# 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

### On random covering of a circle

JPRM-Vol. 1 (2008), Issue 1, pp. 127 – 131 Open Access Full-Text PDF
Abstract: Let $$X_{j}$$, $$j = 1, 2, …, n$$ be the independent and identically distributed random vectors which take the values on the unit circumference. Let $$S_{n}$$ be the area of the convex polygon having $$X_{j}$$ as vertices. The paper by Nagaev and Goldfield (1989) has proved the asymptotic normality of random variableSn. Our main aim is to show that the random variableSn can be represented as a sum of functions of uniform spacings. This allows us to apply known results related to uniform spacings for the analysis of $$S_n$$.

### On the gracefulness of the digraphs $$n − C_{m}$$ for $$m$$ odd

JPRM-Vol. 1 (2008), Issue 1, pp. 118 – 126 Open Access Full-Text PDF
Zhao Lingqi, Jirimutu, Xirong Xu, Wang Lei
Abstract: A digraph D(V, E) is said to be graceful if there exists an injection $$f : V (G) → {0, 1, · · · , |E|}$$ such that the induced function $$f’:E(G) → {1, 2, · · · , |E|}$$ which is defined by $$f'(u, v) = [f(v)−f(u)] (mod |E|+1)$$ for every directed edge $$(u, v)$$ is a bijection. Here, $$f$$ is called a graceful labeling (graceful numbering) of $$D(V, E)$$, while $$f’$$ is called the induced edge’s graceful labeling of D. In this paper we discuss the gracefulness of the digraph $$n − C_{m}$$ and prove that $$n − C_{m}$$ is a graceful digraph for $$m = 5, 7, 9, 11, 13$$ and even n.

### Matrix lie rings that contain an abelian subring

JPRM-Vol. 1 (2008), Issue 1, pp. 113 – 117 Open Access Full-Text PDF
Evgenii L. Bashkirov
Abstract: Let $$k$$ be a field and $$\overline{k}$$ an algebraic closure of $$k$$. The paper is devoted to the description of subrings of the Lie ring $$sl_{2}overline{k}$$ that contain an abelian subring which is a one-dimensional subspace of the $$k$$-vector space $$sl_{2}overline{k}$$.

### Limit sets of weakly contracting relations with eventual condensation

JPRM-Vol. 1 (2008), Issue 1, pp. 101 – 112 Open Access Full-Text PDF
Vasile Glavan, Valeriu Gutu
Abstract: Barnsley’s formula for the attractor of a hyperbolic IFS with condensation is generalized for the omega-limit set of a weakly contracting set-valued map with eventual condensation. The latter need not be a contraction, as well as its omega-limit set need not be an attractor.

### Algebraic properties of special rings of formal series

JPRM-Vol. 1 (2007), Issue 1, pp. 178 – 185 Open Access Full-Text PDF
Azeem Haider
Abstract: The $$K$$-algebra $$K_{S}[[X]]$$ of Newton interpolating series is constructed by means of Newton interpolating polynomials with coefficients in an arbitrary field K (see Section 1) and a sequence S of elements $$K$$. In this paper we prove that this algebra is an integral domain if and only if $$S$$ is a constant sequence. If K is a non-archimedean valued field we obtain that a $$K$$-subalgebra of convergent series of $$K_{S}[[X]]$$ is isomorphic to Tate algebra (see Theorem 3) in one variable and by using this representation we obtain a general proof of a theorem of Strassman (see Corollary 1). In the case of many variables other results can be found in [2].

### ANALYTICAL SOLUTIONS TO BRAJINSKII’S EQUATIONS IN ONE DIMENSION BY USING LAPLACE TRANSFORM TECHNIQUE

JPRM-Vol. 1 (2007), Issue 1, pp. 169 – 177 Open Access Full-Text PDF
S.N.Hosseinimotlagh, M.Roostaie, H.Kazemifard
Abstract: Brajinskii’s equations are the fundamental relations governing the behavior of the plasma produced during a fusion reaction, especially ICF plasma. These equations contains six partial differential coupled together. In this paper we have tried to give analytical solutions to these equations using a one dimensional method. Laplace transform technique is the main tool to do that with an arbitrary boundary and initial conditions for some special cases.