Research ArticleOpen accessPhrase in the titleThe Extended Laplace TransformSabra RamadanThe space of new generalized functions has been constructed. The operation of associative multiplication has been defined on this space. The Extended Laplace Transform has been defined. …Journal of Mathematics and Statistics, Vol. 3, Issue 4 · 31 Dec 2007 · 7,069 accessesView PDFCite
Research ArticleOpen accessIn the keywordsThe Solution to Some Hypersingular Integral EquationsAlexander G. RammGel’fand, I. M., & Shilov, G. E. (1964). Generalized Functions. Volume I: Properties and Operations (1st ed., Vol. 1). Academic Press. Hörmander, L. (1998). The Analysis of Linear Partial Differential Operators I (1st ed.). Springer Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-96750-4 Ramm, A. G. (2022). The Navier-Stokes Problem (2nd ed.). Springer Nature. Ramm, A. G. (2023). Analysis of the Navier-Stokes problem (2nd ed.). … …Journal of Mathematics and Statistics, Vol. 20, Issue 1 · 25 May 2024 · 5,683 accessesView PDFCite
Research ArticleOpen accessIn the keywordsPerturbation Iteration Transform Method for the Solution of Newell-Whitehead-Segel Model EquationsGrace O. Akinlabi, Sunday O. EdekiIn this study, a computational method referred to as Perturbation Iteration Transform Method (PITM), which is a combination of the conventional Laplace Transform Method (LTM) and the Perturbation Iteration Algorithm (PIA) is applied for the solution of Newell-Whitehead-Segel Equations (NWSEs). Three unique examples are considered and the results obtained are compared with their exact solutions graphically. Also, the results agree … …Journal of Mathematics and Statistics, Vol. 13, Issue 1 · 20 Feb 2017 · 6,987 accessesView PDFCite
Research ArticleOpen accessIn the keywordsRandom Sum of Mixtures of Sum of Bivariate Exponential DistributionsAbd El-Moneim A.M. Teamah, Ahmed M.T. Abd El-BarProblem statement: The distributions of R = X+Y and W = X/(X+Y), where X and Y follow Lawrance and Lewis`s bivariate exponential distribution, is generalized. Approach: In this research we found mixtures of sum of bivariate exponential random variables. Results: Also we calculated the probability density function (pdf) of the random sum of mixtures of sum of bivariate exponential random … …Journal of Mathematics and Statistics, Vol. 5, Issue 4 · 31 Dec 2009 · 7,316 accessesView PDFCite
Research ArticleOpen accessIn the abstractThe Study of the Dynamics of a Cebâşev ManipulatorRelly Victoria Virgil PetrescuThe paper presents a new method for determining the dynamic parameters of a Cebâşev conveyor mechanism, solvable in two steps. In the first step, the classic method of preserving the kinetic energy of the entire mechanism is used to determine the rotating mass of the Cebâşev mechanism denoted by J*, this being the dynamic rotating mass of the entire mechanism … …American Journal of Engineering and Applied Sciences, Vol. 15, Issue 4 · 28 Nov 2022 · 5,663 accessesView PDFCite
Research ArticleOpen accessIn the abstractSome Contributions to the Theory of Abstract Degenerate Volterra Integro-Differential EquationsMarko KostićIn this study, we contribute to the existing theory of abstract degenerate Volterra integro-differential equations in sequentially complete locally convex spaces. We investigate a class of abstract degenerate Volterra inclusions by using the multivalued linear operator approach, as well as a class of abstract degenerate multi-term fractional differential equations with Caputo derivatives by using the pure Laplace transform techniques. …Journal of Mathematics and Statistics, Vol. 12, Issue 2 · 17 Jun 2016 · 7,406 accessesView PDFCite
Research ArticleOpen accessIn the abstractCompare Between Two-Unit Cold Standby and Warm Standby Outdoor Electric Power Systems in Changing WeatherG. S. Mokaddis, M. Salah EL-Sherbeny, Entesar Al-EsayehProblem statement: This study presents the reliability analysis of two mathematical models representing electric power systems operating in fluctuating outdoor weather (i.e., normal and stormy weather) and compared between two models. Approach: Model I deals the reliability analysis of a single-server two-unit cold standby, Model II deals the reliability analysis of a single-server two-unit warm standby, for two systems with … …Journal of Mathematics and Statistics, Vol. 6, Issue 1 · 31 Mar 2010 · 7,439 accessesView PDFCite
Research ArticleOpen accessIn the abstractStochastic Behavior of Redundant Complex System with Two Types of FailureG. S. Mokaddis, M. Salah EL-Sherbeny, Entesar Al-EsayehProblem statement: This study presented the reliability and Mean Time To System Failure (MTTF) analysis of a two-state complex with repairable system, consisting of two sub-systems A and B arranged in series, incorporating the concept of hardware and human failures. The failure times of operating units and repair time of failed units were exponential distributed. Approach: Markov-renewal processes and properties … …Journal of Mathematics and Statistics, Vol. 5, Issue 2 · 30 Jun 2009 · 7,100 accessesView PDFCite
Research ArticleOpen accessIn the abstractNew Approach to Compute Integral TransformsA. Adawi, F. AwawdehIntegral transforms find special applicability within scientific and mathematical disciplines. A powerful and efficient homotopy methodology in evaluating integrals arises in integral transforms was presented. The method depends on solving a related first order linear differential equation by homotopy analysis method HAM. The Laplace transform, Fourier transform and the moment generating function of the standard normal distribution were used as … …Journal of Mathematics and Statistics, Vol. 4, Issue 2 · 30 Jun 2008 · 6,716 accessesView PDFCite