Research ArticleOpen accessEvery word in the titleApplications of q-Umbral Calculus to Modified Apostol Type q-Bernoulli PolynomialsMehmet Acikgoz, Resul Ates, Ugur Duran, Serkan AraciThis article aims to identify the generating function of modified Apostol type q-Bernoulli polynomials. With the aid of this generating function, some properties of modified Apostol type q-Bernoulli polynomials are given. It is shown that aforementioned polynomials are q-Appell. Hence, we make use of these polynomials to have applications on q-Umbral calculus. From those applications, we derive some theorems in … …Journal of Mathematics and Statistics, Vol. 14, Issue 1 · 4 Jan 2018 · 8,182 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleUnderstanding a Simple Arabic Stories Using Event CalculusMohamed Abd El-Salam, Ahmed Kamal Hussein, Aly Aly FahmyThis study investigates the use of event calculus for understanding stories written in Arabic natural language. System makes a representation for commonsense knowledge and story events and then performs a commonsense reasoning to infer the details events which are not explicitly described in the story; furthermore it manages changes in objects properties over time and handles the actions synchronizations problem. …American Journal of Applied Sciences, Vol. 10, Issue 10 · 6 Sep 2013 · 6,639 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleFractional Calculus Theoretical Evolution for Radiation QuantitiesAmin Al-Okour, Sherin A. Sareireh, Abdullah Ajlouni, Abdul-Wali AjlouniProblem statement: Radiation dosimetry features depend on semi-empirical formulas that lack a strong mathematical framework. This is due to the fact that the microscopic radiation interaction with matter includes energy losses that have never been described properly in quantum mechanics, which deals with conserved energy systems. Approach: Using the recent theory of the quantization of nonconservative systems using fractional calculus. … …Journal of Mathematics and Statistics, Vol. 8, Issue 1 · 2 Feb 2012 · 6,661 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleFractional Calculus for Certain Integral Operator Involving Logarithmic CoefficientsAabed Mohammed, Maslina Darus, Daniel BreazProblem statement: Some properties of certain integral operators on some subclasses were studied. Approach: Certain classes defined by integral operators were introduced. The well known definitions and preliminaries results were stated. Results: Having new integral operator, the characterization problems were discussed. Thus sufficient conditions were given. Conclusion: Therefore, by having new integral operators, sufficient conditions were determined. In fact, other … …Journal of Mathematics and Statistics, Vol. 5, Issue 2 · 30 Sep 2009 · 7,181 accessesView PDFCite
Research ArticleOpen accessIn the keywordsFormalizing Relations in Type TheoryFarida KachapovaTypetheory plays an important role in the foundations of mathematics as a frameworkfor formalizing mathematics and a base for proof assistants providingsemi-automatic proof checking and construction. Derivation of each theorem intype theory results in a formal term encapsulating the whole proof process.This study uses a variant of type theory, namely the Calculus of Constructionswith Definitions, to formalize the standardtheory of … …Journal of Mathematics and Statistics, Vol. 18, Issue 1 · 29 Oct 2022 · 5,778 accessesView PDFCite
Research ArticleOpen accessIn the keywordsMeasurable Functional Calculi and Spectral TheoryMykola YaremenkoIn this article, the spectral theory is considered, we study the spectral families and their correspondence to the operators on the reflexive Banach spaces; assume A is a well-bounded operator on reflexive Lebesgue spaces then the operator A is a scalar type spectral operator. The main goals are to obtain the characterization of the well-bounded operators in the terms of … …Journal of Mathematics and Statistics, Vol. 18, Issue 1 · 6 Jul 2022 · 6,419 accessesView PDFCite
Research ArticleOpen accessIn the keywordsq-Bernoulli’s EquationSalih Y. Arbab, Sami H. AltoumThe work shows the q-deformation of Bernoulli’s equation, q-derivative and q-calculus are used to form a q-analogous of Bernoulli’s equation. We introduce the theorem of q-Bernoulli’s equation. …American Journal of Applied Sciences, Vol. 17, Issue 1 · 4 Oct 2020 · 7,127 accessesView PDFCite
Research ArticleOpen accessIn the keywordsFormalizing Probability Concepts in a Type TheoryFarida KachapovaIn this paper we formalize some fundamental concepts of probability theory such as the axiomatic definition of probability space, random variables and their characteristics, in the Calculus of Inductive Constructions, which is a variant of type theory and the foundation for the proof assistant COQ. In a type theory every term and proposition should have a type, so in our … …Journal of Mathematics and Statistics, Vol. 14, Issue 1 · 12 Nov 2018 · 8,547 accessesView PDFCite
Research ArticleOpen accessIn the keywordsSufficient Conditions for Subordination of Meromorphic FunctionsRabha W. Ibrahim, Maslina DarusProblem statement: The problem of giving sufficient condition for certain class of meromorphic functions defined as differential operator was studied. Approach: The differential operator of meromorphic functions containing fractional power was proposed and defined. The preliminary concept of subordination was introduced to give sharp proofs for certain sufficient conditions of the differential operator aforementioned. Results: Having new operator, subordination theorems … …Journal of Mathematics and Statistics, Vol. 5, Issue 3 · 30 Sep 2009 · 7,208 accessesView PDFCite