Results 1 to 10 of about 174,264 (177)
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 and Hopf Algebras for Lie Pseudogroups
Axioms, 2023 According 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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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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Generalized Lennard-Jones Potentials, SUSYQM and Differential Galois Theory [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2018 In this paper we start with proving that the Schr\"odinger equation (SE) with the classical $12-6$ Lennard-Jones (L-J) potential is nonintegrable in the sense of the differential Galois theory (DGT), for any value of energy; i.e., there are no solutions ...
Acosta-Humánez, Manuel F. +2 more
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Differential Galois Theory and Isomonodromic Deformations [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2019 We present a geometric setting for the differential Galois theory of $G$-invariant connections with parameters. As an application of some classical results on differential algebraic groups and Lie algebra bundles, we see that the Galois group of a connection with parameters with simple structural group $G$ is determined by its isomonodromic ...
Blázquez-Sanz, David +2 more
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Differential Galois Theory and Integration [PDF]
Texts & Monographs in Symbolic Computation, 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.
Dreyfus, Thomas, Weil, Jacques-Arthur
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Integrability of Stochastic Birth-Death processes via Differential Galois Theory [PDF]
Mathematical Modelling of Natural Phenomena, 2019 Stochastic birth-death processes are described as continuous-time Markov processes in models of population dynamics. A system of infinite, coupled ordinary differential equations (the so-called master equation) describes the time-dependence of the ...
Acosta-Humanez, Primitivo B. +2 more
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Rational KdV Potentials and Differential Galois Theory [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2019 In this work, using differential Galois theory, we study the spectral problem of the one-dimensional Schr dinger equation for rational time dependent KdV potentials. In particular, we compute the fundamental matrices of the linear systems associated to the Schr dinger equation.
Jiménez, S. +3 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 ...
Adamus, Elżbieta +2 more
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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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