Algebra - Science topic

In this article, we study the fractional form of a well-known dynamical system from mathematical biology, namely, the Lotka–Volterra model. This mathematical model describes the dynamics of a predator and a prey, and we consider here the fractional form using the Rabotnov fractional-exponential (RFE) kernel. In this work, we derive an approximate f...

A loop (Q, •) is called Basarab loop if it is both a left and a right Basarab loop; (x • yx ρ) • xz = x • yz and yx • (x λ z • x) = yz • x hold for all x, y, z ∈ Q respectively. In this paper, the characterizations of the Bryant-Schneider group of a Basarab loop are studied using the left and right Basarab loop identities. It is shown that the elem...

In this paper, we study the graph theoretical polynomial known as the Hosoya polynomial obtained from one of the standard classes of graphs called path. Using this polynomial applied for the numerical solution of the nonlinear Fredholm integral equation, which reduces in the algebraic system of equation with collocation points, then solving this sy...

In this paper, we introduce the hyperbolic k-Mersenne and k-Mersenne-Lucas octonions and investigate their algebraic properties. We give Binet's formula and present several interrelations and some well-known identities such as Catalan identity, d'Ocagne identity, Vajda identity, generating functions, etc. of these octo-nions in closed form. Further...

The structure and the existence of maximal subrings in division rings are investigated. We see that if $R$ is a maximal subring of a division ring $D$ with center $F$ and $N(R)\neq U(R)\cup \{0\}$, where $N(R)$ is the normalizer of $R$ in $D$, then either $R$ is a division ring with $[D:R]_l=[D:R]_r$ is finite or $R$ is an Ore $G$-domain with certa...

In this paper, we propose a generalized Lucas matrix (a recursive matrix of higher order) obtained from the generalized Fibonacci sequences. We obtain their algebraic properties such as direct inverse calculation, recursive nature, etc. Then, we propose a modified public key cryptography using the generalized Lucas matrices as a key element that op...

I will be chairing a panel in the The First International Society of Fuzzy Sets Extensions and Applications Conference. ISFSEA Conferences Panel (Attached details): Fuzzification of Algebraic Structures and Hypercompositional Algebra https://conf.isfsea.com/conference-panels/. If you are interested in submitting your paper to my panel, please re...

In algebraic graph theory, Doob graphs $D(m,n)$ are known as distance-regular graphs with the same intersection array as the Hamming graph $H(N,4)$, $N=2m+n$. The Doob graph $D(m,n)$ is the Cartesian product of $m>0$ copies of the Shrikhande graph, which is the srg$(16,6,2,2)$ different from $K_4\square K_4$, and $n\ge 0$ copies of the complete gra...

Nodal integral methods (NIMs) have been proven effective in solving a wide range of scientific and engineering problems by providing accurate solutions with coarser grids. Despite notable advantages, these methods have encountered limited acceptance within the fluid flow community, primarily due to the lack of robust and efficient nonlinear solvers...

In this paper, we define and investigate the concept of the implication-based neutrosophic finite state machine (IB-IFSA) over a finite group. Building upon the framework of neutrosophic logic, we introduce the implication-based neutrosophic kernel and the implication-based neutrosophic subsemiautomaton, establishing their formal definitions and pr...

Concepts such as Fuzzy Sets, Neutrosophic Sets, and Plithogenic Sets have been widely investigated for tackling uncertainty, with numerous applications explored across various domains. As extensions of the Plithogenic Set, the HyperPlithogenic Set and the SuperHyperPlithogenic Set are also recognized. A Symbolic Plithogenic Set (SPS) is a structure...

Neutrosophic Sets are conceptual frameworks designed to address uncertainty. A Neutrosophic TwoFold Algebra is a hybrid algebraic structure defined over a neutrosophic set, combining classical algebraic operations with neutrosophic components. Concepts such as Hyperalgebra and Superhyperalgebra extend classical Algebra using Power Sets and-th power...

Although thermoelectric material performance can be estimated using the dimensionless figure of merit ZT, predicting the performance of thermoelectric generator modules (TGMs) is complex owing to the nonlinearity and nonlocality of the thermoelectric differential equations. Here, we present a simplified thermoelectric algebra framework for predicti...

