Results 61 to 70 of about 2,017 (174)
A Quasigroup Approach for Conservation Laws in Asymptotically Flat Spacetimes
UniverseIn the framework of the quasigroup approach to conservation laws in general relativity, we show how the infinite-parametric Newman–Unti group of asymptotic symmetries can be reduced to the Poincaré quasigroup. We compute Noether’s charges associated with
Alfonso Zack Robles +2 more
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Algebraic Properties of Quasigroup Under Q-neutrosophic Soft Set [PDF]
Neutrosophic Sets and SystemsThe novel concept called neutrosophic set was launched to take care of indeterminate factors in real-life data. The hybrid model of neutrosophic set and soft set has been widely studied in different areas of algebra, especially in associative structures ...
Benard Osoba +2 more
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Mathematical Communications, 2011 In this paper, the concept of an ARH--quasigroup is introduced and identities valid in that quasigroup are studied. The geometrical concept of an affine--regular heptagon is defined in a general ARH--quasigroup and geometrical representation in the quasigroup $\mathbb{C}(2 \cos \frac{\pi}{7})$ is given.
Volenec, Vladimir +2 more
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Discrete Mathematics, 1992 A quasigroup \((Q,.,\setminus,/)\) is a set \(Q\) equipped with three binary operations \(.,\setminus,/\) such that (1) \((x/y).y = x\), \((x.y)/y = x\), (2) \(x.(x\setminus y) = y\), \(x\setminus(x.y) = y\). A right quasigroup \((Q,.,/)\) is a set \(Q\) with two binary operations \(.,/\) satisfying (1). A right quasigroup fulfilling \(x.x = x\) and \((
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Quasigroups and related systems, 2010 In this paper the concept of ARO-quasigroup is introduced and some identities which are valid in a general ARO-quasigroup are proved. The "geometric" concepts of midpoint, parallelogram and affine-regular octagon is introduced in a general ARO-quasigroup.
Kolar-Šuper, Ružica +2 more
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Journal of Algebra, 1996 It is well known that the following four Moufang identities, M1: \((x(yz))x=(xy)(zx)\) and N1: \(((xy)z)y=x(y(zy))\) and their respective mirrors M2 and N2 (obtained by writing them backwards), are equivalent in loops which are then called Moufang loops. The author now shows that every quasigroup satisfying any one of these four identities is a Moufang
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Row‐Hamiltonian Latin squares and Falconer varieties
Proceedings of the London Mathematical Society, Volume 128, Issue 1, January 2024.Abstract A Latin square is a matrix of symbols such that each symbol occurs exactly once in each row and column. A Latin square L$L$ is row‐Hamiltonian if the permutation induced by each pair of distinct rows of L$L$ is a full cycle permutation. Row‐Hamiltonian Latin squares are equivalent to perfect 1‐factorisations of complete bipartite graphs.
Jack Allsop, Ian M. Wanless
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Quasigroups, Braided Hopf (Co)quasigroups and Radford’s Biproducts of Quasi-Diagonal Type
MathematicsGiven the Yetter–Drinfeld category over any quasigroup and a braided Hopf coquasigroup in this category, we first mainly study the Radford’s biproduct corresponding to this braided Hopf coquasigroup.
Yue Gu, Shuanhong Wang
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An Algebraic Approach of Topological Indices Connected with Finite Quasigroups
Journal of Function Spaces, Volume 2024, Issue 1, 2024.In mathematical chemistry, the algebraic polynomial serves as essential for calculating the most accurate expressions of distance‐based, degree‐distance‐based, and degree‐based topological indices. The chemical reactivity of molecules, which includes their tendency to engage in particular chemical processes or go through particular reactions, can be ...
Muhammad Nadeem +4 more
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Quantum Quasigroups and the Quantum Yang–Baxter Equation
Axioms, 2016 Quantum quasigroups are algebraic structures providing a general self-dual framework for the nonassociative extension of Hopf algebra techniques. They also have one-sided analogues, which are not self-dual.
Jonathan Smith
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