December 2024 - 78 articles
In 2012, Chu investigated the generalization of classical Watson–Whipple–Dixon summation theorems in the form of analytical formulas. By employing four generalized Watson summation formulas, the objective of this paper is to evaluate a ne...
This paper presents an innovative numerical technique for specific classes of stochastic heat equations. Our approach uniquely combines a sixth-order compact finite difference algorithm with fast discrete Fourier transforms. While traditional discret...
Binomial series involving harmonic polynomials are expressed in terms of parametric integrals. By evaluating these parametric integrals, we establish several remarkable closed formulae for the infinite series containing both central binomial coeffici...
In this paper, we show the maximal regularity of nonlinear second-order hyperbolic boundary differential equations. We aim to show if the given second-order partial differential operator satisfies the specific ellipticity condition; additionally, if...
This research focuses on biological systems with sexual reproduction in which female and male individuals coexist together, forming female–male couples with the purpose of procreation. The couples can originate new females and males according t...
This paper provides a study on optimal prediction problems in a linear model and its subsample models with linear stochastic restrictions, using matrix theory for precise analytical solutions. It focuses on deriving analytical expressions using block...
We propose a novel approach to fractals by leveraging the approximation of fixed points, emphasizing the deep connections between fractal theory and fixed-point theory. We include a condition of isomorphism, which not only generates traditional fract...
The purpose of this study is to improve the computational efficiency of solvers for nonlinear algebraic problems with simple roots. To this end, a multi-step solver based on Newton’s method is utilized. Divided difference operators are applied...
Consider a commutative Z2-graded ring (R=R0⨁R1). Consequently, each element (x∈R) can be uniquely expressed as x=x0+x1, where x0∈R0 and x1∈R1. For any x∈R, we consider the function N(x)=x02−x12. In this work, we exami...
The present article aims to significantly improve geometric function theory by making an important contribution to p-valent meromorphic and analytic functions. It focuses on subordination, which describes the relationships of analytic functions. In o...
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