# 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

### Some Opial-type inequalities involving fractional integral operators

JPRM-Vol. 17 (2021), Issue 1, pp. 48 – 58 Open Access Full-Text PDF
Abstract: The core idea of this paper is to provide the Opial-type inequalities for Hadamard fractional integral operator and fractional integral of a function with respect to an increasing function $$g$$. Moreover, related extreme cases and counter part of our main results are also given in the paper.

### Reversed degree-based topological indices for Benzenoid systems

JPRM-Vol. 17 (2021), Issue 1, pp. 40 – 47 Open Access Full-Text PDF
Abdul Jalil M. Khalaf, Abaid ur Rehman Virk, Ashaq Ali, Murat Cancan
Abstract: Topological indices are numerical values that correlate the chemical structures with physical properties. In this article, we compute some reverse topological indices namely reverse Atom-bond connectivity index and reverse Geometric-arithmetic index for four different types of Benzenoid systems.

### Determinant Spectrum of Diagonal Block Matrix

JPRM-Vol. 17 (2021), Issue 1, pp. 35 – 39 Open Access Full-Text PDF
Elif OTKUN CEVIK, Zameddin I. ISMAILOV
Abstract: It is known that in mathematical literature one of important questions of spectral theory of operators is to describe spectrum of diagonal block matrices in the direct sum of Banach spaces with the spectrums of their coordinate operators. This problem has been investigated in works [1] and [2]. Also for the singular numbers similar investigation has been made in [3]. In this paper the analogous question is researched. Namely, the relationships between $$\epsilon$$-determinat spectrums of the diagonal block matrices and their block matrices are investigated. Later on, some applications are given.

### Inequalities of Hardy-type for Multiple Integrals on Time Scales

JPRM-Vol. 17 (2021), Issue 1, pp. 21 – 34 Open Access Full-Text PDF
Dawood Ahmad, Khuram Ali Khan, Ammara Nosheen
Abstract: We extend some inequalities of Hardy-type on time scales for functions depending on more than one parameter. The results are proved by using induction principle, properties of integrals on time scales, chain rules for composition of two functions, Hölder’s inequality and Fubini’s theorem in time scales settings.

### On algebraic aspects of SSC associated to the subdivided prism graph

JPRM-Vol. 17 (2021), Issue 1, pp. 7 – 20 Open Access Full-Text PDF
Mehwish Javed, Agha Kashif, Muhammad Javaid
Abstract: In this article, some important combinatorial and algebraic properties of spanning simplicial complex associated to the subdivided prism graph $$P(n,m)$$ are presented. The $${f}-$$vector of the spanning simplicial complex $$\Delta_s(P(n,m))$$ and the Hilbert series for the face ring $$K\big[\Delta_s(P(n,m))\big]$$ are computed. Further, the associated primes of the facet ideal $$I_{\mathcal{F}}(\Delta_s(P(n,m)))$$ are determined. Finally, the Cohen-Macaulay characterization of the SR-ring of $$\Delta_s(P(n,m))$$ is discussed.

### Quantum Painlev´e II solution with approximated analytic solution in form of nearly Yukawa potential

JPRM-Vol. 17 (2021), Issue 1, pp. 1 – 6 Open Access Full-Text PDF
Irfan Mahmood
Abstract: In this article it has been shown that one dimensional non-stationary Schrodinger equation with a specific choice of potential reduces to the quantum Painleve II equation and the solution of its riccati form appears as a dominant term of that potential. Further, we show that Painleve II Riccati solution is an equivalent representation of centrifugal expression of radial Schrodinger potential. This expression is used to derive the approximated to the Yukawa potential of radial Schrodinger equation which can be solved by applying the Nikiforov-Uvarov method. Finally, we express the approximated form of Yukawa potential explicitly in terms of quantum Painleve II solution.