Results 11 to 20 of about 21,477 (310)

Variable-basis Categorically-algebraic Dualities

Fuzzy Information and Engineering, 2014
The manuscript continues our study on developing a categorically-algebraic (catalg) analogue of the theory of natural dualities of D. Clark and B. Davey, which provides a machinery for obtaining topological representations of algebraic structures.
Sergey A. Solovyov
doaj   +2 more sources

Algebraic Cryptanalysis Scheme of AES-256 Using Gröbner Basis [PDF]

Journal of Electrical and Computer Engineering, 2017
The zero-dimensional Gröbner basis construction is a crucial step in Gröbner basis cryptanalysis on AES-256. In this paper, after performing an in-depth study on the linear transformation and the system of multivariate polynomial equations of AES-256 ...
Kaixin Zhao, Jie Cui, Zhiqiang Xie
doaj   +2 more sources

The Algebraic Basis of Classical Multivariate Methods

The Statistician, 1971
Although the classical multivariate techniques are often taught separately, the basic algebra involved in most of them is very similar. This is because many of these methods arise from the optimization of a criterion that can be expressed as a quadratic function, or the ratio of quadratic functions, after an a priori structure has been imposed on the ...
Krzanowski, W. J.
openaire   +2 more sources

An Algebraic-Geometric Parametrization of the Canonical Basis

Advances in Mathematics, 1996
The summary of the author leaves nothing to do. ``One of the observations of \textit{G. Lusztig} [Prog. Math. 123, 531-568 (1994; Zbl 0845.20034)] has been that the canonical basis [\textit{G. Lusztig}, J. Am. Math. Soc. 3, 447-498 (1990; Zbl 0703.17008)] of the + part of a quantized enveloping algebra attached to a Cartan matrix of finite type is ...
Lusztig, George
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Notes on algebraic functions

International Journal of Mathematics and Mathematical Sciences, 2003
Consideration of the monodromy group of the hypergeometric equation z(1−z)w″+[γ−(1+α+β)z]w′−αβw=0, in the case of α=1/6, β=5/6, γ=7/6, shows that the global hypergeometric function solution F(1/6;5/6;7/6;z) is nonalgebraic although it has only algebraic ...
Guan Ke-Ying, Lei Jinzhi
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Research on Granular Conversion Computing in Algebraic Quotient Space [PDF]

Jisuanji kexue yu tansuo, 2022
Granular computing is a problem processing paradigm based on multi-level structure, which has attracted extensive attention of domestic and foreign scholars in recent years.
WEI Zongxuan, WANG Jiayang
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Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real-World Data. [PDF]

Adv Intell Discov
This article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Ren Y, Wei GW.
europepmc   +2 more sources

Analogues of the Newton formulas for the block-symmetric polynomials on $\ell_p(\mathbb{C}^s)$

Karpatsʹkì Matematičnì Publìkacìï, 2020
The classical Newton formulas gives recurrent relations between algebraic bases of symmetric polynomials. They are true, of course, for symmetric polynomials on infinite-dimensional Banach sequence spaces.
V.V. Kravtsiv
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A short history of algebraic statistics [PDF]

, 2008
In algebraic statistics, computational techniques from algebraic geometry become tools to address statistical problems. This, in turn, may prompt research in algebraic geometry. The basic ideas at the core of algebraic statistics will be presented. In
Eva Riccomagno, Riccomagno, Eva
core   +1 more source

Integral Cryptanalysis Using Algebraic Transition Matrices

IACR Transactions on Symmetric Cryptology, 2023
In this work we introduce algebraic transition matrices as the basis for a new approach to integral cryptanalysis that unifies monomial trails (Hu et al., Asiacrypt 2020) and parity sets (Boura and Canteaut, Crypto 2016).
Tim Beyne, Michiel Verbauwhede
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