on the asymptotic behavior for a certain nonlinear evolution equation let x be a real banach space we shall say that an operator a with domain d a and range r a in x is accretive if lx x2 11 0 and yi e axi i 1 2 and that a satisfies the range condition if r z i 1 d a the closure of d a for all a 0 where 1 denotes the identity let g 0 co 0 co be a nonincreasing continuous function such that lim r13 g t 0 let x e x and consider the following initial value problem

unbounded behavior and convergence of solutions of nonlinear volterra equations in banach spaces soit x un espace de banach reel de norme et a un operateur m accretif dans x on etudie le comportement asymptotique des solutions de l equation de volterra non lineaire g t u t b au t t r 0 ou b r r g r x sont donnees et est la convolution

two novel methods and multi mode periodic solutions for the fermi pasta ulam model we introduce two novel methods for studying periodic solutions of the fpu model both numerically and rigorously one is a variational approach based on the dual formulation of the problem and the other involves computer assisted proofs these methods are used e g to construct a new type of solutions whose energy is spread among several modes associated with closely spaced resonances

stability of low dimensional bushes of vibrational modes in the fermi pasta ulam chains bushes of normal modes represent the exact excitations in the nonlinear physical systems with discrete symmetries physica d 117 1998 43 the present paper is the continuation of our previous paper physica d 166 2002 208 where these dynamical objects of new type were discussed for the monoatomic nonlinear chains here we develop a simple crystallographic method for finding bushes in nonlinear chains and investigate stability of one and two dimensional vibrational bushes for both fpu and fpu models in particular of those revealed recently in physica d 175 2003 31

alien attractors and memory annihilation of structured sets in hopfield networks this paper considers the encoding of structured sets into hopfield associative memories a structured set is a set of vectors with equal hamming distance h from one another and its centroid is an external vector that has distance h 2 from every vector of the set structured sets having centroids are not infrequent when such a set is encoded into a noiseless hopfield associative memory using a bipolar outer product connection matrix and the network operates with synchronous neuronal update the memory of all encoded vectors is annihilated even for sets with as few as three vectors in dimension n 5 four for n 5 in such self annihilating structured sets the centroid emerges as a stable attractor we call it an alien attractor for canonical structured sets self annihilation takes place only if h n 2 self annihilation does not occur and alien attractors do not emerge in dimensions less than five

a theoretical investigation into the performance of the hopfield model an analysis is made of the behavior of the hopfield model as a content addressable memory cam and as a method of solving the traveling salesman problem tsp the analysis is based on the geometry of the subspace set up by the degenerate eigenvalues of the connection matrix the dynamic equation is shown to be equivalent to a projection of the input vector onto this subspace in the case of content addressable memory it is shown that spurious fixed points can occur at any corner of the hypercube that is on or near the subspace spanned by the memory vectors analysed is why the network can frequently converge to an invalid solution when applied to the traveling salesman problem energy function with these expressions the network can be made robust and can reliably solve the traveling salesman problem with tour sizes of 50 cities or more

optimal hopfield network for combinatorial optimization with linear cost function an optimal hopfield network is presented for combinatorial optimization problems with linear cost function it is proved that a vertex of the network state hypercube is asymptotically stable if and only if it is an optimal solution to the problem that is one can always obtain an optimal solution whenever the network converges to a vertex in this sense this network can be called the optimal hopfield network it is also shown through simulations of assignment problems that this network obtains optimal or nearly optimal solutions more frequently than other familiar hopfield networks

group invariant pattern recognition abstract in this paper we develop a group theoretical model for the feature extraction part of pattern recognition systems we argue that the features used should reflect the regularities in the environment in which the system exists we develop first a group theoretical model to describe these regularities and then we show how to construct a feature extraction system that reflects these regularities we show why the so found filter functions often appear as solutions to optimality problems and why they often have some nice properties such as invariance under fourier transformation we will mainly investigate problems connected to the group of rotations in 2 d and 3 d space but we will touch other types of symmetries as well

asymptotic behavior of solutions to nonlinear volterra integral equations in section 2 we establish the existence of solutions to 1 1 and to related equations theorems 2 1 and 2 3 in contrast with previous papers e g 7 we do not assume that a is m accretive instead we require a to satisfy a weaker cone condition certain other facts are also included in this section throughout this paper we also assume that b is completely positive 6 in the third section we present two mean ergodic theorems for the solutions of 1 1 in hilbert space the first theorem theorem 3 1 deals with weak almost convergence and the second theorem 3 4 with strong almost convergence these results improve upon those of 1 and include the known results for nonlinear semigroups 191 it is important to establish almost convergence because it then follows that the solution is summed by every strongly regular kernel corollaries 3 3 and 3 5 a weak convergence criterion corollary 3 2 is also obtained if the banach space x is reflexive and strictly convex and 0 e r a then

