# 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

### $$A_19/B_6$$: A new lanczos-type algorithm and its implementation

JPRM-Vol. 1 (2015), Issue 1, pp. 106 – 122 Open Access Full-Text PDF
Zakir Ullah, Muhammad Farooq, Abdellah Salhi
Abstract: Lanczos-type algorithms are mostly derived using recurrence relationships between formal orthogonal polynomials. Various recurrence relations between these polynomials can be used for this purpose. In this paper, we discuss recurrence relations A19 and B6 for the choice $$U_i(x) = P_{i}^{(1)}$$, where $$U_i$$ is an auxiliary family of polynomials of exact degree $$i$$. This leads to new Lanczos-type algorithm $$A_19/B_6$$ that shows superior stability when compared to existing algorithms of the same type. This new algorithm is derived and described here. Computational results obtained with it are compared to those of the most robust algorithms of this type namely $$A_12$$,  (A^{new}_12\) $$A_5/B_{10}$$ and $$A_8/B_{10}$$ on the same test problems. These results are included.

### A study of the flow of non-newtonian fluid between heated parallel plates by HAM

JPRM-Vol. 1 (2015), Issue 1, pp. 93 – 105 Open Access Full-Text PDF
H. A. Wahab, Saira Bhatti, Saifullah Khan, Muhammad Naeem ,Sajjad Hussain
Abstract: This paper presents the heat transfer of a third grade fluid between two heated parallel plates for two models: constant viscosity model and Reynold’s model. In both cases the nonlinear energy and momentum equations have been solved by HAM. The graphs for the velocity and temperature profiles are plotted and discussed for various values of the emerging parameters in the problem. The main effect is governed by whether or not the fluid is non-Newtonian and the temperature effects are being referred to have a less dominant role.

### $$(λ, µ)$$-Fuzzy ideals in ternary semirings

JPRM-Vol. 1 (2015), Issue 1, pp. 85 – 90 Open Access Full-Text PDF
T. Anitha, D. Krishaswamy.
Abstract: In this paper we introduce the notion of $$(λ, µ)$$-Fuzzy ternary subsemirings and $$(λ, µ)$$-Fuzzy ideals in ternary semirings which can be regarded as the generalization of fuzzy ternary subsemirings and fuzzy ideals in ternary semirings.

### On multiplication group of an AG-group

JPRM-Vol. 1 (2015), Issue 1, pp. 77 – 84 Open Access Full-Text PDF
M. Shah, A. Ali, I. Ahmad, V. Sorge
Abstract: We are investigating the multiplication group of a special class of quasigroup called AG-group. We prove some interesting results such as: The multiplication group of an AG-group of order n is a non-abelian group of order 2n and its left section is an abelian group of order n. The inner mapping group of an AG-group of any order is a cyclic group of order 2.

### The $$t$$-pebbling number of squares of cycles

JPRM-Vol. 1 (2015), Issue 1, pp. 61 – 76 Open Access Full-Text PDF
Lourdusamy Arockiam, Mathivanan Thanaraj
Abstract: Let $$C$$ be a configuration of pebbles on a graph $$G$$. A pebbling move (step) consists of removing two pebbles from one vertex, throwing one pebble away, and moving the other pebble to an adjacent vertex. The $$t$$-pebbling number, $$f_t(G)$$, of a connected graph $$G$$, is the smallest positive integer such that from every configuration of $$f_t(G)$$ pebbles, t pebbles can be moved to any specified target vertex by a sequence of pebbling moves. In this paper, we determine the t-pebbling number for squares of cycles.

### The complement of subgroup graph of a group

JPRM-Vol. 1 (2015), Issue 1, pp. 55 – 60 Open Access Full-Text PDF
F. Kakeri, A. Erfanian
Abstract: Let $$G$$ be a finite group and $$H$$ a subgroup of $$G$$. In 2012, David F. Anderson et al. introduced the subgroup graph of $$H$$ in $$G$$ as a simple graph with vertex set consisting all elements of G and two distinct vertices $$x$$ and $$y$$ are adjacent if and only if $$xy ∈ H$$. They denoted this graphby $$Γ_H(G)$$. In this paper, we consider the complement of $$Γ_H(G)$$, denoted by $$\overline{Γ_H(G)}$$ and will give some graph properties of this graph, for instance diameter, girth, independent and dominating sets, regularity. Moreover, the structure of this graph, planerity and 1-planerity are also investigated in the paper.