Results 1 to 10 of about 1,260 (192)
Ternary Associativity and Ternary Lie Algebras at Cube Roots of Unity [PDF]
AxiomsWe 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.
Viktor Abramov
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A fault tolerant routing algorithm based on cube algebra for hypercube systems [PDF]
Journal of Systems Architecture, 2000 We propose an approach to determine the shortest path between the source and the destination nodes in a faulty or a non-faulty hypercube. The number of faulty nodes and links may be rather large and if any path between the nodes exists, the developed algorithm determines it.
Novruz M. Allahverdi +2 more
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The Subpower Membership Problem for Finite Algebras with Cube Terms [PDF]
Logical Methods in Computer Science, 2019 The subalgebra membership problem is the problem of deciding if a given element belongs to an algebra given by a set of generators. This is one of the best established computational problems in algebra.
Andrei Bulatov +2 more
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Existence of cube terms in finite algebras [PDF]
Algebra Universalis, 2021 We study the problem of whether a given finite algebra with finitely many basic operations contains a cube term; we give both structural and algorithmic results. We show that if such an algebra has a cube term then it has a cube term of dimension at most $N$, where the number $N$ depends on the arities of basic operations of the algebra and the size of
Alexandr Kazda, Dmitriy Zhuk
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Associative Ternary Algebras and Ternary Lie Algebras at Cube Roots of Unity
MathematicsWe propose an approach to extend the concept of a Lie algebra to ternary structures based on ω-symmetry, where ω is a primitive cube root of unity. We give a definition of a corresponding structure, called a ternary Lie algebra at cube roots of unity, or
Anti Maria Aader +2 more
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The data cube as a typed linear algebra operator [PDF]
Proceedings of The 16th International Symposium on Database Programming Languages, 2017 There is a need for a typed notation for linear algebra applicable to the fields of econometrics and data mining. In this paper we show that such a notation exists and can be useful in formalizing and reasoning about data aggregation operations.One such operation - the construction of a data cube - is shown to be easily expressible as a linear algebra ...
José Nuno Oliveira, Hugo Daniel Macedo
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A convergence on Boolean algebras generalizing the convergence on the Aleksandrov cube [PDF]
Czechoslovak Mathematical Journal, 2014 We compare the forcing related properties of a complete Boolean algebra B with the properties of the convergences $λ_s$ (the algebraic convergence) and $λ_{ls}$ on B generalizing the convergence on the Cantor and Aleksandrov cube respectively. In particular we show that $λ_{ls}$ is a topological convergence iff forcing by B does not produce new reals ...
Aleksandar Pavlovic +2 more
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Poincaré type inequalities on the discrete cube and in the CAR algebra [PDF]
Probability Theory and Related Fields, 2007 We prove Lp Poincare inequalities for functions on the discrete cube and their discrete gradient. We thus recover an exponential inequality and the concentration phenomenon for the uniform probability on the cube first obtained by Bobkov and Gotze. Inequalities involving the discrete gradient and powers of the discrete Laplacian are also considered ...
Ben Efraim, L., Lust-Piquard, F.
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Visualizing a Cubic Linkage through the Use of CAS and DGS
Mathematics, 2022 Our goal is to discuss the different issues that arise when attempting to visualize a joints-and-bars cube through GeoGebra, a widespread program that combines dynamic geometry (DGS) and computer algebra systems (CAS). As is standard in the DGS framework,
Tomás Recio +3 more
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Algebraic method to recover superpolies in cube attacks [PDF]
IET Information Security, 2020 Cube attacks are an important type of key recovery attacks against nonlinear feedback shift register (NFSR)‐based cryptosystems. The key step in cube attacks closely related to key recovery is recovering superpolies. However, in the previous cube attacks including original, division property based and correlation cube attacks, the algebraic normal form
Chen-Dong Ye, Tian Tian 0004
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