We study the categorical-algebraic condition that internal actions are weakly representable (WRA) in the context of varieties of (non-associative) algebras over a field. Our first aim is to give a complete characterization of action accessible, operadic quadratic varieties of non-associative algebras which satisfy an identity of degree two and to...

The existence of maximal subrings in certain non-commutative rings, especially in rings which are integral over their centers, are investigated. We prove that if a ring $T$ is integral over its center, then either $T$ has a maximal subring or $T/J(T)$ is a commutative Hilbert ring with $|Max(T)|\leq 2^{\aleph_0}$ and $|T/J(T)|\leq 2^{2^{\aleph_0}}$...

Given a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {C}^*$$\end{document}-algebra A with an almost periodic time evolution \documentclass[12pt]{minimal} \usep...

Wahl's local Euler characteristic measures the local contributions of a singularity to the usual Euler characteristic of a sheaf. Using tools from toric geometry, we study the local Euler characteristic of sheaves of symmetric differentials for isolated surface singularities of type $A_n$. We prove an explicit formula for the local Euler characteri...

We give examples of Frobenius algebras of rank two over ground Dedekind rings which are projective but not free and discuss possible applications of these algebras to link homology.

This work uses the modified Extended Direct Algebraic Method (mEDAM) with conformable derivatives to obtain accurate solutions for the diffusion-reaction equation with cubic nonlinearity and the nonlinear fractional generalised density-independent DR problem. We use fractional derivatives in the conformable sense to achieve precise polynomial-form...

We study the properties of the symplectic sp(2N) algebra deformed using Dunkl operators, which describe the dynamical symmetry of the generalized N-particle quantum Calogero model. It contains a symmetry subalgebra formed by the deformed unitary generators as well as the (nondeformed) sl(2,R) conformal subalgebra. An explicit relation among the def...

We prove a comparison theorem between the étale cohomology of algebraic varieties over Stein compacta and the singular cohomology of their analytifications. We deduce that the field of meromorphic functions in a neighborhood of a connected Stein compact subset of a normal complex space of dimension \documentclass[12pt]{minimal} \usepackage{amsmath}...

In this paper, we considered the problem of the simultaneous approximation of a function and its derivatives by means of the well‐known neural network (NN) operators activated by the sigmoidal function. Other than a uniform convergence theorem for the derivatives of NN operators, we also provide a quantitative estimate for the order of approximatio...

Let M be a Kähler manifold with complex structure J and Kähler metric g . A c-projective vector field is a vector field on M whose flow sends J -planar curves to J -planar curves, where J -planar curves are analogs of what (unparametrised) geodesics are for pseudo-Riemannian manifolds (without complex structure). The c-projective symmetry algebras...

In this article, an exterior differential form and its dual form are developed to represent both gravitational and electromagnetic interactions, thereby achieving a mathematical unification of gravity and electromagnetism by their algebraic topologic properties. As an application, it is demonstrated through numerations of the derived exterior diffe...

In this paper, we introduce the Hermite wavelet method (HWM), a numerical method for the fractional-order Bagley–Torvik equation (BTE) solution. The recommended method is based on a polynomial called the Hermite polynomial. This method uses collocation points to turn the given differential equation into an algebraic equation system. We can find the...

En esta presentación se definirá un nuevo operador de Dirac fraccionario construido con un conjunto estructural φ para posteriormente obtener una descomposición de Fischer en términos de funciones (φ,ψ)-inframonogénicas. Este operador de Dirac y la variable fraccionaria generan una superálgebra de Lie isomorfa a osp(1|2). Dicha álgebra se presenta...

Controlled ordinary differential equations driven by continuous bounded variation curves can be considered a continuous time analogue of recurrent neural networks for the construction of expressive features of the input curves. We ask up to which extent well known signature features of such curves can be reconstructed from controlled ordinary diffe...

Granular rough sets (GRST) from axiomatic algebraic perspective perspectives are potentially capable of solving the problem of meaning in AI (specifically generative AI) through the following specific interrelated methodologies: 1. Representations of dependence between subsets of attributes by other subsets of attributes (and a related new theory o...

