on nonstability of the linear recurrence of order one abstract we show that under some assumptions the linear recurrence or difference equation of order one in a banach space is nonstable in the hyers ulam sense our results are also connected with the notion of shadowing in dynamical systems and computer sciences

on the unification of line processes outlier rejection and robust statistics with applications in early vision the modeling of spatial discontinuities for problems such as surface recovery segmentation image reconstruction and optical flow has been intensely studied in computer vision while line process models of discontinuities have received a great deal of attention there has been recent interest in the use of robust statistical techniques to account for discontinuities this paper unifies the two approaches to achieve this we generalize the notion of a line process to that of an analog outlier process and show how a problem formulated in terms of outlier processes can be viewed in terms of robust statistics we also characterize a class of robust statistical problems for which an equivalent outlier process formulation exists and give a straightforward method for converting a robust estimation problem into an outlier process formulation we show how prior assumptions about the spatial structure of outliers can be expressed as constraints on the recovered analog outlier processes and how traditional continuation methods can be extended to the explicit outlier process formulation these results indicate that the outlier process approach provides a general framework which subsumes the traditional line process approaches as well as a wide class of robust estimation problems examples in surface reconstruction image segmentation and optical flow are presented to illustrate the use of outlier processes and to show how the relationship between outlier processes and robust statistics can be exploited an appendix provides a catalog of common robust error norms and their equivalent outlier process formulations

data imputation through the identification of local anomalies we introduce a comprehensive and statistical framework in a model free setting for a complete treatment of localized data corruptions due to severe noise sources e g an occluder in the case of a visual recording within this framework we propose 1 a novel algorithm to efficiently separate i e detect and localize possible corruptions from a given suspicious data instance and 2 a maximum a posteriori estimator to impute the corrupted data as a generalization to euclidean distance we also propose a novel distance measure which is based on the ranked deviations among the data attributes and empirically shown to be superior in separating the corruptions our algorithm first splits the suspicious instance into parts through a binary partitioning tree in the space of data attributes and iteratively tests those parts to detect local anomalies using the nominal statistics extracted from an uncorrupted clean reference data set once each part is labeled as anomalous versus normal the corresponding binary patterns over this tree that characterize corruptions are identified and the affected attributes are imputed under a certain conditional independency structure assumed for the binary patterns we analytically show that the false alarm rate of the introduced algorithm in detecting the corruptions is independent of the data and can be directly set without any parameter tuning the proposed framework is tested over several well known machine learning data sets with synthetically generated corruptions and experimentally shown to produce remarkable improvements in terms of classification purposes with strong corruption separation capabilities our experiments also indicate that the proposed algorithms outperform the typical approaches and are robust to varying training phase conditions

stability of multi additive mappings in β banach spaces abstract in this paper we prove the generalized hyers ulam stability of the system defining multi additive mappings and an equation which characterizes these mappings in banach spaces we thus generalize some previous results obtained in classical banach spaces in order to get our outcomes we use both direct and fixed point methods

stability of a general mixed additive cubic functional equation in non archimedean fuzzy normed spaces we establish some stability results concerning the general mixed additive cubic functional equation in non archimedean fuzzy normed spaces in addition we establish some results of approximately general mixed additive cubic mappings in non archimedean fuzzy normed spaces the results improve and extend some recent results

a fixed point theorem and the hyers ulam stability in non archimedean spaces abstract we prove a fixed point theorem in complete non archimedean normed spaces and show its applications in the hyers ulam stability of some functional equations

on the general solution and hyperstability of the general radical quintic functional equation in quasi β banach spaces abstract the goal of this paper is to study the general solution of the following general radical quintic functional equation f a x 5 b y 5 5 r f x s f y for f a mapping from the field of real numbers into a vector space where a b r s are fixed nonzero reals also we prove the generalized hyperstability results for the general radical quintic functional equation by using the fixed point theorem cf dung and hang 2018 15 theorem 2 1 in quasi banach spaces namely we show under some weak natural assumptions functions satisfying the above equation approximately in some sense must be actually solutions to it

on the pressure transfer function for solitary water waves with vorticity in this paper we analyse the role which the pressure function on the sea bed plays in determining solitary waves with vorticity we prove that the pressure function on the flat bed determines a unique real analytic solitary wave solution to the governing equations given a real analytic vorticity distribution in particular the pressure function on the flat bed prescribes a unique surface profile for the resulting solitary water wave

stability of multi jensen mappings in non archimedean normed spaces in this paper we study the stability of the multi jensen mappings in non archimedean normed spaces the results improve and extend some recent results