a review of hopfield neural networks for solving mathematical programming problems the hopfield neural network hnn is one major neural network nn for solving optimization or mathematical programming mp problems the major advantage of hnn is in its structure can be realized on an electronic circuit possibly on a vlsi very large scale integration circuit for an on line solver with a parallel distributed process the structure of hnn utilizes three common methods penalty functions lagrange multipliers and primal and dual methods to construct an energy function when the function reaches a steady state an approximate solution of the problem is obtained under the classes of these methods we further organize hnns by three types of mp problems linear non linear and mixed integer the essentials of each method are also discussed in details some remarks for utilizing hnn and difficulties are then addressed for the benefit of successive investigations finally conclusions are drawn and directions for future study are provided

admissible pairs and integral equations abstract the aim of this paper is to show how a general convergence principle of bruck and reich can be applied to the study of the asymptotic behavior of solutions to nonlinear volterra integral equations

harmonic analysis of homogeneous networks we introduce a generalization of mutually inhibitory networks called homogeneous networks such networks have symmetric connection strength matrices that are circulant one dimensional case or block circulant with circulant blocks two dimensional case fourier harmonics provide universal eigenvectors and we apply them to several homogeneous examples k wta k cluster on center off surround and the assignment problem we also analyze one nonhomogeneous case the subset sum problem we present the results of 10000 trials on a 50 node k cluster problem and 100 trials on a 25 node subset sum problem

asymptotic behavior of solutions of nonlinear volterra equations and mean points abstract in this paper we study the asymptotic behavior of solutions to a nonlinear volterra equation in banach spaces first we deal with the mean point concerning an invariant mean on 0 for the unbounded behavior of solutions in a reflexive banach space using the mean point we obtain the weak and strong convergences for the unbounded behavior of solutions in a reflexive and strictly convex banach space and in the dual space which has a frechet differentiable norm respectively

stability for second order abstract evolution equations on presente une methode generale qui semble bonne pour etudier les proprietes de stabilite d une grande classe d equations non lineaires et qui n a pas besoin de propriete de compacite

nonlinear constructive interference in electrical lattices we analyze the constructive interference of input signals in nonlinear discrete two dimensional media the media consist of inductor capacitor lattices with saturating voltage dependent capacitors we find that nonlinearity significantly boosts the ability of such media to generate large amplitude output signals from small amplitude inputs to understand this boosting we develop a general perturbative method suitable for finding the steady state solution of a damped n ifmmode times else texttimes fi n nonlinear lattice that is driven at a single frequency we verify our theory using extensive numerical simulations

higher order averaging periodic solutions linear systems and an application existence and stability of periodic solutions by using second order averaging when the vector field by first order averaging vanishes will be studied in this paper as well as its generalization to higher order a special averaging algorithm for the computation of higher approximations of the fundamental matrix of linear equations with periodic coefficients is given as an application the existence and stability of periodic solutions of an inhomogeneous second order equation with time dependent damping coefficient are studied

the asymptotic behavior of the solutions of the cauchy problem generated by ϕ accretive operators abstract the purpose of this paper is to study the asymptotic behavior of the solutions of certain type of differential inclusions posed in banach spaces in particular we obtain the abstract result on the asymptotic behavior of the solution of the boundary value problem u t p u u 1 u f on 0 u u on 0 u 0 x u 0 x in where is a bounded open domain in r n with smooth boundary f t x is a given l 1 function on 0 1 and 1 p p represents the p laplacian operator is the associated neumann boundary operator and a maximal monotone graph in r r with 0 0

asymptotic behavior of solutions of a nonlinear evolution equation the purpose of this paper is to study the asymptotic behavior of the solutions of a certain nonlinear evolution equation in banach spaces see 1 below this time dependent initial value problem involves an accretive operator a and a function g r f r it was first considered by browder in 11 and was the basis of the iterative procedures for constructing zeros of accretive operators presented in 2 and 5 these papers treat only the case when 0 e r a we begin with several results e g theorems 3 and 6 that are of interest when 0 r a these results are in some sense analogs of known results for nonlinear semigroups and resolvents there is however a difference see for example corollary 4 then we show that under certain mild restrictions 0 e r a if and only if the solutions to 1 are bounded theorem 7 when an additional condition is imposed on g we can shown that a is zero free if and only if lim u t co for each solution of 1 theorem 8 and proposition 9 in the last part of the paper we assume that 0 e r a and obtain several strong convergence results for solutions of 1 e g theorem 12 these results show that the asymptotic behavior of the solutions to 1 resembles the behavior of resolvents more than that of nonlinear semigroups theorem 12 yields improvements of the convergence results for the iterative procedure of s and leads to a geometric result concerning the fixed point set of a nonexpansive mapping corollary 13 we also mention that the sequence constructed from the iterative procedure of 5 imitates the behavior of the solutions of 1 not only when 0 e r a but also when a is zero free finally we remark that many of our results are new even in hilbert space let e be a real banach space and let i denote the identity operator recall that a subset a of e x e with domain d a and range r a is said to be accretive if lx x2 0 we denote the closure of a subset d of e by cl d its closed convex hull by clco d and its distance from a point x in e by d x 0 we 43 0022 247x 81 090043 11 02 00 0

