In this paper, we generalize a sequence of positive linear operators introduced by Ismail and May study some their approximation properties for different classes continuous functions. First, estimate the error in terms usual modulus continuity second-order Ditzian Totik. Then, characterize bounded functions that can be approximated uniformly these new operators. last section, obtain most import...

The relativistic harmonic oscillator represents a unique energy-conserving oscillatory system. detailed characteristics of the solution this are displayed in both weak- and extreme-relativistic limits using different expansion procedures, for each limit. In weak-relativistic limit, Normal Form is developed, which yields an approximation to that significantly better than traditional asymptotic p...

The Poisson Boltzmann equation is a model that describes electrostatic interactions between molecules in ionic solutions. As the mathematical base for the Gouy Chapman double layer (interfacial) theory, it was first proposed by Gouy in 1910 and then complemented by Chapman in 1913. The equation is extraordinarily important in the fields of molecular dynamics and biophysics, because it can be us...

The problems of asymptotic expansion for solutions of PDE and PDE systems were studied by many authors. A lot of references could be found in [5]. As a rule, border problems are studied with the small parameter being denoted at the higher derivative by t. For example, in [8, page 155] the system of first-order equations is studied with the small parameter denoted by t and x that corresponds to ...

Whenever real particle production occurs in quantum field theory, the imaginary part of the Hadamard elementary function G (1) is non-vanishing. A method is presented whereby the imaginary part of G (1) may be calculated for a charged scalar field in a static spherically symmetric spacetime with arbitrary curvature coupling and a classical electromagnetic field A. The calculations are performed...

The density functional theory DFT provides a powerful and reliable approach to the electronic structures of manyelectron systems.1,2 The DFT has been extended so that various physical quantities can be chosen as basic variables.3–5 For instance, the spin-density functional theory,6,7 the current-density functional theory CDFT ,8–11 and LDA+U method12–15 are regarded as examples of such extensio...

1.1. Topological derivatives in shape optimization. Topological derivatives are introduced for linear problems in (Sokolowski and Zochowski, 1999) and for variational inequalities in (Sokolowski and Zochowski, 2005). The mathematical theory of asymptotic analysis is applied in (Nazarov and Sokolowski, 2003; 2006) for the derivation of topological derivatives in shape optimization of elliptic bo...

We study the renormalisation of non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric scalar field theory with interaction $\phi^2(i\phi)^\varepsilon$ using Wilsonian approach and without any expansion in $\varepsilon$. Specifically, we solve Wetterich equation local potential approximation, both ultraviolet regime loop expansion. calculate scale-dependent effective its infrared limit. The is found ...

Abstract In this paper, we study local approximation properties of certain gamma-type operators. They generalize the Post–Widder operators and Rathore operators, approximate locally integrable functions satisfying a growth condition on infinite interval $$[0,\infty )$$ [ 0 , <...