Axioms, Volume 13, Issue 12

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 ${\mathbb{Z}}_2$-graded ring ($R=R_0⨁R_1$). Consequently, each element ($x\in R$) can be uniquely expressed as $x=x_0+x_1$, where $x_0\in R_0$ and $x_1\in R_1$. For any $x\in R$, we consider the function $N\left(x\right)=x_0^2-x_1^2$. 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...

This paper gives a thorough characterization of chain rings with index of nilpotency 5 and residue field ${\mathbb{F}}_{p^m},$ where p represents a prime number, contributing valuable insights to the field of algebraic structures. It carefully identifies and categori...

This study explores the application of generalized conformable derivatives in modeling hotel demand dynamics in Mexico, using the Gompertz-type model. The research focuses on customizing conformable functions to fit the unique characteristics of the...

This paper offers an approach to computing Radial Basis Function–Finite Difference (RBF-FD) weights by integrating a kernel-based function. We derive new weight sets that effectively approximate both the first and second differentiations of a f...

This work explores the geometric properties of the Turanian of the modified Bessel function of the first kind (TMBF). Using the properties of the digamma function, we establish conditions under which the normalized TMBF satisfies starlikeness, convex...

In this paper, we examine the interplay between the structural and spectral properties of the unit graph $G\left({\mathbb{Z}}_n\right)$ for $n=p_1^{r_1}{p}_2^{r_2}\dots p_k^{r_k}$, where $p_1,p_2,\dots ,p_k$ are distinct primes and $k,r_1,r_2,\dots ,r_k$ are positive integers such that at least on...

This study employs a novel physics-informed neural network (PINN) approach, the standard explicit finite difference method (EFDM) and unconditionally positivity preserving FDM to tackle the one-dimensional Sine–Gordon equation (SGE). Two test p...

The study of long-term behavior in stochastic systems is critical for understanding the dynamics of complex processes influenced by randomness. This paper addresses the existence and uniqueness of Stepanov-like pseudo S-asymptotically $(\omega ,c)$-per...

This study presents a novel category of nonconvex functions in Banach spaces, referred to as quasi-lower $C^2$ functions on nonempty closed sets. We establish the existence of solutions for nonconvex variational problems involving quasi-lower $C^2$ functio...

In this paper, we consider a viscoelastic Kirchhoff equation with a delay term in the internal feedback. By using the Faedo–Galerkin approximation method, we prove the well posedness of the global solutions. Introducing suitable energy, we prov...

Rigged Hilbert spaces (RHSs) are the right mathematical context that include many tools used in quantum physics, or even in some chaotic classical systems. It is particularly interesting that in RHS, discrete and continuous bases, as well as an abstr...

This paper introduces the idea of a cone m-hemi metric space, which extends the idea of an m-hemi metric space. By presenting non-trivial examples, we demonstrate the superiority of cone m-hemi metric spaces over m-hemi metric spaces. Further, we ext...

For the constructive analysis of locally Lipschitzian system of non-linear differential equations with mixed periodic and two-point non-linear boundary conditions, a numerical-analytic approach is developed, which allows one to study the solvability...

: In this study, we introduce a novel class of generalized neutrosophic open sets, referred to as neutrosophic strongly preopen sets. Building on this foundation, we propose a new type of continuity and several new types of mappings. These concepts a...

In this paper, we investigate the stochastic Heisenberg ferromagnetic equation (SHFE) derived by a multiplicative Wiener process. We use a suitable transformation to change the SHF equation into another Heisenberg ferromagnetic equation with random v...

The regularity of the n-P-V-rings and n-P-V’-rings is systematically investigated in this paper. Employing the notions of quasi-ideals, weakly left (or right) ideals, and generalized weak ideals, we focus on investigating the strong $\pi$-regula...

This work explores the geometry of extremal Kerr-Newman black holes by analyzing their mass/energy relationships and the conditions ensuring black hole existence. Using differential geometry in $E^3$, we examine the topology of the event horizon surface...

Based on allometric theory and scaling laws, numerous mathematical models have been proposed to study ontogenetic growth patterns of animals. Although deterministic models have provided valuable insight into growth dynamics, animal growth often devia...

In the study, the authors introduce Qi’s normalized remainder of the Maclaurin power series expansion of the function $\ln \sec x=-\ln \cos x$; in view of a monotonicity rule for the ratio of two Maclaurin power series and by virtue of the logarith...

This paper explores the operational principles and monomiality principles that significantly shape the development of various special polynomial families. We argue that applying the monomiality principle yields novel results while remaining consisten...

