In quantum secure multi-party summation protocols, some attackers can impersonate legitimate participants in the summation process, and easily steal the summation results from the participants. This is often overlooked for existing secure multi-party...
The Kadomtsev–Petviashvili equation is known to be the leading term of a semi-infinite hierarchy of integrable equations with evolutions given by times with positive numbers. Here, we introduce new hierarchy directed to negative numbers of times. The...
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...
The purpose of this study is to obtain the commutativity of a 3-prime near ring satisfying some differential identities on Jordan ideals involving derivations and multiplicative derivations. Further, herein we discuss some examples to show the necess...
Social and economic development leads to the continuous urbanization process, accompanied by the increasingly prominent traffic congestion problem. Traffic congestion also brings problems such as serious environmental pollution and intensified social...
This paper reviews results about discrete physics and non-commutative worlds and explores further the structure and consequences of constraints linking classical calculus and discrete calculus formulated via commutators. In particular, we review how...
We propose a new approach to extend the notion of commutator and Lie algebra to algebras with ternary multiplication laws. Our approach is based on the ternary associativity of the first and second kinds. We propose a ternary commutator, which is a l...
We study two types of dynamical extensions of Lucas sequences and give elliptic solutions for them. The first type concerns a level-dependent (or discrete time-dependent) version involving commuting variables. We show that a nice solution for this sy...
Let A be a self-adjoint standard operator algebra on a real or complex Hilbert space of dimension ≥2, and let k∈{1,2,3}. The k-skew commutator for A,B∈A is defined by [A,B]1∗=AB−BA∗ and [A,B]k∗=[A,[A,[A,B]k&min...
A multiscale dynamic analysis of the commutation error, based on the filtering approach is performed. The similarity multiscale hypothesis proposed by Bardina (1983) and extended by Geurts and Holm (2006) to the commutation error is examined in detai...
This paper examines the commutativity of the quotient ring F/Y by utilizing specific differential identities in a general ring F that contains a semiprime ideal Y. This study particularly focuses on the role of a multiplicative generalized semideriva...
We study the local commutation relation between the Lefschetz operator and the exterior differential on an almost complex manifold with a compatible metric. The identity that we obtain generalizes the backbone of the local Kähler identities to t...
In this paper, we consider the problem of classifying commutative rings according to the genus number of its associating zero-divisor graphs. The zero-divisor graph of R, where R is a commutative ring with nonzero identity, denoted by Γ(R), is...
A topological index is a numeric quantity associated with a chemical structure that attempts to link the chemical structure to various physicochemical properties, chemical reactivity, or biological activity. Let R be a commutative ring with identity,...
This paper proposes a convex quadratic optimization commutation method to raise the equalization degree of power loss distribution of coil array for magnetic levitation planar motors. Starting with the modeling of electromagnetic forces/torques and c...
This article examines the commutativity of rings with antiautomorphisms, specifically when they are equipped with derivations that satisfy certain algebraic identities. Moreover, we present examples to demonstrate the necessity of the various restric...
This paper investigates the relationship between the commutativity of rings and the properties of their multiplicative generalized derivations. Let F be a ring with a semiprime ideal Π. A map ϕ:F→F is classified as a multiplicative gener...
Symmetric structures are key in non-associative algebras. A Mock-Lie algebra, defined by commutativity and the Jacobi identity, shows strong algebraic symmetry. This paper studies the quasi-centroid, which captures the symmetry of linear operators co...
In this paper, some new properties of Abel Grassmann‘s Neutrosophic Extended Triplet Loop (AG-NET-Loop) were further studied. The following important results were proved: (1) an AG-NET-Loop is weakly commutative if, and only if, it is a commuta...
The numerical invariants of a variation of Hodge structure over a smooth quasi-projective variety are a measure of complexity for the global twisting of the limit-mixed Hodge structure when it degenerates. These invariants appear in formulas that may...
In 1940 Naimark showed that if a set of quantum observables are positive semi-definite and sum to the identity then, on a larger space, they have a joint resolution as commuting projectors. In 1955 Sz.-Nagy showed that any set of observables could b...
Generalizing bicommutant theorem to the higher-order commutator case is very useful for representation theory of Lie algebras, which plays an important role in symmetry analysis. In this paper, we mainly prove that for any spectral operator A on a co...
Let R be a commutative ring with identity and S a (not necessarily saturated) multiplicative subset of R. We call the ring R to be a weakly S-Noetherian ring if every S-finite proper ideal of R is an S-Noetherian R-module. In this article, we study s...
In this article, we investigate the fundamental properties of coalgebras with coalgebra comultiplications, counits, and coalgebra homomorphisms of coalgebras over a commutative ring R with identity 1R based on digital images with adjacency relations....
Let R be a commutative ring with identity, and let S be a (not necessarily saturated) multiplicative subset of R. We define R to be a nonnil-S-Noetherian ring if each nonnil ideal of R is S-finite. In this paper, we study some properties of nonnil-S-...
Let R ⊆ T be an extension of commutative rings with identity and H ( R , T ) (respectively, h ( R , T ) ) the composite Hurwitz series ring (respectively, composite Hurwitz polynomial ring). In this article, we study equiv...
