33 Results Found

Starting from the 2001 Thomas Friedrich’s work on $\mathrm{Spin}\left(9\right)$ , we review some interactions between $\mathrm{Spin}\left(9\right)$ and geometries related to octonions. Several topics are discussed in this respect: explicit descriptions of the $\mathrm{Spin}(9$...

The aim of this work is to study the method of the normalized systems of functions. The normalized systems of functions with respect to the Dirac operator in the umbral Clifford analysis are constructed. Furthermore, the solutions of umbral Dirac-typ...

We develop a rigorous algebraic–analytic framework for multidual complex numbers ${\mathbb{DC}}_n$ within the setting of Clifford analysis and establish a comprehensive theory of hyperholomorphic multidual complex-valued functions. Our main contributions are...

In practical engineering, the use of Pauli algebra can provide a computational advantage, transforming conventional vector algebra to straightforward matrix manipulations. In this work, the Pauli matrices in cylindrical and spherical coordinates are...

By means of Clifford Algebra, a unified language and tool to describe the rules of nature, this paper systematically discusses the dynamics and properties of spinor fields in curved space-time, such as the decomposition of the spinor connection, the...

Isothermic surfaces are defined as immersions with the curvture lines admitting conformal parameterization. We present and discuss the reconstruction of the iterated Darboux transformation using Clifford numbers instead of matrices. In particulalr, w...

New-generation power networks, such as microgrids, are being affected by the proliferation of nonlinear electronic systems, resulting in harmonic disturbances both in voltage and current that affect the symmetry of the system. This paper presents a m...

This paper develops a theoretical framework for the computation of higher-order derivatives based on the algebra of hyper-dual numbers. Extending the classical dual number system, hyper-dual numbers provide a natural and rigorous mechanism for encodi...

Clifford algebras are an active area of mathematical research having numerous applications in mathematical physics and computer graphics, among many others. This paper demonstrates algorithms for the computation of characteristic polynomials, inverse...

In this paper, we explore the finite-time synchronization of Clifford-valued neural networks with finite-time distributed delays. To address the problem associated with non-commutativity pertaining to the multiplication of Clifford numbers, the origi...

This work addresses a significant gap in the existing literature by developing integral representation formulas for extended quaternion-valued functions within the framework of Clifford analysis. While classical Cauchy-type and Borel–Pompeiu fo...

We present the emergence of a root system in six dimensions from the tetrahedra of an icosahedral core known as the 20-group (20G) within the framework of Clifford’s geometric algebra. Consequently, we establish a connection between a three-dimension...

In this article, as a new mathematical approach to origin of the laws of nature, using a new basic algebraic axiomatic (matrix) formalism based on the ring theory and Clifford algebras (presented in Section 2), “it is shown that certain mathematical...

We investigate the modeling capabilities of sets of coupled classical harmonic oscillators (CHO) in the form of a modeling game. The application of the simple but restrictive rules of the game lead to conditions for an isomorphism between Lie-algebra...

This paper explains a method of constructing algebras, starting with the properties of discrimination in elementary discrete systems. We show how to use points of view about these systems to construct what we call iterant algebras and how these algeb...

A group is an algebraic system that characterizes symmetry. As a generalization of the concept of a group, semigroups and various non-associative groupoids can be considered as algebraic abstractions of generalized symmetry. In this paper, the notion...

We investigate a generalization of the equation $curl\overrightarrow{w}=\overrightarrow{g}$ to an arbitrary number n of dimensions, which is based on the well-known Moisil–Teodorescu differential operator. Explicit solutions are derived for a particular problem in bounded domains of...

The main purpose of this paper was to study the almost anti-periodic oscillation caused by external inputs and the global exponential synchronization of Clifford-valued recurrent neural networks with mixed delays. Since the space consists of almost a...

Neutrosophic extended triplet group is a new algebra structure and is different from the classical group. In this paper, the notion of generalized neutrosophic extended triplet group is proposed and some properties are discussed. In particular, the f...

There is a divergence between religion and its modes of application, or religion and religiosity. This essay provides a critical analysis of Clifford Geertz’s book Islam Observed and tries to attempt the question of whether Islam is better unde...

We investigate the emergence of different effective geometries in stochastic Clifford circuits with sparse coupling. By changing the probability distribution for choosing two-site gates as a function of distance, we generate sparse interactions that...

Scators form a linear space equipped with a specific non-distributive product. In the elliptic case they can be interpreted as a kind of hypercomplex number. The requirement that the scator partial derivatives are direction-independent leads to a gen...

The Geometric Algebra Fulcrum Library (GA-FuL) version 1.0 is introduced in this paper as a comprehensive computational library for geometric algebra (GA) and Clifford algebra (CA), in addition to other classical algebras. As a sophisticated software...

This paper explores the question of how religious symbolism functions to provide a more meaningful or enriched experience of life. It examines a common and highly influential view, referred to here as the “source model”, for which this fu...

This article examines how ethnographic methodology and literary theory can advance research engines and artificial intelligence systems beyond the reductive computational approaches that dominate contemporary AI development. Drawing on recent Stanfor...

The simulation of multidimensional wave propagation with variable material parameters is a computationally intensive task, with applications from seismology to electromagnetics. While quantum computers offer a promising path forward, their algorithms...

Motivation. Analytic function theory on commutative complex extensions calls for an operator–theoretic calculus that simultaneously sees the algebra-induced coupling among components and supports boundary-to-interior mechanisms. Gap. While Dira...

A method of the Riemann–Hilbert problem is applied for Zhang’s conjecture 1 proposed in Philo. Mag. 87 (2007) 5309 for a ferromagnetic three-dimensional (3D) Ising model in the zero external field and the solution to the Zhang’s conjecture 1 is const...

Noncommutativity in physics has a long history, tracing back to classical mechanics. In recent years, many new developments in theoretical physics, and in practical applications rely on different techniques of noncommutative algebras. In this review,...

The Ising model describes a many-body interacting spin (or particle) system, which can be utilized to imitate the fundamental forces of nature. Although it is the simplest many-body interacting system of spins (or particles) with Z₂ symmetry, the phe...

Since 1892, the electrical engineering scientific community has been seeking a power theory for interpreting the power flow within electric networks under non-sinusoidal conditions. Although many power theories have been proposed regarding non-sinuso...

Very recently, a different generalization of real-valued neural networks (RVNNs) to multidimensional domains beside the complex-valued neural networks (CVNNs), quaternion-valued neural networks (QVNNs), and Clifford-valued neural networks (ClVNNs) ha...

The common feature for a nontrivial hard problem is the existence of nontrivial topological structures, non-planarity graphs, nonlocalities, or long-range spin entanglements in a model system with randomness. For instance, the Boolean satisfiability...