This review is devoted to the universal algebraic and geometric properties of the non-relativistic quantum current algebra symmetry and to their representations subject to applications in describing geometrical and analytical properties of quantum an...
We review a non-relativistic current algebra symmetry approach to constructing the Bogolubov generating functional of many-particle distribution functions and apply it to description of invariantly reduced Hamiltonian systems of the Boltzmann type ki...
Based on the G. Goldin’s quantum current algebra symmetry representation theory, have succeeded in explaining a hidden relationship between the quantum many-particle Hamiltonian operators, defined in the Fock space, their factorized structure a...
Let \(\mathbf{H}\) be the quaternion algebra. Let \(\mathfrak{g}\) be a complex Lie algebra and let \(U(\mathfrak{g})\) be the enveloping algebra of \(\mathfrak{g}\). The quaternification \(\mathfrak{g}^{\mathbf{H}}=\)\(\,(\,\mathbf{H}\otimes U(\math...
Non-linear loads in circuits cause the appearance of harmonic disturbances both in voltage and current. In order to minimize the effects of these disturbances and, therefore, to control the flow of electricity between the source and the load, passive...
We review some recent progress in the theory of electroweak radiative corrections in semileptonic decay processes. The resurrection of the so-called Sirlin’s representation based on current algebra relations permits a clear separation between the per...
The position operator
This paper proposes an approach for computing the network’s equilibrium point related to the fault clearing time in transient stability studies. The computation of this point is not a trivial task, particularly when the algebraic network’...
We apply a well known technique of theoretical physics, known as geometric algebra or Clifford algebra, to linear electrical circuits with nonsinusoidal voltages and currents. We rederive from the first principles the geometric algebra approach to th...
We generalize the property of complex numbers to be closely related to Euclidean circles by constructing new classes of complex numbers which in an analogous sense are closely related to semi-antinorm circles, ellipses, or functionals which are homog...
These notes are an informal overview of techniques related to deformation theory in the context of physics. Beginning from motivation for the concept of a sheaf, they build up through derived functors, resolutions, and the functor of points to the no...
This paper deals with the optimal reconfiguration problem of DC distribution networks by proposing a new mixed-integer nonlinear programming (MINLP) formulation. This MINLP model focuses on minimising the power losses in the distribution lines by ref...
The Lie algebraic scheme for constructing Hamiltonian operators is differential-algebraically recast and an effective approach is devised for classifying the underlying algebraic structures of integrable Hamiltonian systems. Lie–Poisson analysi...
Evolution algebras are currently widely studied due to their importance not only “per se” but also for their many applications to different scientific disciplines, such as Physics or Engineering, for instance. This paper deals with these types of alg...
Currently, researching the Yang–Baxter equation (YBE) is a subject of great interest among scientists of diverse areas in mathematics and other sciences. One of the fundamental open problems is to find all of its solutions. The investigation de...
In this review, we present a general framework for the construction of Kac–Moody (KM) algebras associated to higher-dimensional manifolds. Starting from the classical case of loop algebras on a circle
This paper addresses the problem of computing the family of two-filiform Lie algebra laws of dimension nine using three Lie algebra properties converted into matrix form properties: Jacobi identity, nilpotence and quasi-filiform property. The interes...
In the algebra of single-valued structures, cyclicity is one of the fundamental properties of groups. Therefore, it is natural to study it also in the algebra of multivalued structures (algebraic hyperstructure theory). However, when one considers th...
This is a noticeably short biography and introductory paper on multiplier Hopf algebras. It delves into questions regarding the significance of this abstract construction and the motivation behind its creation. It also concerns quantum linear groups,...
The Hochschild cohomological dimension of any commutative k-algebra is lower-bounded by the least-upper bound of the flat-dimension difference and its global dimension. Our result is used to show that for a smooth affine scheme X satisfying Pointcar&...
Introduced by S.A. Lomov, the concept of a pseudoanalytic (pseudoholomorphic) solution laid the foundation for the development of the singular perturbation analytical theory. In order for this concept to work in case of linear problems, an apparatus...
Point orthogonal projection onto planar algebraic curve plays an important role in computer graphics, computer aided design, computer aided geometric design and other fields. For the case where the test point
In this study some algebraic transformations on hypercube system are proposed. The presented transformations of forbidden subcubes provide defining set of all maximal and nonfaulty subcubes, and subset of minimal and nonfaulty subcubes included certa...
Point orthogonal projection onto an algebraic surface is a very important topic in computer-aided geometric design and other fields. However, implementing this method is currently extremely challenging and difficult because it is difficult to achieve...