a new feature extractor invariant to intensity rotation and scaling of color images this paper proposes a new method for extracting the invariant features of an image based on the concept of principal component analysis and a competitive learning algorithm the proposed algorithm can be applied to binary gray level or colored texture images with a size greater than 256x256 pixels in addition to translation scaling and rotation invariant extraction the extraction of a feature invariant to color intensity can be implemented by using this method in our experiment the proposed method shows the capability to differentiate images having the same shape but different colored textures the experimental results report the effectiveness of this technique and its performance as measured by recognition accuracy rate and computational time these results are also compared with those obtained by classical techniques

on the complexity of computing and learning with multiplicative neural networks in a great variety of neuron models neural inputs are combined using the summing operation we introduce the concept of multiplicative neural networks that contain units that multiply their inputs instead of summing them and thus allow inputs to interact nonlinearly the class of multiplicative neural networks comprises such widely known and well studied network types as higher order networks and product unit networks we investigate the complexity of computing and learning for multiplicative neural networks in particular we derive upper and lower bounds on the vapnik chervonenkis vc dimension and the pseudodimension for various types of networks with multiplicative units as the most general case we consider feedforward networks consisting of product and sigmoidal units showing that their pseudo dimension is bounded from above by a polynomial with the same order of magnitude as the currently best known bound for purely sigmoidal networks moreover we show that this bound holds even when the unit type product or sigmoidal may be learned crucial for these results are calculations of solution set components bounds for new network classes as to lower bounds we construct product unit networks of fixed depth with superlinear vc dimension for sigmoidal networks of higher order we establish polynomial bounds that in contrast to previous results do not involve any restriction of the network order we further consider various classes of higher order units also known as sigma pi units that are characterized by connectivity constraints in terms of these we derive some asymptotically tight bounds multiplication plays an important role in both neural modeling of biological behavior and computing and learning with artificial neural networks we briefly survey research in biology and in applications where multiplication is considered an essential computational element the results we present here provide new tools for assessing the impact of multiplication on the computational power and the learning capabilities of neural networks

on the asymptotic behavior of nonlinear semigroups and the range of accretive operators ii abstract it is known that certain problems in partial differential equations may be interpreted as initial value problems for ordinary differential equations in banach spaces when such an evolution equation is governed by an accretive operator then its solutions give rise to a nonlinear contraction semigroup in this paper we study certain aspects of the asymptotic behavior of nonlinear semigroups and or resolvents of accretive operators we also derive new results on their behavior at the origin it turns out that the behavior of a nonlinear semigroup resembles that of the resolvent of its generator both at infinity and at the origin author

image normalization by complex moments the role of moments in image normalization and invariant pattern recognition is addressed the classical idea of the principal axes is analyzed and extended to a more general definition the relationship between moment based normalization moment invariants and circular harmonics is established invariance properties of moments as opposed to their recognition properties are identified using a new class of normalization procedures the application of moment based normalization in pattern recognition is demonstrated by experiment

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

rotation and scale independent pattern recognition through optimization this paper presents a two dimensional pattern recognition paradigm which is independent of rotation and scale it uses a hopfield neural network with a configuration similar to that employed for the traveling salesman problem tsp enhancements to the original hopfield design are included which are based on the eigenvalues of the connection matrix and on modifications suggested by simulations the goal of the method is to determine the underlying linear transformation between a test image and an observed input pattern by minimizing the energy of a hopfield network this procedure is easy to implement and is well suited for sparse binary images e g skeletalized representations or the output from vertex detection algorithms in this work the effects of noise are studied both analytically and through monte carlo techniques yielding some useful performance guidelines and greatly increasing the utility of the method experiments show that this technique performs successfully on a variety of rotated and scaled images and is robust against additive noise

geometric and illumination invariants for object recognition we propose invariant formulations that can potentially be combined into a single system in particular we describe a framework for computing invariant features which are insensitive to rigid motion affine transform changes of parameterization and scene illumination perspective transform and view point change this is unlike most current research on image invariants which concentrates on either geometric or illumination invariants exclusively the formulations are widely applicable to many popular basis representations such as wavelets short time fourier analysis and splines exploiting formulations that examine information about shape and color at different resolution levels the new approach is neither strictly global nor local it enables a quasi localized hierarchical shape analysis which is rarely found in other known invariant techniques such as global invariants furthermore it does not require estimating high order derivatives in computing invariants unlike local invariants whence is more robust we provide results of numerous experiments on both synthetic and real data to demonstrate the validity and flexibility of the proposed framework

