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Open Journal of Mathematical Sciences (OMS)

The Open Journal of Mathematical Sciences (OMS) ISSN: 2523-0212 (Online) | 2616-4906 (Print) is partially supported by the National Mathematical Society of Pakistan, is a single-blind peer-reviewed and open-access journal dedicated to publishing original research articles, review papers, and survey articles in all areas of mathematics.

  • Diamond Open Access: OMS follows the Diamond Open Access model—completely free for both authors and readers, with no article processing charges (APCs).
  • Rapid Publication: Accepted papers are published online as soon as they are ready, ensuring timely dissemination of research findings.
  • Scope: The journal welcomes high-quality contributions across all branches of mathematics, offering a broad platform for scholarly exchange.
  • Publication Frequency: While articles are available online throughout the year, OMS publishes one annual print volume in December for readers who prefer physical copies
  • Indexing: ROAD, J-Gate Portal, AcademicKeys, Crossref (DOI prefix: 10.30538), Scilit, Directory of Research Journals Indexing, JournalSeek (to be added in next update).
    Under review for: JSTOR, zbMATH, Publication Forum.
  • Publisher: Ptolemy Scientific Research Press (PSR Press), part of the Ptolemy Institute of Scientific Research and Technology.

Latest Published Articles

Kifilideen L. Osanyinpeju1
1 Agricultural and Bio-Resources Engineering Department, College of Engineering, Federal University of Agriculture Abeokuta, Ogun State.
Abstract:

The generation of coefficients of terms of positive and negative powers of \(n\) and \(-n\) of Kifilideen trinomial theorem as the terms are progress is stressful and time-consuming which the same problem is identified with coefficients of terms of binomial theorem of positive and negative powers of \(n\) and \(-n\). This slows the process of producing the series of any particular trinomial expansion. This study established Kifilideen coefficient tables for positive and negative powers of \(n\) and \(-n\) of the Kifilideen trinomial theorem and other developments based on matrix and standardized methods. A Kifilideen theorem of matrix transformation of the positive power of \(n\) of trinomial expression in which three variables \(x,y\), and \(z\) are found in parts of the trinomial expression was originated. The development would ease evaluating the trinomial expression’s positive power of \(n\). The Kifilideen coefficient tables are handy and effective in generating the coefficients of terms and series of the Kifilideen expansion of trinomial expression of positive and negative powers of \(n\) and \(-n.\)

Gianluca Viggiano1
1Bank of Italy, Regional Economic Research, Milan, Italy.
Abstract:

The Taylor expansion is a widely used and powerful tool in all branches of Mathematics, both pure and applied. In Probability and Mathematical Statistics, however, a stronger version of Taylor’s classical theorem is often needed, but only tacitly assumed. In this note, we provide an elementary proof of this measurable Taylor’s theorem, which guarantees that the interpolating point in the Lagrange form of the remainder can be chosen to depend measurably on the independent variable.

Abd Raouf Chouikha1
14, Cour des Quesblais 35430 Saint-Pere, FRANCE.
Abstract:

In this paper, we establish sharp inequalities for trigonometric functions. We prove in particular for \(0 < x < \frac{\pi}{2}\) and any \(n \geq 5\) \[0 < P_n(x)\ <\ (\sin x)^2- x^3\cot x < P_{n-1}(x) + \left[\left(\frac{2}{\pi}\right)^{2n} – \sum_{k=3}^{n-1} a_k \left(\frac{2}{\pi}\right)^{2n-2k}\right] x^{2n} \] where \(P_n(x) = \sum_{3=k}^n a_k x^{2k+1}\) is a \(n\)-polynomial, with positive coefficients (\(k \geq 5\)), \(a_{{k}}=\frac{{2}^{2\,k-2}}{\ \left( 2\,k-2 \right) ! } \left( \left| {B}_{ 2\,k-2} \right| +{\frac { \left( -1\right) ^{k+1}}{ \left( 2\,k-1 \right) k}} \right),\) \( B_{2k} \) are Bernoulli numbers. This improves a lot of lower bounds of \( \frac{\sin(x)}{x}\) and generalizes inequalities chains.
Moreover, bounds are obtained for other trigonometric inequalities as Huygens and Cusa inequalities as well as for the function
\[g_n(x) = \left(\frac{\sin(x)}{x}\right)^2 \left( 1 – \frac{2\left(\frac{2 x}{\pi}\right)^{2n+2}}{1-(\frac{2x}{\pi})^2}\right) +\frac{\tan(x)}{x}, \ n\geq 1 \].

Ly Van An1
1Faculty of Mathematics Teacher Education, Tay Ninh University, Tay Ninh, Vietnam.
Abstract:

In this manuscript, our primary focus revolves around extending the inequalities associated with the Quadratic \(\varphi(\delta_{1},\delta_{2})-\)function. Our approach involves leveraging the general quadratic functional equation encompassing \(2k\)-variables within the context of the fuzzy Banach space. Our main contribution lies in the expansion of these inequalities, representing a significant result within this study.

