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43 articles for “Generating Function”
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Research ArticleOpen accessIn the keywordsApplications 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 accessIn the keywordsTransient Solution to an infinite Server Queue with Varying Arrival and Departure RateA. A. El-SherbinyProblem statement: In many potential application of queueing theory, the transient solution of queueing system is important. Approach: This study presented the transient solution for infinite server queues with Poisson arrivals and exponential service times when the parameters of both distributions are allowed to vary with time. Based on generating functions technique which results in a simple differential equation. Using … …Journal of Mathematics and Statistics, Vol. 6, Issue 1 · 31 Mar 2010 · 7,977 accessesView PDFCite
Research ArticleOpen accessIn the keywordsTransient Solution of the M/M/C1 Queue with Additional C2 Servers for Longer Queues and BalkingR. O. Al-Seedy, A. A. El-Sherbiny, S. A. EL-Shehawy, S. I. AmmarThe goal of this research is to discuss the M/M/C1 queue with additional C2 servers for longer queues and balking. By using generating function technique the transient probabilities are derived in terms of the modified Bessel function. …Journal of Mathematics and Statistics, Vol. 4, Issue 1 · 31 Mar 2008 · 7,416 accessesView PDFCite
Research ArticleOpen accessIn the keywordsA General Probability Distribution Using Burmann Power SeriesRichard F. Patterson, Pali SenThe goal of this study is to present a general power series distribution that exhibits the properties of some well known distributions. To accomplish this goal we examine an infinite sequence of independent random variables having a Bürmann’s power series distribution. Consequently, we derive moment generating function of the distribution and establish the maximum likelihood estimate of the component that … …Journal of Mathematics and Statistics, Vol. 1, Issue 3 · 30 Sep 2005 · 6,290 accessesView PDFCite
Research ArticleOpen accessIn the keywordsThe Dual Exponentiated Weibull ModelMona Mustafa ElbielyA new lifetime model with various shapes of the hazard rate function for modeling uni-modal and bimodal data sets is introduced and studied along with its statistical properties. Before using the maximum likelihood method for estimating the unknown model parameters, we assessed its performance via a simulation study. The flexibility of the new model is illustrated via plots of the … …Journal of Mathematics and Statistics, Vol. 15, Issue 1 · 29 Jun 2019 · 6,511 accessesView PDFCite
Research ArticleOpen accessIn the keywordsOn Generalized Some (p, q)-Special PolynomialsUgur Duran, Mehmet Acikgoz, Serkan AraciIn this study, we introduce a new class of generalized (p, q)-Bernoulli, (p, q)-Euler and (p, q)-Genocchi polynomials and investigate their some properties. We derive (p, q)-generalizations of some familiar formulae belonging to classical Bernoulli, Euler and Genocchi polynomials. We also obtain a (p, q)-extension of the Srivastava-Pintér addition theorem. …Journal of Mathematics and Statistics, Vol. 14, Issue 1 · 18 May 2018 · 7,437 accessesView PDFCite
Research ArticleOpen accessIn the abstractEnhancing Data Transmission Security through the Modified Hill Cipher and Henon Map Chaos FunctionSamsul Arifin, Kevin Tan, Felix Indra Kurniadi et al.The advancement and sophistication of technology in the present era have resulted in millions of people interacting and sharing data through the internet using various platforms such as email, chat applications, and others. This has led to the dissemination of personal information and data worldwide through the internet, which also poses the possibility of data interception by unauthorized parties. Data … …Journal of Computer Science, Vol. 21, Issue 6 · 28 Jun 2025 · 3,638 accessesView PDFCite
Research ArticleOpen accessIn the abstractCloning and Expression of SCAMP3 in Transgenic Silkworm (Bombyx mori)Selly S. Rajagukguk, Sabar Pambudi, Astari Dwiranti et al.SCAMP3 (Secretory Carrier Membrane Protein 3) is a crucial component of vesicular trafficking pathways and plays important roles in endocytosis and protein recycling. Previous studies demonstrate SCAMP3 dysregulation in various cancers, suggesting potential applications as a biomarker and therapeutic target. Understanding SCAMP3 expression and post-translational processing provides insights into its biological functions and potential applications in cancer diagnostics and therapy. … …OnLine Journal of Biological Sciences, Vol. 25, Issue 4 · 16 Feb 2026 · 1,521 accessesView PDFCite
Research ArticleOpen accessIn the abstractRadial Basis Function Neural Networks Towards Electronic Trust QuantificationSmitha Zacaria, Tiny du ToitTrust is a broad term applicable in various contexts. Trust between electronic entities is complex to quantify, particularly in intricate networks. Traditional trust algorithms rely on historical trust values, requiring storage and access to past transaction details. Contextual variations further complicate trust calculation. Challenges in calculating trust include heightened computational complexities, managing information storage, and securing access to extensive datasets … …Journal of Computer Science, Vol. 20, Issue 11 · 26 Sep 2024 · 4,791 accessesView PDFCite
Research ArticleOpen accessIn the abstractEnhancing Lifetime Data Modeling With the Modified Version of Weibull Distribution: A Comparative ApproachArjun Kumar Gaire, Shahid Mohammad, Yogendra Bahadur GurungThis study introduces a new two-parameter univariate distribution, a modified version of the Weibull distribution, for a non-negative realm. Originating from a framework introduced by Azzalini and Capitanio, the distribution exhibits a monotonically increasing hazard rate. It offers closed-form expressions for key statistical properties, including reliability functions, moments, moment-generating functions, and order statistics. An expression for random number generation is … …Journal of Mathematics and Statistics, Vol. 21, Issue 1 · 8 Oct 2025 · 3,085 accessesView PDFCite