note on nonstability of the linear functional equation of higher order we provide a complete solution of the problem of hyers ulam stability for a large class of higher order linear functional equations in single variable with constant coefficients we obtain this by showing that such an equation is nonstable in the case where at least one of the roots of the characteristic equation is of module 1 our results are related to the notions of shadowing in dynamical systems and computer science and controlled chaos they also correspond to some earlier results on approximate solutions of functional equations in single variable

hyers ulam stability of a first order partial differential equation abstract we prove that the existence of a global prime integral leads in appropriate conditions to the hyers ulam stability of a linear partial differential equation of first order

on the quotient stability of a family of functional equations abstract we show some stability results for a family of functional equations that contains the exponential and the golab schinzel functional equations

intuitionistic fuzzy stability of a general mixed additive cubic equation we establish some stability results concerning the general mixed additive cubic functional equation f kx y f kx y kf x y kf x y 2f kx 2kf x in intuitionistic fuzzy normed spaces in addition we show under some suitable conditions that an approximately mixed additive cubic function can be approximated by a mixed additive and cubic mapping

prior learning and gibbs reaction diffusion this article addresses two important themes in early visual computation it presents a novel theory for learning the universal statistics of natural images and it proposes a general framework of designing reaction diffusion equations for image processing we studied the statistics of natural images including the scale invariant properties then generic prior models were learned to duplicate the observed statistics based on minimax entropy theory the resulting gibbs distributions have potentials of the form u i spl lambda s spl sigma sub spl alpha 1 sup k spl sigma sub x y spl lambda sup spl alpha f sup spl alpha i x y with s f sup 1 f sup 2 f sup k being a set of filters and spl lambda spl lambda sup 1 spl lambda sup 2 spl lambda sup k the potential functions the learned gibbs distributions confirm and improve the form of existing prior models such as line process but in contrast to all previous models inverted potentials were found to be necessary we find that the partial differential equations given by gradient descent on u i spl lambda s are essentially reaction diffusion equations where the usual energy terms produce anisotropic diffusion while the inverted energy terms produce reaction associated with pattern formation enhancing preferred image features we illustrate how these models can be used for texture pattern rendering denoising image enhancement and clutter removal by careful choice of both prior and data models of this type incorporating the appropriate features

on the generalized hyers ulam stability of multi quadratic mappings a mapping f v email protected w where v is a commutative group w is a linear space and n 2 is an integer is called multi quadratic if it is quadratic in each variable in this paper we prove the generalized hyers ulam stability of multi quadratic mappings in banach spaces and complete non archimedean spaces

stability of a mixed functional equation in several variables on banach modules abstract in this paper we establish the general solution of the functional equation i 1 n f x i 1 n j 1 n x j i 1 n f x i n f 1 n i 1 n x i n 2 and use a fixed point method to prove its generalized hyers ulam stability in banach modules over a unital banach algebra

a fixed point technique for investigating the stability of α β γ derivations on lie c algebras abstract we apply a fixed point theorem to investigate some new stability results for derivations on lie c algebras associated with the generalized cauchy jensen type additive functional equation i 1 n f x i 1 n 1 j 1 j i n x j 2 i 1 n f x i

on approximate roots of polynomials and systems of polynomials in ultrametric banach algebras abstract we present methods that allow to estimate the distance between the approximate and exact zeros of some polynomial equations and systems of them also infinite in ultrametric banach algebras to make our results more useful we consider that issue in a more general situation i e for some functional equations of polynomial form moreover we do it almost everywhere with respect to a given ideal as an auxiliary tool we prove an ultrametric version of a fixed point theorem in some function spaces also almost everywhere our investigations have been motivated by several previous outcomes and the notion of ulam stability

hyers ulam rassias stability of a linear recurrence abstract in this paper we give a hyers ulam rassias stability result for the first order linear recurrence in banach spaces

image denoising using scale mixtures of gaussians in the wavelet domain we describe a method for removing noise from digital images based on a statistical model of the coefficients of an overcomplete multiscale oriented basis neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables a gaussian vector and a hidden positive scalar multiplier the latter modulates the local variance of the coefficients in the neighborhood and is thus able to account for the empirically observed correlation between the coefficient amplitudes under this model the bayesian least squares estimate of each coefficient reduces to a weighted average of the local linear estimates over all possible values of the hidden multiplier variable we demonstrate through simulations with images contaminated by additive white gaussian noise that the performance of this method substantially surpasses that of previously published methods both visually and in terms of mean squared error

