random attractors for singular stochastic evolution equations abstract the existence of random attractors for singular stochastic evolution equations see perturbed by general additive noise is proven the drift is only assumed to satisfy the standard assumptions of the variational approach to see with compact embeddings in the gelfand triple and singular coercivity for ergodic monotone contractive random dynamical systems it is proven that the random attractor consists of a single random point in case of real linear multiplicative noise finite time extinction is obtained applications include stochastic generalized fast diffusion equations and stochastic generalized singular p laplace equations perturbed by levy noise with jump measure having finite first and second moments

one dimensional random attractor and rotation number of the stochastic damped sine gordon equation abstract this paper is devoted to the study of the asymptotic dynamics of the stochastic damped sine gordon equation with homogeneous neumann boundary condition it is shown that for any positive damping and diffusion coefficients the equation possesses a random attractor and when the damping and diffusion coefficients are sufficiently large the random attractor is a one dimensional random horizontal curve regardless of the strength of noise hence its dynamics is not chaotic it is also shown that the equation has a rotation number provided that the damping and diffusion coefficients are sufficiently large which implies that the solutions tend to oscillate with the same frequency eventually and the so called frequency locking is successful

random attractors for the stochastic benjamin bona mahony equation on unbounded domains abstract we prove the existence of a compact random attractor for the stochastic benjamin bona mahony equation defined on an unbounded domain this random attractor is invariant and attracts every pulled back tempered random set under the forward flow the asymptotic compactness of the random dynamical system is established by a tail estimates method which shows that the solutions are uniformly asymptotically small when space and time variables approach infinity

convergence theorems for the kohonen feature mapping algorithms with vlrps abstract the convergence of the kohonen feature mapping algorithm with vanishing learning rate parameters vlrps is considered which includes the simple competitive learning algorithm as a special case a few examples show that the learning fails to converge to global minima in general then we present a novel approach which enables us to find out a new family of vlrps such that the corresponding learning algorithm converges to the set of global minima with probability one the new vlrps is a generalization of the well known rate parameters used in the simulated annealing a numerical example is also included to confirm our theoretical approach we believe that this discovery is of importance for a large class of learning algorithms in neural networks and statistics

tempered random attractors for parabolic equations in weighted spaces this paper deals with the asymptotic behavior of solutions of parabolic equations on unbounded domains which contain stochastic terms as well as non autonomous deterministic terms we define a continuous random dynamical system for the equations in weighted sobolev spaces that allow functions to have certain polynomial growth rate at infinity and hence include all bounded solutions we prove pullback asymptotic compactness of solutions as well as the existence and uniqueness of tempered random attractors in the weighted spaces the structures of the tempered attractors are fully characterized by tempered complete solutions in the case where the non autonomous deterministic terms are periodic in time we show that the tempered random attractors are also periodic in time to overcome the difficulty of non compactness of sobolev embeddings on unbounded domains the idea of uniform pathwise estimates on the tails of solutions is employed to show asymptotic compactness

the empirical mode decomposition and the hilbert spectrum for nonlinear and non stationary time series analysis a new method for analysing nonlinear and non stationary data has been developed the key part of the method is the empirical mode decomposition method with which any complicated data set can be dec

attractors for random dynamical systems a criterion for existence of global random attractors for rds is established existence of invariant markov measures supported by the random attractor is proved for spde this yields invariant measures for the associated markov semigroup the results are applied to reation diffusion equations with additive white noise and to navier stokes equations with multiplicative and with additive white noise

random attractors for a class of stochastic partial differential equations driven by general additive noise abstract the existence of random attractors for a large class of stochastic partial differential equations spde driven by general additive noise is established the main results are applied to various types of spde as e g stochastic reaction diffusion equations the stochastic p laplace equation and stochastic porous media equations besides classical brownian motion we also include space time fractional brownian motion and space time levy noise as admissible random perturbations moreover cases where the attractor consists of a single point are also investigated and bounds for the speed of attraction are obtained