cluster based blind nonlinear channel estimation a cluster based maximum likelihood sequence estimator mlse for nonlinear channels was described which consists of a clustering network and an mlse implemented by the viterbi algorithm the cluster based mlse can be used for digital communication through nonlinear finite length channels because channel mapping estimation is used instead of channel estimation in the conventional mlse the clustering network of the cluster based mlse which estimates the channel mapping between the signal input vectors and the noiseless channel outputs is a supervised network and requires a training sequence we propose a blind channel mapping estimator to estimate the channel mapping without using the training sequence the blind channel mapping estimator has a clustering block and a mapping block the clustering block estimates the channel outputs which represent the channel mapping subject to an unknown permutation operation because no training sequence is utilized that permutation operation is resolved by the mapping block and therefore the channel mapping is obtained introducing the blind channel mapping estimator into the cluster based mlse a blind cluster based mlse for nonlinear channels can be done computer simulations of the blind channel mapping estimator and the blind mlse for nonlinear channels are presented

commutativity as prior knowledge in fuzzy modeling in fuzzy modeling fm the quantity and quality of the training set is crucial to properly grasp the behavior of the system being modeled however the available data are often not large enough or are deficiently distributed along the input space not revealing the system behavior completely in such cases the consideration of any prior knowledge about the system can be decisive for the accuracy achieved by the fuzzy modeling this paper faces with the integration of mathematical properties satisfied by a system as prior knowledge in fm focusing on the commutativity property as a starting point with this aim several measures are developed to evaluate the commutativity in a fuzzy environment dealing with different elements involved in fm then several approaches are proposed to measure the commutativity degrees of a fuzzy rule with respect to the training set and a simple method is presented to integrate these degrees into the fm task the experimental results show the accuracy improvement gained by the proposed method

approximating maximum clique with a hopfield network in a graph a clique is a set of vertices such that every pair is connected by an edge max clique is the optimization problem of finding the largest clique in a given graph and is np hard even to approximate well several real world and theory problems can be modeled as max clique in this paper we efficiently approximate max clique in a special case of the hopfield network whose stable states are maximal cliques we present several energy descent optimizing dynamics both discrete deterministic and stochastic and continuous one of these emulates as special cases two well known greedy algorithms for approximating max clique we report on detailed empirical comparisons on random graphs and on harder ones mean field annealing an efficient approximation to simulated annealing and a stochastic dynamics are the narrow but clear winners all dynamics approximate much better than one which emulates a naive greedy heuristic

a hybrid neural network model for solving optimization problems a hybrid neural network model for solving optimization problems is proposed an energy function which contains the constraints and cost criteria of an optimization problem is derived and then the neural network is used to find the global minimum or maximum of the energy function which corresponds to a solution of the optimization problem the network contains two subnets a constraint network and a goal network the constraint network models the constraints of an optimization problem and computes the gradient updating value of each neuron such that the energy function monotonically converges to satisfy all constraints of the problem the goal network points out the direction of convergence for finding an optimal value for the cost criteria these two subnets ensure that the neural network finds feasible as well as optimal or near optimal solutions the traveling salesman problem and the hamiltonian cycle problem are used to demonstrate the method

existence results and asymptotic behavior for nonlocal abstract cauchy problems the purpose of this paper is to study the existence and asymptotic behavior of solutions for cauchy problems with nonlocal initial datum generated by accretive operators in banach spaces

extraction of shift invariant wavelet features for classification of images with different sizes an effective shift invariant wavelet feature extraction method for classification of images with different sizes is proposed the feature extraction process involves a normalization followed by an adaptive shift invariant wavelet packet transform an energy signature is computed for each subband of these invariant wavelet coefficients a reduced subset of energy signatures is selected as the feature vector for classification of images with different sizes experimental results show that the proposed method can achieve high classification accuracy of 98 5 percent and outperforms the other two image classification methods

asymptotic behavior of solutions of nonlinear volterra equations 0 recently baillon and clement 3 established mean ergodic theorems for solutions of nonlinear volterra equations in hilbert space in the present paper we study the asymptotic behavior of solutions of 1 1 by using nonlinear ergodic theorems the first mean ergodic theorem was given by baillon l and it was improved by several authors 3 8 141 163

almost convergence of solutions of nonlinear volterra equations in banach space a l aide d un theoreme ergodique on etudie le comportement asymptotique des solutions des problemes aux valeurs initiales dans des espaces de banach on applique le resultat obtenu a l etude du comportement asymptotique des solutions des equations de volterra non lineaires dans des espaces de banach

periodic attractor for reactiondiffusion high order hopfield neural networks with time varying delays this paper is concerned with a class of reactiondiffusion high order hopfield neural networks with time varying delays subject to the dirichlet boundary condition in a bounded domain easily verifiable delay independent criteria are established to ensure the existence of periodic mild solutions and the global exponential stability of the periodic mild solutions is also discussed by using the exponential dissipation property of semigroup of operators the obtained results are easy to check and they effectually complement previously known results a numerical example is given to show the effectiveness of theoretical results

