Related papers: Inverse Langevin and Brillouin functions: mathemat…
In this paper we review the physical applications of the generalized Lambert function recently defined by the first author. Among these applications we mention the eigenstate anomaly of the $H_2^+$ ion, the two dimensional two-body problem…
The inverse Langevin function is a fundamental part of the statistical chain models used to describe the behavior of polymeric-like materials, appearing also in other fields such as magnetism, molecular dynamics and even biomechanics. In…
We introduce a new type of Bernstein operators, which can be used to approximate the functions with inner singularities. The direct and inverse results of the weighted approximation of this new type of combinations are given.
This paper uses the convolution theorem of the Laplace transform to derive new inverse Laplace transforms for the product of two parabolic cylinder functions in which the arguments may have opposite sign. These transforms are subsequently…
Inversion of function sinc(x) is studied. New series and integral representations of branches of inverse function are obtained using Fourier analysis.
The Lambert W(x) function and its possible applications in physics are presented. The actual numerical implementation in C++ consists of Halley's and Fritsch's iterations with initial approximations based on branch-point expansion,…
We prove an inversion theorem for the Fourier transform defined for normal functions, in the case when such functions are of moderate decrease, and in dimensions 2 and 3. This improves on Carleson's general almost everywhere convergence…
We have derived some new results for the Mellin transform formulas, as well as for the Gauss hypergeometric function. Also, we have found the connection between the Legendre functions of the second kind. Some of the results obtained we used…
We prove a novel inversion theorem for functionals given as power series in infinite-dimensional spaces and apply it to the inversion of the density-activity relation for inhomogeneous systems. This provides a rigorous framework to prove…
In terms of the best approximations of functions and generalized moduli of smoothness, direct and inverse approximation theorems are proved for Besicovitch almost periodic functions whose Fourier exponent sequences have a single limit point…
The purpose of this note is to compare various approximation methods as applied to the inverse of the Bessel function of the first kind, in a given domain of the complex plane.
This article handles in a short manner a few Laplace transform pairs and some extensions to the basic equations are developed. They can be applied to a wide variety of functions in order to find the Laplace transform or its inverse when…
In Musilak-Orlicz type spaces ${\mathcal S}_{\bf M}$, direct and inverse approximation theorems are obtained in terms of the best approximations of functions and generalized moduli of smoothness. The question of the exact constants in…
A recognized trend of research investigates generalizations of the Hadamard's inversion theorem to functions that may fail to be differentiable. In this vein, the present paper explores some consequences of a recent result about the…
The Bregman divergence (Bregman distance, Bregman measure of distance) is a certain useful substitute for a distance, obtained from a well-chosen function (the "Bregman function"). Bregman functions and divergences have been extensively…
The Lorentz Integral Transform approach allows microscopic calculations of electromagnetic reaction cross sections without explicit knowledge of final state wave functions. The necessary inversion of the transform has to be treated with…
We connect the well-known theory of functional forms of variational bicomplex with the theory of antiexact differential forms. We identify antiexact functional forms as an obstruction to the variationality of differential equations. The…
Different practical problems, espesially, problems of hydrodynamics, elasticity theory, geophysics and aerodynamics can be reduced to finding of an optimal shape. The investigation of these problems is based on the study of depending domain…
The applications of the recent results obtained in the theory of generalized Lambert functions, to the mean field theory of ferromagnetism are presented. As a consequence, all the predictions of the Weiss theory of ferromagnetism can be…
We study physical aspects for a new nonlinear electrodynamics (inverse electrodynamics). It is shown that this new electrodynamics displays the vacuum birefringence phenomenon in the presence of external magnetic field, hence we compute the…