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

Exact solutions of generalized Oldroyd-B fluid subject to a time-dependent shear stress in a pipe

JPRM-Vol. 1 (2009), Issue 1, pp. 139 – 148 Open Access Full-Text PDF
Qammar Rubbab, Syed Muhammad Husnine, Amir Mahmood
Abstract: The velocity field and the shear stress corresponding to the unsteady flow of a generalized Oldroyd-B fluid in an infinite circular cylinder subject to a longitudinal time-dependent shear stress are determined by means of Hankel and Laplace transforms. The exact solutions, written in terms of the generalized \(G\)-functions, satisfy all imposed initial and boundary conditions. The similar solutions for ordinary Oldroyd-B, ordinary and generalized Maxwell, ordinary and generalized second grade as well as for Newtonian fluids are obtained as limiting cases of our general solutions.
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On the Ramsey number for paths and beaded wheels

JPRM-Vol. 1 (2009), Issue 1, pp. 133 – 138 Open Access Full-Text PDF
Kashif Ali, Edy Tri Baskoro, Ioan Tomescu
Abstract: For given graphs \(G\) and \(H\), the Ramsey number \(R(G, H)\) is the least natural number n such that for every graph \(F\) of order \(n\) the following condition holds: either \(F\) contains \(G\) or the complement of \(F\) contains \(H\). Beaded wheel \(BW_{2,m}\) is a graph of order \(2m + 1\) which is obtained by inserting a new vertex in each spoke of the wheel \(W_m\). In this paper, we determine the Ramsey number of paths versus Beaded wheels: \(R(P_n, BW_{2,m}) = 2n − 1\) or \(2n\) if \(m ≥ 3\) is even or odd, respectively, provided \(n ≥ 2m^2 − 5m + 4\).
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JPRM-Vol. 1 (2009), Issue 1, pp. 124 – 132 Open Access Full-Text PDF
T. Shojaeizadeh, Z. Abadi, E. Golpar Raboky
Abstract: This paper presents a computational technique for Fredholm and Volterra integral equations of the second kind. The method based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and legendre polynomials are presented. The operational matrices of integration and product are utilized to reduce the computation of integral equation into some algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.
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\(C^2\) Rational quintic function

JPRM-Vol. 1 (2009), Issue 1, pp. 115 – 126 Open Access Full-Text PDF
Maria Hussain, Malik Zawwar Hussain, Robert J. Cripps
Abstract: A two-parameter family of piecewise \(C^2\) rational quintic functions is presented along with an error investigation for the approximation of an arbitrary \(C^3\) function. The two parameters have a direct geometric interpretation making their use straightforward. Illustrations of their effect on the shape of the rational function are given. The relaxed continuity constraints and the increased flexibility via the two parameters make the
proposed function a suitable candidate for interactive CAD.
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The connected vertex geodomination number of a graph

JPRM-Vol. 1 (2009), Issue 1, pp. 101 – 114 Open Access Full-Text PDF
A. P. Santhakumaran, P. Titus
Abstract: For a connected graph \(G\) of order \(p ≥ 2\), a set \(S ⊆ V (G)\) is an \(x\)-geodominating set of \(G\) if each vertex \(v ∈ V (G)\) lies on an \(x-y\) geodesic for some element y in \(S\). The minimum cardinality of an \(x\)-geodominating set of G is defined as the \(x\)-geodomination number of \(G\), denoted by gx(G). An \(x\)-geodominating set of cardinality \(g_x(G)\) is called a \(g_x\)-set of \(G\). A connected \(x\)-geodominating set of G is an \(x\)-geodominating set S such that the subgraph \(G[S]\) induced by \(S\) is connected. The minimum cardinality of a connected \(x\)-geodominating set of \(G\) is defined as the connected \(x\)-geodomination number of \(G\) and is denoted by \(cg_x(G)\). A connected \(x\)-geodominating set of cardinality \(cg_x(G)\) is called a \(cg_x\)-set of \(G\). We determine bounds for it and find the same for some special classes of graphs. If \(p, a\) and \(b\) are positive integers such that \(2 ≤ a ≤ b ≤ p − 1\), then there exists a connected graph G of order \(p\), \(g_x(G) = a\) and \(cg_x(G) = b\) for some vertex \(x\) in \(G\). Also, if \(p\), \(d\) and \(n\) are integers such that \(2 ≤ d ≤ p − 2\) and \(1 ≤ n ≤ p\), then there exists a connected graph \(G\) of order \(p\), diameter \(d\) and \(cg_x(G) = n\) for some vertex \(x\) in \(G\). For positive integers \(r\), \(d\) and \(n\) with \(r ≤ d ≤ 2r\), there exists a connected graph \(G\) with rad \(G = r\), \(diam G = d\) and \(cg_x(G) = n\) for some vertex \(x\) in \(G\).
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Mathematical modeling of thrombus growth in microvessels

JPRM-Vol. 1 (2008), Issue 1, pp. 195 – 205 Open Access Full-Text PDF
A. G. Alenitsyn, A. S. Kondratyev, I. Mikhailova, I. Siddique
Abstract: Richardson’s phenomenological mathematical model of the thrombi growth in microvessels is extended to describe more realistic features of the phenomenon. Main directions of the generalization of Richardson’s model are: 1) the dependence of platelet activation time on the distance from the injured vessel wall; 2) the nonhomogeneity of the platelet distribution in blood flow in the vicinity of the vessel wall. The generalization of the model corresponds to the main experimental results concerning thrombi formation obtained in recent years. The extended model permits to achieve a numerical agreement between model and experimental data.
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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)