Journal of Progressive Research in Mathematics Journal of Progressive Research in Mathematics en-US (Managing Editor) (JPRM Support Team) Thu, 12 Jan 2023 14:20:16 +0000 OJS 60 On the computation of zeros of Bessel functions <p>The zeros of some chosen Bessel functions of different orders is revised using the well-known bisection method , McMahon formula is also reviewed and the calculation of some zeros are carried out implementing a recent version of MATLAB software.</p> <p>The obtained results are analyzed and discussed on the lights of previous calculations.</p> Tahani E. Ahmed, Muna S. Akrim, Khadiga S. Abdeen, Ali M. Awin ##submission.copyrightStatement## Thu, 12 Jan 2023 14:19:24 +0000 Generalized Pierre Numbers <p>In this paper, we introduce and investigate the generalized Pierre sequences for the first time and we deal with, in detail, two special cases, namely, Pierre and Pierre-Lucas sequences. We present Binet's formulas, generating functions, Simson formulas, and the summation formulas for these sequences. Moreover, we give some identities and matrices related with these sequences. Furthermore, we show that there are close relations between Pierre, Pierre-Lucas and Tribonacci, Tribonacci-Lucas numbers.</p> YĆ¼ksel Soykan ##submission.copyrightStatement## Sun, 19 Feb 2023 07:40:34 +0000 Numerical Methods for Convex Quadratic Programming with Nonnegative Constraints <p>This paper deals with some problems in numerical simulation for convex quadratic programming with nonnegative constraints. For systems of ordinary differential equations which derived from the above mentioned problem, we construct a kind of new numerical method: the modified implicit Euler method. Under some restrictions for step-size, we obtained the numerical solution which satisfied with the termination condition. Compared with the classical Matlab command ODE23, the new method has ideal computation cost.</p> Qi Wang ##submission.copyrightStatement## Sun, 05 Mar 2023 12:19:43 +0000 The Galerkin Approximation to Forward-Backward Stochastic Partial Differential Equations <p>In this paper, the authors utilized the Galerkin approximation scheme approach to solve a class of fully coupled forward-backward stochastic partial differential equations in an infinite dimensional functional setup.</p> Shilun Li, Hong Yin ##submission.copyrightStatement## Sun, 23 Apr 2023 10:39:02 +0000 New Types of Pythagorean Fuzzy Modules and Applications in Medical Diagnosis <p>In this article, we discuss several distinct categories of pythagorean fuzzy modules, study pythagorean fuzzy relations, and provide applications in the field of medical diagnosis. The concept of pythagorean fuzzy prime modules, along with its characteristics, is presented. In addition,an investigation is conducted into a pythagorean fuzzy multiplication module. Moreover, pythagorean fuzzy relations and pythagorean fuzzy homomorphisms are introduced. By making use of pythagorean fuzzy sets and pythagorean fuzzy relations., we propose a novel approach to the medical diagnosis process. This approach is achieved by pointing the smallest distance between the symptoms of the patients and the symptoms related to diseases.</p> Areej Almuhaimeed ##submission.copyrightStatement## Mon, 24 Apr 2023 01:20:51 +0000 Quantum Conversation <p>This article is a sequel to the paper published earlier entitled (A new approach to gauge theory and variational principal). It is assumed that atoms are engaged in a perpetual conversation called Quantum Conversation,<br>and the behavior of an atom varies based on the syntax, and the tonality, derived from the spectral terms. Accepting this premise, it is then explored how to identify Quantum Conversation, (QC). Quantum<br>Conversation could be identied through looking at atom from a fresh point of view. Mainly this includes re-interpreting spin, and split identied by the spectral terms which is the other behavioral characteristic of quantum particles. Split is dened both as the change in the orbit level, and the division of an atom into smaller elements. Spin, and split change as a result of Q.C. Q.C. has two major elements, 1) syntax, and 2) tonality.<br>Given the dynamics and the diverse nature of syntax combined with tonality, it makes it possible to imagine and analyze a great number of scenarios for the behavior of the elements of an atom that would not be<br>possible to observe through laboratory experiments. This would open the door to a deeper understanding of the life of an atom.</p> M.M. Khoshyaran ##submission.copyrightStatement## Tue, 25 Apr 2023 16:17:26 +0000 Some identities involving degenerate Cauchy numbers and polynomials of the fourth kind <p>In this paper, we study the constant equations associated with the degenerate Cauchy polynomials of the fourth kind using the generating function and Riordan array. By using the generating function method and the Riordan array method, we establish some new constants between the degenerate Cauchy polynomials of the fourth kind and two types of Stirling numbers, Lab numbers, two types of generalized Bell numbers, Daehee numbers, Bernoulli numbers and polynomials.</p> Xiao-Qian Tian, Wuyungaowa . ##submission.copyrightStatement## Tue, 27 Jun 2023 00:00:00 +0000 Modelling The Impact of Screening, Treatment and Underlying Health Conditions on Dynamics of Covid-19 <p>This study formulated a SIRS classical mathematical model which is modified to incorporate the exposed and the treated individuals where COVID-19 is modelled. The model stratifies the population into two categories depending whether they have underlying health conditions or not, and describes disease transmission within or between the groups. Five compartments are considered in the model for each group that is; Susceptible individuals, exposed population, Infected individuals, treated population and the Recovered population. The objectives were to; Formulate a mathematical deterministic model based on classical SIRS model incorporating screening, treatment and underlying health conditions on covid-19 dynamics. Determine the Reproduction number and use it to analyze the model. Determining sensitivity analysis and Bifurcation. Simulating the model using data from the ministry of health. The Next generation matrix method was used to determine the basic reproduction number denoted &nbsp;of the proposed model. The results of the simulation indicated that the Disease Free Equilibrium is locally asymptotically stable whenever &nbsp;and globally asymptotically stable if&nbsp; . On the other hand, Endemic Equilibrium was globally asymptotically stable if .The results obtained showed that increasing the rate of screening and treatment on the exposed population and weakening the disease transmission route between the susceptible, exposed and infected population are crucial to curb the spread of COVID-19 virus. The Government of Kenya should advocate treatment and screening of the exposed and infected individuals.</p> Jeremiah Savali Kilonzi, Cyrus Gitonga Ngari, Stephen Karanja ##submission.copyrightStatement## Wed, 04 Oct 2023 08:53:42 +0000 Meromorphic solutions to certain differential-difference equations <p>The aim of this paper is to investigate the growth and constructions of meromorphic solutions of the nonlinear differential-difference equation<br>$$f^n(z)+h(z)\Delta_cf^{(k)}(z)=A_0(z)+A_1(z)e^{\alpha_1z^q}+\cdots+A_m(z)e^{\alpha_mz^q},$$<br>where $n, m, q\in \mathbb{N}^+$, $\alpha_1,\cdots,\alpha_m$ are distinct nonzero complex numbers, $h(z)$ is a nonzero entire function and $A_j(z)~(0\leq j\leq m)$ are meromorphic functions. In particular, for $A_0(z)\equiv 0$, we give the exact form of meromorphic solutions of the above equation under certain conditions. In addition, our results are shown to be sharp.</p> Yezhou Li, Wenxiao Niu ##submission.copyrightStatement## Sun, 24 Dec 2023 14:10:28 +0000