Meet the editor

Dr. Kamal Shah is a senior researcher in the Department of Mathematics & Sciences, Prince Sultan University, Riyadh, Saudi Arabia. From 2007 to 2021, he was an associate professor in the Department of Mathematics, University of Malakand, Chakdara, Pakistan. He obtained a master's in Mathematics from Government Post Graduate Jahanzeb College, Swat, Pakistan, in 2005. He joined the University of Malakand as a lecturer in 2007

and obtained his Ph.D. in Fractional Calculus in 2016 from the same university. Dr. Shah has published numerous articles in scientific journals and has supervised many MPhil and Ph.D. students.

Contents

Characteristic Polynomials

over Finite Fields

*by Jerome A. Adepoju*

*by Sándor Kovács, Szilvia György and Noémi Gyúró*

*by Mritunjay Kumar Singh and Rajesh P. Singh*

Irreducible Polynomials: Non-Binary Fields *by Mani Shankar Prasad and Shivani Verma*

in Sheet Metal Forming Analysis

to Extensions of Absolute Values

Scenarios

of Fractional Order

*and Thabet Abdeljawad*

*by Lhoussain El Fadil and Mohamed Faris*

Some Proposed Problems on Permutation Polynomials

Effectiveness of Basic Sets of Goncarov and Related Polynomials

On the Use of Homogeneous Polynomial Yield Functions

*by Mehmet Firat, Bora Şener, Toros Arda Akşen and Emre Esener*

On the Irreducible Factors of a Polynomial and Applications

The Efficiency of Polynomial Regression Algorithms and Pearson Correlation (r) in Visualizing and Forecasting Weather Change

Using Shifted Jacobi Polynomials to Handle Boundary Value Problems

*by Okba Weslati, Samir Bouaziz and Mohamed Moncef Serbaji*

*by Kamal Shah, Eiman, Hammad Khalil, Rahmat Ali Khan* 

**Preface III**

**Chapter 1 1**

**Chapter 2 37**

**Chapter 3 47**

**Chapter 4 75**

**Chapter 5 85**

**Chapter 6 99**

**Chapter 7 113**

**Chapter 8 133**

## Contents


Preface

A polynomial in mathematics is an expression consisting of coefficients and variables that involves only the operations of addition, subtraction, and multiplication with a non-negative integer power. Polynomials have significant applications in the description of many real-world problems. Various polynomial-type expressions are being used to describe the various chemical, biological, social, and economic problems. Further, polynomials are increasingly being used in numerical computations of large numbers of nonlinear problems. They are also used in calculus and numerical analysis to approximate other functions. In linear algebra during spectral analysis, eigen values are computed through characteristic polynomials, which further help in finding the radius of convergence of various matrices. In stability analysis, eigen values are computed through the help of minimal polynomials of the Jacobian matrix. Polynomials are powerful tools in approximation theory and advanced numerical analysis.

Chapter 1 discusses some characteristic functions and various valuable relations

Chapter 2 presents some problems of permutations and their applications, various

Chapter 3 discusses the effectiveness of basic sets of Gončarov polynomials and

Chapter 5 describes the use of homogenous polynomials yield function and various

Chapter 8 describes the use of shifted Jacobi polynomials in some fractional order

**Kamal Shah**

Prince Sultan University, Riyadh, Saudi Arabia

Department of Mathematics, University of Malakand, Chakdara, Pakistan

Department of Mathematics and Sciences,

Chapter 4 reviews irreducible factors of polynomials as well as discusses the irreducibility of polynomials with specific requirements on their coefficients.

Chapter 6 examines the irreducibility of polynomials in non-binary fields.

Chapter 7 presents the efficiency of polynomial regression algorithms.

differential equations under initial and boundary conditions.

of polynomials.

results.

relations, and results.

their different properties.
