# 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 newton interpolating series and their applications

JPRM-Vol. 1 (2007), Issue 1, pp. 120 – 128 Open Access Full-Text PDF
Ghiocel Groza
Abstract: Newton interpolating series are constructed by means of Newton interpolating polynomials with coefficients in an arbitrary field $$K$$ (see Section 1). If $$K = \mathbb{C}$$ is the field of complex numbers with the ordinary absolute value, particular convergent series of this form were used in number theory to prove the transcendence of some values of exponential series (see Theorem 1). Moreover, if $$K = \mathbb{R}$$, by means of these series it can be obtained solutions of a multipoint boundary value problem for a linear ordinary differential equation (see Theorem 2). If $$K = \mathbb{C}_{P}$$, some particular convergent series of this type (so-called Mahler series) are used to represent all continuous functions from $$\mathbb{Z}_{P}$$ in $$\mathbb{C}_{P}$$ (see [4]). For an arbitrary field K, with respect to suitable addition and multiplication of two elements the set of Newton interpolating series becomes a commutative K-algebra $$K_{S}[[X]]$$ which generalizes the canonical $$K$$-algebra of formal power series. If we consider K a local field, we construct a subalgebra of $$K_{S}[[X]]$$, even for more variables, which is a generalization of Tate algebra used in rigid analytic geometry (see Section 3).

### 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.