Zobrazeno 1 - 10
of 112
pro vyhledávání: '"Barkatou, Moulay A."'
Polyhedral affinoid algebras have been introduced by Einsiedler, Kapranov and Lind to connect rigid analytic geometry (analytic geometry over non-archimedean fields) and tropical geometry.In this article, we present a theory of Gr{\"o}bner bases for
Externí odkaz:
http://arxiv.org/abs/2403.13382
We extend Petkov\v{s}ek's algorithm for computing hypergeometric solutions of scalar difference equations to the case of difference systems $\tau(Y) = M Y$, with $M \in {\rm GL}_n(C(x))$, where $\tau$ is the shift operator. Hypergeometric solutions a
Externí odkaz:
http://arxiv.org/abs/2401.08470
We establish a real version of Turrittin's result on polynomial and formal normal forms of linear systems of ODEs with meromorphic coefficients. Both the normal forms or the transformations used have only real coefficients. In order to adapt the proo
Externí odkaz:
http://arxiv.org/abs/2305.08211
Publikováno v:
SIGMA 19 (2023), 016, 29 pages
Darboux developed an ingenious algebraic mechanism to construct infinite chains of ''integrable'' second-order differential equations as well as their solutions. After a surprisingly long time, Darboux's results were rediscovered and applied in many
Externí odkaz:
http://arxiv.org/abs/2101.07470
For linear recurrence systems, the problem of finding rational solutions is reduced to the problem of computing polynomial solutions by computing a content bound or a denominator bound. There are several bounds in the literature. The sharpest bound l
Externí odkaz:
http://arxiv.org/abs/2007.02926
Autor:
El Khessaimi, Yassine, El Hafiane, Youssef, Smith, Agnès, Peyratout, Claire, Tamine, Karim, Adly, Samir, Barkatou, Moulay
Publikováno v:
In Journal of Building Engineering 1 October 2023 76
Publikováno v:
SIGMA 16 (2020), 054, 13 pages
Generalizing the main result of [Aparicio-Monforte A., Compoint E., Weil J.-A., J. Pure Appl. Algebra 217 (2013), 1504-1516], we prove that a linear differential system is in reduced form in the sense of Kolchin and Kovacic if and only if any differe
Externí odkaz:
http://arxiv.org/abs/1912.10567
Autor:
Barkatou, Moulay A., Gontsov, Renat R.
Publikováno v:
SIGMA 15 (2019), 058, 15 pages
We study the problem of solvability of linear differential systems with small coefficients in the Liouvillian sense (or, by generalized quadratures). For a general system, this problem is equivalent to that of solvability of the Lie algebra of the di
Externí odkaz:
http://arxiv.org/abs/1901.09951
It is well known that for a first order system of linear difference equations with rational function coefficients, a solution that is holomorphic in some left half plane can be analytically continued to a meromorphic solution in the whole complex pla
Externí odkaz:
http://arxiv.org/abs/1802.01150