Results 1 to 10 of about 16,934 (193)
A density theorem for parameterized differential Galois theory [PDF]
Pacific Journal of Mathematics, 2014 We study parameterized linear differential equations with coefficients depending meromorphically upon the parameters. As a main result, analogously to the unparameterized density theorem of Ramis, we show that the parameterized monodromy, the ...
Dreyfus, Thomas
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LARGE FIELDS IN DIFFERENTIAL GALOIS THEORY [PDF]
Journal of the Institute of Mathematics of Jussieu, 2020 AbstractWe solve the inverse differential Galois problem over differential fields with a large field of constants of infinite transcendence degree over $\mathbb{Q}$. More generally, we show that over such a field, every split differential embedding problem can be solved.
Annette Bachmayr +3 more
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Differential Galois Theory and Lie Symmetries [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2015 We study the interplay between the differential Galois group and the Lie algebra of infinitesimal symmetries of systems of linear differential equations. We show that some symmetries can be seen as solutions of a hierarchy of linear differential systems.
David Blázquez-Sanz +5 more
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Jacobian Conjecture via Differential Galois Theory [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2019 We prove that a polynomial map is invertible if and only if some associated differential ring homomorphism is bijective. To this end, we use a theorem of Crespo and Hajto linking the invertibility of polynomial maps with Picard-Vessiot extensions of partial differential fields, the theory of strongly normal extensions as presented by Kovacic and the ...
Elżbieta Adamus +3 more
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Differential Galois Theory and Hopf Algebras for Lie Pseudogroups [PDF]
AxiomsAccording to a clever but rarely quoted or acknowledged work of E. Vessiot that won the prize of the Académie des Sciences in 1904, “Differential Galois Theory” (DGT) has mainly to do with the study of “Principal Homogeneous Spaces” (PHSs) for finite ...
Jean-Francois Pommaret
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Differential Galois Theory and Integration [PDF]
, 2021 In this paper, we present methods to simplify reducible linear differential systems before solving. Classical integrals appear naturally as solutions of such systems. We will illustrate the methods developed in a previous paper on several examples to reduce the differential system.
Thomas Dreyfus, Jacques-Arthur Weil
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RGB image encryption using SPN with a novel block cipher over simple graph adjacency matrices and Galois fields [PDF]
Scientific ReportsThis paper presents a construction of a secure image encryption scheme with graph theory, Galois field, and substitution-permutation network (SPN) for enhanced multimedia data security.
Muhammad Sajjad, Nawaf A. Alqwaifly
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Generalized differential Galois theory [PDF]
Transactions of the American Mathematical Society, 2008 71 pages, part of author's Phd ...
Peter Landesman
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Differential Galois Theory of Linear Difference Equations [PDF]
Mathematische Annalen, 2008 We present a Galois theory of difference equations designed to measure the differential dependencies among solutions of linear difference equations.
Hardouin, Charlotte, Singer, Michael F.
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Differential Galois theory I [PDF]
Annals of Pure and Applied Logic, 1998 This paper proposes a generalization of Kolchin's Galois theory of differential fields. In the Kolchin theory, the Galois groups correspond to algebraic groups over the subfield of constants; moreover every algebraic group can arise in this way. In this paper, the constants are replaced by an arbitrary differential algebraic set \(X\). Accordingly, \(X\
Anand Pillay
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