learn the optimal projection matrix instead of recomputing the dcv again when new sample is added into the training set theoretical analysis denotes that idcv is much more efficient that dcv experiments on orl pie and ar face databases demonstrate the efficiency of our proposed idcv algorithm over the original batch dcv algorithm

minimal wave speed in a diffusive epidemic model with temporal delay abstract taking incubation period into account we modify capasso et al s epidemic model and consider a reaction diffusion system with time delay by the method of upper and lower solutions to a related second order ordinary differential equation with infinite time delay we establish the existence of the minimal wave speed for the modified epidemic model and show that incubation period reduces the minimal wave speed of epidemic model indeed

solving the small sample size problem in face recognition using generalized discriminant analysis the goal of face recognition is to distinguish persons via their facial images each person s images form a cluster and a new image is recognized by assigning it to the correct cluster since the images are very high dimensional it is necessary to reduce their dimension linear discriminant analysis lda has been shown to be effective at dimension reduction while preserving the cluster structure of the data it is classically defined as an optimization problem involving covariance matrices that represent the scatter within and between clusters the requirement that one of these matrices be nonsingular restricts its application to datasets in which the dimension of the data does not exceed the sample size for face recognition however the dimension typically exceeds the number of images in the database resulting in what is referred to as the small sample size problem recently the applicability of lda has been extended by using the generalized singular value decomposition gsvd to circumvent the nonsingularity requirement thus making lda directly applicable to face recognition data our experiments confirm that lda gsvd solves the small sample size problem very effectively as compared with other current methods

asymptotic speeds of spread and traveling waves for integral equations and delayed reaction diffusion models abstract the theory of asymptotic speeds of spread and monotone traveling waves is generalized to a large class of scalar nonlinear integral equations and is applied to some time delayed reaction and diffusion population models

dynamics of a class of delayed reaction diffusion systems with neumann boundary condition abstract this paper considers a class of delayed reaction diffusion systems under the neumann boundary condition which arise in epidemiology and can describe the temporal and spatial evolutionary phenomena for the bacteria population and the human infective population with the help of the iterative properties of interval mapping and dynamical system approaches some positively invariant sets and attractive basins of the considered systems are analyzed detailedly in addition combining the global attractivity of interval mapping we provide some sufficient conditions to ensure local or global attractivity of steady states of the systems finally we apply these theoretical results to some models with different nonlinearity demonstrating force of infection and then obtain some sufficient conditions about force of infection to describe the survival and extinction of bacteria and infective populations

nonlocal dispersal cooperative systems acceleration propagation among species abstract we focus on the influences of nonlocal dispersal kernels on the spatial propagation in nonlocal dispersal cooperative systems with initial values having nonempty compact supports it is well known that the solution of a monostable nonlocal dispersal scalar equation spreads at a finite speed when the kernel is thin tailed and propagates by accelerating when the kernel has a heavy tail the fat tailed however in such systems we find that one species can propagate by accelerating although its dispersal kernel is thin tailed which is a new and interesting phenomenon more precisely we show that the spatial propagation of every species at large time is mainly determined by the tail of the maximum of their dispersal kernels which further implies that their spatial propagation is accelerated by each other because of the cooperation relation between them this gives us a new understanding of the cooperation relation in the spatial propagation of nonlocal dispersal cooperative systems

entire solutions in bistable reaction diffusion equations with nonlocal delayed nonlinearity this paper is concerned with entire solutions for bistable reaction diffusion equations with nonlocal delay in one dimensional spatial domain here the entire solutions are defined in the whole space and for all time t r assuming that the equation has an increasing traveling wave solution with nonzero wave speed and using the comparison argument we prove the existence of entire solutions which behave as two traveling wave solutions coming from both ends of the x axis and annihilating at a finite time furthermore we show that such an entire solution is unique up to space time translations and is liapunov stable a key idea is to characterize the asymptotic behavior of the solutions as t in terms of appropriate subsolutions and supersolutions in order to illustrate our main results two models of reaction diffusion equations with nonlocal delay arising from mathematical biology are considered