pullback attractors of non autonomous stochastic degenerate parabolic equations on unbounded domains abstract this paper is concerned with pullback attractors of the stochastic p laplace equation defined on the entire space r n we first establish the asymptotic compactness of the equation in l 2 r n and then prove the existence and uniqueness of non autonomous random attractors this attractor is pathwise periodic if the non autonomous deterministic forcing is time periodic the difficulty of non compactness of sobolev embeddings on r n is overcome by the uniform smallness of solutions outside a bounded domain

flattening squeezing and the existence of random attractors the study of qualitative properties of random and stochastic differential equations is now one of the most active fields in the modern theory of dynamical systems in the deterministic case the properties of flattening and squeezing in infinite dimensional autonomous dynamical systems require the existence of a bounded absorbing set and imply the existence of a global attractor the flattening property involves the behaviour of individual trajectories while the squeezing property involves the difference of trajectories it is shown here that the flattening property is implied by the squeezing property and is in fact weaker since the attractor in a system with the flattening property can be infinite dimensional whereas it is always finite dimensional in a system with the squeezing property the flattening property is then generalized to random dynamical systems for which it is called the pullback flattening property it is shown to be weaker than the random squeezing property but equivalent to pullback asymptotic compactness and pullback limit set compactness and thus implies the existence of a random attractor the results are also valid for deterministic non autonomous dynamical systems formulated as skew product flows

dynamics of the non autonomous stochastic p laplace equation driven by multiplicative noise we investigate the asymptotic behavior of solutions of the p laplace equation driven simultaneously by non autonomous deterministic forcing and multiplicative white noise on r n we show the tails of solutions of the equation are uniformly small outside a bounded domain which is used to derive asymptotic compactness of solution operators in l 2 r n by overcoming the non compactness of sobolev embeddings on unbounded domains we then prove existence and uniqueness of random attractors and further establish upper semicontinuity of attractors as the intensity of noise approaches zero

generalized pencil of function method for extracting poles of an em system from its transient response a generalized pencil of function gpof method is developed for extracting the poles of an electromagnetic system from its transient response the gpof method needs the solution of a generalized eigenvalue problem to find the poles subspace decomposition is also used to optimize the performance of the gpof method the gpof method has advantages over the prony method in both computation and noise sensitivity and approaches the cramer rao bound when the signal to noise ratio snr is above threshold an application of the gpof method to a thin wire target is presented

limiting dynamics for stochastic wave equations abstract in this paper relations between the asymptotic behavior for a stochastic wave equation and a heat equation are considered by introducing almost surely d contracting property for random dynamical systems we obtain a global random attractor of the stochastic wave equation u t t u t u f u w endowed with dirichlet boundary condition for any 0 1 the upper semicontinuity of this global random attractor and the global attractor of the heat equation z t z f z 0 with dirichlet boundary condition as goes to zero is investigated furthermore we show the stationary solutions of the stochastic wave equation converge in probability to some stationary solution of the heat equation

high order differentiation filters that work reliable derivatives of digital images have always been hard to obtain especially but not only at high orders we analyze the sources of errors in traditional filters such as derivatives of the gaussian that are used for differentiation we then study a class of filters which is much more suitable for our purpose namely filters that preserve polynomials up to a given order we show that the errors in differentiation can be corrected using these filters we derive a condition for the validity domain of these filters involving some characteristics of the filter and of the shape our experiments show a very good performance for smooth functions

decomposition of one dimensional waveform using iterative gaussian diffusive filtering methods the gaussian smoothing method is shown to have a wide transition zone around the cutoff frequency selected to filter a given dataset we proposed two iterative gaussian smoothing methods to tighten the transition zone one being approximately diffusive and the other being strictly diffusive the first version smoothes repeatedly the remaining high frequency parts and the second version requires an additional step to further smooth the resulting smoothed response in each of the smoothing operation based on the choice of the criterion for accuracy the smoothing factor and the number of iterations are derived for an infinite data length in both methods by contrast for a finite length data string results of the interior points sufficiently away from the two endpoints obtained by both methods can be shown to exhibit an approximate diffusive property the upper bound of the distance affected by the error propagation inward due to the lack of data beyond the two ends is numerically estimated numerical experiments also show that results of employing the iterative gaussian smoothing method are almost the same as those obtained by the strict diffusive version except that the error propagation distance induced by the latter is slightly deeper than that of the former the proposed method has been successfully applied to decompose the wave formation of a number of test cases including two sets of real experimental data

