# 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 four issues in March, June, September 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

### HYBRID FUNCTIONS APPROACH FOR SOLVING FREDHOLM AND VOLTERRA INTEGRAL EQUATIONS

JPRM-Vol. 1 (2009), Issue 1, pp. 124 – 132 Open Access Full-Text PDF
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.

### $$C^2$$ 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.

### 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 $$G$$.

### 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.

### Almost periodic functions defined on $$\mathbb{R}^n$$ with values in locally convex spaces

JPRM-Vol. 1 (2008), Issue 1, pp. 181 – 194 Open Access Full-Text PDF
Abstract: In this paper we develop the theory of almost periodic functions defined on $$\mathbb{R}^n$$ with values in locally convex spaces and Frechet spaces.

### Exact solutions for some unsteady flows of generalized second grade fluids in cylindrical domains

JPRM-Vol. 1 (2008), Issue 1, pp. 171 – 180 Open Access Full-Text PDF
Amir Mahmood, Constantin Fetecau, Imran Siddique
Abstract: The velocity field and the adequate shear stress, corresponding to the unsteady flow of generalized second grade fluids due to a constantly accelerating circular cylinder, are determined by means of the Hankel and Laplace transforms. The solutions that have been obtained satisfy all imposed initial and boundary conditions and for $$β → 1$$ reduce to the similar solutions for the second grade fluids performing the same motion.