Journal of Progressive Research in Mathematics

On the computation of zeros of Bessel functions

Tahani E. Ahmed, Muna S. Akrim, Khadiga S. Abdeen, Ali M. Awin — Thu, 12 Jan 2023 14:19:24 +0000

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.

The obtained results are analyzed and discussed on the lights of previous calculations.

Generalized Pierre Numbers

Yüksel Soykan — Sun, 19 Feb 2023 07:40:34 +0000

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.

Numerical Methods for Convex Quadratic Programming with Nonnegative Constraints

Qi Wang — Sun, 05 Mar 2023 12:19:43 +0000

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.

The Galerkin Approximation to Forward-Backward Stochastic Partial Differential Equations

Shilun Li, Hong Yin — Sun, 23 Apr 2023 10:39:02 +0000

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.

New Types of Pythagorean Fuzzy Modules and Applications in Medical Diagnosis

Areej Almuhaimeed — Mon, 24 Apr 2023 01:20:51 +0000

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.

Quantum Conversation

M.M. Khoshyaran — Tue, 25 Apr 2023 16:17:26 +0000

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,
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
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.
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
possible to observe through laboratory experiments. This would open the door to a deeper understanding of the life of an atom.

Some identities involving degenerate Cauchy numbers and polynomials of the fourth kind

Xiao-Qian Tian, Wuyungaowa . — Tue, 27 Jun 2023 00:00:00 +0000

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.