remarks on the hyers ulam stability of some systems of functional equations abstract in this paper we present a method that allows to study the hyers ulam stability of some systems of functional equations connected with the cauchy jensen and quadratic equations in particular we generalize and extend some already known results

selections of generalized convex set valued functions satisfying some inclusions abstract the main purpose of this article is to determine the existence of a unique selection of convex set valued functions satisfying some generalized set valued inclusions from radstrom s cancelation lemma and the main result of piszczek 20 we extend the same conclusions as in 19 but under weaker assumptions finally we present a few applications of set valued dynamics

a generalization of the hyers ulam rassias stability of jensen s equation in this paper we prove a generalization of the stability of the jensen s equation in the spirit of hyers ulam rassias and g vruta

remarks on stability and non stability of the linear functional equation of the first order abstract we prove some results on stability and non stability of the linear functional equation of the first order in single variable moreover we suggest some possible definitions of stability and non stability

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

fixed point theorems and the ulam hyers stability in non archimedean cone metric spaces abstract let x p be a metric space with a k valued non archimedean metric p in this paper we prove the existence and approximation of a fixed point for operators f x x satisfying the contractive condition in the form p f x f y q p x y where q k k is an increasing operator then we study the generalized ulam hyers stability of fixed point equations we next obtain an extension of the krasnoselskii fixed point theorem for the sum of two operators finally an application to functional equations is given

learning to represent spatial transformations with factored higher order boltzmann machines to allow the hidden units of a restricted boltzmann machine to model the transformation between two successive images memisevic and hinton 2007 introduced three way multiplicative interactions that use the intensity of a pixel in the first image as a multiplicative gain on a learned symmetric weight between a pixel in the second image and a hidden unit this creates cubically many parameters which form a three dimensional interaction tensor we describe a low rank approximation to this interaction tensor that uses a sum of factors each of which is a three way outer product this approximation allows efficient learning of transformations between larger image patches since each factor can be viewed as an image filter the model as a whole learns optimal filter pairs for efficiently representing transformations we demonstrate the learning of optimal filter pairs from various synthetic and real image sequences we also show how learning about image transformations allows the model to perform a simple visual analogy task and we show how a completely unsupervised network trained on transformations perceives multiple motions of transparent dot patterns in the same way as humans

on the stability of the first order linear recurrence in topological vector spaces abstract suppose that x is a sequentially complete hausdorff locally convex space over a scalar field k v is a bounded subset of x a n n 0 is a sequence in k 0 with the property lim inf n a n 1 and b n n 0 is a sequence in x we show that for every sequence x n n 0 in x satisfying x n 1 a n x n b n v n 0 there exists a unique sequence y n n 0 satisfying the recurrence y n 1 a n y n b n n 0 and for every q with 1 q lim inf n a n there exists n 0 n such that x n y n 1 q 1 c o n v v b n n 0

explicit and exact solutions concerning the antarctic circumpolar current with variable density in spherical coordinates we use spherical coordinates to devise a new exact solution to the governing equations of geophysical fluid dynamics for an inviscid and incompressible fluid with a general density distribution and subjected to forcing terms the latter are of paramount importance for the modeling of realistic flows that is flows that are observed in some averaged sense in the ocean owing to the employment of spherical coordinates we do not need to resort to approximations e g of f and plane type that simplify the geometry in the governing equations our explicit solution represents a steady purely azimuthal stratified flow with a free surface that thanks to the inclusion of forcing terms and the consideration of the earth s geometry via spherical coordinates makes it suitable for describing the antarctic circumpolar current and enables an in depth analysis of the structure of this flow in line with the latter aspect we employ functional analytical techniques to prove that the free surface distortion is defined in a unique and implicit way by means of the pressure applied at the free surface we conclude our discussion by setting out relations between the monotonicity of the surface pressure and the monotonicity of the surface distortion that concur with the physical expectations

products of gaussians and probabilistic minor component analysis recently hinton introduced the products of experts architecture for density estimation where individual expert probabilities are multiplied and renormalized we consider products of gaussian pancakes equally elongated in all directions except one and prove that the maximum likelihood solution for the model gives rise to a minor component analysis solution we also discuss the covariance structure of sums and products of gaussian pancakes or one factor probabilistic principal component analysis models

a fixed point approach to stability of functional equations abstract we prove a simple fixed point theorem for some not necessarily linear operators and derive from it several quite general results on the stability of a very wide class of functional equations in single variable

