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

Hamiltonicity in directed Toeplitz graphs having increasing edges of length 1, 3 and 7

JPRM-Vol. 20 (2024), Issue 2, pp. 64 – 76 Open Access Full-Text PDF
Shabnam Malik, Farzaneh Ramezani
Abstract: A directed Toeplitz graph Tn⟨a1, . . . , ap; b1, . . . , bq⟩ with vertices 1, 2, . . . , n, where the edge (i, j) occurs if and only if j − i = as or i − j = bt for some 1 ≤ s ≤ p and 1 ≤ t ≤ q, is a digraph whose adjacency matrix is a Toeplitz matrix. In this paper, we study hamiltonicity in directed Toeplitz graphs having increasing edges of length 1, 3 and 7, only.
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Invariant and Preserving Transforms for Cross Ratio of 4-Points in a line on Desargues Affine Plane

JPRM-Vol. 20 (2024), Issue 2, pp. 48 – 63 Open Access Full-Text PDF
Orgest ZAKA, James F. Peters
Abstract: This paper introduces advances in the geometry of the transforms for cross ratio of four points in a line in the Desargues affine plane. The results given here have a clean, based Desargues affine plan axiomatics and definitions of addition and multiplication of points on a line in this plane, and for skew field properties. In this paper are studied, properties and results related to the some transforms for cross ratio for 4-points, in a line, which we divide into two categories, Invariant and Preserving transforms for cross ratio. The results in this paper are (1) the cross-ratio of four points is Invariant under transforms: Inversion, Natural Translation, Natural Dilation, Mobi¨us Transform, in a line of Desargues affine plane. (2) the cross-ratio of four points is Preserved under transforms: parallel projection, translations and dilation’s in the Desargues affine plane.
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A common generalization of Dickson polynomials, Fibonacci polynomials, and Lucas polynomials and applications

JPRM-Vol. 20 (2024), Issue 2, pp. 30 – 47 Open Access Full-Text PDF
Said Zriaa, Mohammed Moucouf
Abstract: In this work, we define a more general family of polynomials in several variables satisfying a linear recurrence relation. We provide explicit formulas and determinantal expressions. Our results are then applied to secondorder recurrent polynomials, presenting several relationships and identities involving Fibonacci polynomials of order 2, Lucas polynomials of order 2, classical Fibonacci polynomials, classical Lucas polynomials, Fibonacci numbers, Lucas numbers, and both kinds of Dickson polynomials. Our findings offer a unified generalization of various existing works, with several well-known results emerging as special cases.
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Analysing MHD Heat-Mass Transfer model for-Oldroyd-B Fluid Using Fractional Order Prabhakar Derivative

JPRM-Vol. 20 (2024), Issue 2, pp. 10 – 29 Open Access Full-Text PDF
Azhar Ali Zafar, Sajjad Hussain, Khurram Shabbir
Abstract: The manuscript explores a fractional order heat-mass transfer model for Oldroyd-B fluid on a vertical plate employing the Prabhakar derivative operator. It investigates the MHD flow of Oldroyd-B fluid induced by natural convection and the general motion of the plate. Well known integral transform i.e. Laplace transform and Tzou’s numerical inversion algorithm are employed to simulate the model under generalized constraints. Several scenarios involving the generalized motion of the plate and general boundary conditions are investigated. A comprehensive graphical analysis is conducted to investigate the control of system parameters, and valuable findings are concluded that can help to optimize and foster various processes.
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Complexity of Monad graphs generated by the function f(g) = g5

JPRM-Vol. 20 (2024), Issue 2, pp. 1 – 9 Open Access Full-Text PDF
Hayder B . Shelash, Hayder R. Hashim, Ali A. Shukur
Abstract: A Monad graph is a graph Γ in which each of its vertices belongs to a finite group G and connects with its image under the action of a linear map f. This kind of graph was introduced by V. Arnold in 2003. In this paper, we compute the Monad graphs in which G is isomorphic to a cyclic group Cn of order n and f the fifth power function, i.e. f(g) = g5. Furthermore, some algebraic and dynamical properties of the studied Monad graphs are obtained. The proofs of our results are based on various tools and results with regard to the fields of number theory, algebra and graph theory.
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Category Of Grey Sets

JPRM-Vol. 20 (2024), Issue 1, pp. 89 – 96 Open Access Full-Text PDF
Masoomeh Hezarjaribi, Davood Darvishi Solokolaei, Zohreh Habibi
Abstract: In this paper, we introduce the concept of morphisms between two grey sets and defined a new category, namely, GSet, of grey sets and grey morphisms. We investigate some categorical notions such product, coproduct, pullback, and pushout. Additionally, we study equalizer and coequalizer for pairs of grey morphisms and show that any grey set has an injective hull.
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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)