in this paper at first , we discuss about nonlinear pseudoparabolic equations with nonlocalboundary conditions and their results.at second we use an effective error estimation for this method altough has not yet beendiscussed. the aim of this paper is to fill this gap.

The paper is concerned with the problem of shape preserving interpolatory subdivision. For arbitrarily spaced, planar input data an efficient non-linear subdivision algorithm reproducing conic sections and respecting the convexity properties of the initial data, is here presented. Significant numerical examples are included to illustrate the effectiveness of the proposed method and the smoothne...

A problem of learning a prediction rule that is approximated in a linear span of a large number of reproducing kernel Hilbert spaces is considered. The method is based on penalized empirical risk minimization with `1type complexity penalty. Oracle inequalities on excess risk of such estimators are proved showing that the method is adaptive to unknown degree of “sparsity” of the target function.

In the study of Hilbert spaces of analytic functions, it is noticed that complete interpolating sequences and Riesz bases of reproducing kernels are dual notions. In this work we make this duality explicit by identifying sequences of complex numbers with linear operators.

Let μ be a measure with compact support, with orthonormal polynomials {pn}, and associated reproducing kernels {Kn}. We show that bulk universality holds in measure in {ξ : μ (ξ) > 0}. More precisely, given ε, r > 0, the linear Lebesgue measure of the set of ξ with μ (ξ) > 0 and for which

An extension of reproducing kernel Hilbert space (RKHS) theory provides a new framework for modeling functional regression models with functional responses. The approach only presumes a general nonlinear regression structure as opposed to previously studied linear regression models. Generalized cross-validation (GCV) is proposed for automatic smoothing parameter estimation. The new RKHS estimat...

Starting from linear equations for the complex scalar field, the twoand three-point Green’s functions are obtained in the infrared approximation. We show that the infrared singularity factorizes in the vertex function as in spinorial QED, reproducing in a straightforward way the result of lenghty perturbative calculations. PACS. 11.10 Field theory, 12.20 Models of electromagnetic interactions.

We model the non-linear gain characteristics of a Fabry-Perot semiconductor optical amplifier using a modified photon density rate equation. Good agreement is found with experimental results, with the simulation accurately reproducing all the major characteristics of the amplifier. To our knowledge, this is the first calculation using only the rate equations that accurately predicts the gain an...

We study some relations between a reproducing cone K in a linear space V over a fully ordered field F and the cone I(K) in Hom( V, V) consisting of all operators A such that AK G K. In particular, indecomposable cones are considered.

The “kernel trick” is well established as a means of constructing nonlinear algorithms from linear ones, by transferring the linear algorithms to a high dimensional feature space: specifically, a reproducing kernel Hilbert space (RKHS). Recently, it has become clear that a potentially more far reaching use of kernels is as a linear way of dealing with higher order statistics, by embedding proba...