Dempster–Shafer Theory (DST) relies significantly on belief and plausibility measures to handle ambiguity and uncertainty; however, DST has been extended to fuzzy sets (FSs) and intuitionistic fuzzy sets (IFSs) with only a few extensions focusi...

This paper proposes a novel sine step size for warm-restart stochastic gradient descent (SGD). For the SGD based on the new proposed step size, we establish convergence rates for smooth non-convex functions with and without the Polyak–Łoja...

This paper deals with the second-order semi-linear degenerate elliptic equation $y{u}_{yy}+b{u}_y+{\Delta }_{x}u+{|u|}^{\alpha -1}u=0,(x,y)\in {\mathbb{R}}^n\times (0,\infty )$, where $n\ge 1,\alpha >1$. We establish a Liouville theorem of stable solution of the degenerate...

In this paper, we study nonlinear differential equations with Caputo fractional derivatives with respect to other functions and impulses. The main characteristic of the impulses is that the time between two consecutive impulsive moments is defined by...

In this paper, a new numerical scheme, which we call the impulsive linearly implicit Euler method, for the SIR epidemic model with pulse vaccination strategy is constructed based on the linearly implicit Euler method. The sufficient conditions for gl...

The aim of the article is to create a method for studying the asymptotics of solutions to second-order differential equations with irregular singularities. The method allows us to prove the convergence of formal series included in the asymptotics of...

This paper reports the research work carried out with the goal of geometrically and algebraically describing, as well as topologically classifying, the curves resulting from the intersection of a torus with families of parabolic and elliptical cylind...

Motivated by recent advancements in the quantum detection problem employing both discrete and continuous frames, this paper delves into a quantum detection problem utilizing g-frames within the context of quaternionic Hilbert spaces. We offer several...

In this article, we examine and investigate various variants of Julia set patterns for complex exponential functions $W\left(z\right)=\alpha e^{z^n}+{\displaystyle \frac{\beta }{z^m}}+log{c}^t,$ and $T\left(z\right)=\alpha e^{z^n}+{\displaystyle \frac{\beta }{z^m}}+\gamma$ (which are analytic except at $z=0$) where $n\ge 2,$ $m,n\in \mathbb{N}$...

Our study presents an innovative variational Bayesian parameter estimation method for the Quantile Nonlinear Dynamic Latent Variable Model (QNDLVM), particularly when dealing with missing data and nonparametric priors. This method addresses the compu...

The efficiency and quality of the manufacturing industry are greatly influenced by production scheduling, which makes it a crucial aspect. A well-designed production scheduling scheme can significantly enhance manufacturing efficiency and reduce ente...

The goal of this study is to derive new conditions that improve the testing of the oscillatory and asymptotic features of fourth-order differential equations with an advanced neutral term. By using Riccati techniques and comparison with lower-order e...

This manuscript presents set-theoretical solutions to the Yang–Baxter equation within the framework of GE-algebras by constructing mappings that satisfy the braid condition and exploring the algebraic properties of GE-algebras. Detailed proofs...

Understanding shear flow behavior in compressible, viscous, micropolar real gases is essential for both theoretical advancements and practical engineering applications. This study develops a comprehensive model that integrates micropolar fluid theory...

The study of the Hankel determinant generated by the Maclaurin series of holomorphic functions belonging to particular classes of normalized univalent functions is one of the most significant problems in geometric function theory. Our goal in this st...

This study computationally examined the Richtmyer–Meshkov instability (RMI) evolution in a helium backward-triangular bubble immersed in monatomic argon, diatomic nitrogen, and polyatomic methane under planar shock wave interactions. Using high...

This article investigates the applications of the q-Carlson–Shaffer operator on subclasses of q-uniformly starlike functions, introducing the class $S{T}_q(m,c,d,\beta )$. The study establishes a necessary condition for membership in this class and...

The objective of this research article is to introduce Kikkawa and Suzuki-type contractions in the setting of topological vector space-valued cone metric space with a solid cone and establish some new fixed point results for multi-valued mappings. Th...

The field of indices has been explored and advanced by various researchers for different purposes. One purpose is the optimization of indices in various problems. In this work, the general power-sum connectivity index is considered. The general power...

In this paper, we consider various aspects of the Schur problem for a square complex matrix A, namely the similarity unitary transformation of A into upper triangular form containing the eigenvalues of A on its diagonal. Since the profound work of I....

Quantitative bisimulations between weighted finite automata are defined as solutions of certain systems of matrix-vector inequalities and equations. In the context of fuzzy automata and max-plus automata, testing the existence of bisimulations and th...