We consider some recently constructed examples of simple finite-dimensional right-alternative superalgebras and right-symmetric algebras. We prove that the central order in any of these algebras and superalgebras is embedded in a finite module over its center (or over the even part of its center in the case of superalgebras)

In this paper, we provide a unified definition of mediated graph, a combinatorial structure with multiple applications in mathematical optimization. We study some geometric and algebraic properties of this family of graphs and analyze extremal mediated graphs under the partial order induced by the cardinalty of their vertex sets. We derive mixed in...

von Neumann algebras have been playing an increasingly important role in the context of gauge theories and gravity. The crossed product presents a natural method for implementing constraints through the commutation theorem, rendering it a useful tool for constructing gauge-invariant algebras. The crossed product of a Type III algebra with its modul...

This paper concerns the relation between imperative process algebra and rely/guarantee logic. An imperative process algebra is complemented by a rely/guarantee logic that can be used to reason about how data change in the course of a process. The imperative process algebra used is the extension of ACP (Algebra of Communicating Processes) that is us...

A. Weil identified a 2-dimensional space of rational classes of Hodge type (n,n) in the middle cohomology of every 2n-dimensional abelian variety with a suitable complex multiplication by an imaginary quadratic number field. These abelian varieties are said to be of Weil type and these Hodge classes are known as Weil classes. We prove that the Weil...

We geometrize the mod p Satake isomorphism of Herzig and Henniart–Vignéras using Witt vector affine flag varieties for reductive groups in mixed characteristic. We deduce this as a special case of a formula, stated in terms of the geometry of generalized Mirković–Vilonen cycles, for the Satake transform of an arbitrary parahoric mod p Hecke algebra...

We show that Klemenc's stable envelope of exact $\infty$-categories induces an equivalence between stable $\infty$-categories with a bounded heart structure and weakly idempotent complete exact $\infty$-categories. Moreover, we generalise the Gillet-Waldhausen theorem to the connective algebraic K-theory of exact $\infty$-categories and deduce a un...

We discuss the relationship between o-minimality and the so called Zilber-Pink conjecture. Since the work of Pila and Zannier, algebraization theorems in o-minimal geometry had profound impacts in Diophantine geometry (most notably on the study of special points in abelian and Shimura varieties). We will first focus on functional transcendence, dis...

This article presents new constructions of quantum error correcting Calderbank-Shor-Steane (CSS for short) codes. These codes are mainly obtained by Sloane's classical combinations of linear codes applied here to the case of self-orthogonal linear codes. A new algebraic decoding technique is also introduced. This technique is exemplified on CSS cod...

We obtain general criteria for giving a lower bound on the degree of numbers of the form $\prod_{n=1}^\infty \left(1+\frac{b_n}{\alpha_n}\right)$ or of the form $\prod_{m=1}^\infty \left(1+ \sum_{n=1}^\infty \frac{b_{n,m}}{\alpha_{n,m}}\right)$, where the $\alpha_n$ and $\alpha_{n,m}$ are assumed to be algebraic integers, and the $b_n$ and $b_{n,m}...

A bstract We continue our analysis of open string field theory based on A ∞ -algebras obtained from Witten’s theory by attaching stubs to the elementary vertex. Classical solutions of the new theory can be obtained from known analytic solutions in Witten’s theory by applying a cohomomorphism. In a previous work two such cohomomorphisms were found,...

We reconsider the equivalence theorem from an algebraic viewpoint, using an extended Becchi-Rouet-Stora-Tuytin symmetry. This version of the equivalence theorem is then used to reexpress the Abelian Higgs model action, originally written in terms of undesirable gauge variant field excitations, in terms of gauge-invariant, physical variables, corres...

This paper introduces a novel numerical algorithm for solving pantograph differential equations and Volterra functional integro‐differential equations including the piecewise fractional derivative. The proposed algorithm combines the piecewise Gegenbauer functions, the Ritz method, and operational matrices. These functions have great flexibility to...

Mathematical knowledge of geometric and arithmetic progressions is fundamental to the education of students in basic education, since the development of algebraic thinking requires the identification of patterns in numerical sequences and the investigation of generalizations. The aim of this article is to define a recurrence sequence that uses the...

