Journal of Prime Research in Mathematics

Journal of Prime Research in Mathematics (JPRM) ISSN: 1817-3462 (Online) 1818-5495 (Print) is an HEC recognized, Scopus indexed, open access journal which provides a plate forum to the international community all over the world to publish their work in mathematical sciences. JPRM is very much focused on timely processed publications keeping in view the high frequency of upcoming new ideas and make those new ideas readily available to our readers from all over the world for free of cost. Starting from 2020, we publish one Volume each year containing two issues in June and December. The accepted papers will be published online immediate in the running issue. All issues will be gathered in one volume which will be published in December of every year.

Latest Published Articles

Optimal System, Group Invariant Solutions and Conservation Laws of the Non-linear Elastic Wave Equation and Damped Elastic Wave Equation

JPRM-Vol. 19 (2023), Issue 1, pp. 55 – 72 Open Access Full-Text PDF
M. Usman, A. Razzaq, Ali Raza, F.D. Zaman
Abstract: Non-linear wave equations are created by the elastic wave propagation through inelastic material. We obtain the Lie point symmetries for the non-linear elastic wave equation and the optimal system of the symmetry algebra using Lie symmetry approach. Numerous solutions that are group invariant are obtained under the optimal system of subalgebras of Lie algebra. Additionally, the variational symmetries are obtained via Noether approach and the corresponsing conservation laws are presented. The non-linear elastic wave equation with a damping term is also studied. The local conservation laws using the direct approach are also discussed in this study.
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Zagreb Connection Numbers on Different Networks

JPRM-Vol. 19 (2023), Issue 1, pp. 44 – 54 Open Access Full-Text PDF
Muhammad Mubashar, Asad Zubair, Muhammad Hussain
Abstract: The first Zagreb index formulated in its approximate form for -electron energy in 1972 and second Zagreb index formulated in 1975 for branching of molecules. Some modification of these indices was proposed in three different ways naming as novel modification, connection indices and leap Zagreb indices. In this paper we proposed and calculated connection indices for Honey Comb Network and triangular benezoid structures. Furthermore as an extension of our work we also formulated connection indices for line graph of subdivision of Honey Comb and triangular benezoid networks.
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On the representations of the braid group and the welded braid group

JPRM-Vol. 19 (2023), Issue 1, pp. 34 – 43 Open Access Full-Text PDF
Rana S. Kahil, Mohammad N. Abdulrahim
Abstract: We study the composition of F. R. Cohen’s map Bn → Bnk with the standard representation of Bnk, where Bn is the braid group on n strings. We prove that the obtained representation of Bn is isomorphic to the direct sum of k copies of the standard representation of Bn. A similar work is done for the welded braid group 𝓌Bn.
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On the solutions of 2x + 2y = z2 in the Fibonacci and Lucas numbers

JPRM-Vol. 19 (2023), Issue 1, pp. 27 – 33 Open Access Full-Text PDF
Hayder R. Hashim
Abstract: Consider the Diophantine equation 2x + 2y = z2, where x, y and z are nonnegative integers. As thisequation has infinitely many solutions, in this paper we study its solutions in case where the unknowns represent Fibonacci and/or Lucas numbers. In other words, we completely resolve the equation in case of (x, y, z) ∈ {(Fi, Fj , Fk),(Fi, Fj ,Lk),(Li,Lj ,Lk),(Li,Lj , Fk),(Fi,Lj ,Lk),(Fi,Lj , Fk)} with i, j, k ≥ 1 and Fn and Ln denote the general terms of Fibonacci and Lucas numbers, respectively.
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Sombor indices of molecular graphs and some derived graphs of V -phenylenic nanotubes and nanotori

JPRM-Vol. 19 (2023), Issue 1, pp. 14 – 26 Open Access Full-Text PDF
Setareh Javame, Massoud Ghods
Abstract: Carbon nanotubes are widely used in various fields such as composites, energy devices, electronic applications, and medical applications. The most commonly used nanotubes and nanotubes are V -phenylenic nanotubes and nanotori. Topological analysis of a molecule involves translating its molecular structure into a unique number. In this article, Sombor indices for molecular graph, line graph, and subdivision graph of the V -phenylenic nanotubes and nanotori are calculated.
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Solving Split Equality Fixed Point of Nonexpansive Semigroup and split equality minimization Problems in real Hilbert Space

JPRM-Vol. 19 (2023), Issue 1, pp. 1 – 13 Open Access Full-Text PDF
Hammed Anuoluwapo Abassa, Ojen Kumar Narain
Abstract: In this article, we study the split equality problem involving nonexpansive semigroup and convex minimization problem. Using a Halpern iterative algorithm, we establish a strong convergence result for approximating a common solution of the aforementioned problems. The iterative algorithm introduced in this paper is designed in such a way that it does not require the knowledge of the operator norm. We display a numerical example to show the relevance of our result. Our result complements and extends some related results in literature.
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Volume 20 (2024)

Volume 19 (2023)

Volume 18 (2022)

Volume 17 (2021)

Volume 16 (2020)

Volume 15 (2019)

Volume 14 (2018)

Volume 13 (2017)

Volume 12 (2016)

Volume 11 (2015)

Volume 10 (2014)

Volume 09 (2013)

Volume 08 (2012)

Volume 07 (2011)

Volume 06 (2010)

Volume 05 (2009)

Volume 04 (2008)

Volume 03 (2007)

Volume 02 (2006)

Volume 01 (2005)