symmetries conservation laws and multisoliton perturbation theory on the basis of action angle variables for multisolitons new symmetries mastersymmetries are constructed for systems with known hierarchies of nonhamiltonian mastersymmetries hierarchies of hamiltonian mastersymmetries are constructed and for systems with known hamiltonian mastersymmetries a hierarchy of non hamiltonian mastersymmetries are constructed moreover with the help of the action angle variables the n soliton perturbation theory on the soliton submanifold adiabatic approximation is formulated an explicit form of the time evolution of asymptotic data under the influence of perturbation is presented

master symmetries and point particle representation of solitons hierarchies of soliton equations generated by an appropriate recursion operator are considered n non interacting galilean like point particles are connected with an n soliton solution of an arbitrary equation from the hierarchy the method of finding the particle representation of solitons is closely related to eigenstates of the recursion operator and master symmetries of the soliton equations

comparison and stability of solutions to a class of quasilinear parabolic problems on presente des resultats de comparaison et d unicite pour les solutions de problemes aux valeurs limites quasilineaires paraboliques avec et sans obstacles un resultat de stabilite dans l 1 donne la stabilisation asymptotique dans cet espace quand t vers le probleme elliptique correspondant

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

the fractal neighbor distance measure fractal image coding has been used successfully to compress and segment images and more recently utilized in a new distance measure to recognize objects this paper discusses how the process of decoding a set of region based contractive transformations has invariance properties that can be advantageous in object recognition we will show that the recognition ability of the proposed fractal neighbor classifier fnc utilizing the fractal neighbor distance fnd measure is a function of the contrast scaling factor and the illumination shift factor our investigation of the fnd required accurate control over the convergence of a fractal decoding process convergence can be determined by examining the contractivity and eventual contractivity factors we have derived theorems that allow these two factors to be calculated for a general class of fractal codes consisting of affine transformations with integral geometric scaling experiments were performed that verified our ability to control and modify these convergence properties furthermore experiments on human face recognition revealed that the performance of the fnc improved through the use of eventual convergence and the imposition of limits on the illumination shift factor

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

factorization of the 2 2 matrix recursion operator of the coupled kdv equation the recursion operator for the infinitesimal transformations about solutions of the coupled kdv equation is a 2 2 matrix whose elements are of the fourth order this formidable looking operator is written as the product of four 2 2 matrix operators whose elements are of the first order auxiliary functions introduced to factorize the recursion operator lead to the scattering equation for the equation the factorization of the recursion operator for the sine gordon equation is also presented

soliton point particles of extended evolution equations a hamiltonian formulation of the particle representation of solitons of extended hierarchies of evolution equations is presented the extension is related to the addition of new terms with x dependent coefficients

the painleve property and backlund transformations for the sequence of boussinesq equations we investigate the sequence of boussinesq equations by the method of singular manifolds for the boussinesq equation which is known to possess the painleve property a backlund transformation is defined this backlund transformation which is formulated in terms of the schwarzian derivative obtains the system of modified boussinesq equations and the resulting miura type transformation the modified boussinesq equations are found to be invariant under a discrete group of symmetries acting on the dependent variables by linearizing the miura transformation and modified equations the lax pair is readily obtained furthermore by a result of fokas and anderson the recursion operators defining the sequence of higher order boussinesq equations may be constructed from the miura transformation this allows the recursive definition of backlund transformations for this sequence of equations the recursion operator is found to preserve the discrete symmetries of the modified boussinesq equations this leads to the conclusion that the sequences of boussinesq and modified boussinesq equations identically possess the painleve property are meromorphic we also find that by a simple reduction the sequences of caudrey dodd gibbon and kuperschmidt equations are contained within the boussinesq sequence rational solutions are iteratively constructed for the boussinesq equation and a criterion is proposed for the existence of rational solutions of general integrable systems

a review of the fractal image coding literature fractal image compression is a technique based on the representation of an image by a contractive transform on the space of images for which the fixed point is close to the original image this broad principle encompasses a very wide variety of coding schemes many of which have been explored in the rapidly growing body of published research while certain theoretical aspects of this representation are well established relatively little attention has been given to the construction of a coherent underlying image model that would justify its use most purely fractal based schemes are not competitive with the current state of the art but hybrid schemes incorporating fractal compression and alternative techniques have achieved considerably greater success this review represents a survey of the most significant advances both practical and theoretical since the publication of jacquin s 1990 original fractal coding scheme

geometric theory of local and non local conservation laws for the sine gordon equation in previous work one of the authors gave a geometric theory of those nonlinear evolution equations n e es that can be solved by the zakharov shabat 1972 inverse scattering scheme as generalized by ablowitz kaup newell segur 1973b 1974 in this paper we extend the geometric theory to include the hamiltonian structure of those n e es solvable by the method and we indicate the connection between the geometric theory and the theory of prolongation structures and pseudopotentials due to wahlquist estabrook 1975 1976 we exploit a gauge invariance of the geometric theory to derive both the well known polynomial conserved densities of the sine gordon equation and a non local set of conserved densities these act as hamiltonian densities for a hierarchy of sine gordon equations which is analogous to that found by lax 1968 for the korteweg de vries equation and appears to be new in an appendix we derive an expression for the equation of motion for an arbitrary member of the sine gordon hierarchy by methods which can be applied in larger context the results for the sine gordon equation lead to the conclusion that a complete set of conserved densities for an arbitrary n e e solvable by the a k n s z s scheme must include non local conserved densities