In recent work, we demonstrated that a spectral variety for the Berry connection of a 2d \mathcal{N}=(2,2) 𝒩 = ( 2 , 2 ) GLSM with Kähler vacuum moduli space X X and Abelian flavour symmetry is the support of a sheaf induced by a certain action on the equivariant quantum cohomology of X X . This action could be quantised to first-order matrix diffe...

We discuss many-body fermionic and bosonic systems subject to dissipative particle losses in arbitrary spatial dimensions d d , within the Keldysh path-integral formulation of the quantum master equation. This open quantum dynamics represents a generalisation of classical reaction-diffusion dynamics to the quantum realm. We first show how initial c...

We construct countable groups \(G\) with the following new degree of \(\mathrm{W}^{*}\)-superrigidity: if \(L(G)\) is virtually isomorphic, in the sense of admitting a bifinite bimodule, with any other group von Neumann algebra \(L(\Lambda )\), then the groups \(G\) and \(\Lambda \) must be virtually isomorphic. Moreover, we allow both group von Ne...

In a recent paper, W. Ou generalized the algebraic integrability criteria of Campana-P\u{a}un and Druel to the compact K\"ahler setting. A key ingredient in his proof is an algebraicity criterion, extends the algebraicity criteria of Bost, Bogomolov-McQuillan. In this note, we explain a proof of his criterion.

Various problems of mathematical physics consider octonions and split-octonions as a mathematical structure, which underpins the eight-dimensional nature of these problems. Therefore, it is not surprising that octonionic analysis has become an area of active research in recent years. One of the main goals of octonionic analysis is to develop tools...

The present article aims to develop a categorical duality for the category of bounded complete J-algebraic lattices. In terms of the lattice of weak ideals, we first construct a left adjoint to the forgetful functor Sup\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsb...

We compute scalar static response coefficients (Love numbers) of non-dilatonic black $p$-brane solutions in higher dimensional supergravity. This calculation revels a fine-tuning behavior similar to that of higher dimensional black holes, which we explain by ``hidden'' near-zone Love symmetries. In general, these symmetries act on equations for per...

The condition number of a generator matrix of an ideal lattice derived from the ring of integers of an algebraic number field is an important quantity associated with the equivalence between two computational problems in lattice-based cryptography, the “Ring Learning With Errors (RLWE)” and the “Polynomial Learning With Errors (PLWE)”. In this work...

This paper introduces fuzzy subalgebras of autometrized algebras and studies their properties. Also, we present fuzzy ideals of autometrized algebras and provide examples to illustrate our findings. We examine the homomorphisms of both the images and the inverse images of fuzzy subalgebras and ideals. Furthermore, we introduce fuzzy congruences on...

A notable feature of the anomalous sub-solution equation is its solution’s algebraic decay over extended time periods, a phenomenon commonly associated with Mittag-Leffler type stability. For power-nonlinear sub-diffusion models with variable coefficients, we prove Mittag-Leffler stability under natural decay assumptions on the source functions, wi...

In the field of many valued logic, lattice valued logic (especially ideals) plays an important role. Now days lattice valued logic becomes a research area. Researchers introduced weak LI-ideals of lattice implication algebra. Furthermore, other scholars researched LI-ideals of implicative almost dis-tributive lattice. Therefore, the target of this...

In this paper, based on Hida’s methods, we establish p-stability results for the critical L-values of algebraic Hecke characters over CM fields in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin...

We analytically study interacting Dirac fermions, described by the Thirring model, under weak local particle number measurements with monitoring rate $\gamma$. This system maps to a bosonic replica field theory, analyzed via the renormalization group. For a nonzero attractive interaction, a phase transition occurs at a critical measurement strength...

We initiate the algebraic study of the semigroup of one-to-one order-preserving partial contraction mappings of a totally ordered set {1, 2,. .. , n}, which we denote by OCI n. In particular, we characterise the Green's relations and their starred analogues in OCI n. We also compute the rank of OCI n as 2n − 1.