regularized discriminant analysis abstract linear and quadratic discriminant analysis are considered in the small sample high dimensional setting alternatives to the usual maximum likelihood plug in estimates for the covariance matrices are proposed these alternatives are characterized by two parameters the values of which are customized to individual situations by jointly minimizing a sample based estimate of future misclassification risk computationally fast implementations are presented and the efficacy of the approach is examined through simulation studies and application to data these studies indicate that in many circumstances dramatic gains in classification accuracy can be achieved

travelling fronts and entire solutions of the fisher kpp equation in ℝn this paper is devoted to time global solutions of the fisher kpp equation in n where f is a c 2 concave function on 0 1 such that f 0 f 1 0 and f 0 on 0 1 it is well known that this equation admits a finite dimensional manifold of planar travelling fronts solutions by considering the mixing of any density of travelling fronts we prove the existence of an infinite dimensional manifold of solutions in particular there are infinite dimensional manifolds of nonplanar travelling fronts and radial solutions furthermore up to an additional assumption a given solution u can be represented in terms of such a mixing of travelling fronts

entire solutions in a time delayed and diffusive epidemic model this paper is concerned with entire solutions in the following time delayed and diffusive epidemic model email protected tu 1 x t d email protected u 1 x t a 1 1u 1 x t a 1 2u 2 x t email protected tu 2 x t d email protected u 2 x t a 2 2u 2 x t gu 1x email protected where d i 0 i 1 2 using comparison arguments we establish the existence and its properties of entire solutions for the above system here an entire solution means a classical solution defined for all email protected r

rapid and brief communication face recognition based on 2d fisherface approach two dimensional 2d discrimination analysis using methods such as 2d pca and image lda is of interest in face recognition because it extracts discriminative features faster than one dimensional 1d discrimination analysis however existing 2d methods generally use more discriminative features and take longer to test than 1d methods 2d pca in particular cannot make full use of the fisher discriminant criterion image lda also has drawbacks in that it cannot perform 2d principal component analysis and discards components with poor discriminative capabilities in addition existing 2d methods cannot provide an automatic strategy to choose 2d principal components or discriminant vectors in this paper we propose 2d fisherface a novel discrimination approach that combines the two stage pca lda strategy and 2d discrimination techniques it can extract face discriminative features by automatically selecting two dimensional principal components and discriminant vectors using the ar database as the test data it is shown that the proposed approach is faster and more effective than several representative 1d and 2d discrimination methods

ermakov systems of arbitrary order and dimension structure and linearization ermakov systems of arbitrary order and dimension are constructed these inherit an underlying linear structure based on that recently established for the classical ermakov system as an application alignment of a 2 1 dimensional ermakov and integrable ernst system is shown to produce a novel integrable hybrid of a 2 1 dimensional sinh gordon system and of a conventional ermakov system

traveling wave solutions of lotka volterra competition systems with nonlocal dispersal in periodic habitats this paper is concerned with space periodic traveling wave solutions of the following lotka volterra competition system with nonlocal dispersal and space periodic dependence partial derivative u 1 partial derivative t integral r n kappa y x u 1 t y dy u 1 t x u 1 a 1 x b 1 x u 1 c 1 x u 1 x is an element of r n partial derivative u 2 partial derivative t integral r n kappa y x u 2 t y dy u 1 t x u 2 a 2 x b 2 x u 2 c 2 x u 2 x is an element of r n under suitable assumptions the system admits two semitrivial space periodic equilibria u 1 x 0 and 0 u 2 x where u 1 x 0 is linearly and globally stable and 0 u 2 x is linearly unstable with respect to space periodic perturbations by sub and supersolution techniques and comparison principals we show that for any given xi is an element of sn 1 there exists a continuous periodic traveling wave solution of the form u 1 t x u 2 t x phi 1 x ct xi ct xi 4 phi 2 x ct xi ct xi connecting u 1 0 and 0 u 2 and propagating in the direction of xi with speed c c xi where c xi is the spreading speed of the system in the direction of moreover for c c xi we also prove the asymptotic stability and uniqueness of traveling wave solution using squeezing techniques c 2016 elsevier inc all rights reserved