We propose numerical algorithms which can be integrated with modern computer algebra systems in a way that is easily implemented to approximate the sine and cosine functions with an arbitrary accuracy. Our approach is based on Taylor’s expansio...
This paper presents a new framework based on geometric algebra (GA) to solve and analyse three-phase balanced electrical circuits under sinusoidal and non-sinusoidal conditions. The proposed approach is an exploratory application of the geometric alg...
The NTRU (Number Theory Research Unit) is a prominent post-quantum public key cryptography algorithm and a current focus of research. Although many NTRU variants have been proposed, a comprehensive generalization of these variants is still lacking. T...
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...
Quantum anomalies are traditionally understood as classical symmetries that fail to survive quantization, while experimental “anomalies” denote deviations between theoretical predictions and measured values. In this work, we develop a uni...
Using complex network analysis methods to analyze the internal structure of geographic networks is a popular topic in urban geography research. Statistical analysis occupies a dominant position in the current research on geographic networks. This per...
In 2005, Philippe Guillot presented a new construction of Boolean functions using linear codes as an extension of the Maiorana–McFarland’s (MM) construction of bent functions. In this paper, we study a new family of Boolean functions with cryptograph...
Symmetry-related problems can be addressed by means of group theory, and ring theory can be seen as an extension of additive group theory. Ring theory, a significant topic in abstract algebra, is currently active in a diverse range of study domains a...
In the current work, we analyze the spectral distribution of the geometric mean of two or more matrix-sequences constituted by Hermitian positive definite matrices, under the assumption that all input matrix-sequences belong to the same Generalized L...
The present paper employs a numerical method based on the improved block–pulse basis functions (IBPFs). This was mainly performed to resolve the Volterra–Fredholm integral equations of the second kind. Those equations are often simplified into a line...
We develop detailed quaternionic and octonionic frameworks for quantum computation grounded on normed division algebras. Our central result is to prove the polynomial computational equivalence of quaternionic and complex quantum models: Computation o...
Currently, wind turbines utilize doubly fed induction machines that incorporate a frequency converter in the rotor circuit to manage slip energy. This setup ensures a stable voltage amplitude and frequency that align with the alternating current. It...
In this article, the authors propose to investigate the numerical solutions of several fractional-order models of the multi-space coupled Korteweg–De Vries equation involving many different kernels. In order to transform these models into a set...
This article deals with the implementation of fuzzy differential transform method for solving a system of nonlinear fuzzy integro-differential equations. This system appears in a model of biological species living together. Though the differential tr...
Long electromagnetic transients occur in electrical systems because of switching and impulse actions As a result, the simulation time of such processes can be long, which is undesirable. Simulation time is significantly increased if the circuit in th...
The coupling of baryonic current to the derivative of the curvature scalar, R, inherent to gravitational baryogenesis (GBG), leads to a fourth-order differential equation of motion for R instead of the algebraic one of general relativity (GR). The fo...
Probabilistic safety assessment (PSA) of nuclear facilities on external multi-hazards has become a major issue after the Fukushima accident in 2011. However, the existing external hazard PSA methodology is for single hazard events and cannot cover th...
In this paper, a current that is called spin current and corresponds to the variation of the matter action in BF theory with respect to the spin connection A which takes values in Lie algebra
Current mathematics curricula have as one of their fundamental objectives the development of number sense. This is understood as a set of skills. Some of them have an algebraic nature such as acquiring an abstract understanding of relations between n...
The rapid evolution of virtual reality systems and the broader metaverse landscape has prompted growing research interest in biometric authentication methods for user verification. These solutions offer an additional layer of access control that surp...
The singularities of serial robotic manipulators are those configurations in which the robot loses the ability to move in at least one direction. Hence, their identification is fundamental to enhance the performance of current control and motion plan...
This paper deals with the problem of optimal location and reallocation of battery energy storage systems (BESS) in direct current (dc) microgrids with constant power loads. The optimization model that represents this problem is formulated with two ob...
In this paper, we propose a methodology for the step-by-step solution of problems, which can be incorporated into a computer algebra system. Our main aim is to show all the intermediate evaluation steps of mathematical expressions from the start to t...
This paper begins with the introduction of biquaternion algebra and its properties in compact, profound and comprehensible approach. The Schrödinger equation including both the scalar Aharonov-Bohm(sAB) and Aharonov-Casher(AC) effects, that are curre...
In the current study, we explore digital homology modules, and investigate their fundamental properties on (pointed) digital images as one of the developments of symmetries. We also examine pointed digital Hopf spaces and base point preserving digita...
As the space of solutions of the first-order Hamiltonian field theory has a presymplectic structure, we describe a class of conserved charges associated with the momentum map, determined by a symmetry group of transformations. A gauge theory is dealt...
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