a fast learning algorithm for deep belief nets we show how to use complementary priors to eliminate the explaining away effects that make inference difficult in densely connected belief nets that have many hidden layers using complementary priors we derive a fast greedy algorithm that can learn deep directed belief networks one layer at a time provided the top two layers form an undirected associative memory the fast greedy algorithm is used to initialize a slower learning procedure that fine tunes the weights using a contrastive version of the wake sleep algorithm after fine tuning a network with three hidden layers forms a very good generative model of the joint distribution of handwritten digit images and their labels this generative model gives better digit classification than the best discriminative learning algorithms the low dimensional manifolds on which the digits lie are modeled by long ravines in the free energy landscape of the top level associative memory and it is easy to explore these ravines by using the directed connections to display what the associative memory has in mind

on the hyers ulam stability of linear mappings abstract let e1 be a real normed vector space and e2 a real banach space s m ulam posed the problem when does a linear mapping near an approximately linear mapping e1 e2 exist we give a new generalized solution to this problem an example illustrates when the answer to this question is negative the behaviour of bounded approximately additive mappings which do not satisfy hyers uiam stability is also investigated

on the cauchy rassias stability of a generalized additive functional equation let x and y be banach spaces and f x y an odd mapping we solve the following generalized additive functional equation rf j 1dxjr j 0 1 j 1d j lrf j 1d 1 j xjr cld 1 cl 1d 1 1 j 1df xj for all x1 xd x moreover we deal with the above functional equation in banach modules over a c algebra and obtain generalizations of the cauchy rassias stability the concept of cauchy rassias stability for the linear mapping was originated from th m rassias s stability theorem that appeared in his paper th m rassias on the stability of the linear mapping in banach spaces proc amer math soc 72 1978 297 300

a fixed point theorem in n banach spaces and ulam stability abstract motivated by some issues in ulam stability we prove a fixed point theorem for operators acting on some classes of functions with values in n banach spaces we also present applications of it to ulam stability of eigenvectors and some functional and difference equations

energy based models for sparse overcomplete representations we present a new way of extending independent components analysis ica to overcomplete representations in contrast to the causal generative extensions of ica which maintain marginal independence of sources we define features as deterministic linear functions of the inputs this assumption results in marginal dependencies among the features but conditional independence of the features given the inputs by assigning energies to the features a probability distribution over the input states is defined through the boltzmann distribution free parameters of this model are trained using the contrastive divergence objective hinton 2002 when the number of features is equal to the number of input dimensions this energy based model reduces to noiseless ica and we show experimentally that the proposed learning algorithm is able to perform blind source separation on speech data in additional experiments we train overcomplete energy based models to extract features from various standard data sets containing speech natural images hand written digits and faces

a generalization of the hyers ulam rassias stability of approximately additive mappings abstract in this paper we prove a generalization of the stability of approximately additive mappings in the spirit of hyers ulam and rassias

monotone solutions of a nonlinear differential equation for geophysical fluid flows abstract we prove the existence of monotone bounded solutions of a recently derived nonlinear differential equation of geophysical relevance our approach relies on functional analytic techniques and the obtained results have wide applicability which we illustrate by some examples

hyers ulam stability of the linear differential operator with nonconstant coefficients abstract we obtain some stability results for the linear differential operator of order one in banach spaces as a consequence we derive a result on hyers ulam stability for the linear differential operator of higher order with nonconstant coefficients

construction of continuous solutions and stability for the polynomial like iterative equation abstract most of known results such as existence uniqueness and stability for polynomial like iterative equations were given under the assumption that the coefficient of the first order iteration term does not vanish the existence with a non zero leading coefficient was therefore raised as an open problem it was positively answered for local c 1 solutions later in this paper this problem is answered further by constructing c 0 solutions moreover we discuss the stability of those c 0 solutions which consequently implies a result of the stability for iterative roots

selections of set valued maps satisfying a linear inclusion in a single variable abstract we prove that a set valued map satisfying a linear functional inclusion in a single variable admits in appropriate conditions a unique selection satisfying a linear functional equation in a single variable as a consequence there follow results on the hyers ulam stability of the linear functional equation in a single variable and the equation of homomorphism of square symmetric groupoids

hyersulam stability of the iterative equation with a general boundary restriction hyersulam stability has played an important role not only in the theory of functional equations but also in a variety of branches of mathematics such as differential equations integral equations and linear operators in the present paper we will discuss the hyersulam stability of the iterative equation with a general boundary restriction by the construction of a uniformly convergent sequence of functions we prove that for every approximate solution of such an equation there exists an exact solution near it