analysis of a reaction diffusion system modeling man environment man epidemics in this paper an old model for the temporal and spatial evolution of orofecal transmitted disease is reexamined it consists of a system of two coupled reaction diffusion equations for the concentration of bacteria and infective humans under the assumptions that the total population of humans is unaffected by the disease and only a small proportion of the population is affected at any one time the force of infection on healthy humans is assumed to be a sigmoidal function of bacterial concentration tending to some finite limit and with zero gradient at zero this last feature models an immune response to low concentrations of the infectious agent in practice the diffusion coefficient for infective humans ismuch smaller than that of bacteria and is therefore set to zero a detailed analysis of the steady state bifurcation pattern is then performed for the case of homogeneous dirichlet boundary conditions applied at the endpoints of a one dimensional interval particular attention is paid to the limiti

global attractivity spreading speeds and traveling waves of delayed nonlocal reaction diffusion systems abstract the purpose of this work is to study the spatial dynamics of some delayed nonlocal reaction diffusion systems in whole space we first establish a series of comparison theorems to investigate the global attractivity of the equilibria for a delayed nonlocal reaction diffusion system with and without quasi monotonicity then we show that the spreading speed of a general system without quasi monotone conditions is coincident with the minimal wave speed applying a fluctuation method we further provide some sufficient conditions to ensure the upward convergence of the spreading speed and traveling wave solutions finally we point out the effects of the delay and nonlocality on the spreading speed of the non quasi monotone systems

nonlinear superposition higher order nonlinear equations and classical linear invariants we find a class of nonlinear ordinary differential equations in of any order m 2 whose solutions are given by the nonlinear superposition law t x t r d t dt where dmr d m f r r and x t satisfies a special self adjoint linear equation of order m the coefficients of the self adjoint equation in x which are identical to those of the nonlinear equations in can be deduced from the well known invariants of the classical theory of linear differential equations

dynamical behavior of an epidemic model with a nonlinear incidence rate abstract in this paper we study the global dynamics of an epidemic model with vital dynamics and nonlinear incidence rate of saturated mass action by carrying out global qualitative and bifurcation analyses it is shown that either the number of infective individuals tends to zero as time evolves or there is a region such that the disease will be persistent if the initial position lies in the region and the disease will disappear if the initial position lies outside this region when such a region exists it is shown that the model undergoes a bogdanov takens bifurcation i e it exhibits a saddle node bifurcation hopf bifurcations and a homoclinic bifurcation existence of none one or two limit cycles is also discussed

saddle point behavior for monotone semiflows and reaction diffusion models the saddle point behavior is established for monotone semiflows with weak bistability structure and then these results are applied to three reaction diffusion systems modeling man environment man epidemics single loop positive feedback and two species competition respectively

traveling wave solutions in partially degenerate cooperative reaction diffusion systems abstract we study the existence of traveling wave solutions for partially degenerate cooperative reaction diffusion systems that can have three or more equilibria we show via integral systems that there exist traveling wave solutions in a partially degenerate reaction diffusion system with speeds above two well defined extended real numbers we prove that the two numbers are the same and may be characterized as the spreading speed as well as the slowest speed of a class of traveling wave solutions provided that the linear determinacy conditions are satisfied we demonstrate our theoretical results by examining a partially degenerate lotka volterra competition model with advection terms

traveling waves for epidemic models with nonlocal dispersal in time and space periodic habitats abstract this paper deals with the spatial spreading speed and traveling wave solutions of a general epidemic model with nonlocal dispersal in time and space periodic habitats it should be mentioned that the existence of spreading speed and traveling wave solutions of nonlocal dispersal cooperative system in space time periodic habitats have been established previously in this paper we further show that the epidemic system has a spreading speed c and for any c c there exist a unique continuous space time periodic traveling wave solution 1 x c t t c t 2 x c t t c t of epidemic model in the direction of with speed c and there is no such solution for c c