on the asymptotic behavior of solutions of nonlinear volterra equations where a is an m accretive operator in x b is a given real kernel and g is a given x valued function in what follows we make the same assumptions on b and g as in 2 5 71 hl beac r r b o o b ebv r r h2 ge w r y g el r x g o ed a h3 b is completely positive on r and b m 0 we may assume without loss of generality that b 0 1 sine b t and a may be replaced by b t b o and b o a respectively note that if h 1 holds the first statement in h3 is equivalent to the fact that there exists a k e l r r nonnegative and nonincreasing satisfying b t k b t 1 for t e r moreover in this case lim o b t b cc exists and b m 0 if and only if kel r r see 2 5 71 now define g u for u e c r x or c 0 t x t 0 as follows

translation rotation and scale invariant pattern recognition by high order neural networks and moment classifiers the classification and recognition of two dimensional patterns independently of their position orientation and size by using high order networks are discussed a method is introduced for reducing and controlling the number of weights of a third order network used for invariant pattern recognition the method leads to economical networks that exhibit high recognition rates for translated rotated and scaled as well as locally distorted patterns the performance of these networks at recognizing types and handwritten numerals independently of their position size and orientation is compared with and found superior to the performance of a layered feedforward network to which image features extracted by the method of moments are presented as input

polyhedral combinatorics and neural networks the often disappointing performance of optimizing neural networks can be partly attributed to the rather ad hoc manner in which problems are mapped onto them for solution in this paper a rigorous mapping is described for quadratic 0 1 programming problems with linear equality and inequality constraints this being the most general class of problem such networks can solve the problem s constraints define a polyhedron p containing all the valid solution points and the mapping guarantees strict confinement of the network s state vector to p however forcing convergence to a 0 1 point within p is shown to be generally intractable rendering the hopfield and similar models inapplicable to the vast majority of problems a modification of the tabu learning technique is presented as a more coherent approach to general problem solving with neural networks when tested on a collection of knapsack problems the modified dynamics produced some very encouraging results

three dimensional shape analysis using moments and fourier descriptors a procedure for using moment based feature vectors to identify a three dimensional object from a two dimensional image recorded at an arbitrary viewing angle and range is presented a moment form called standard moments rather than the usual moment invariants is considered a standard six airplane experiment was used to compare different techniques fourier descriptors and moment invariants were both compared to the present scheme for normalized moments various experiments were conducted using mixtures of silhouette and boundary moments and different normalization techniques standard moments gave slightly better results than fourier descriptors for this experiment both of these techniques were much better than moment invariants

radial and angular moment invariants for image identification radial and angular moments of images are presented and methods are shown for deriving moment functions that are invariant with respect to rotation translation reflection and size changes without the aid of the theory of algebraic invariants hu s invariants are expressed in terms of these radial and angular moments and it is claimed that this facilitates visual inspection of invariance properties

a lagrange multiplier and hopfield type barrier function method for the traveling salesman problem a lagrange multiplier and hopfield type barrier function method is proposed for approximating a solution of the traveling salesman problem the method is derived from applications of lagrange multipliers and a hopfield type barrier function and attempts to produce a solution of high quality by generating a minimum point of a barrier problem for a sequence of descending values of the barrier parameter for any given value of the barrier parameter the method searches for a minimum point of the barrier problem in a feasible descent direction which has a desired property that lower and upper bounds on variables are always satisfied automatically if the step length is a number between zero and one at each iteration the feasible descent direction is found by updating lagrange multipliers with a globally convergent iterative procedure for any given value of the barrier parameter the method converges to a stationary point of the barrier problem without any condition on the objective function theoretical and numerical results show that the method seems more effective and efficient than the softassign algorithm

natural discriminant analysis using interactive potts models natural discriminant analysis based on interactive potts models is developed in this work a generative model composed of piece wise multivariate gaussian distributions is used to characterize the input space exploring the embedded clustering and mixing structures and developing proper internal representations of input parameters the maximization of a log likelihood function measuring the fitness of all input parameters to the generative model and the minimization of a design cost summing up square errors between posterior outputs and desired outputs constitutes a mathematical framework for discriminant analysis we apply a hybrid of the mean field annealing and the gradient descent methods to the optimization of this framework and obtain multiple sets of interactive dynamics which realize coupled potts models for discriminant analysis the new learning process is a whole process of component analysis clustering analysis and labeling analysis its major improvement compared to the radial basis function and the support vector machine is described by using some artificial examples and a real world application to breast cancer diagnosis

classical waves on nonlinear lattices ii qn exact analytical solutions are found for classical vibrations of nonlinear oscillators with higher powers of spring constants such as q6 and q8 the solutions are based on a new type of elliptic function that has been created to solve these problems