Tristram de Piro1
1Flat 3, Redesdale House, 85 The Park, Cheltenham, GL50 2RP;
Abstract:

We classify particle paths for systems in thermal equilibrium satisfying the usual relations and prove that the only solutions are given by straight line parallel paths with speed \(c\).

Joel N. Ndam1, Stephen T. Agba2
1Department of Mathematics, University of Jos, Nigeria;
2Department of Mathematics and Computer Science, Federal University of Health Sciences, Otukpo, Nigeria
Abstract:

It is on record that rolling out COVID-19 vaccines has been one of the fastest for any vaccine production worldwide. Despite this prompt action taken to mitigate the transmission of COVID-19, the disease persists. One of the reasons for the persistence of the disease is that the vaccines do not confer immunity against the infections. Moreover, the virus-causing COVID-19 mutates, rendering the vaccines less effective on the new strains of the disease. This research addresses the multi-strains transmission dynamics and herd immunity threshold of the disease. Local stability analysis of the disease-free steady state reveals that the pandemic can be contained when the basic reproduction number, \(R_{0}\) is brought below unity. The results of numerical simulations also agree with the theoretical results. The herd immunity thresholds for some of the vaccines against COVID-19 were computed to guide the management of the disease. This model can be applied to any strain of the disease.

Mansouria Saidani1, Benharrat Belaïdi1
1Department of Mathematics, Laboratory of Pure and Applied Mathematics, University of Mostaganem (UMAB), B. P. 227 Mostaganem-(Algeria)
Abstract:

The purpose of this paper is the study of the growth of solutions of higher order linear differential equations \(f^{\left( k\right) }+\left( A_{k-1,1}\left( z\right) e^{P_{k-1}\left(z\right) }+A_{k-1,2}\left( z\right) e^{Q_{k-1}\left( z\right) }\right)f^{\left( k-1\right) }+\cdots +\left( A_{0,1}\left( z\right) e^{P_{0}\left( z\right)
}+A_{0,2}\left( z\right) e^{Q_{0}\left( z\right) }\right) f=0\) and \(f^{\left( k\right) }+\left( A_{k-1,1}\left( z\right) e^{P_{k-1}\left(z\right) }+A_{k-1,2}\left( z\right) e^{Q_{k-1}\left( z\right) }\right)f^{\left( k-1\right) }+\cdots +\left( A_{0,1}\left( z\right) e^{P_{0}\left( z\right)}+A_{0,2}\left( z\right) e^{Q_{0}\left( z\right) }\right) f=F\left( z\right),\) where \(A_{j,i}\left( z\right) \left( \not\equiv 0\right) \left(j=0,…,k-1;i=1,2\right) ,\) \(F\left( z\right) \) are meromorphic functions of finite order and \(P_{j}\left( z\right) ,Q_{j}\left( z\right) \) \((j=0,1,…,k-1;i=1,2)\) are polynomials with degree \(n\geq 1\). Under some others conditions, we extend the previous results due to Hamani and Belaïdi [1].

David Raske1
1 1210 Washtenaw, Ypsilanti, MI, 48197, USA.
Abstract:

In this paper we prove large-time existence and uniqueness of high regularity weak solutions to some initial/boundary value problems involving a nonlinear fourth order wave equation. These sorts of problems arise naturally in the study of vibrations in beams that are hinged at both ends. The method used to prove large-time existence is the Galerkin approximation method.

Tristram de Piro1
1 Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter (550), Woodstock Road, Oxford, OX2 6GG, England.
Abstract:

In this paper, we proved that solutions \((\rho,J)\) exist for the 1-dimensional wave equation on \([-\pi,\pi]\). When \((\rho,J)\) is extended to a smooth solution \((\rho,\overline{J})\) of the continuity equation on a vanishing annulus \(Ann(1,\epsilon)\) containing the unit circle \(S^1\), a corresponding causal solution \((\rho,\overline{J}’ \overline{E}, \overline{B})\) to Maxwell’s equations can be obtained from Jefimenko’s equations. The power radiated in a time cycle from any sphere \(S(r)\) with \(r>0\) is \(O\left(\frac{1}{r}\right)\), which ensure that no power is radiated at infinity over a cycle.

Edouard Singirankabo1, Emmanuel Iyamuremye1, Alexis Habineza2, Yunvirusaba Nelson2
1Department of Mathematics, College of Education, University of Rwanda, Rwanda.
2Department of Mathematics, Jomo Kenyatta University of Agriculture and Technology, Kenya.
Abstract:

This study aims to model the statistical behaviour of extreme maximum temperature values in Rwanda. To achieve such an objective, the daily temperature data from January 2000 to December 2017 recorded at nine weather stations collected from the Rwanda Meteorological Agency were used. The two methods, namely the block maxima (BM) method and the Peaks Over Threshold (POT), were applied to model and analyse extreme temperatures in Rwanda. Model parameters were estimated, while the extreme temperature return periods and confidence intervals were predicted. The model fit suggests that Gumbel and Beta distributions are the most appropriate for the annual maximum daily temperature. Furthermore, the results show that the temperature will continue to increase as estimated return levels show it.

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