140 Results Found

The Lambert W function, implicitly defined by $W\left(x\right){}^{}$...

In the theory of special functions, finding correlations between different types of functions is of great interest as unifying results, especially when considering issues such as analytic continuation. In the present paper, the relation between Lambe...

Schröder based series for the principal and negative one branches of the Lambert W function are defined; the series are generic and are in terms of an initial, arbitrary, approximating function. Upper and lower bounds for the initial approximati...

The relationship between the inverse Langevin function and the proposed r₀-r₁-Lambert W function is defined. The derived relationship leads to new approximations for the inverse Langevin function with lower relative error bounds than comparable publi...

We consider a series which combines two Dirichlet series constructed from the coefficients of a Laurent series and derive a general integral representation of the series as a Mellin transform. As an application, we obtain a family of Mellin integral...

The purpose of this note is to propose an application of the Lambert W function in linear viscoelasticity based on the Bernstein and Stieltjes properties of this function. In particular, we recognize the role of its main branch, $W_0\left(t\right)$, in a peculiar...

Spectral line shapes are a key ingredient of hot-plasma opacity calculations. Since resorting to elaborate line-shape models remains prohibitive for intensive opacity calculations involving ions in different excitation states, with L, M, etc., shells...

This paper presents a new approach to stabilize the first order neutral delay differential systems with two time delays. First, we provided a few oscillation and non-oscillation criteria for the neutral delay differential equations using spectrum ana...

The aim of this paper is to define the linear operator based on the generalized Mittag-Leffler function and the Lambert series. By using this operator, we introduce a new subclass of β-uniformly starlike functions ${\mathsf{{\rm T}}}_{\mathcal{J}}\left({\alpha }_i\right)$. Further, we o...

This paper develops a unified framework for continuous distributional characterizations based on conditional expectations of functions of a random variable. The proposed framework expresses several characterization identities through a single differe...

Studies of the dynamics of linear and nonlinear differential equations with delays described by mathematical models play a crucial role in various scientific domains, including economics and biology. In this article, the Lambert function method, whic...

Due to the high dependence of photovoltaic energy efficiency on environmental conditions (temperature, irradiation...), it is quite important to perform some analysis focusing on the characteristics of photovoltaic devices in order to optimize energy...

Semi-empirical models remain among the most widely used tools for analyzing proton exchange membrane fuel cells (PEMFCs) because they provide a practical balance between physical interpretability and computational efficiency. Existing reviews primari...

In this paper, the explicit equation of the single diode model (SDM) expressed by the Lambert W function was reduced to its simplified form through variable replacement; then the simplified explicit equation was combined with an intelligent optimizat...

There are three standard equivalent circuit models of solar cells in the literature—single-diode, double-diode, and triple-diode models. In this paper, first, a modified version of the single diode model, called the Improved Single Diode Model...

In this paper, we study a two-parameter family of Stieltjes transformations related to holomorphic Lambert–Tsallis functions, which are a two-parameter generalization of the Lambert function. Such Stieltjes transformations appear in the study o...

The aim of this paper is to study the use of Lambert W functions in the analysis of nonlinear dynamics and bifurcations of a new two-dimensional $\gamma$-Ricker population model. Through the use of such transcendental functions, it is possible to stud...

The Colebrook equation is a popular model for estimating friction loss coefficients in water and gas pipes. The model is implicit in the unknown flow friction factor, $f$ . To date, the captured flow friction factor, $f$ , can be extracted...

The Lambert W is a Bernstein function and hence the cumulant function of a positive infinitely divisible law, the Lambert law $L(\Lambda )$. The Lambert law is self-decomposable with a unit rate compound Poisson background driving Lévy process (...

In this article, we introduce a new probability distribution generator called the Lambert-F generator. For any continuous baseline distribution F, with positive support, the corresponding Lambert-F version is generated by using the new generator. The...

We compare the classical viscoelastic models due to Becker and Lomnitz with respect to a recent viscoelastic model based on the Lambert W function. We take advantage of this comparison to derive new analytical expressions for the relaxation spectrum...

In this note we discuss the development of a new Gamma exponentiated functional $\mathrm{GE}(\alpha ,h)$ distribution, using the Gamma baseline distribution generating method by Zografos and Balakrishnan. The raw moments of the Gamma exponentiated functi...

This article numerically analyzes the distribution of the zeros of Riemann’s zeta function along the critical line (CL). The zeros are distributed according to a hierarchical two-layered model, one deterministic, the other stochastic. Following...

In this paper, we study a quadratic nonlinear equation from the fractional point of view. An explicit solution is given in terms of the Lambert special function. A new phenomenon appears involving the collapsing of the solution and the blow-up of the...

The current–voltage characteristics of the double diode and triple diode models of solar cells are highly nonlinear functions, for which there is no analytical solution. Hence, an iterative approach for calculating the current as a function of...