a fixed point theorem and the ulam stability in generalized dq metric spaces abstract we prove a fixed point theorem for function spaces that is a very efficient and convenient tool for the investigations of various operator inequalities connected to ulam stability issues in classes of functions taking values in various spaces e g in ultrametric spaces dq metric spaces quasi banach spaces and p banach spaces the theorem is a natural generalization and extension of the classical banach contraction principle and some other more recent results

generalized hyers ulam stability for general additive functional equations in quasi β normed spaces abstract in 1940 s m ulam proposed the famous ulam stability problem in 1941 d h hyers solved the well known ulam stability problem for additive mappings subject to the hyers condition on approximately additive mappings the first author of this paper investigated the hyers ulam stability of cauchy and jensen type additive mappings in this paper we generalize results obtained for jensen type mappings and establish new theorems about the hyers ulam stability for general additive functional equations in quasi normed spaces

continuity of iteration and approximation of iterative roots motivated by computing iterative roots for general continuous functions in this paper we prove the continuity of the iteration operators t n defined by t nf f n we apply the continuity and introduce the concept of continuity degree to answer positively the approximation question if lim m f m f can we find an iterative root f m of f m of order n for each email protected n such that the sequence f m tends to the iterative root of f of order n associated with a given initial function we not only give the construction of such an approximating sequence f m but also illustrate the approximation of iterative roots with an example some remarks are presented in order to compare our approximation with the hyers ulam stability

on the existence of solutions and the pressure function related to the antarctic circumpolar current abstract this paper is concerned with the analysis of an incompressible inviscid fluid moving only in the azimuthal direction with no variations in this direction but allowing for a depth dependent variation as such this permits the consideration of the antarctic circumpolar current the most significant current in earth s oceans and the only current that encircles the polar axis more precisely working in spherical coordinates accounting thus for the geometry of the earth we derive an implicit equation for the function describing the free surface which is related to the pressure function we use this equation to prove by means of the implicit function theorem that any small deviation from the pressure required to maintain the free surface undisturbed gives rise to a unique veritable wave solution our approach comprises also a body force which is shown to have significant influence on the monotonicity properties of the pressure function and the height function describing the free surface

modeling the shape of the scene a holistic representation of the spatial envelope in this paper we propose a computational model of the recognition of real world scenes that bypasses the segmentation and the processing of individual objects or regions the procedure is based on a very low dimensional representation of the scene that we term the spatial envelope we propose a set of perceptual dimensions naturalness openness roughness expansion ruggedness that represent the dominant spatial structure of a scene then we show that these dimensions may be reliably estimated using spectral and coarsely localized information the model generates a multidimensional space in which scenes sharing membership in semantic categories e g streets highways coasts are projected closed together the performance of the spatial envelope model shows that specific information about object shape or identity is not a requirement for scene categorization and that modeling a holistic representation of the scene informs about its probable semantic category

on approximate solutions of the linear functional equation of higher order abstract we show that under some assumptions every approximate solution of the linear functional equation of higher order in single variable generates a solution of the equation that is close to it we also give a description of a procedure that yields such a solution estimate the distance between those approximate and exact solutions to the equation and discuss the problem of uniqueness moreover as a consequence we obtain some results concerning the hyers ulam stability of the equation

stability of multi additive mappings in non archimedean normed spaces abstract a function f v n w where v is a commutative semigroup w is a linear space and n 1 is an integer is called multi additive if it is additive in each variable in this paper we prove the generalized hyers ulam stability of multi additive mappings in non archimedean normed spaces using the so called direct method

generalization of functional equation for the square root spiral abstract in the paper we give the general solution of the linear functional equation p 1 p x c x h x furthermore we discuss its hyers ulam rassias stability and the stability in the sense of ger for the equation p 1 p x c x our results are applied to the square root spiral so that the related results by heuvers et al k j heuvers d s moak b boursaw the functional equation of the square root spiral in th m rassias ed functional equations and inequalities kluwer 2000 pp 111 117 and results by jung and sahoo stability of functional equation for square root spirals appl math lett 15 2002 435 438 are generalized

the trajectories of particles in stokes waves analyzing a free boundary problem for harmonic functions we show that there are no closed particle paths in an irrotational inviscid traveling wave propagating at the surface of water over a flat bed within a period each particle experiences a backward forward motion with a slight forward drift