invariant pattern recognition a review in this document we review and compare some of the classical and modern techniques for solving the problem of invariant pattern recognition such techniques include integral transforms construction of algebraic moments and the use of structured neural networks in all cases we assume that the nature of the invariance group is known a priori many of the methods described apply to specific geometrical transformation groups however some of the techniques are highly general and applicable to large classes of invariance groups we also review some results regarding the existence and structure of invariants under certain kinds of groups

rates of convergence and metastability for abstract cauchy problems generated by accretive operators abstract we extract rates of convergence and rates of metastability in the sense of tao for convergence results regarding abstract cauchy problems generated by accretive at zero operators a d a x 2 x where x is a real banach space proved in 8 by proof theoretic analysis of the proofs in 8 and having assumed a new stronger notion of uniform accretivity at zero yielding a new notion of modulus of accretivity we compute the rate of metastability for the convergence of the solution of the abstract cauchy problem generated by a uniformly accretive at zero operator to the unique zero of a via proof mining based on a result by the first author finally we apply our results to a special class of cauchy problems considered in 8 this work is the first application of proof mining to the theory of partial differential equations

a unified approach to the asymptotic almost equivalence of evolution systems without lipschitz conditions abstract we study the asymptotic behavior of almost orbits of evolution systems in banach spaces without any continuity assumptions on either the space or the time dependence we establish in a unified framework standard convergence ergodic convergence and almost convergence of almost orbits for both the weak and the strong topologies on the basis of the analogue behavior of orbits

on the asymptotic behaviour of solutions of volterra equations in hilbert space u 0 x 1 1 where a is a nonlinear maximal monotone possibly multi valued operator on a real hilbert space h f z 0 4 h x e d a and g is a given mapping g c o d a o t h vo t 0 1 2 by a recent result of crandall nohel 5 theorem 11 the problem 1 1 has a unique generalized solution u e c o 0 h p rovided that g satisfies a lipschitz type condition the present note is concerned with the asymptotic behaviour as t m of generalized solutions of 1 1 at the expense of appropriate assumptions on g see 2 3 2 4 below we are able to derive natural analogs of results by several authors concerning the asymptotic properties of nonlinear contraction semigroups in hilbert space the plan of the paper is as follows the results are presented in section 2 and the proofs are given in section 3 although we deal with solutions of l l we have always in mind the related nonlinear volterra equation

energy function analysis of dynamic programming neural networks all analytical examination of the energy function associated with a dynamic programming neural network is presented the analysis is carried out in two steps first the locations and numbers of the minimum states for different components of the energy function are investigated in the extreme cases a clearer insight into the energy function can be gained through the minimum states of different components secondly the locations of the minimum states of the energy function using different parameter values are derived it is shown that the minimum states can reside in regions which are regarded as valid solutions with certain conditions examples and simulation results are given to justify the validity of the theories developed

weak asymptotic almost periodicity for semigroups of operators abstract we address the question as to when a motion or almost orbit of a strongly continuous semigroup of operators in a banach space is weakly asymptotically almost periodic our results on existence and representation are applied to the study of weak stability properties of operator semigroups and the problem of existence of almost periodic motions for a uniformly bounded co semigroups of linear operators and b nonlinear contraction semigroups

weak convergence of almost orbits of asymptotically nonexpansive commutative semigroups we give three equivalent conditions for weak convergence of almost orbits of an asymptotically nonexpansive commutative semigroup acting on a nonempty bounded closed convex subset of a uniformly convex banach space whose dual has the kadec property

stability analysis of dynamical regimes in nonlinear systems with discrete symmetries we present a theorem that allows one to simplify the linear stability analysis of periodic and quasiperiodic nonlinear regimes in n particle mechanical systems with different kinds of discrete symmetry this theorem suggests a decomposition of the linearized system arising in the standard stability analysis into a number of subsystems whose dimensions can be considerably less than the dimension of the full system as an example of such a simplification we discuss the stability of bushes of modes invariant manifolds for the fermi pasta ulam chains and prove another theorem about the maximal dimension of the above mentioned subsystems

asymptotic behavior of the solutions of a class of functional differential equations remarks on a related volterra equation on etudie la convergence asymptotique forte quand t des solutions de u t au t g u t f t t 0 u 0 u 0 a est un operateur monotone maximal defini sur un sous ensemble d a contenu dans un espace de hilbert reel h u 0 d a f l 1 0 h et g est une application donnee

nonlinear ergodic theorems for semigroups of non lipschitzian mappings in banach spaces let c be a nonempty closed convex subset of a uniformly convex banach space and let s t t t 0 be a nonlinear semi group of non lipschitzian mappings on c which is asymptotically non expansive in the intermediate sense in this paper we study weak almost convergence of almost orbits of s

