Related papers: Rational approximation to the Thomas--Fermi equati…
We announce here that Fermat's Last theorem was solved, but there is an easy proof of it on the basis of elemetary undergraduate mathematics. We shall disclose such an easy proof.
A rational approximation by a ratio of polynomial functions is a flexible alternative to polynomial approximation. In particular, rational functions exhibit accurate estimations to nonsmooth and non- Lipschitz functions, where polynomial…
Approximations to the Kruskal-Katona theorem are stated and proven. These approximations are weaker than the theorem, but much easier to work with numerically.
Using the $\hbar$-expansion of the Green's function of the Hartree-Fock-Bogoliubov equation, we extend the second-order Thomas-Fermi approximation to generalized superfluid Fermi systems by including the density-dependent effective mass and…
We survey key techniques and results from approximation theory in the context of uniform approximations to real functions such as e^{-x}, 1/x, and x^k. We then present a selection of results demonstrating how such approximations can be used…
We introduce a lazy approach to the explanation-based approximation of probabilistic logic programs. It uses only the most significant part of the program when searching for explanations. The result is a fast and anytime approximate…
This article describes a sequence of rational functions which converges locally uniformly to the zeta function. The numerators (and denominators) of these rational functions can be expressed as characteristic polynomials of matrices that…
In this paper, we prove that the Max-Morse Matching Problem is approximable, thus resolving an open problem posed by Joswig and Pfetsch. We describe two different approximation algorithms for the Max-Morse Matching Problem. For…
Computing the probability of a formula given the probabilities or weights associated with other formulas is a natural extension of logical inference to the probabilistic setting. Surprisingly, this problem has received little attention in…
We compute the constant of approximation for an arbitrary rational point on an arbitrary smooth cubic hypersurface $X$ over a number field $k$, provided that there is a $k$-rational line somewhere on $X$. In the process, we verify the Coba…
We describe an approximate rational arithmetic with round-off errors (both absolute and relative) controlled by the user. The rounding procedure is based on the continued fraction expansion of real numbers. Results of computer experiments…
The proofs first generated by automated theorem provers are far from optimal by any measure of simplicity. In this paper I describe a technique for simplifying automated proofs. Hopefully this discussion will stimulate interest in the…
Quantum corrections to Thomas-Fermi (TF) theory are investigated for noninteracting one-dimensional fermions with known uniform semiclassical approximations to the density and kinetic energy. Their structure is analyzed, and contributions…
This paper proposes a unique optimization approach for estimating the minimax rational approximation and its application for evaluating matrix functions. Our method enables the extension to generalized rational approximations and has the…
Given strong uniqueness for an It\^o's stochastic equation, we prove that its solution can beconstructed on "any" probability space by using, for example, Euler's polygonal approximations. Stochastic equations in $\mathbb{R}^{d}$ and in…
We present a proof of the Chevalley-Weil Theorem that is somewhat different from the proofs appearing in the literature and with somewhat weaker hypotheses, of purely topological type. We also provide a discussion of the assumptions, and an…
We prove the first correction to the leading Thomas-Fermi energy for the ground state energy of atoms and molecules in a model where the kinetic energy of the electrons is treated relativistically. The leading Thomas-Fermi energy,…
The goal of this paper is to introduce a simple finite element method to solve the Stokes and the Navier-Stokes equations. This method is in primal velocity-pressure formulation and is so simple such that both velocity and pressure are…
An alternative form of Fermats equation[1] is proposed. It represents a portion of the identity that includes three terms of Fermats original equation. This alternative form permits an elementary and compact proof of the first case of…
We seek random versions of some classical theorems on complex approximation by polynomials and rational functions, as well as investigate properties of random compact sets in connection to complex approximation.