综合数学
This paper introduces an extension to the Python Neutrosophic Sets (PYNS) framework, originally detailed in Nordo et al. 2024, with the addition of the NSfamily class for constructing and manipulating neutrosophic topologies. Building on…
This paper presents some concepts of the theory of interactive fuzzy numbers, and mainly, a class of interactive fuzzy numbers, called $f$-correlated fuzzy numbers. We start from the foundations of general fuzzy mathematics and go through…
We found a counterexample to the conjecture of Karvatskyi and Pratsiovytyi concerning the topological type of the achievement set of an intermediate series (Proceedings of the International Geometry Center, 2023.…
This study incorporates mathematical analysis, focusing on developing theories and conducting numerical simulations of Influenza virus transmission using real-world data. The terms in the equations introduce parameters which are determined…
In this study, a spatially distributed reaction-diffusion-advection (RDA) model with harvesting is investigated to signify the outcome of a competition between two competing species in a heterogeneous environment. The study builds upon the…
This study is a modification of the McKendrick equation into a growth model with fractional order to predict the abalone length growth. We have shown that the model is a special case of Taylor's series after it was analysed using Adomian…
Two classes of infinite series involving harmonic numbers and the binomial coefficient $C(3n,n)$ are evaluated in closed form using integrals. Several remarkable integral values and difficult series identities are stated as special cases of…
Carleman linearization is a technique that embeds systems of ordinary differential equations with polynomial nonlinearities into infinite dimensional linear systems in a procedural way. In this paper we generalize the method for systems of…
We present a new Clifford-valued linear canonical Stockwell transform aimed at providing efficient and focused representation of Clifford-valued functions in high-dimensional time-frequency analysis. This transform improves upon the…
There are two permutation groups that they share the same character table of order 1344. We take up natural representations on 8 and 14 letters respectively. The purpose of this paper is to examine the semi-simple structure of centralizing…
The Fernandez-Guasti squircle is a plane algebraic curve that is an intermediate shape between the circle and the square. It has qualitative features that are similar to the more famous Lam\'e curve. However, unlike the Lam\'e curve which…
The formal term-by-term differentiation with respect to parameters is demonstrated to be legitimate for the Mittag-Leffler type functions. The justification of differentiation formulas is made by using the concept of the uniform…
We introduce a new approach for generating combinatorial identities and formulas by the application of Kronecker substitution to polynomial expansions within quotient rings. Our main result enables the derivation of elementary arithmetic…
We investigate a class of combinatorial sums involving reciprocals of central binomial coefficients , employing generating functions as the primary solution technique to formulate and analyze series involving the Catalan's constant. Using a…
Our aim is to develop a general approach for the dynamics of material bodies of dimension d represented by a mater manifold of dimension (d + 1) embedded into the space-time. It can be declined for d = 0 (pointwise object), d = 1 (arch if…
The problem of finding the sum of a polynomial's values is considered. In particular, for any $n\geq 3$, the explicit formula for the sum of the $n$th powers of natural numbers $S_n=\sum_{x=1}^{m}x^{n}$ is proved:…
Consider that $\mathbb{G}=(\mathbb{X}, \mathbb{Y})$ is a simple, connected graph with $\mathbb{X}$ as the vertex set and $\mathbb{Y}$ as the edge set. The atom-bond connectivity ($ABC$) index is a novel topological index that Estrada…
In this work we derive a functional equation in terms of the Hurwitz-Lerch zeta function along with definite integrals in terms of the incomplete gamma and Hurwitz-Lerch zeta functions. The method used in these derivations is contour…
We consider a SICA model for HIV transmission on time scales. We prove permanence of solutions and we derive sufficient conditions for the existence and uniform asymptotic stability of a unique positive almost periodic solution of the…
This paper presents an advanced mathematical analysis and simplification of the quadratic programming problem arising from fuzzy clustering with generalized capacity constraints. We extend previous work by incorporating broader balancing…