Chaotic time series can well reflect the nonlinearity and non-stationarity of real environment changes. The traditional kernel adaptive filter (KAF) with second-order statistical characteristics suffers performance degeneration dramatically for predicting chaotic containing noises outliers. In order to improve robustness filters in presence impulsive noise, a nonlinear similarity measure named ...

D.V. Chudnovsky and G.V. Chudnovsky [CH] introduced a generalization of the FrobeniusStickelberger determinantal identity involving elliptic functions that generalize the Cauchy determinant. The purpose of this note is to provide a simple essentially non-analytic proof of this evaluation. This method of proof is inspired by D. Zeilberger’s creative application in [Z1]. AMS Subject Classificatio...

This paper focus on the study of existence and uniqueness of distributional and classical solutions to the Cauchy Boltzmann problem for the soft potential case assuming Sn−1 integrability of the angular part of the collision kernel (Grad cut-off assumption). For this purpose we revisit the Kaniel–Shinbrot iteration technique to present elementary proofs of existence when the initial data is nea...

We consider the Cauchy problem for generalized Fornberg–Whitham equation with dissipation. This is one of nonlinear, nonlocal and dispersive-dissipative equations. The main topic this paper an asymptotic analysis solutions to problem. prove that solution converges modified heat kernel. Moreover, we construct second term asymptotics depending on degree nonlinearity. In view those profiles, inves...

We consider a hydrodynamic model of flocking-type with all-to-all interaction kernel in one-space dimension and establish global existence entropy weak solutions concentration to the Cauchy problem for any [Formula: see text] initial data that has finite total mass confined bounded interval density uniformly positive therein. In addition, under suitable condition on data, we show admit time-asy...

A recently introduced fast algorithm for the computation of the first N terms in an expansion of an analytic function into ultraspherical polynomials consists of three steps: Firstly, each expansion coefficient is represented as a linear combination of derivatives; secondly, it is represented, using the Cauchy integral formula, as a contour integral of the function multiplied by a kernel; final...

This paper algorithmically and empirically studies two major types of nonparametric multivariate density estimation techniques, where no assumption is made about the data being drawn from any of known parametric families of distribution. The first type is the popular kernel method (and several of its variants) which uses locally tuned radial basis (e.g., Gaussian) functions to interpolate the m...

Abstract In his celebrated article, Aronson established Gaussian bounds for the fundamental solution to Cauchy problem governed by a second order divergence form operator with uniformly elliptic coefficients. We extend Aronson’s proof of upper heat kernel estimates nonlocal operators whose jumping satisfies pointwise bound and energy is coercive. A detailed given in Euclidean space extensions d...

where / i s the boundary function for jpand da is Lebesgue measure on the sphere. When m = 1, (1) easily transforms into the Cauchy integral formula. In dimension m9 the formula extends to be defined on all / in L , always yielding holomorphic functions. If we identify holomorphic functions with their boundary values, the extended operator can be regarded as the orthogonal projection from L to ...