# 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

### On existence of canonical number system in certain classes of pure algebraic number fields

JPRM-Vol. 1 (2011), Issue 1, pp. 19 – 24 Open Access Full-Text PDF
Abstract: Canonical Number System can be considered as natural generalization of radix representation of rational integers to algebraic integers. We determine the existence of Canonical Number System in two classes of pure algebraic number fields of degree $$2^n$$ and $$n$$.

### Outputs in random $$f$$-ary recursive circuits

JPRM-Vol. 1 (2011), Issue 1, pp. 09 – 18 Open Access Full-Text PDF
Abstract: This paper extends the study of outputs for random recursive binary circuits in Tsukiji and Mahmoud (Algorithmica 31(2001), 403). We show via martingales that a suitably normalized version of the number of outputs in random f-ary recursive circuits converges in distribution to a normal random variate.

### The domination cover pebbling number of the square of a path

JPRM-Vol. 1 (2011), Issue 1, pp. 01 – 08 Open Access Full-Text PDF
A. Lourdusamy, T. Mathivanan
Abstract: Given a configuration of pebbles on the vertices of a connected graph $$G$$, a pebbling move (or pebbling step) is defined as the removal of two pebbles from a vertex and placing one pebble on an adjacent vertex. The domination cover pebbling number, $$ψ(G)$$, of a graph $$G$$ is the minimum number of pebbles that have to be placed on $$V (G)$$ such that after a sequence of pebbling moves, the set of vertices with pebbles forms a dominating set of $$G$$, regardless of the initial configuration. In this paper, we determine the domination cover pebbling number for the square of a path.

### $$λ$$-fractional schwarzian derivative and $$λ$$-fractional mobius transformation

JPRM-Vol. 1 (2010), Issue 1, pp. 56 – 61 Open Access Full-Text PDF
Y. Polatoglu
Abstract: We denote by A the class of all analytic functions in the open unit disk $$\mathbb{D} = {z | |z| < 1}$$ which satisfy the conditions $$f(0) = 0$$, $$f'(0) = 1$$. In this paper we define a new concept of $$λ$$− fractional Schwarzian derivative and $$λ$$− fractional Mobius transformation for the class A. We also formulate the criterion for a function to be univalent using the fractional Schwarzian.

### Some exact solutions for the flow of a Newtonian fluid with heat transfer via prescribed vorticity

JPRM-Vol. 1 (2010), Issue 1, pp. 38 – 55 Open Access Full-Text PDF
M. Jamil, N. A. Khan, A. Mahmood, G. Murtaza, Q. Din
Abstract: Two-dimensional , steady, laminar equations of motion of an incompressible fluid with variable viscosity and heat transfer equations are considered. The problem investigated is the flow for which the vorticity distribution is proportional to the stream function perturbed by a sinusoidal stream. Employing transformation variable, the governing Navier-Stokes Equations are transformed into the ordinary differential equations and exact solutions are obtained. Finally, the influence of different parameters of interest on the velocity, temperature and pressure profiles are plotted and discussed.

### Some distributional properties of the concomitants of record statistics for bivariate pseudo–exponential distribution and characterization

JPRM-Vol. 1 (2010), Issue 1, pp. 32 – 37 Open Access Full-Text PDF
Abstract: A new class of distributions known as Bivariate Pseudo–Exponential distribution has been defined. The distribution of r–th concomitant and joint distribution of r–th and s–th concomitant of record statistics of the resulting distribution have been derived. Expression for single and product moments has also been obtained for the resulting distributions. A characterization of the k-th concomitant of record statistics for the Pseudoexponential distribution by the conditional expectation is presented.