Results 21 to 30 of about 21,477 (310)
A Basis for Free Assosymmetric Algebras
Journal of Algebra, 1996 The authors exhibit a natural basis for free assosymmetric algebras, i.e. algebras in which the associator \(\{x,y,z\}\) satisfies \(\{a,b,c\} = \{p(a),p(b),p(c)\}\) for all permutations \(p\) on \(a,b,c\). If \(F\) is a field of characteristic \(\neq 2\) and 3, \(S\) a set of generators, \(F[S]\) the free nonassociative algebra over \(F\) generated by
Hentzel, Irvin Roy +2 more
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A message recovery attack on multivariate polynomial trapdoor function [PDF]
PeerJ Computer Science, 2023 Cybersecurity guarantees the exchange of information through a public channel in a secure way. That is the data must be protected from unauthorized parties and transmitted to the intended parties with confidentiality and integrity. In this work, we mount
Rashid Ali +4 more
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Fast change of basis in algebras
Applicable Algebra in Engineering, Communication and Computing, 1992 The \(n\)-dimensional algebra \({\mathcal A}\) has basis \({\mathbf b}\). The structure constants relative to a new basis \({\mathbf c}\), with \({\mathbf b}Q={\mathbf c}\), can be computed in \(O(n^ 5)\) arithmetic operations. However, the authors show that the problem can be solved in time \(O(n^ 4)\).
Hentzel, Irvin, Jacobs, David
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Algebraic Description and Simultaneous Linear Approximations of Addition in Snow 2.0. [PDF]
, 2008 In this paper we analyse the algebraic properties over the field GF(2) of the addition modulo 2pn. We look at implicit quadratic equations describing this operation, and at probabilistic conditional linear equations.
Nicolas T. Courtois +3 more
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Some new operations on fuzzy soft sets and their applications in decision-making [PDF]
Songklanakarin Journal of Science and Technology (SJST), 2022 This paper aims to introduce various types of useful operations on fuzzy soft sets (FSSs), such as Einstein sum, Einstein product, algebraic sum, algebraic product, bounded product, bounded sum, and the basic properties of these new operations have ...
Ajoy Kanti Das +2 more
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An algebraic characterization of the affine canonical basis [PDF]
Duke Mathematical Journal, 1999 The canonical basis for quantized universal enveloping algebras associated to the finite--dimensional simple Lie algebras, was introduced by Lusztig. The principal technique is the explicit construction (via the braid group action) of a lattice over $\bz[q^{-1}]$.
Beck, Jonathan +2 more
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Positive basis for surface skein algebras [PDF]
Proceedings of the National Academy of Sciences, 2014 Significance The Jones polynomial of knots is one of the simplest and most powerful knot invariants, at the center of many recent advances in topology; it is a polynomial in a parameter q . The skein algebra of a surface is a natural generalization of the Jones polynomial to knots that live in a thickened ...
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Free integro-differential algebras and Groebner-Shirshov bases [PDF]
, 2014 The notion of commutative integro-differential algebra was introduced for the algebraic study of boundary problems for linear ordinary differential equations. Its noncommutative analog achieves a similar purpose for linear systems of such equations.
Guo, Li +5 more
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Invariant Basis Number for $C^{*}$-algebras [PDF]
Illinois Journal of Mathematics, 2015 We develop the ring-theoretic notion of Invariant Basis Number in the context of unital $C^*$-algebras and their Hilbert $C^*$-modules. Characterization of $C^*$-algebras with Invariant Basis Number is given in $K$-theoretic terms, closure properties of the class of $C^*$-algebras with Invariant Basis Number are investigated, and examples of $C ...
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Algebraic basis of the algebra of block-symmetric polynomials on $\ell_1 \oplus \ell_{\infty}$
Karpatsʹkì Matematičnì Publìkacìï, 2019 We consider so called block-symmetric polynomials on sequence spaces $\ell_1\oplus \ell_{\infty}, \ell_1\oplus c, \ell_1\oplus c_0,$ that is, polynomials which are symmetric with respect to permutations of elements of the sequences.
V.V. Kravtsiv
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