Polyadic Analogs of Direct Product by Steven Duplij

“…We propose a generalization of the external direct product concept to polyadic algebraic structures which introduces novel properties in two ways: the arity of the product can differ from that of the constituents, and the elements from different multipliers can be “entangled” such that the product is no longer componentwise. …”
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Pattern Graph Rewrite Systems by Kissinger, A, Merry, A, Soloviev, M

“…We then provide examples demonstrating the expressive power of pattern graphs and how they can be applied to study interacting algebraic structures that are central to categorical quantum mechanics.…”

f-Grouplikes by Hooshmand, M. H., Sarmin, Nor Haniza

“…A nice example for associative function,$f$-multiplication and such algebraic structures are $b$-decimal part functions$(\; )_b$, $b$-addition $+_b$, and the real $b$-grouplike $(\mathbb{R},+_b)$.In this paper, we introduce an important type of grouplikes (namely $f$-grouplike) that is motivated fromthe both topics. …”

Mass Formula for Self-Orthogonal and Self-Dual Codes over Non-Unital Rings of Order Four by Adel Alahmadi, Altaf Alshuhail, Rowena Alma Betty, Lucky Galvez, Patrick Solé

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Nano topology induced by Lattices by M. Lellis Thivagar, V. Sutha Devi

“…On the other hand, the lower and upper approximations have also been studied within the context various algebraic structures.…”
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A new approach to the study of fixed points based on soft rough covering graphs by Imran Shahzad Khan, Nasir Shah, Abdullah Shoaib, Poom Kumam, Kanokwan Sitthithakerngkiet

“…Applications of the algebraic structures available in covering soft sets to soft graphs may reveal new facets of graph theory.…”
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Oriented Fuzzy Numbers vs. Fuzzy Numbers by Krzysztof Piasecki, Anna Łyczkowska-Hanćkowiak

“…For this purpose, we examine algebraic structures composed of numerical spaces equipped with addition, dot multiplication, and subtraction determined in a usual way. …”
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Weak separation, pure domains and cluster distance by Farber, Miriam, Galashin, Pavel

“…We apply our result to calculate the cluster distance and to give lower bounds on the mutation distance between cluster variables in the cluster algebra structure on the coordinate ring of the Grassmannian. …”
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Type-II polyadic constacyclic codes over finite fields by Jitman, Somphong, Ling, San, Tharnnukhroh, Jareena

“…Polyadic constacyclic codes over finite fields have been of interest due to their nice algebraic structures, good parameters, and wide applications. …”
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On the Adequacy of Psychophysical Measurements by V.M. Romanchuk

“…The theoretical justification of equivalence is the isomorphism of algebraic structures. Such a solution to the Fechner-Stevens problem is constructive since it contains the possibility of experimental verification of the adequacy of the measurement results. …”
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Dynamical l-bits and persistent oscillations in Stark many-body localization by Buca, B, Gunawardana, TM

“…We explain and analytically prove all these observations by rigorously perturbatively showing the existence of novel algebraic structures that are exponentially stable in time, which we call dynamical l-bits. …”

On Hamming Distance Distributions of Repeated-Root Cyclic Codes of Length 5p^s Over F_p ^m + uF_p ^m by Hai Q. Dinh, Bac T. Nguyen, Hiep L. Thi, Woraphon Yamaka

“…Let <inline-formula> <tex-math notation="LaTeX">$p\not =5$ </tex-math></inline-formula> be any odd prime. Using the algebraic structures of all cyclic codes of length <inline-formula> <tex-math notation="LaTeX">$5p^{s}$ </tex-math></inline-formula> over the finite commutative chain ring <inline-formula> <tex-math notation="LaTeX">${\mathcal{ R}}=\mathbb F_{p^{m}}+u\mathbb F_{p^{m}}$ </tex-math></inline-formula>, in this paper, the exact values of Hamming distances of all cyclic codes of length <inline-formula> <tex-math notation="LaTeX">$5p^{s}$ </tex-math></inline-formula> over <inline-formula> <tex-math notation="LaTeX">$\cal R$ </tex-math></inline-formula> are established. …”
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Perfectly Secure Shannon Cipher Construction Based on the Matrix Power Function by Eligijus Sakalauskas, Lina Dindienė, Aušrys Kilčiauskas, Kȩstutis Lukšys

“…This property was obtained by the special selection of algebraic structures to define the MPF. In an earlier paper we demonstrated, that certain MPF can be treated as a conjectured one-way function. …”
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An efficient approach to study multi-polar fuzzy ideals of semirings by Shahida Bashir, Talal Alharbi, Rabia Mazhar, Issra Khalid, Muneeb ul Hassan Afzal, Nauman Riaz Chaudhry

“…This paper introduces innovative extensions to algebraic structures. We present the definitions and some important results of m-polar fuzzy subsemirings (m-PFSSs), m-polar fuzzy ideals (m-PFIs), m-polar fuzzy generalized bi-ideals (m-PFGBIs), m-polar fuzzy bi-ideals (m-PFBIs) and m-polar fuzzy quasi-ideals (m-PFQIs) in semirings. …”
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The Structure Theorems of Pseudo-BCI Algebras in Which Every Element is Quasi-Maximal by Xiaoying Wu, Xiaohong Zhang

“…For mathematical fuzzy logic systems, the study of corresponding algebraic structures plays an important role. Pseudo-BCI algebra is a class of non-classical logic algebras, which is closely related to various non-commutative fuzzy logic systems. …”
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Irreducible modules over finite simple Lie pseudoalgebras II. Primitive pseudoalgebras of type K by Bakalov, Bojko, D’Andrea, Alessandro, Kac, Victor

“…One of the algebraic structures that has emerged recently in the study of the operator product expansions of chiral fields in conformal field theory is that of a Lie conformal algebra. …”
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The monotone wrapped Fukaya category and the open-closed string map by Ritter, A, Smith, I

“…The module and unital algebra structures, and the generation criterion, also hold for the compact Fukaya category F(E), and also hold for closed monotone symplectic manifolds. …”

Graphical calculi and their conjecture synthesis by Miller-Bakewell, H

“…This work continues the exploration of graphical calculi, inside and outside of the quantum computing setting, by investigating the algebraic structures with which we label diagrams. The initial aim for this was Conjecture Synthesis; the algorithmic process of creating theorems. …”

Dualizable tensor categories by Douglas, C, Schommer-Pries, C, Snyder, N

“…There is furthermore a correspondence between algebraic structures on tensor categories and homotopy fixed point structures, which in turn provide structured field theories; we describe the expected connection between pivotal tensor categories and combed fixed point structures, and between spherical tensor categories and oriented fixed point structures.…”

Dualizable tensor categories by Douglas, CL, Schommer-Pries, C, Snyder, N

“…There is furthermore a correspondence between algebraic structures on tensor categories and homotopy fixed point structures, which in turn provide structured field theories; we describe the expected connection between pivotal tensor categories and combed fixed point structures, and between spherical tensor categories and oriented fixed point structures.…”