traditional heuristic versus hopfield neural network approaches to a car sequencing problem this paper considers the problem of optimally sequencing different car models along an assembly line according to some contiguity constraints while ensuring that the demands for each of the models are satisfied this car sequencing problem csp is a practical np hard combinatorial optimisation problem the csp is formulated as a nonlinear integer programming problem and it is shown that exact solutions to the problem are difficult to obtain due to the indefinite quadratic form of the csp objective function two traditional heuristics steepest descent and simulated annealing are employed to solve the csp approximately several hopfield neural network hnn approaches are also presented the process of mapping an optimisation problem onto a hnn is demonstrated explicitly and modifications to the existing neural approaches are presented which guarantee feasibility of solutions further modifications are proposed to improve the solution quality by permitting escape from local minima in an attempt to locate the global optimum results from all solutions techniques are compared on a set of instances of the csp and conclusions drawn

statistical physics algorithms that converge in recent years there has been significant interest in adapting techniques from statistical physics in particular mean field theory to provide deterministic heuristic algorithms for obtaining app

using zernike moments for the illumination and geometry invariant classification of multispectral texture we develop a method for recognizing color texture independent of rotation scale and illumination color texture is modeled using spatial correlation functions defined within and between sensor bands using a linear model for surface spectral reflectance with the same number of parameters as the number of sensor classes we show that illumination and geometry changes in the scene correspond to a linear transformation of the correlation functions and a linear transformation of their coordinates a several step algorithm that includes scale estimation and correlation moment computation is used to achieve the invariance the key to the method is the new result that illumination rotation and scale changes in the scene correspond to a specific transformation of correlation function zernike moment matrices these matrices can be estimated from a color image this relationship is used to derive an efficient algorithm for recognition the algorithm is substantiated using classification results on over 200 images of color textures obtained under various illumination conditions and geometric configurations

linear and logarithmic capacities in associative neural networks a model of associate memory incorporating global linearity and pointwise nonlinearities in a state space of n dimensional binary vectors is considered attention is focused on the ability to store a prescribed set of state vectors as attractors within the model within the framework of such associative nets a specific strategy for information storage that utilizes the spectrum of a linear operator is considered in some detail comparisons are made between this spectral strategy and a prior scheme that utilizes the sum of kronecker outer products of the prescribed set of state vectors which are to function nominally as memories the storage capacity of the spectral strategy is linear in n the dimension of the state space under consideration whereas an asymptotic result of n 4 log n holds for the storage capacity of the outer product scheme computer simulated results show that the spectral strategy stores information more efficiently the preprocessing costs incurred in the two algorithms are estimated and recursive strategies are developed for their computation

numerical analysis of the one mode solutions in the fermi pasta ulam system the stability of the one mode nonlinear solutions of the fermi pasta ulam ensuremath beta system is numerically investigated no external perturbation is considered for the one mode exact analytical solutions the only perturbation being that introduced by computational errors in the numerical integration of motion equations the threshold energy for the excitation of the other normal modes and the dynamics of this excitation are studied as a function of the parameter ensuremath mu characterizing the nonlinearity the energy density ensuremath epsilon and the number n of particles of the system the results achieved confirm in part previous ones obtained with a linear analysis of the problem of the stability and clarify the dynamics by which a one mode exchanges energy with the other modes with increasing energy density in a range of energy density near the threshold value and for various values of the number of particles n the nonlinear one mode exchanges energy with the other linear modes for a very short time immediately recovering all its initial energy this sort of recurrence is very similar to fermi recurrences even if in the fermi recurrences the energy of the initially excited mode changes continuously and only periodically recovers its initial value a tentative explanation for this intermittent behavior in terms of floquet s theorem is proposed preliminary results are also presented for the fermi pasta ulam ensuremath alpha system which show that there is a stability threshold for large n independent of n

on image analysis by the methods of moments various types of moments have been used to recognize image patterns in a number of applications a number of moments are evaluated and some fundamental questions are addressed such as image representation ability noise sensitivity and information redundancy moments considered include regular moments legendre moments zernike moments pseudo zernike moments rotational moments and complex moments properties of these moments are examined in detail and the interrelationships among them are discussed both theoretical and experimental results are presented

neural networks translation rotation and scale invariant pattern recognition a neural network model which is capable of recognising transformed versions of a set of learnt patterns is proposed the group of transformations includes global translations rotations and scale transformations the neural firing thresholds are used as additional degrees of freedom

a novel optimizing network architecture with applications we present a novel optimizing network architecture with applications in vision learning pattern recognition and combinatorial optimization this architecture is constructed by combining the following techniques 1 deterministic annealing 2 self amplification 3 algebraic transformations 4 clocked objectives and 5 softassign deterministic annealing in conjunction with self amplification avoids poor local minima and ensures that a vertex of the hypercube is reached algebraic transformations and clocked objectives help partition the relaxation into distinct phases the problems considered have doubly stochastic matrix constraints or minor variations thereof we introduce a new technique softassign which is used to satisfy this constraint experimental results on different problems are presented and discussed

