# 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

### g-noncommuting graph of some finite groups

JPRM-Vol. 1 (2016), Issue 1, pp. 16 – 23 Open Access Full-Text PDF
M. Nasiri, A. Erfanian, M. Ganjali, A. Jafarzadeh
Abstract: Let $$G$$ be a finite non-abelian group and $$g$$ a fixed element of $$G$$. In 2014, Tolue et al. introduced the g-noncommuting graph of $$G$$, which was denoted by $$Γ^{g}_G$$ with vertex set $$G$$ and two distinct vertices $$x$$ and $$y$$ join by an edge if $$[x, y] \neq g$$ and $$g^{−1}$$. In this paper, we consider induced subgraph of $$Γ^{g}_{G}$$ on $$G /Z(G)$$ and survey some graph theoretical properties like connectivity, the chromatic and independence numbers of this graph associated to symmetric, alternating and dihedral groups.

### A note on self-dual AG-groupoids

JPRM-Vol. 1 (2016), Issue 1, pp. 01 – 15 Open Access Full-Text PDF
Abstract: In this paper, we enumerate self-dual AG-groupoids up to order 6, and classify them on the basis of commutativity and associativity. A self-dual AG-groupoid-test is introduced to check an arbitrary AG-groupoid for a self-dual AG-groupoid. We also respond to an open problem regarding cancellativity of an element in an AG-groupoid. Some features of ideals in self-dual AG-groupoids are explored. Some desired algebraic structures are constructed from the known ones subject to certain conditions and some subclasses of self-dual AG-groupoids are introduced.

### On the mixed hodge structure associated hypersurface singularities

JPRM-Vol. 1 (2015), Issue 1, pp. 137 – 161 Open Access Full-Text PDF
Abstract: Let $$f : \mathbb{C}^{n+1} → \mathbb{C}$$ be a germ of hypersurface with isolated singularity. One can associate to f a polarized variation of mixed Hodge structure $$H$$ over the punctured disc, where the Hodge filtration is the limit Hodge filtration of W. Schmid and J. Steenbrink. By the work of M. Saito and P. Deligne the VMHS associated to cohomologies of the fibers of $$f$$ can be extended over the degenerate point $$0$$ of disc. The new fiber obtained in this way is isomorphic to the module of relative differentials of $$f$$ denoted $$Ω_f$$ . A mixed Hodge structure can be defined on $$Ω_f$$ in this way. The polarization on \mathcal{H} deforms to Grothendieck residue pairing modified by a varying sign on the Hodge graded pieces in this process. This also proves the existence of a Riemann-Hodge bilinear relation for Grothendieck pairing and allow to calculate the Hodge signature of Grothendieck pairing.

### Existence and non existence of mean cordial labeling of certain graphs

JPRM-Vol. 1 (2015), Issue 1, pp. 123 – 136 Open Access Full-Text PDF
R. Ponraj, S. Sathish Narayanan
Abstract: Let f be a function from the vertex set $$V (G)$$ to $${0, 1, 2}$$. For each edge $$uv$$ assign the label $$\frac{f(u)+f(v)}{2}$$. $$f$$ is called a mean cordial labeling if $$|v_f (i) − v_f (j)| ≤ 1$$ and $$|e_f (i) − e_f (j)| ≤ 1$$, $$i, j ∈ {0, 1, 2}$$, where $$v_f (x)$$ and $$e_f (x)$$ respectively denote the number of vertices and edges labeled with $$x$$ $$(x = 0, 1, 2)$$. A graph with a mean cordial labeling is called a mean cordial graph. In this paper we investigate mean cordial labeling behavior of prism, $$K_2 +\overline{K_m}$$, $$K_n + \overline{2K_2}$$, book $$B_m$$ and some snake graphs.

### $$A_19/B_6$$: 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
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.