nonlinear component analysis as a kernel eigenvalue problem a new method for performing a nonlinear form of principal component analysis is proposed by the use of integral operator kernel functions one can efficiently compute principal components in high dimensional feature spaces related to input space by some nonlinear map for instance the space of all possible five pixel products in 16 16 images we give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition

two dimensional time dependent hamiltonian systems with an exact invariant we present a direct approach to investigate the existence of an exact invariant for two dimensional hamiltonians in which the potential depends explicitly on time the method is based on an expansion of the invariant in the velocities the problem is solved completely for invariants linear and quadratic in the momenta our results contain as a particular case the results of lewis and leach on one dimensional systems

existence and uniqueness of entire solutions for a reaction diffusion equation abstract we consider entire solutions of u t u xx f u i e solutions that exist for all x t r 2 where f 0 f 1 0 f 0 in particular we are interested in the entire solutions which behave as two opposite wave fronts of positive speed s approaching each other from both sides of the x axis and then annihilating in a finite time in the case f 1 0 we show that such entire solution exists and is unique up to space time translations in the case f 1 0 we derive two families of such entire solutions in the first family one cannot be any space time translation of the other yet all entire solutions in the second family only differ by a space time translation

spreading speeds of a partially degenerate reaction diffusion system in a periodic habitat abstract this paper is devoted to the study of the spreading speeds of a partially degenerate reaction diffusion system with monostable nonlinearity in a periodic habitat we first obtain sufficient conditions for the existence of principal eigenvalues in the case where solution maps of the associated linear systems lack compactness and prove a threshold type result on the global dynamics for the periodic initial value problem then we establish the existence and computational formulae of spreading speeds for the general initial value problem it turns out that the spreading speed is linearly determinate

stability and periodicity in coupled pinney equations abstract we show that the coupled pinney equations with periodic coefficient constitute a class of nonlinear coupled hill s equations for which the problems of stability and periodicity of the solutions reduce to those for a pair of uncoupled linear hill s equations one of which is of ince type

global bifurcation of steady state solutions in this paper we study the bifurcation of steady state solutions of a reaction diffusion equation in one space variable the steady state solutions satisfy the equation a f u 0 on the interval l 0 or 0 for some nonzero function c c a for the neumann problem we use entirely different techniques to prove that s is never critical for any cubic polynomial j this implies at once that the neumann problem can have at most one nonconstant solution having a given number of maxima or minima this solution is necessarily strongly nondegenerate in the sense that zero is not contained in the spectrum of the linearized operator see 2 for the dirichlet problem the situation is far more complicated and the bifurcation diagrams undergo qualitative changes depending on the positions of the roots off for example fig 1 shows the bifurcation diagram for the positive solutions for two different cubic functions of the form f u a u u b u c it is interesting to note however that in every case we study there are at most three solutions to the dirichlet problem for each

traveling wavefronts for delayed reaction diffusion systems via a fixed point theorem abstract by using schauder s fixed point theorem we prove some existence results for traveling wavefronts of reaction diffusion systems with quasimonotonicity reactions more precisely we reduce the existence of traveling wavefronts to the existence of an admissible pair of supersolution and subsolution which are easy to construct in practice finally to illustrate our main results we study the existence of traveling wavefronts for a delayed predator prey model with diffusion as well as the reaction diffusion system with the well known belousov zhabotinskii reaction and the obtained results improve the existing ones

a two stage linear discriminant analysis via qr decomposition linear discriminant analysis lda is a well known method for feature extraction and dimension reduction it has been used widely in many applications involving high dimensional data such as image and text classification an intrinsic limitation of classical lda is the so called singularity problems that is it fails when all scatter matrices are singular many lda extensions were proposed in the past to overcome the singularity problems among these extensions pca lda a two stage method received relatively more attention in pca lda the lda stage is preceded by an intermediate dimension reduction stage using principal component analysis pca most previous lda extensions are computationally expensive and not scalable due to the use of singular value decomposition or generalized singular value decomposition in this paper we propose a two stage lda method namely lda qr which aims to overcome the singularity problems of classical lda while achieving efficiency and scalability simultaneously the key difference between lda qr and pca lda lies in the first stage where lda qr applies qr decomposition to a small matrix involving the class centroids while pca lda applies pca to the total scatter matrix involving all training data points we further justify the proposed algorithm by showing the relationship among lda qr and previous lda methods extensive experiments on face images and text documents are presented to show the effectiveness of the proposed algorithm

