Results 21 to 30 of about 154,581 (190)
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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Nonintegrability of the Axisymmetric Bianchi IX Cosmological Model via Differential Galois Theory [PDF]
SIAM Journal on Applied Dynamical Systems, 2021 We investigate the integrability of an anisotropic universe with matter and cosmological constant formulated as Bianchi IX models. The presence of the cosmological constant causes the existence of a critical point in the finite part of the phase space ...
P. Acosta-Hum'anez +2 more
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Darboux Transformations for Orthogonal Differential Systems and Differential Galois Theory [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2021 Darboux developed an ingenious algebraic mechanism to construct infinite chains of ''integrable'' second-order differential equations as well as their solutions.
P. Acosta-Humánez +3 more
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Differential Galois theory III: Some inverse problems [PDF]
Illinois Journal of Mathematics, 1997 [For Part I see ibid. 42, No. 4, 678-699 (1998; Zbl 0916.03028). Part II is reviewed above.] In Part I, the author developed a theory of differential Galois extensions, generalizing Kolchin's theory of strongly normal extensions. It was shown that arbitrary finite-dimensional differential algebraic groups can arise as differential Galois groups for ...
David Marker, Anand Pillay
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Galois theory of differential schemes [PDF]
Added the theory of geometric quotients and several applications and ...
Ivan Tomašić, Behrang Noohi
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IEEE Access, 2022 Since its birth in 2000, authenticated encryption (AE) has been a hot research topic, and many new features have been proposed to boost its security or performance.
Mohamud Ahmed Jimale +6 more
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Algebraic D-groups and differential Galois theory [PDF]
Pacific Journal of Mathematics, 2004 The author gives another exposition of his new differential Galois theory. As he thinks, a previous presentation [Ill. J. Math. 42, No. 4, 678--699 (1998; Zbl 0916.03028)] was too model-theoretic and so somewhat obscure to differential algebraists. This new representation is based on some generalization of \(G\)-primitive extensions of \textit{E.
A. Pillay
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Non-integrability on AdS3 supergravity backgrounds
Journal of High Energy Physics, 2020 We investigate classical integrability on two recently discovered classes of back- grounds in massive IIA supergravity. These vacua are of the form AdS3 × S2 × ℝ × CY2, they preserve small N $$ \mathcal{N} $$ = (0, 4) supersymmetry and are associated ...
Kostas Filippas
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Galois theory of aigebraic and differential equations [PDF]
Nagoya Mathematical Journal, 1996 This paper will be the first part of our works on differential Galois theory which we plan to write. Our goal is to establish a Galois Theory of ordinary differential equations. The theory isinfinite dimensionalby nature and has a long history. The pioneer of this field is S. Lie who tried to apply the idea of Abel and Galois to differential equations.
Hiroshi Umemura
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A new discretization of the Euler equation via the finite operator theory [PDF]
Open Communications in Nonlinear Mathematical PhysicsWe propose a novel discretization procedure for the classical Euler equation, based on the theory of Galois differential algebras and the finite operator calculus developed by G.C. Rota and collaborators.
Miguel A. Rodríguez +1 more
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