Let R be a finite commutative ring with nonzero identity 1. In this paper, domination parameters, the domination number and the total dominating number, of the unit graph G(R) or the closed unit graph G¯(R) of R are investigated. To study the do...
In this article, for a prime ideal ρ of an arbitrary ring ℜ, we study the commutativity of the quotient ring ℜ/ρ, whenever ℜ admits a generalized reverse derivation ϑ associated with a reverse derivation ∂ that sa...
Using survey data from three dwelling types in Jakarta, we examine how dwelling type, socioeconomic identity, and commuting distance affect women’s travel-mode choices and motivations behind women’s choices for nearby and distant non-work...
The use of advanced switching technologies, including hybrid and fully semiconductor-based circuit breakers, enables a significant reduction in the prospective short-circuit current. This enhances the level of circuit protection by minimizing thermal...
This work explores the unit graph of the commutative ring Zp for prime p and explores the significance of the Sombor index and the Sombor polynomial in comprehending its structural details. We systematically investigate the unit graph and the identit...
The evolution of the internet has led to the growth of smart application requirements on the go in the vehicular ad hoc network (VANET). VANET enables vehicles to communicate smartly among themselves wirelessly. Increasing usage of wireless technolog...
In this note, we investigate algebraic loop structures and inverses of elements of a set of all homomorphisms of Lie algebras with a binary operation derived from a Lie algebra comultiplication. As a symmetry phenomenon, we show that if...
Let Γ(V,E) be a simple connected graph with more than one vertex, without loops or multiple edges. A nonempty subset S⊆V is a global offensive alliance if every vertex v∈V−S satisfies that δS(v)≥δS¯(v)+1. The...
In this paper, we consider the digital cohomology modules of a digital image consisting of a bounded and finite subset of Zn and an adjacency relation. We construct a contravariant functor from the category of digital images and digital continuous fu...
Let R be a commutative ring with nonzero identity and k≥2 be a fixed integer. The k-zero-divisor hypergraph Hk(R) of R consists of the vertex set Z(R,k), the set of all k-zero-divisors of R, and the hyperedges of the form {a1,a2,a3,…,ak}, where a1,a2...
With its unique geopolitical status and multicultural setting, Hong Kong has harbored different youth groups generated from cross-border migration with mainland China who are tied to different cultural values and identifications. This study aims to i...
This note is intended as a contribution to the study of quantitative measures of graph complexity that use entropy measures based on symmetry. Determining orbit sizes of graph automorphism groups is a key part of such studies. Here we focus on an ext...
We derive some quantum central limit theorems for the expectation values of macroscopically coarse-grained observables, which are functions of coarse-grained Hermitian operators consisting of non-commuting variables. Thanks to the Hermiticity constra...
Let R be a commutative ring with identity 1≠0 and let Z(R)′ be the set of all non-unit and non-zero elements of ring R. Γ′(R) denotes the cozero-divisor graph of R and is an undirected graph with vertex set Z(R)′, w∉z...
Given a commutative ring R with identity 1≠0, let the set Z(R) denote the set of zero-divisors and let Z*(R)=Z(R)∖{0} be the set of non-zero zero-divisors of R. The zero-divisor graph of R, denoted by Γ(R), is a simple graph whose vertex set is Z*(R)...
In this paper, we present some generalizations of Jacobi–Jordan algebras. More concretely, we will focus on noncommutative Jacobi–Jordan algebras, Malcev–Jordan algebras, and general Jacobi–Jordan algebras. We adapt a method,...
The canonical commutation relation, [Q,P]=iℏ, stands at the foundation of quantum theory and the original Hilbert space. The interpretation of P and Q as observables has always relied on the analogies that exist between the unitary transformati...
In order to be able to use methods of universal algebra for investigating posets, we assigned to every pseudocomplemented poset, to every relatively pseudocomplemented poset and to every sectionally pseudocomplemented poset, a certain algebra (based...
A new three-dimensional Lie algebra and its loop algebra are proposed by us, whose commutator is a vector product. Based on this, a positive flow and a negative flow are obtained by introducing a new kind of spectral problem expressed by the vector p...
This paper explores the impact of choice of ventilation setting (“window open”, “new (external) air” and “recirculate”) on in-vehicle carbon monoxide exposures for commuters travelling by car at different times of the day (morning, midday, and evenin...
As climate change concerns, urban congestion, and environmental degradation intensify, cities prioritise cycling as a sustainable transport option to reduce CO2 emissions and improve quality of life. However, rampant bicycle theft and poor security i...
A Novikov–Poisson algebra (A,∘,·) is a vector space with a Novikov algebra structure (A,∘) and a commutative associative algebra structure (A,·) satisfying some compatibility conditions. Give a Novikov–Poisson al...
For a finite commutative ring R with identity 1≠0, the weakly zero-divisor graph of R denoted as WΓ(R) is a simple undirected graph having vertex set as a set of non-zero zero-divisors of R and two distinct vertices a and b are adjacent if a...
A finite ring with an identity whose lattice of ideals forms a unique chain is called a finite chain ring. Let R be a commutative chain ring with invariants p,n,r,k,m. It is known that R is an Eisenstein extension of degree k of a Galois ring S=GR(pn...
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