characterizations of common fixed points of one parameter nonexpansive semigroups and convergence theorems to common fixed points we first prove characterizations of common fixed points of one parameter nonexpansive semigroups we next present convergence theorems to common fixed points

asymptotic properties of solutions of time dependent volterra integral equations abstract the asymptotic properties of the bounded solutions of a time dependent nonlinear volterra equation are studied in a hilbert space an application of physical interest is also given

asymptotic behavior of uniformly asymptotically almost nonexpansive curves in a hilbert space abstract we extend the notion of uniformly asymptotically almost nonexpansive curves which was first introduced in rouhani and kim j nonlinear convex anal 4 2003 175 for a commutative semigroup to a general semitopological semigroup study the asymptotic behavior of such curves in a hilbert space and apply our results to study the asymptotic behavior for almost orbits of semigroups of asymptotically nonexpansive type mappings over a general semitopological semigroup in a hilbert space since in this case the semigroup is not directed the proofs in rouhani and kim j nonlinear convex anal 4 2003 175 do not extend to this case and new methods have to be used for the proofs in addition to rouhani j math anal appl 147 1990 465 j math anal appl 151 1990 226 nonlinear anal 44 2001 627 nonlinear anal 51 2002 735 and rouhani and kim j nonlinear convex anal 4 2003 175 our results extend and unify many previously known results j math anal appl 127 1987 206 proc amer math soc 104 1988 431 nonlinear anal 29 1997 539 topol methods nonlinear anal 5 1995 305 j math anal appl 105 1985 514 nonlinear anal 26 1996 1411 pacific j math 126 1987 277 j math anal appl 206 1997 451 chinese ann math 6 1996 729 nonlinear anal 14 1990 69 j math anal appl 85 1982 172 proc amer math soc 81 1981 253 proc amer math soc 97 1986 55 canad j math 44 1992 880 j math anal appl 142 1989 242 proc amer math soc 117 1993 385

some remarks on the set of common fixed points of one parameter semigroups of nonexpansive mappings in banach spaces with the opial property abstract in this paper we discuss the necessary and sufficient condition for common fixed points of one parameter nonexpansive semigroups in banach spaces with the opial property we next prove the convergence theorem to a common fixed point finally we discuss the existence of nonexpansive retraction onto the set of common fixed points in these theorems we may not assume that the strict uniform convexity of a banach space

the zone boundary mode in periodic nonlinear electrical lattices abstract we study the existence and linear stability of the zone boundary mode in a nonlinear electrical lattice consisting of n inductors and n voltage dependent capacitors with periodic boundary conditions the inductances are allowed to alternate while the capacitors are identical and each have a quadratic dependence on voltage by block diagonalizing a 2 n 2 n floquet problem we reduce the question of the stability of the mode to a single hill s equation that is analyzed using methods of perturbation theory and averaging we show that periodicity of the lattice inductances degrades stability and also show that the instability threshold is proportional to n 2 numerical computations validate the perturbative results

asymptotic behavior for almost orbits of a reversible semigroup of non lipschitzian mappings in a metric space let m be a metric space and a hausdorff topology on m such that m is compact let s be a right reversible semitopological semigroup and t s s s a representation of s as asymptotically nonexpansive type self mappings of m and u a bounded almost orbit of we study the convergence of the net u s s s in m when the triplet m satisfies various types of opial conditions our results extend and unify many previously known results 2002 elsevier science usa all rights reserved

asymptotic behavior of almost orbits of reversible semigroups of lipschitzian mappings abstract let c be a nonempty closed convex subset of a hilbert space h g a right reversible semitopological semigroup and s s t t g a continuous representation of g as lipschitzian mappings of c into itself then we deal with the asymptotic behavior of an almost orbit u t t g of s s t t g we first prove that if limsupt kt 1 then the closed convex subset s e g co u t t s f s consists of at most one point where kt is the lipschitzian constant of s t t g then we apply this result to study the problem of weak convergence of the net u t t g

on the asymptotic behavior of solutions of evolution equations associated with nonlinear volterra equations soit x un espace de banach reel on considere le probleme aux valeurs initiales f t du t dt au t g u t r 0 u 0 u 0 ou a est un operateur m accretif dans x f l loc 1 r x u 0 d a et g une application donnee

weak almost periodicity and the strong ergodic limit theorem for periodic evolution systems the first ergodic theorems for semigroups of nonlinear operators date back to work done by j b baillon cl 23 in 1975 1976 where he proved in 2 that i i lim l t j t s i x dt exists for an odd nonlinear contraction semigroup s t a 0 in real hilbert space in subsequent years various authors have extended his results to motions and almost orbits of nonlinear strongly continuous semigroups in uniformly convex banach spaces e g see 4 10 22 24 26 27 30 31 33 351 as well as 4 10 241 for yet further references these results apply to strong and integral solutions of the quasi autonomous nonlinear cauchy problem