internal null stabilization for some diffusive models of population dynamics we investigate the large time behavior of the solutions to some fisher type models with nonlocal terms describing the dynamics of biological populations with diffusion logistic term and migration two types of logistic terms are taken into account a necessary condition and a sufficient condition for the internal null stabilizability of the solution to a fisher model with nonlocal term are provided in case of null stabilizability with state constraints a feedback stabilizing control of harvesting type is proposed the rate of stabilization corresponding to the feedback stabilizing control is dictated by the principal eigenvalue to a certain linear but not selfadjoint operator a large principal eigenvalue leads to a fast stabilization to zero another goal is to approximate this principal eigenvalue using a method suggested by the theoretical result concerning the large time behavior of the solution to a certain fisher model with a special logistic term an iterative method to improve the position by translations of the support of the feedback stabilizing control in order to get a larger principal eigenvalue and consequently a faster stabilization to zero is derived numerical tests illustrating the effectiveness of the theoretical results are given

dynamical algebraic approach and invariants for time dependent hamiltonian systems in two dimensions dynamical invariants for time dependent td oscillator systems in two dimensions are derived the applications of the dynamical algebraic approach known already for one dimensional td systems r s kaushal and h j korsch j math phys 22 1904 1981 are now carried out to two dimensional td systems a possible generalization of ermakov systems to higher dimensions is discussed

feature extraction using two dimensional maximum embedding difference in this paper we propose a novel method combining graph embedding and difference criterion techniques for image feature extraction namely two dimensional maximum embedding difference 2dmed this method directly extracts the optimal projective vectors from 2d image matrices by simultaneously considering characteristic that is the intraclass compactness graph the margin graph and inter class separability graph respectively in this method it is not necessary to convert the image matrix into high dimensional image vector so that much computational time would be saved in addition the proposed method preserves the manifold reconstruction relationships in the low dimensional subspace experimental results on the orl yale face and usps database show the effectiveness of the proposed method

an efficient algorithm to solve the small sample size problem for lda in this paper we present an efficient algorithm to solve the most discriminant vectors of lda for high dimensional data set the experiments on orl face database confirm the effectiveness of the proposed method

rapid and brief communication two dimensional fld for face recognition this paper presents a new scheme of face image feature extraction namely the two dimensional fisher linear discriminant experiments on the orl and the umist face databases show that the new scheme outperforms the pca and the conventional pca fld schemes not only in its computational efficiency but also in its performance for the task of face recognition

face recognition using laplacianfaces we propose an appearance based face recognition method called the laplacianface approach by using locality preserving projections lpp the face images are mapped into a face subspace for analysis different from principal component analysis pca and linear discriminant analysis lda which effectively see only the euclidean structure of face space lpp finds an embedding that preserves local information and obtains a face subspace that best detects the essential face manifold structure the laplacianfaces are the optimal linear approximations to the eigenfunctions of the laplace beltrami operator on the face manifold in this way the unwanted variations resulting from changes in lighting facial expression and pose may be eliminated or reduced theoretical analysis shows that pca lda and lpp can be obtained from different graph models we compare the proposed laplacianface approach with eigenface and fisherface methods on three different face data sets experimental results suggest that the proposed laplacianface approach provides a better representation and achieves lower error rates in face recognition

