A fresh study on the perturbative expansion is presented with the help of Heaviside transform with respect to the mass. We apply Heaviside transform to the effective potential in the Gross-Neveu model and carry out perturbative approximation of the massless potential by dealing with the resulting Heaviside function. We find that accurate values of the dynamical mass can be obtained from the Hea...

In this paper we design and analyze a class of high order numerical methods to two dimensional Heaviside function integrals. Inspired by our high order numerical methods to two dimensional delta function integrals [19], the methods comprise approximating the mesh cell restrictions of the Heaviside function integral. In each mesh cell the two dimensional Heaviside function integral can be rewrit...

This paper introduces a new approach to the recursive propagation of probability density functions through discrete-time stochastic nonlinear dynamic systems. An efficient recursive procedure is proposed that is based on the optimal approximation of the posterior densities after each prediction step by means of Dirac mixtures. The parameters of the individual components are selected by systemat...

Unconventional way of handling the perturbative series is presented with the help of Heaviside transformation with respect to the mass. We apply Heaviside transform to the e ective potential in the massive Gross-Neveu model and carry out perturbative approximation of the massless potential by dealing with the resulting Heaviside function. We nd that accurate values of the dynamical mass can be ...

It is shown that cartesian product and pointwise-sum with a fixed compact set preserve various approximation-theoretic properties. Results for pointwise-sum are proved for F -spaces and so hold for any normed linear space, while the other results hold in general metric spaces. Applications are given to approximation of Lp-functions on the d-dimensional cube, 1 ≤ p < ∞, by linear combinations of...

In Lp-spaces with p an integer from [1, infinity) there exists a best approximation mapping to the set of functions computable by Heaviside perceptron networks with n hidden units; however for p an integer from (1, infinity) such best approximation is not unique and cannot be continuous.

In this paper we study the one-sided Hausdorff distance between the Heaviside function and some transmuted activation functions. Precise upper and lower bounds for the Hausdorff distance have been obtained. Numerical examples are presented throughout the paper using the computer algebra system MATHEMATICA. The results can be successfully used in the field of applied insurance mathematics.