Results 21 to 30 of about 554 (70)

A Reduction Method for Higher Order Variational Equations of Hamiltonian Systems [PDF]

, 2011
Let $\mathbf{k}$ be a differential field and let $[A]\,:\,Y'=A\,Y$ be a linear differential system where $A\in\mathrm{Mat}(n\,,\,\mathbf{k})$. We say that $A$ is in a reduced form if $A\in\mathfrak{g}(\bar{\mathbf{k}})$ where $\mathfrak{g}$ is the Lie ...
Aparicio, Ainhoa, Weil, Jacques-Arthur
core   +2 more sources

Computing abelian subalgebras for linear algebras of upper-triangular matrices from an algorithmic perspective

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2016
In this paper, the maximal abelian dimension is algorithmically and computationally studied for the Lie algebra hn, of n×n upper-triangular matrices. More concretely, we define an algorithm to compute abelian subalgebras of hn besides programming its ...
Ceballos Manuel, Núñez Juan, Tenorio Ángel F.   +2 more
doaj   +1 more source

A generalization of Kruskal–Katona’s theorem

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2020
Let K be a field, E the exterior algebra of a finite dimensional K-vector space, and F a finitely generated graded free E-module with homogeneous basis g1, . . ., gr such that deg g1 ≤ deg g2 ≤ · · · ≤ deg gr.
Amata Luca, Crupi Marilena
doaj   +1 more source

Symbolic computation of optimal systems of subalgebras of three- and four-dimensional real Lie algebras [PDF]

Open Communications in Nonlinear Mathematical Physics
The complete optimal systems of subalgebras of all nonisomorphic three- and four-dimensional real Lie algebras are analyzed by the program \symbolie running in the computer algebra system \emph{Wolfram Mathematica}\texttrademark.
Luca Amata, Francesco Oliveri, Emanuele Sgroi   +2 more
doaj   +1 more source

Cryptanalysis of matrix conjugation schemes

Journal of Mathematical Cryptology, 2014
In this paper we cryptanalyze two protocols: the Grigoriev–Shpilrain authentication protocol and a public key cryptosystem due to Wang, Wang, Cao, Okamoto and Shao.
Myasnikov Alex D., Ushakov Alexander
doaj   +1 more source

An extension of Turán's inequality

, 2015
Let pm(x) = P (λ) m (x)/P (λ) m (1) be the m -th ultraspherical polynomial normalized by pm(1) = 1 . We prove the inequality |x|pn(x)− pn−1(x)pn+1(x) 0 , x ∈ [−1,1] , for −1/2 < λ 1/2 .
G. Nikolov, V. Pillwein
semanticscholar   +1 more source

Solving Schubert Problems with Littlewood-Richardson Homotopies

, 2010
We present a new numerical homotopy continuation algorithm for finding all solutions to Schubert problems on Grassmannians. This Littlewood-Richardson homotopy is based on Vakil's geometric proof of the Littlewood-Richardson rule. Its start solutions are
Sottile, Frank, Vakil, Ravi, Verschelde, Jan   +2 more
core   +2 more sources

Analysis of a key exchange protocol based on tropical matrix algebra

Journal of Mathematical Cryptology, 2018
In this paper, we consider a two party key-exchange protocol proposed in [D. Grigoriev and V. Shpilrain, Tropical cryptography, Comm. Algebra 43 (2014), 2624–2632, Section 2], which uses tropical matrix algebra as the platform.
Kotov Matvei, Ushakov Alexander
doaj   +1 more source

A Constructive Characterization of Solvable Polynomial Algebras [PDF]

, 2013
For the solvable polynomial algebras introduced and studied by Kandri-Rody and Weispfenning [J. Symbolic Comput., 9(1990)], a constructive characterization is given in terms of Gr\"obner bases for ideals of free algebras, thereby solvable polynomial ...
Li, Huishi
core  

Isomorphism and isotopism classes of filiform Lie algebras of dimension up to seven

, 2015
Since the introduction of the concept of isotopism of algebras by Albert in 1942, a prolific literature on the subject has been developed for distinct types of algebras.
Falcón, O. J., Falcón, R. M., Núñez, J.   +2 more
core   +1 more source