an optimization criterion for generalized discriminant analysis on undersampled problems an optimization criterion is presented for discriminant analysis the criterion extends the optimization criteria of the classical linear discriminant analysis lda through the use of the pseudoinverse when the scatter matrices are singular it is applicable regardless of the relative sizes of the data dimension and sample size overcoming a limitation of classical lda the optimization problem can be solved analytically by applying the generalized singular value decomposition gsvd technique the pseudoinverse has been suggested and used for undersampled problems in the past where the data dimension exceeds the number of data points the criterion proposed in this paper provides a theoretical justification for this procedure an approximation algorithm for the gsvd based approach is also presented it reduces the computational complexity by finding subclusters of each cluster and uses their centroids to capture the structure of each cluster this reduced problem yields much smaller matrices to which the gsvd can be applied efficiently experiments on text data with up to 7 000 dimensions show that the approximation algorithm produces results that are close to those produced by the exact algorithm

ermakov and non ermakov systems in quantum dissipative models via the hydrodynamical formulation of quantum mechanics a unified protocol to treat the quantum time dependent harmonic oscillator with friction is presented described by two different models an explicitly time dependent linear schrodinger equation caldirola kanai model and a logarithmic nonlinear schrodinger equation kostin model for the former model an ermakov system that makes it possible to obtain an invariant of ermakov lewis type is derived for the latter model a non ermakov system is derived instead and it is shown that neither an exact nor an approximate invariant of ermakov lewis type exists

a new lda based face recognition system which can solve the small sample size problem a new lda based face recognition system is presented in this paper linear discriminant analysis lda is one of the most popular linear projection techniques for feature extraction the major drawback of applying lda is that it may encounter the small sample size problem in this paper we propose a new lda based technique which can solve the small sample size problem we also prove that the most expressive vectors derived in the null space of the within class scatter matrix using principal component analysis pca are equal to the optimal discriminant vectors derived in the original space using lda the experimental results show that the new lda process improves the performance of a face recognition system signi cantly 2000 pattern recognition society published by elsevier science ltd all rights reserved

2d 2pcalda an efficient approach for face recognition in this paper we propose a novel method for image feature extraction namely 2d 2pcalda this method directly extracts the optimal projective vectors from 2d image matrices by simultaneously considering row direction 2dpca and column direction 2dlda the proposed method not only avoids huge feature matrix problem in 2dpca and 2dlda but also take full advantage of the discriminant information and descriptive information of the images experiment results on yale face database and orl face databases demonstrate the effectiveness and robustness of the proposed method

entire solutions in nonlocal dispersal equations with bistable nonlinearity abstract we consider entire solutions of nonlocal dispersal equations with bistable nonlinearity in one dimensional spatial domain a two dimensional manifold of entire solutions which behave as two traveling wave solutions coming from both directions is established by an increasing traveling wave front with nonzero wave speed furthermore we show that such an entire solution is unique up to space time translations and liapunov stable a key idea is to characterize the asymptotic behaviors of the solutions as t in terms of appropriate subsolutions and supersolutions we have to emphasize that a lack of regularizing effect occurs

efficient and robust feature extraction by maximum margin criterion in pattern recognition feature extraction techniques are widely employed to reduce the dimensionality of data and to enhance the discriminatory information principal component analysis pca and linear discriminant analysis lda are the two most popular linear dimensionality reduction methods however pca is not very effective for the extraction of the most discriminant features and lda is not stable due to the small sample size problem in this paper we propose some new linear and nonlinear feature extractors based on maximum margin criterion mmc geometrically feature extractors based on mmc maximize the average margin between classes after dimensionality reduction it is shown that mmc can represent class separability better than pca as a connection to lda we may also derive lda from mmc by incorporating some constraints by using some other constraints we establish a new linear feature extractor that does not suffer from the small sample size problem which is known to cause serious stability problems for lda the kernelized nonlinear counterpart of this linear feature extractor is also established in the paper our extensive experiments demonstrate that the new feature extractors are effective stable and efficient

laplacian eigenmaps for dimensionality reduction and data representation one of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data we consider the problem of constructing a representation for data lying on a low dimensional manifold embedded in a high dimensional space drawing on the correspondence between the graph laplacian the laplace beltrami operator on the manifold and the connections to the heat equation we propose a geometrically motivated algorithm for representing the high dimensional data the algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality preserving properties and a natural connection to clustering some potential applications and illustrative examples are discussed