In this paper, we propose very simple analytical methodologies for modeling the behavior of photovoltaic (solar cells/panels) using a one-diode/two-resistor (1-D/2-R) equivalent circuit. A value of a = 1 for the ideality factor is shown to be very re...

Schröder approximations of the first kind, modified for the inverse function approximation case, are utilized to establish general analytical approximation forms for an inverse function. Such general forms are used to establish arbitrarily accur...

Standard models of “regular black holes” typically have asymptotically de Sitter regions at their cores. Herein, we shall consider novel “hollow” regular black holes, those with asymptotically Minkowski cores. The reason for d...

The transformation formula under the action of a general linear fractional transformation for a generalized Dedekind eta function has been the subject of intensive study since the works of Rademacher, Dieter, Meyer, and Schoenberg et al. However, the...

Two-dimensional (2D) correlation functions are central to understanding structural crossovers in soft-core fluids; however, their asymptotic analysis is hindered by the Hankel-transform kernel, whose asymptotic representation introduces a term that b...

The classical Lotka–Volterra predator–prey system is often used in modeling species competition. The two-species nonlinear system is expressed in terms of a single positive coupling parameter $\lambda$. Based on a standard functional trans...

Even a relatively simple equation such as Colebrook’s offers a lot of possibilities to students to increase their computational skills. The Colebrook’s equation is implicit in the flow friction factor and, therefore, it needs to be solved...

The most commonly used model of solar cells is the single-diode model, with five unknown parameters. First, this paper proposes three variants of the single-diode model, which imply the voltage dependence of the series resistance, parallel resistance...

The symmetric Kullback–Leibler centroid, also called the Jeffreys centroid, of a set of mutually absolutely continuous probability distributions on a measure space provides a notion of centrality which has proven useful in many tasks, including...

The mouse neuromuscular junction (NMJ) has long been used as a model synapse for the study of neurotransmission in both healthy and disease states of the NMJ. Neurotransmission from these neuromuscular nerve terminals occurs at highly organized struc...

This paper presents new analytical expressions for the maximum power point voltage, current, and power that have an explicit dependence on the series resistance. An explicit expression that relates the series resistance to well-known solar cell param...

In this paper we will be concerned with zeta-symmetry—the functional equation for the (Riemann) zeta-function (equivalents to which are called modular relations)—and reveal the reason why so many results are intrinsic to PFE (Partial Frac...

The SIR (Susceptible-Infected-Removed) model is a simple mathematical model of epidemic outbreaks, yet for decades it evaded the efforts of the mathematical community to derive an explicit solution. The present paper reports novel analytical results...

Assuming the in vitro conditions for the enzyme-catalyzed reactions, the basic Michaelis-Menten description is modified in a logistic (mathematical) manner such that the inherent limitations that appear in the previous method are removed. Beside its...

In this reply, we present updated approximations to the Colebrook equation for flow friction. The equations are equally computational simple, but with increased accuracy thanks to the optimization procedure, which was proposed by the discusser, Dr. M...

This reply gives two corrections of typographical errors in respect to the commented article, and then provides few comments in respect to the discussion and one improved version of the approximation of the Colebrook equation for flow friction, based...

Classical black holes contain a singularity at their core. This has prompted various researchers to propose a multitude of modified spacetimes that mimic the physically observable characteristics of classical black holes as best as possible, but that...

Low Density Parity Check (LDPC) codes are currently being deeply analyzed through algorithms that require the capability of addressing their iterative decoding convergence performance. Since it has been observed that the probability distribution func...

Motivated by a problem proposed by Seiffert a quarter of century ago, we explicitly evaluate binomial sums with Pell and Lucas polynomials as weight functions. Their special cases result in several interesting identities concerning Fibonacci and Luca...

A bounded form of the Teissier distribution, namely the unit Teissier distribution, is introduced. It is subjected to a thorough examination of its important properties, including shape analysis of the main functions, analytical expression for moment...

A Regge–Wheeler analysis is performed for a novel black hole mimicker ‘the regular black hole with asymptotically Minkowski core’, followed by an approximation of the permitted quasi-normal modes for propagating waveforms. A first-order WKB approxima...

Here I investigate some mathematical aspects of the maximum entropy theory of ecology (METE). In particular I address the geometrical structure of METE endowed by information geometry. As novel results, the macrostate entropy is calculated analytical...

This article presents the solution to an optimization problem concerning the longest wooden log that can be floated through two perpendicularly intersecting water canals. This application problem is further generalized and solved using a graphical me...

In this paper, an energy efficient power allocation scheme is proposed for a distributed massive multiple-input multiple-output (MIMO) system with a circular antenna array. Single-antenna users simultaneously transmit signal to the base station (BS)...

Detailed simulations have indicated optimum insulation thicknesses of walls’ insulation for a variety of cases. Simplified analytical relations have also been proposed to the same aim, allowing the extraction of more general results, with limited acc...