Gaussian quadrature rules are commonly used to approximate integrals with respect to a non-negative measure dσ^. It is important to be able to estimate the quadrature error in the Gaussian rule used. A common approach to estimating this error is to evaluate another quadrature rule that has more nodes and higher algebraic degree of precision than th...

We answer in the negative Siegel's problem for $G$-functions, as formulated by Fischler and Rivoal. Roughly, we prove that there are $G$-functions that cannot be written as polynomial expressions in algebraic pullbacks of hypergeometric functions; our examples satisfy differential equations of order two, which is the smallest possible. In fact, we...

We consider the quantum analog of the generalized Zernike systems given by the Hamiltonian: $$ \hat{\mathcal{H}} _N =\hat{p}_1^2+\hat{p}_2^2+\sum_{k=1}^N \gamma_k (\hat{q}_1 \hat{p}_1+\hat{q}_2 \hat{p}_2)^k , $$ with canonical operators $\hat{q}_i,\, \hat{p}_i$ and arbitrary coefficients $\gamma_k$. This two-dimensional quantum model, besides the c...

The path to the solution of Feder-Vardi dichotomy conjecture by Bulatov and Zhuk led through showing that more and more general algebraic conditions imply polynomial-time algorithms for the finite-domain Constraint Satisfaction Problems (CSPs) whose templates satisfy them. These investigations resulted in the discovery of the appropriate height 1 M...

Chiral algebras have gained significant attention in modern theoretical physics, particularly in the context of conformal field theories (CFTs), string theory, and topological quantum field theories (TQFTs). These algebras, which involve the structure of left-and right-moving modes of quantum fields, offer deep insights into the symmetries of quant...

Assume that B(X) is the algebra of all bounded linear operators on a complex Banach space X, and let W in B(X) is such that cl(W(X)) is not equal to X or W=zI, where z is a complex number and I is the identity operator. We show that if f: B(X) --> B(X) is an additive mapping Lie centralizable at W, then f(A)=kA+h(A) for all A in B(X), where k is a...

Dimensional reduction of gravity theories to $D=2$ along commuting Killing isometries is well-known to be classically integrable. The resulting system typically features a coset $\sigma$-model coupled to a dilaton and a scale factor of the dimensional reduction. In this article, we construct two families of deformations of dimensionally reduced gra...

The explosive dispersal of particles is an important problem in multiphase physics and is of considerable interest due to its many applications. Simulations that examine particulate dispersal in such flows have employed a variety of methods, including Euler–Lagrange, Euler–Euler, and dusty gas. The appropriate choice of methodology depends on the b...

Algebraic symplectic cobordism is the universal symplectically oriented cohomology theory for schemes, represented by the motivic commutative ring spectrum $\text{MSp}$ constructed by Panin and Walter. The graded algebraic diagonal $\text{MSp}^*$ of the coefficient ring of $\text{MSp}$ is unknown. Through a symplectic version of the Pontryagin-Thom...

Numeracy skills are fundamental abilities that every student must possess to understand mathematical concepts. Indonesia ranks 74th out of 79 countries in terms of numeracy proficiency, indicating the low ability of students to comprehend basic mathematical concepts and solve numeracy-based problems. According to the 2024 National Assessment result...

Este artículo analiza la pertinencia del contenido de álgebra en el marco de prácticas situadas en el contexto social, destacando su relación con el desarrollo de habilidades y la generación de reglas y principios algebraicos. El objetivo es valorar cómo estas prácticas contribuyen al aprendizaje significativo, conectando los contenidos algebraicos...

We answer an open problem of arXiv:1204.1760 and arXiv:1205.4293, extending their work to irreducible well--generated complex reflection groups $W$. We define a combinatorial $W$-noncrossing parking space and an algebraic $W$-parking space for such $W$, and exhibit a $(W \times C)$-equivariant isomorphism between the two. As a consequence of this i...

This paper aims to investigate the benthic-drift population model in both open and closed advective environments, focusing on the logistic growth of benthic populations. We obtain the threshold dynamics using the monotone iteration method, and show that the zero solution is globally attractive straightforward when linearly stable. When unstable, li...

