相关论文: A Robust Approximation to a Lambert-Type Function

We discuss classical and quantum algorithms for solvability testing and finding integer solutions x,y of equations of the form af^x + bg^y = c over finite fields GF(q). A quantum algorithm with time complexity q^(3/8) (log q)^O(1) is…

We present an algorithm for generating approximations for the logarithm of Barnes $G$-function in the half-plane $Re(z)\ge 3/2$. These approximations involve only elementary functions and are easy to implement. The algorithm is based on a…

We establish a rigorous mathematical framework connecting graphene nanoribbon quantum sensing to the Lambert W function through the finite square well (FSW) analogy. The Lambert W function, defined as the inverse of $f(W) = We^W$, provides…

The GW approximation is widely used for reliable and accurate modeling of single-particle excitations. It also serves as a starting point for many theoretical methods, such as its use in the Bethe-Salpeter equation (BSE) and dynamical…

We present a new method for approximating real-valued functions on ${\mathbb R}^+$ by linear combinations of exponential functions with complex coefficients. The approach is based on a multi-point Pad\'e approximation of the Laplace…

Function approximation is a generic process in a variety of computational problems, from data interpolation to the solution of differential equations and inverse problems. In this work, a unified approach for such techniques is…

In this article, we provide a comprehensive analysis of the asymptotic behavior of Bell numbers, enhancing and unifying various results previously dispersed in the literature. We establish several explicit lower and upper bounds. The main…

We show that the equations underlying the $GW$ approximation have a large number of solutions. This raises the question: which is the physical solution? We provide two theorems which explain why the methods currently in use do, in fact,…

Modular graph functions associate to a graph an $SL(2,Z)$-invariant function on the upper half plane. We obtain the Fourier series of modular graph functions of arbitrary weight $w$ and two-loop order. The motivation for this work is to…

We consider a sequence of polynomials appearing in expressions for the derivatives of the Lambert W function. The coefficients of each polynomial are shown to form a positive sequence that is log-concave and unimodal. This property implies…

We present a simple and accurate GW implementation based on a combination of a Laplace transformation (LT) and other acceleration techniques used in post-SCF quantum chemistry, namely, natural auxiliary functions and the frozen-core…

Given a model in algebraic statistics and some data, the likelihood function is a rational function on a projective variety. Algebraic algorithms are presented for computing all critical points of this function, with the aim of identifying…

In computational molecular science, calculation of electrostatic interactions involving charged atoms - the strongest interactions in condensed phases, is a major bottleneck. We propose a quantum-classical algorithm for fast, yet, accurate…

Although the GW approximation is recognized as one of the most accurate theories for predicting materials excited states properties, scaling up conventional GW calculations for large systems remains a major challenge. We present a powerful…

There has been much recent attention on $h$-functions, so named since they describe the distribution of harmonic measure for a given multiply connected domain with respect to some basepoint. In this paper, we focus on a closely related…

We study some series expansions for the Lambert $W$ function. We show that known asymptotic series converge in both real and complex domains. We establish the precise domains of convergence and other properties of the series, including…

The aim of this paper is to treat the constant coefficients functional-differential equation $y'(x)=ay(qx)+by(x)$ with the help of the analytic theory of linear $q$-difference equations. When $ab\not=0$, the associated Cauchy problem with…

In classical physics, calculating the slack of a hanging chain is a problem that has attracted interest. This study aims to solve this problem through experiment and theory. When the length and distance of both the ends of a hanging chain…

The calculation of one-loop Wilson coefficients for general Beyond the Standard Model (BSM) scenarios is a technical challenge often addressed by doing long and error prone analytical calculations by hand. Several software programs already…

After defining in detail the Lambert $W$-function branches, we give a large number of exact identities involving (infinite) symmetric functions of these branches, as well as geometrically convergent series for all the branches. In doing so,…