# 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 comparison of perturbation techniques for nonlinear problems

JPRM-Vol. 1 (2014), Issue 1, pp. 59 – 79 Open Access Full-Text PDF
H. A. Wahab, Saira Bhatti, Muhammad Naeem
Abstract: The present paper presents the comparison of analytical techniques. We establish the existence of the phenomena of the noise terms in the perturbation series solution and find the exact solution of the nonlinear problems. If the noise terms exist, the Homotopy perturbation method gives the same series solution as in Adomian Decomposition Method and we get the exact solution using two iterations only.

### Magnetohydrodynamics of rotating fractional second grade fluid in porous medium

JPRM-Vol. 1 (2014), Issue 1, pp. 45 – 58 Open Access Full-Text PDF
Azhar Ali Zafar, Dumitru Vieru, Shahraz Akhtar
Abstract: Exact solution for the unsteady flow of a fractional second grade fluid through the porous medium under the influence of magnetic field in the direction normal to the flow has been investigated using the integral transforms. Expressions for dimensionless velocity have been obtained and are presented in terms of Fox’s H–function. The influence of the fractional parameter on the fluid motion is studied and a comparison between velocity of the fractional and classical fluid is made.

### A numerical approach for solving hammerstein integral equations in banach spaces

JPRM-Vol. 1 (2014), Issue 1, pp. 37 – 44 Open Access Full-Text PDF
Abstract: In this work, we give a weaker conditions guarantee the boundedness of the Hammerstein integral equation in $$L^p$$ spaces, also we study conditions of the convergence of the approximate solution to the exact one of the integral equation using the successive approximations method. Finally, we treat numerical examples compared with other papers in order to confirm the efficiency of our results.

### Some characterizations of semigroups in terms of intuitionistic fuzzy interior ideals

JPRM-Vol. 1 (2014), Issue 1, pp. 19 – 36 Open Access Full-Text PDF
Hidayat Ullah Khan, Nor Haniza Sarmin, Asghar Khan,Faiz Muhammad Khan
Abstract: The importance of semigroups and their fuzzy subsystems is evident from their applications and significant role in several applied disciplines like computer sciences, control engineering, error-correcting codes and fuzzy automata theory. In this paper, we give generalizations of intuitionistic fuzzy interior ideals of semigroups and introduced the notions of intuitionistic fuzzy interior ideals of type $$(\overline{∈}, \overline{∈} ∨ \overline{q}_{k})$$ and $$(\overline{∈}, \overline{∈})$$ of semigroups. The important mile stone of the present paper is to link ordinary intuitionistic fuzzy interior ideals, $$(\overline{∈}, \overline{∈})$$-intuitionistic fuzzy interior ideals and $$(\overline{∈}, \overline{∈} ∨ \overline{q}_{k})$$-intuitionistic fuzzy interior ideals. Moreover semigroups are characterized by the properties of these notions.

### Wiener index of the tensor product of cycles

JPRM-Vol. 1 (2014), Issue 1, pp. 01 – 18 Open Access Full-Text PDF
K. Pattabiraman
Abstract: The Wiener index, denoted by $$W(G)$$, of a connected graph $$G$$ is the sum of all pairwise distances of vertices of the graph, that is, $$W(G)=\frac{1}{2}\sum_{u,v\in V(G)}d(u,v)$$. In this paper, we obtain the Wiener index of the tensor product of two cycles.

### Elementary calculus in chevalley groups over rings

JPRM-Vol. 1 (2013), Issue 1, pp. 79 – 95 Open Access Full-Text PDF
Alexei Stepanov
Abstract: The article studies structure theory of Chevalley groups over commutative rings. Main results of the article are relative dilation and local-global principles. and an economic set of generators of relative elementary subgroup. These statements proved by computations with elementary unipotents (hence the title) are very important in further development of the subject. No restrictions on the ground ring or the root system $$Φ$$ are imposed except that the rank of $$Φ$$ is not less than 2. The results improve previous results in the area. The article contains a brief survey of the subject, some gaps in proofs or incorrect references are discussed. Proofs of some known related results are substantially simplified.