The wind-driven ocean circulation comprises the oceanic currents that are visible at the surface. In this paper, we use algebraic topology concepts and methods to study a highly simplified model of the evolution of this circulation subject to periodic winds. The low-order spectral model corresponds to a midlatitude ocean basin. For steady forcing,...

It is well-known that in the logic of quantum mechanics disjunctions and conjunctions can be represented by joins and meets, respectively, in an orthomodular lattice provided their entries commute. This was the reason why J. Pykacz introduced new derived operations called ''sharp'' and ''flat'' coinciding with joins and meets, respectively, for com...

A novel short-term time series forecasting scheme based on evolutionary interpolation of Chebyshev polynomials is presented in this paper. The uniqueness of the proposed scheme lies in the higher density of Chebyshev nodes at the ends of the interpolation interval. Thus, the structural representation of the algebraic interpolant closer to the prese...

Every state on the algebra $M_n$ of complex nxn matrices restricts to a state on any matrix system. Whereas the restriction to a matrix system is generally not open, we prove that the restriction to every *-subalgebra of $M_n$ is open. This simplifies topology problems in matrix theory and quantum information theory.

We demonstrate that the direct sum of ideals satisfying the strong $\ell$-exchange property is of fiber type. Furthermore, we provide Gr\"obner bases of the presentation ideals of multi-Rees algebras and the corresponding special fibers, when they are associated with an $n$-dimensional Ferrers diagram that is standardizable. In particular, we show...

We classify four-dimensional connected simply-connected indecomposable Lorentzian symmetric spaces $M$ with connected nontrivial isotropy group furnishing solutions of the Einstein-Yang-Mills equations. Those solutions with respect to some invariant metric connection $\Lambda$ in the bundle of orthonormal frames of $M$ and some diagonal metric on t...

String-net models describe a vast family of topological orders in two spatial dimensions, but fail to produce all the expected anyonic excitations. Following arXiv:1502.03433, we consider an extended string-net model by attaching one tail to each plaquette of the lattice, allowing all anyons to emerge as elementary plaquette excitations for arbitra...

It is shown that every algebraic quantum field theory has an underlying functorial field theory which is defined on a suitable globally hyperbolic Lorentzian bordism pseudo-category. This means that globally hyperbolic Lorentzian bordisms between Cauchy surfaces arise naturally in the context of algebraic quantum field theory. The underlying functo...

In (Davydov et al. Selecta Mathematica (N.S.) 19, 237–269 2013, Rem. 3.4) the authors asked the question if any étale subalgebra of an étale algebra in a braided fusion category is also étale. We give a positive answer to this question if the braided fusion category \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage...

We describe Rota-Baxter operators on split octonions. It turns out that up to some transformations there exists exactly one such non-splitting operator over any field. We also obtain a description of all decompositions of split octonions over a quadratically closed field of characteristic different from 2 into a sum of two subalgebras, which descri...

In this paper, we present the concept of Rota-Baxter operators and Reynolds operators within the framework of trusses. We then introduce and examine dendriform trusses, post-trusses, and NS-trusses as the fundamental algebraic structures underlying these classes of operators. Finally, we extend the notion of averaging operators to trusses, explorin...

We prove that the variety of flexes of algebraic curves of degree $3$ in the projective plane is an ideal theoretic complete intersection in the product of a two-dimensional and a nine-dimensional projective spaces.

We generalize the concept of a field by allowing addition to be a partial operation. We show that elements of such a "partially additive field" share many similarities with physical quantities. In particular, they form subsets of mutually summable elements (similar to physical dimensions), dimensionless elements (those summable with 1) form a field...

It has been establish that the locally finitely separability of any universal algebra represented over a given uniformly computably separable equivalence is equivalent to the immune of the characteristic transversal of this equivalence. Examples are presented that demonstrate the infidelity of this criterion for finitely separable algebras, as well...

Let $f_1(z),\ldots, f_m(z)$ be power series in $\mathbb{Q}_p[[z]]$ such that, for every $1\leq i\leq m$, $f_i(z)$ is solution of a differential operator $\mathcal{L}_i\in E_p[d/dz]$, where $E_p$ is the field of analytic elements. We prove that if, for every $1\leq i\leq m$, $\mathcal{L}_i$ has a strong Frobenius structure and has maximal order mult...