inverse scattering variables of the kdv equation from the point of view of galilean mechanics the galilean invariance of the korteweg de vries equation is applied in order to characterize the structure of degrees of freedom displayed by the inverse scattering transform method it is found that the dynamical systems associated with the discrete scattering data variables admit a description in terms of mass position and momentum variables similar to the systems of free galilean particles on the other hand the radiation component of the kdv field associated with the continuous part of the set of scattering data turns out to be described by a new field evolving according to a linear partial differential equation

existence results for some quasilinear parabolic equations on considere le probleme de cauchy pour une equation dont la partie principale est un operateur parabolique quasilineaire le terme non lineaire additionnel a au plus une croissance quadratique par rapport au gradient de la solution on demontre l existence d une solution bornee faible sous des hypotheses de regularite minimales en supposant l existence d une sous solution et d une supersolution pour le probleme

a nonlinear model for fractal image coding after a very promising start progress in fractal image coding has been relatively slow recently most improvements have been concentrating on better adaptive coding algorithms and on search strategies to reduce the encoding time very little has been done to challenge the linear model of the fractal transformations used so far in practical applications in this paper we explain why effective nonlinear transformations are not easy to find and propose a model based on conformal mappings in the geometric domain that are a natural extension of the affine model our compression results show improvements over the linear model and support the hope that a deeper understanding of the notion of self similarity would further advance fractal image coding

solitons and discrete eigenfunctions of the recursion operator of non linear evolution equations i the caudrey dodd gibbon sawada kotera equation the solution of the third order isospectral equation of the caudrey dodd gibbon sawada kotera equation cdgske for soliton potential is obtained recursively from the riccati equation derived by iterating once the auto backlund transformation it is then shown that the discrete eigenfunctions of the sixth order recursion operator for this equation can be written in terms of the solutions of the isospectral equation the behaviour of the 1 soliton solution which has certain novel features is studied a sine gordon like equation resembling the double sine gordon equation is derived from the cdgske

hamiltonian and recursion operator for the reduced maxwell bloch equations the hamiltonian of the reduced maxwell bloch equations rmbe an integrable nonlinear evolution equation is derived the recursion operator its inverse and also the hierarchy of higher order rmbe are obtained

symmetries of the massive thirring model for a hamiltonian system every non hamiltonian symmetry gives rise to a recursion operator for symmetries using this method two recursion operators for symmetries of the massive thirring model are constructed the structure of the lie algebra of symmetries generated by these operators is given

image coding based on a fractal theory of iterated contractive image transformations the author proposes an independent and novel approach to image coding based on a fractal theory of iterated transformations the main characteristics of this approach are that i it relies on the assumption that image redundancy can be efficiently exploited through self transformability on a block wise basis and ii it approximates an original image by a fractal image the author refers to the approach as fractal block coding the coding decoding system is based on the construction for an original image to encode of a specific image transformation a fractal code which when iterated on any initial image produces a sequence of images that converges to a fractal approximation of the original it is shown how to design such a system for the coding of monochrome digital images at rates in the range of 0 5 1 0 b pixel the fractal block coder has performance comparable to state of the art vector quantizers

recursion operators for infinitesimal transformations and their inverses for certain nonlinear evolution equations recursion operators generating infinitesimal transformations have been obtained systematically for certain nonlinear evolution equations their inverses have been evaluated and a double infinity of infinitesimal transformations and nonlinear equations generated

rearrangement relatif dans les equations elliptiques quasi lineaires avec un second membre distribution application a un theoreme d existence et de regularite abstract in this paper we are concerned with quasilinear elliptic equations that is p au f u u t in r u w01 p l where a is an operator of leray lions type which is defined on w 0 1 p l 1 f is a non linear map having a suitable growth and t is a distribution of w 1 r r n p 1 and r p p 1 using the techniques of the relative rearrangement ann scuola norm sup pisa cl sci 4 in press we give a precise a priori estimate of the solution u of p in l norm these estimates allow us to prove an existence theorem for p and to get the holder continuity of the solution u

existence of bounded solutions of some nonlinear parabolic equations on demontre l existence d au moins une solution de l equation suivante u t i 1 n a i x t u x t u x t f x t u x t u x t 0 dans 7b d q u x o u 0 x l u l p o t w 0 1p l q q o t 1 p

a wavelet based analysis of fractal image compression why does fractal image compression work what is the implicit image model underlying fractal block coding how can we characterize the types of images for which fractal block coders will work well these are the central issues we address we introduce a new wavelet based framework for analyzing block based fractal compression schemes within this framework we are able to draw upon insights from the well established transform coder paradigm in order to address the issue of why fractal block coders work we show that fractal block coders of the form introduced by jacquin 1992 are haar wavelet subtree quantization schemes we examine a generalization of the schemes to smooth wavelets with additional vanishing moments the performance of our generalized coder is comparable to the best results in the literature for a jacquin style coding scheme our wavelet framework gives new insight into the convergence properties of fractal block coders and it leads us to develop an unconditionally convergent scheme with a fast decoding algorithm our experiments with this new algorithm indicate that fractal coders derive much of their effectiveness from their ability to efficiently represent wavelet zero trees finally our framework reveals some of the fundamental limitations of current fractal compression schemes

infinitely many commuting symmetries and constants of motion in involution for explicitly time dependent evolution equations the existing symmetry approach to exactly solvable time evolution equations in one spatial dimension is extended to the case that the equation depends explicitly on the time and space coordinates in this context commuting symmetries constants of motion in involution strong and hereditary symmetries squared eigenfunction operators and hamiltonian structures are discussed the cylindrical korteweg de vries equation is used as an illustrative example

infinitesimal transformations about soliton solutions of sine gordon and modified korteweg de vries equations infinitesimal transformations about n soliton solutions of sine gordon and modified korteweg de vries equations are obtained using respective backlund transformations we also obtain the eigenfunctions of corresponding generalized zakharov shabat systems