fixed points of a mapping and hyers ulam stability abstract we show that many general results on hyers ulam stability of some functional equations in a single variable follow immediately from a simple fixed point theorem the theorem is formulated for self maps of some subsets of the space of functions from a nonempty set into the set of reals we also give some applications of that theorem e g in investigations of solutions of some difference equations and functional inequalities

modeling natural images using gated mrfs this paper describes a markov random field for real valued image modeling that has two sets of latent variables one set is used to gate the interactions between all pairs of pixels while the second set determines the mean intensities of each pixel this is a powerful model with a conditional distribution over the input that is gaussian with both mean and covariance determined by the configuration of latent variables which is unlike previous models that were restricted to using gaussians with either a fixed mean or a diagonal covariance matrix thanks to the increased flexibility this gated mrf can generate more realistic samples after training on an unconstrained distribution of high resolution natural images furthermore the latent variables of the model can be inferred efficiently and can be used as very effective descriptors in recognition tasks both generation and discrimination drastically improve as layers of binary latent variables are added to the model yielding a hierarchical model called a deep belief network

stability of functional equations in single variable abstract this paper discusses hyers ulam stability for functional equations in single variable including the forms of linear functional equation nonlinear functional equation and iterative equation surveying many known and related results we clarify the relations between hyers ulam stability and other senses of stability such as iterative stability continuous dependence and robust stability which are used for functional equations applying results of nonlinear functional equations we give the hyers ulam stability of bottcher s equation we also prove a general result of hyers ulam stability for iterative equations

instability of internal equatorial water waves abstract in the following paper we present criteria for the hydrodynamical instability of internal equatorial water waves we show by way of the short wavelength perturbation approach that certain geophysical waves propagating above the equatorial thermocline are linearly unstable when the wave steepness exceeds a given threshold

fuzzy density weight based support vector regression for image denoising support vector machine svm is a popular machine learning technique and its variant least squares support vector regression ls svr is effective for image denoising however conventional ls svr does not fully consider the sampling distribution of noisy images which may degrade the performance of the algorithm in this paper we propose a new fuzzy density weight svr fdw svr denoising algorithm which assigns fuzzy priority to each sample according to its density weight fdw is designed to estimate the joint probability density function via the fuzzy theory based on the pixel density and neighborhood density extensive experimental results show that fdw svr is superior to those state of the art denoising techniques in light of both subjective and objective evaluations

stability of the multi jensen equation abstract in this paper we study the stability in the sense of th m rassias of multi jensen equation

probabilistic principal component analysis principal component analysis pca is a ubiquitous technique for data analysis and processing but one which is not based upon a probability model in this paper we demonstrate how the principal axes of a set of observed data vectors may be determined through maximum likelihood estimation of parameters in a latent variable model closely related to factor analysis we consider the properties of the associated likelihood function giving an em algorithm for estimating the principal subspace iteratively and discuss the advantages conveyed by the definition of a probability density function for pca

on the stability of the linear differential equation of higher order with constant coefficients abstract we obtain a result on stability of the linear differential equation of higher order with constant coefficients in aoki rassias sense as a consequence we obtain the hyers ulam stability of the above mentioned equation a connection with dynamical sytems perturbation is established

a fixed point approach to the stability of functional equations in non archimedean metric spaces abstract in this note we prove a simple fixed point theorem for a special class of complete metric spaces namely complete non archimedean metric spaces which are connected with some problems coming from quantum physics p adic strings and superstrings we also show that this theorem is a very efficient and convenient tool for proving the hyers ulam stability of a quite wide class of functional equations in a single variable

approximation solution of nonlinear stratonovich volterra integral equations by applying modification of hat functions in this paper we studied the hyers ulam rassias stability for nonlinear stratonovich volterra integral equations also we obtained stochastic operational matrix of modification of hat functions mhfs to numerically solve the nonlinear stratonovich volterra integral equations the main advantage of the proposed method is that it transforms problems under consideration into nonlinear systems of algebraic equations which can be simply solved finally numerical examples are presented to certify convergence and accuracy of the method

hyers ulam stability and discrete dichotomy abstract let m be a given positive integer and let a be an m m complex matrix we prove that the discrete system x n 1 a x n n z is hyers ulam stable if and only if the matrix a possesses a discrete dichotomy also we prove that the scalar difference equation of order m x n m a 1 x n m 1 a 2 x n m 2 a m x n n z is hyers ulam stable if and only if the algebraic equation z m a 1 z m 1 a m 1 z a m z c has no roots on the unit circle this latter result is essentially known for further details see for example 24 and 2 however our proofs are completely different and moreover it seems that our approach opens the way to obtain many other results in this topic