Exploring Roughness in Left Almost Semigroups and Its Connections to Fuzzy Lie Algebras by Abdullah Assiry, Amir Baklouti

“…We highlight the fundamental properties and structures of Generalized Roughness, examining its relationships with Fuzzy Lie Algebras, Order Theory, Lattice Structures, Algebraic Structures, and Categorical Perspectives. Moreover, we investigate the potential of mathematical modeling, optimization techniques, data analysis, and machine learning in the context of Generalized Roughness. …”
Get full text

Higher gauge theory and M-theory by Palmer, S

“…Recently, a class of models with N=(1,0) supersymmetry have been found, with significant overlap with algebraic structures in higher gauge theory. This overlap suggests that the full N=(2,0) theory could involve semistrict L∞-algebras. …”

On degenerations and invariants of low-dimensional complex nilpotent Leibniz algebras by Mohamed, Nurul Shazwani, Said Husain, Sharifah Kartini, Yunos, Faridah

“…Throughout the paper we are dealing with mathematical background with abstract algebraic structures. The present paper is devoted to the degenerations of low-dimensional nilpotent Leibniz algebras over the field of complex numbers. …”
Get full text

Resonance-based schemes for dispersive equations via decorated trees by Yvain Bruned, Katharina Schratz

“…The key idea to control the nonlinear frequency interactions in the system up to arbitrary high order thereby lies in a tailored decorated tree formalism. Our algebraic structures are close to the ones developed for singular stochastic PDEs (SPDEs) with regularity structures. …”
Get full text

Codes over matrix rings for space-time coded modulations by Oggier, Frederique, Sole, Patrick, Belfiore, Jean-Claude

“…When the inner code has a cyclic algebra structure over a number field, as for perfect space-time codes, an outer code can be designed via coset coding, more precisely, by taking the quotient of the algebra by a two-sided ideal which leads to matrices over finite alphabets for the outer code. …”
Get full text
Get full text

Enhanced Matrix Power Function for Cryptographic Primitive Construction by Eligijus Sakalauskas

“…The main results are the following: (1) the proposition of infinite, nonsymmetric, and noncommuting algebraic structures for the construction of the enhanced MPF, satisfying associativity conditions, which are necessary for cryptographic applications; (2) the proof that MPF inversion is polynomially equivalent to the solution of a certain kind of generalized multivariate quadratic (MQ) problem which can be reckoned as hard; (3) the estimation of the effectiveness of direct MPF value computation; and (4) the presentation of preliminary security analysis, the determination of the security parameter, and specification of its secure value. …”
Get full text

إنشاء مخطط هاس لشبكات القواسم برمجيا by أحمد الغصين, عبد القادر شيخ إبراهيم

“…This algorithm is an important step to develop software applications on algebraic structures, especially on lattices, because of the great importance of Hass diagram in the study of lattices theory. …”
Get full text

Prime Graph over Cartesian Product over Rings and Its Complement by Farah Maulidya Fatimah, Vira Hari Krisnawati, Noor Hidayat

“…There is currently a bridge between graphs and algebra, especially an algebraic structures, namely theory of graph algebra. One of researchs on graph algebra is a graph that formed by prime ring elements or called prime graph over ring R. …”
Get full text

An introduction to C-infinity schemes and C-infinity algebraic geometry by Joyce, D

“…Thus, C^∞(X) actually has a far richer structure than the obvious R-algebra structure.</p> <p>We explain a version of algebraic geometry in which rings or algebras are replaced by C^∞-rings. …”

Applications of Supersymmetric Polynomials in Statistical Quantum Physics by Iryna Chernega, Mariia Martsinkiv, Taras Vasylyshyn, Andriy Zagorodnyuk

“…We consider a relation of equivalence for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mo mathvariant="script">ℓ</mo><mn>1</mn></msub><mrow><mo>(</mo><msub><mi mathvariant="double-struck">Z</mi><mn>0</mn></msub><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, induced by the supersymmetric polynomials, and the semi-ring algebraic structures on the quotient set with respect to this relation. …”
Get full text

An Enhanced Approach for the Multiple Vehicle Routing Problem with Heterogeneous Vehicles and a Soft Time Window by He-Yau Kang, Amy H. I. Lee

“…In the area of mathematics, the theories of linear and non-linear algebraic structures and information technology are adopted. …”
Get full text

Solving the elusiveness of word meanings: two arguments for a continuous meaning space for language by Maria M. Piñango

“…Supporting it is a parameterized space that gives rise to lexico-conceptual representations: generalized algebraic structures necessary for the identification, processing, and encoding of an individual's understanding of the world.…”
Get full text

From the Lorentz Transformation Group in Pseudo-Euclidean Spaces to Bi-gyrogroups by Abraham A. Ungar

“…The aim of this article is to extend the study of the ‎Lorentz transformation of order (m,n) from m=1 and n≥1 to ‎all m,n∈N‎, ‎obtaining algebraic structures called ‎a bi-gyrogroup and a  bi-gyrovector space‎. ‎…”
Get full text

Higher Order Geometric Theory of Information and Heat Based on Poly-Symplectic Geometry of Souriau Lie Groups Thermodynamics and Their Contextures: The Bedrock for Lie Group Machin... by Frédéric Barbaresco

“…The poly-symplectic approach generalizes the Noether theorem, the existence of moment mappings, the Lie algebra structure of the space of currents, the (non-)equivariant cohomology and the classification of G-homogeneous systems. …”
Get full text

An approach to $$(\mu ,\nu ,\omega )$$ ( μ , ν , ω ) -single-valued neutrosophic submodules by Muhammad Shazib Hameed, Zaheer Ahmad, Shahbaz Ali, Muhammad Kamran, Alphonse-Roger Lula Babole

“…The goals of this research are to comprehend the algebraic structures of a $$(\mu ,\nu ,\omega )$$ ( μ , ν , ω ) -single-valued neutrosophic submodule of a classical module and enhance the legitimacy of this technique by discussing numerous essential aspects. …”
Get full text

Some Results on Neutrosophic Triplet Group and Their Applications by Tèmítópé Gbóláhàn Jaíyéolá, Florentin Smarandache

“…Distinguishing features between an NTG and some other algebraic structures such as: generalized group (GG), quasigroup, loop and group were investigated. …”
Get full text

Surjective Identifications of Convex Noetherian Separations in Topological (<i>C</i>, <i>R</i>) Space by Susmit Bagchi

“…The interplay of symmetry of algebraic structures in a space and the corresponding topological properties of the space provides interesting insights. …”
Get full text

Geometric Structures Generated by the Same Dynamics. Recent Results and Challenges by Víctor Ayala, Adriano Da Silva, José Ayala

“…Since the involved dynamic comes from algebraic structures on Lie groups, symmetries are present throughout the paper.…”
Get full text

Thom-Sebastiani and duality for matrix factorizations, and results on the higher structures of the Hochschild invariants by Preygel, Anatoly

Get full text

Higher linear algebra in topology and quantum information theory by Reutter, D

“…<p>We investigate categorifications of linear algebra, and their applications to the construction of 4-manifold invariants, to the construction of a variety of linear algebraic structures in quantum information theory, and to the classification of certain instances of `quantum pseudo-telepathy', a phenomenon in quantum physics where two non-communicating parties can use pre-shared entanglement to perform tasks classically impossible without communicating. …”