rapid and brief communication two dimensional locality preserving projections 2dlpp with its application to palmprint recognition this paper proposes a novel algorithm for image feature extraction namely the two dimensional locality preserving projections 2dlpp which directly extracts the proper features from image matrices based on locality preserving criterion experimental results on the polyu palmprint database show the effectiveness of the proposed algorithm

dynamics of a non local delayed reaction diffusion equation without quasi monotonicity this paper is concerned with the dynamics of a non local delayed reaction diffusion equation without quasi monotonicity on an infinite n dimensional domain which can be derived from the growth of a stage structured single species population we first prove that solutions of the cauchy type problem are positively preserving and bounded if the initial value is non negative and bounded then by establishing a comparison theorem and a series of comparison arguments we prove the global attractivity of the positive equilibrium when there exist no positive equilibria we prove that the zero equilibrium is globally attractive in particular these results are still valid for the non local delayed reaction diffusion equation on a bounded domain with the neumann boundary condition finally we establish the existence of new entire solutions by using the travelling wave solutions of two auxiliary equations and the global attractivity of the positive equilibrium

local and global bifurcations in an sirs epidemic model this paper studies the existence and stability of the disease free equilibrium and endemic equilibria for the sirs epidemic model with the saturated incidence rate considering the factor of population dynamics such as the disease related the natural mortality and the constant recruitment of population analytical techniques are used to show for some parameter values the periodic solutions can arise through the hopf bifurcation which is important to carry different strategies for the controlling disease then the codimension two bifurcation i e bt bifurcation is investigated by using a global qualitative method and the curves of saddle node bifurcation hopf bifurcation and homoclinic bifurcation are obtained at the degenerate equilibrium moreover several numerical simulations are given to support the theoretical analysis

on 2 1 dimensional ermakov systems ermakov type systems in 2 1 dimensions are introduced multiwave solutions of a 2 1 dimensional pinney equation and a modulated 2 1 dimensional sine gordon equation are thereby constructed

discussion comment on two dimensional locality preserving projections 2dlpp with its application to palmprint recognition this paper proposes a novel algorithm for image feature extraction namely the two dimensional locality preserving projections 2dlpp which directly extracts the proper features from image matrices based on locality preserving criterion experimental results on the polyu palmprint database show the effectiveness of the proposed algorithm

fast propagation for reaction diffusion cooperative systems abstract this paper deals with the spatial propagation for reaction diffusion cooperative systems it is well known that the solution of a reaction diffusion equation with monostable nonlinearity spreads at a finite speed when the initial condition decays to zero exponentially or faster and propagates fast when the initial condition decays to zero more slowly than any exponentially decaying function however in reaction diffusion cooperative systems a new possibility happens in which one species propagates fast although its initial condition decays exponentially or faster the fundamental reason is that the growth sources of one species come from the other species simply speaking we find a new interesting phenomenon that the spatial propagation of one species is accelerated by the other species this is a unique phenomenon in reaction diffusion systems we present a framework of fast propagation for reaction diffusion cooperative systems

existence and uniqueness of traveling waves for non monotone integral equations with application abstract this paper is concerned with the traveling waves in a class of non monotone integral equations first we establish the existence of traveling waves the approach is based on the construction of two associated auxiliary monotone integral equations and a profile set in a suitable banach space then we show that the traveling waves are unique up to translations under some reasonable assumptions the exact asymptotic behavior of the profiles as and the existence of minimal wave speed are also obtained finally we apply our results to an epidemic model with non monotone force of infection

canonical transformations and exact invariants for dissipative systems a simple treatment to the problem of finding exact invariants and related auxiliary equations for time dependent oscillators with friction is presented the treatment is based on the use of a time dependent canonical transformation and an auxiliary transformation

