# 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

### Matrix lie rings that contains a one-dimentional lie algebra of semi-simple matrices

JPRM-Vol. 1 (2007), Issue 1, pp. 111 – 119 Open Access Full-Text PDF
Evgenii L. Bashkirov
Abstract: Let $$k$$ be a field and $$\overline{k}$$ an algebraic closure of $$k$$. Suppose that $$k$$
contains more than five elements if char $$k \neq 2$$. Let $$h$$ be a one-dimensional subalgebra of the Lie $$k-$$algebra $$sl_{2}\overline{k}$$ consisting of semi-simple matrices. In this paper, it is proved that if g is a subring of the Lie ring $$sl_{2}\overline{k}$$ containing h, then g is either solvable or there exists a quaternion algebra A over a subfield $$F$$ of $$\overline{k}$$ such that $$F ⊇ k$$ and g is isomorphic to the Lie $$F-$$algebra of all elements in A that are skew-symmetric with respect to a symplectic type involution defined on A.

### Towards classification of simple nite dimensional modular lie super agebras

JPRM-Vol. 1 (2007), Issue 1, pp. 101 – 110 Open Access Full-Text PDF
Dimitry Leites

### Probability of the moderate deviations for the sum-functions of spacing

JPRM-Vol. 1 (2006), Issue 1, pp. 217 – 230 Open Access Full-Text PDF
Sherzod Mira, Zam Mirakhmedov, Syed Ikram Abbas Tirmizi
Abstract: Let $$0=U_{0,n}\leq U_{1,n}\leq … \leq U_{n,n}=1$$ be an ordered sample from uniform [0,1] distribution $$D_{in}=U_{i,n}-U_{i-1,n}$$, $$i=1,2,..,n$$, $$n=1,2,…$$ , be their spacings,and let $$f_{1n},…,f_{nn}$$ be a set of measurable functions. In this paper theorems on the probabilities of deviations in the moderate zones for $$R_{n}D=f_{1n}(nD_{1n}, … , f_{nn}(nD_{nn}$$ are presented. Application of these results to study an intermediate efficiencies of the tests based on statistic $$R_{n}(D)$$ are also considered.

### Open-loop control of quantum particle motion: effective splitting in momentum space

JPRM-Vol. 1 (2006), Issue 1, pp. 208 – 216 Open Access Full-Text PDF
Babar Ahmad, Sergei Borisenok, Saifullah, Yuri Rozhdestvensky
Abstract: In this paper an effective quantum particle beam-splitter in the momentum space is realized in the frame of open-loop control scheme. We demonstrate for small interaction time that the splitting effect $$±40\hbar k$$ with summarized relative intensity in both main components is about 50 per cent from initial intensity of the atomic beam.

### On some numerical invariants associated to a compact sets (in metric spaces)

JPRM-Vol. 1 (2006), Issue 1, pp. 203 – 207 Open Access Full-Text PDF
Abstract: In this note we associate to a compact subset of a metric space a subset of natural numbers. We give some interesting properties of this last subset. We also introduce a configuration matrix for a given compact set and propose a conjecture related to this.

### On the arithmetic of the rational function field $$K(X)$$

JPRM-Vol. 1 (2006), Issue 1, pp. 198 – 202 Open Access Full-Text PDF
Abstract: Let $$K$$ be a commutative field. In this paper we study the action of the automorphism group of the rational function field $$K(X)$$ on the set of all valuations of $$K(X)$$ which are trivial on $$K$$. We apply this study in finding a classification of some simple algebraic extension of $$K$$.