the existence and exponential behavior of solutions to stochastic delay evolution equations with a fractional brownian motion abstract in this paper we investigate the existence uniqueness and exponential asymptotic behavior of mild solutions to stochastic delay evolution equations perturbed by a fractional brownian motion b q h t d x t a x t f t x t d t g t d b q h t with hurst parameter h 1 2 1 we also consider the existence of weak solutions

sufficient and necessary criteria for existence of pullback attractors for non compact random dynamical systems abstract we study pullback attractors of non autonomous non compact dynamical systems generated by differential equations with non autonomous deterministic as well as stochastic forcing terms we first introduce the concepts of pullback attractors and asymptotic compactness for such systems we then prove a sufficient and necessary condition for existence of pullback attractors we also introduce the concept of complete orbits for this sort of systems and use these special solutions to characterize the structures of pullback attractors for random systems containing periodic deterministic forcing terms we show the pullback attractors are also periodic under certain conditions as an application of the abstract theory we prove the existence of a unique pullback attractor for reaction diffusion equations on r n with both deterministic and random external terms since sobolev embeddings are not compact on unbounded domains the uniform estimates on the tails of solutions are employed to establish the asymptotic compactness of solutions

the laplacian pyramid as a compact image code we describe a technique for image encoding in which local operators of many scales but identical shape serve as the basis functions the representation differs from established techniques in that the code elements are localized in spatial frequency as well as in space pixel to pixel correlations are first removed by subtracting a lowpass filtered copy of the image from the image itself the result is a net data compression since the difference or error image has low variance and entropy and the low pass filtered image may represented at reduced sample density further data compression is achieved by quantizing the difference image these steps are then repeated to compress the low pass image iteration of the process at appropriately expanded scales generates a pyramid data structure the encoding process is equivalent to sampling the image with laplacian operators of many scales thus the code tends to enhance salient image features a further advantage of the present code is that it is well suited for many image analysis tasks as well as for image compression fast algorithms are described for coding and decoding

asymptotic behavior of stochastic wave equations with critical exponents on mathbb r 3 the existence of a random attractor in h 1 3 x l 2 3 is proved for the damped semilinear stochastic wave equation defined on the entire space 3 the nonlinearity is allowed to have a cubic growth rate which is referred to as the critical exponent the uniform pullback estimates on the tails of solutions for large space variables are established the pullback asymptotic compactness of the random dynamical system is proved by using these tail estimates and the energy equation method

random attractors for stochastic reaction diffusion equations on unbounded domains the existence of a pullback attractor is established for a stochastic reaction diffusion equation on all n dimensional space the nonlinearity is dissipative for large values of the state and the stochastic nature of the equation appears as spatially distributed temporal white noise the reaction diffusion equation is recast as a random dynamical system and asymptotic compactness for this is demonstrated by using uniform a priori estimates for far field values of solutions

scale based description and recognition of planar curves and two dimensional shapes the problem of finding a description at varying levels of detail for planar curves and matching two such descriptions is posed and solved in this paper a number of necessary criteria are imposed on any candidate solution method path based gaussian smoothing techniques are applied to the curve to find zeros of curvature at varying levels of detail the result is the generalized scale space image of a planar curve which is invariant under rotation uniform scaling and translation of the curve these properties make the scale space image suitable for matching the matching algorithm is a modification of the uniform cost algorithm and finds the lowest cost match of contours in the scale space images it is argued that this is preferable to matching in a so called stable scale of the curve because no such scale may exist for a given curve this technique is applied to register a landsat satellite image of the strait of georgia b c manually corrected for skew to a map containing the shorelines of an overlapping area