pulsating fronts and front like entire solutions for a reaction advection diffusion competition model in a periodic habitat abstract this paper is devoted to the study of pulsating fronts and pulsating front like entire solutions for a reaction advection diffusion model of two competing species in a periodic habitat under certain assumptions the competition system admits a leftward and a rightward pulsating fronts in the bistable case in this work we construct some other types of entire solutions by interacting the leftward and rightward pulsating fronts some of these entire solutions behave as the two pulsating fronts approaching each other from both sides of the x axis which turn out to be unique and liapunov stable 2 dimensional manifolds of solutions furthermore the leftward and rightward pulsating fronts are on the boundary of these 2 dimensional manifolds the others behave as the two pulsating fronts propagating from one side of the x axis the faster one then invades the slower one as t these kinds of pulsating front like entire solutions then provide some new spreading ways other than pulsating fronts for two strongly competing species interacting in a heterogeneous habitat

equilibrium solutions of a semilinear reaction diffusion system on etudie le systeme u 1 t d 1 u 1 a 11 u 1 a 12 u 2 dans 0 u 2 t a 22 u 2 g u 1 dans 0 avec les conditions aux limites u 1 u 2 0 dans 0 ou est un sous ensemble ouvert borne de r n n 2 et est assez reguliere sous de bonnes hypotheses on peut trouver au moins une deux ou trois solutions d equilibre

entire solutions of the kpp equation this paper deals with the solutions defined for all time of the kpp equation ut uxx f u 0 0 f 0 1 0i n 0 1 and f 0 s f 0 0 in 0 1 this equation admits infinitely many traveling wave type solutions increasing or decreasing in x i t also admits solutions that depend only on t in this paper we build four other manifolds of solutions one is 5 dimensional one is 4 dimensional and two are 3 dimensional some of these new solutions are obtained by considering two traveling waves that come from both sides of the real axis and mix furthermore the traveling wave solutions are on the boundary of these four manifolds c 1999 john wiley sons inc

higher order special self adjoint equations and particle dynamics we exhibit a remarkable connection between a hierarchy of higher order special self adjoint ordinary differential equations and the description of motion of a cluster of particles in classical mechanics the cluster is assumed to consist of equal mass particles all moving in one dimension in a perturbation schema based on the first order equation of motion of the center of mass point the time evolution of the moments of order m 1 is governed by the solution of a special self adjoint equation of order m a similar connection exists for the moments of a wave packet in quantum mechanics

entire solutions in monostable reaction diffusion equations with delayed nonlinearity abstract entire solutions for monostable reaction diffusion equations with nonlocal delay in one dimensional spatial domain are considered a comparison argument is employed to prove the existence of entire solutions which behave as two traveling wave solutions coming from both directions some new entire solutions are also constructed by mixing traveling wave solutions with heteroclinic orbits of the spatially averaged ordinary differential equations and the existence of such a heteroclinic orbit is established using the monotone dynamical systems theory key techniques include the characterization of the asymptotic behaviors of solutions as t in term of appropriate subsolutions and supersolutions two models of reaction diffusion equations with nonlocal delay arising from mathematical biology are given to illustrate main results

solving the inverse problem of an sis epidemic reaction diffusion model by optimal control methods in this contribution a novel inverse problem on an sis epidemic reaction diffusion model is investigated by employing the optimal control methods by setting a proper regular cost functional and choosing the coefficients to be identified as control variables we embed the original inverse problem which is very difficult to solve into an optimal control problem the existence of the optimal controls and the first order necessary optimality condition satisfied by the optimal controls are established respectively in particular the local uniqueness and stability of the identification of the coefficients are proved by using analytical techniques

feature extraction using two dimensional local graph embedding based on maximum margin criterion in this paper we propose a novel method for image feature extraction namely the two dimensional local graph embedding which is based on maximum margin criterion and thus not necessary to convert the image matrix into high dimensional image vector and directly avoid computing the inverse matrix in the discriminant criterion this method directly learns the optimal projective vectors from 2d image matrices by simultaneously considering local graph embedding and maximum margin criterion the proposed method avoids huge feature matrix problem in eigenfaces fisherfaces laplacianfaces maximum margin criterion mmc and inverse matrix in 2d fisherfaces 2d laplacianfaces and 2d local graph embedding discriminant analysis 2dlgeda so that computational time would be saved for feature extraction experimental results on the yale and the usps databases show the effectiveness of the proposed method under various experimental conditions