# 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

### Modified beta generalized linear failure rate distribution: theory and applications

JPRM-Vol. 1 (2019), Issue 1, pp. 21 – 48 Open Access Full-Text PDF
Farrukh Jamal, Ibrahim Elbatal, Christophe Chesneau, Mohammed Elgarhy, Amal S. Hassan
Abstract: In this paper we introduce a new comprehensive six-parameter distribution called the modified beta generalized linear failure rate distribution. One of the interest of this distribution is to generalize some well-known flexible distributions discussed in the literature, such as (i) the beta linear failure rate distribution, (ii) the generalized linear failure rate distribution, (iii) the beta exponential distribution, (iv) the beta Rayleigh distribution and (v) the generalized exponential distribution, among others. We derive some of its statistical properties, including the moments, the moment generating function, the quantile function, the order statistics and the mean deviations. We propose the method of maximum likelihood for estimating the model parameters. A simulation study is performed in order to investigate the performance of the maximum likelihood estimators. A real data set is used to illustrate the importance and the flexibility of the new distribution.

### Advanced algorithm for solving a transportation problem with five indicators and fixed cost

JPRM-Vol. 1 (2019), Issue 1, pp. 05 – 20 Open Access Full-Text PDF
Benoumelaz Farouk, Abed Samira, Khelil Nacer, Rebiai Belgacem, Kamal Houam.
Abstract: In this paper, we studied an advanced algorithm for obtaining the best solution to a transportation problem a fixed-charge with five indicators (AATPI5FC) , the procedure itself is very quick; the proposed method solves FCTPI5 by analyze the problem into partial subsections, solution algorithm is coupling between our technique and simplex algorithm (the technique on the fifth index to guarantee improved service), which is novel and can be useful to researchers solved these problems, the advantages of the proposed advanced algorithm are discussed on the existing methods in the context of the application model, the results showed that the proposed advanced algorithm is simple ,accurate and more computational methods found in literature.

### Quasi invo-regular rings

JPRM-Vol. 1 (2019), Issue 1, pp. 01 – 04 Open Access Full-Text PDF
Peter V. Danchev
Abstract: We define the class of quasi invo-regular rings and prove that they curiously coincide with the so-called invo-regular rings, recently introduced and explored by the present author in Ann. Univ. Mariae CurieSklodowska – Sect. Math. (2018).

### Connective eccentricity index of certain path-thorn graphs

JPRM-Vol. 1 (2018), Issue 1, pp. 87 – 99 Open Access Full-Text PDF
M. Javaid, M. Ibraheem, A. A. Bhatti
Abstract: Let $$G$$ be a simple connected graph with $$V (G)$$ and $$E(G)$$ as the vertex set and edge set respectively. A topological index is a numeric quantity by which we can characterize the whole structure of a molecular graph or a network to predict the physical or chemical activities of the involved chemical compounds in the molecular graph or network. The connective eccentricity index of the graph $$G$$ is defined as $$ξ^{ce}(G) = \sum_{v∈G}\frac{d(v)}{e(v)}$$, where $$d(v)$$ and $$e(v)$$ denote the degree and eccentricity of the vertex $$v ∈ G$$ respectively. In this paper, we compute the connective eccentricity index of the various families of the path-thorn graphs and present the obtained results with the help of suitable mathematical expressions consisting on various summations. More precisely, the computed results are general extensions of the some known results.

### Solving differential equations by wavelet transform method based on the mother wavelets & differential invariants

JPRM-Vol. 1 (2018), Issue 1, pp. 74 – 86 Open Access Full-Text PDF
Hamid Reza Yazdani, Mehdi Nadjafikhah, Megerdich Toomanian
Abstract: Nowadays, wavelets have been widely used in various fields of science and technology. Meanwhile, the wavelet transforms and the generation of new Mother wavelets are noteworthy. In this paper, we generate new Mother wavelets and analyze the differential equations by using of their corresponding wavelet transforms. This method by Mother wavelets and the corresponding wavelet transforms produces analytical solutions for PDEs and ODEs.

### K Banhatti and k hyper banhatti indices of the line graphs of h-pantacenic nanotubes

JPRM-Vol. 1 (2018), Issue 1, pp. 62 – 73 Open Access Full-Text PDF
Abdur Rehman, Muhammad Nawaz, Waqas Nazeer, Wei Gao
Abstract: Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. Topological indices are used for example in the development of quantitative structureactivity relationships (QSARs) in which the biological activity or other properties of molecules are correlated with their chemical structure. The aim of this report is to compute the first and second K Banhatti indices of the Line Graphs of H-Pantacenic Nanotubes. We also compute the first and second K hyper Banhatti indices of the Line Graphs of H-Pantacenic Nanotubes.