Concepts such as Fuzzy Sets, Neutrosophic Sets, and Plithogenic Sets have been widely investigated for tackling uncertainty, with numerous applications explored across various domains. As extensions of the Plithogenic Set, the HyperPlithogenic Set and the SuperHyperPlithogenic Set are also recognized. A Symbolic Plithogenic Set (SPS) is a structure...

Diophantine approximation explores how well irrational numbers can be approximated by rationals, with foundational results by Dirichlet, Hurwitz, and Liouville culminating in Roth's theorem. Schmidt's subspace theorem extends Roth's results to higher dimensions, with profound implications to Diophantine equations and transcendence theory. This arti...

This work presents a mathematical framework based on uncertain numbers to address the inherent uncertainty in nonlinear systems, a challenge that traditional mathematical frameworks often struggle to fully capture. By establishing five axioms, a formal system of uncertain numbers is developed and embedded within set theory, providing a comprehensiv...

We study Vaidya-type solutions in Weyl conformal gravity (WCG) using Eddington--Finkelstein-like coordinates. Our considerations focus on spherical as well as hyperbolic and planar symmetries. In particular, we find all vacuum dynamical solutions for the aforementioned symmetries. These are, in contrast to general relativity, structurally quite non...

The aim of this paper is to give a categorical equivalence for Stone algebras. We introduce the variety of Stone-Kleene algebras with intuitionistic negation, or Stone KAN-algebras for short, and explore Kalman's construction for Stone algebras. We examine the centered algebras within this new variety and prove that the category of Stone algebras i...

Integer factorization is a fundamental problem in computational number theory with significant applications in cryptography, computational algebra, and primality testing. Classical algorithms such as the Quadratic Sieve (QS) and Number Field Sieve (NFS) operate by collecting smooth numbers and solving linear congruences, typically mod 2. In this pa...

A BG-algebra is defined as a non-empty set that includes a constant 0 and a binary operation which adheres to the following axioms: (𝐵G1) , (𝐵G2) , and (𝐵G3) for all . Pseudo BG-algebra is a generalization of BG-algebra, which is an algebra that satisfies the following axioms: (pBG1) , (pBG2) , and (pBG3) for all . In BG-algebra introduced an (l, r...

We introduce the notion of bounded quasi-inversion closed semiprime f-algebras and we prove that, if A is such an algebra, then any intermediate algebra in A is an order ideal of A. This extends a recent result by Dominguez who has dealt with the unital case (the problem on C(X)-type spaces has been solved earlier by Dominguez, Gomez-Perez, and Mul...

Many information-theoretic quantities have corresponding representations in terms of sets. Many of these information quantities do not have a fixed sign—for example, the co-information can be both positive and negative. In previous work, we presented a signed measure space for entropy where the smallest sets (called atoms) all have fixed signs. In...

Basic algebraic and combinatorial properties of finite vector spaces in which individual vectors are allowed to have multiplicities larger than 1 are derived. An application in coding theory is illustrated by showing that multispace codes that are introduced here may be used in random linear network coding scenarios, and that they generalize standa...

Given a squarefree monomial ideal $I$ of a polynomial ring $Q$, we show that if the minimal free resolution $\mathbb{F}$ of $Q/I$ admits the structure of a differential graded (dg) algebra, then so does any "pruning" of $\mathbb{F}$. As an application, we show that if $Q/\mathcal{F}(\Delta)$, the quotient of the ambient polynomial ring by the facet...

This paper proposes a numerical technique to solve the time-fractional generalized Kawahara differential equation (TFGKDE). Certain shifted Lucas polynomials are utilized as basis functions. We first establish some new formulas concerned with the introduced polynomials and then tackle the equation using a suitable collocation procedure. The integer...

We construct explicit examples that are algebraic varieties in positive characteristic to show that locally trivial moduli functors do not always satisfy Schlessinger's condition $(H_1)$ in [3], in contrast to the complex/characteristic $0$ case. The first example is an algebraic curve, and the second is a normal rational projective surface with on...