Results 61 to 70 of about 16,850 (158)
, 2020 Galois Theory is a powerful tool to study the roots of polynomials. In this sense, the differential Galois theory is the analogue of Galois theory for linear differential equations. In this thesis, we will construct the notion of a differential field and Picard-Vessiot extension of a linear differential equation as the analogue of a field and the ...
openaire +1 more source
Differential Galois theory of infinite dimension [PDF]
Nagoya Mathematical Journal, 1996 This paper is the second part of our work on differential Galois theory as we promised in [U3]. Differential Galois theory has a long history since Lie tried to apply the idea of Abel and Galois to differential equations in the 19th century (cf. [U3], Introduction). When we consider Galois theory of differential equation, we have to separate the finite
openaire +3 more sources
Galois theory of differential schemes
Added the theory of geometric quotients and several applications and ...
Tomašić, Ivan, Noohi, Behrang
openaire +2 more sources
Galois theory of differential fields of positive characteristic [PDF]
Pacific Journal of Mathematics, 1989 Strongly normal extensions of a differential field \(K\) of positive characteristic are defined. On the set \(G\) of all differential isomorphisms of a strongly normal extension \(N\) of \(K\), a structure of an algebraic group is induced. Correspondences between subgroups of \(G\) and intermediate differential fields of \(N\) and \(K\) are studied ...
openaire +3 more sources
, 2012 We introduce the parameterized generic Galois group of a q-difference module, that is a differential group in the sense of Kolchin. It is associated to the smallest differential tannakian category generated by the q-difference module, equipped with the ...
Di Vizio, Lucia, Hardouin, Charlotte
core +1 more source
$p$-adic differential Galois theory and Galois cohomology
, 2021 [en] The goal of this project has been to give a classification of the forms of Picard-Vessiot extensions defined over a differential field with field of constants $\mathbb{Q}_{p}$, which is not algebraically closed, and with differential Galois group $O\left(2, \mathbb{Q}_{p}\right)$ or $S O\left(2, \mathbb{Q}_{p}\right)$.
openaire +1 more source
Splitting differential equations using Galois theory
Transactions of the American Mathematical SocietyThis article is interested in pullbacks under the logarithmic derivative of algebraic ordinary differential equations. In particular, assuming the solution set of an equation is internal to the constants, we would like to determine when its pullback is itself internal to the constants.
Eagles, Christine, Jimenez, Léo
openaire +2 more sources
Differential galois theory and mechanics
, 2017 This paper is a natural continuation with applications of the recent differential algebraic section of the paper hal-01570516 (arxiv:1707.09763)
openaire +2 more sources
Differential Galois theory and tensor products
Indagationes Mathematicae, 1990 The author gives a short and selfcontained proof of the fundamental theorems of differential Galois theory. The ideas of the paper build upon lecture notes from 1984 by M. van der Put (unpublished), where one also finds proofs of these theorems. The motivation of the paper is that selfcontained proofs are almost impossible to find in the literature ...
openaire +2 more sources
A Novel Cipher-Based Data Encryption with Galois Field Theory. [PDF]
Sensors (Basel), 2023 Hazzazi MM +3 more
europepmc +1 more source