Results 31 to 40 of about 51,885 (183)
Advances in Mathematics, 2016 We introduce an abstract topos-theoretic framework for building Galois-type theories in a variety of different mathematical contexts; such theories are obtained from representations of certain atomic two-valued toposes as toposes of continuous actions of a topological group.
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From Galois to Hopf Galois: theory and practice
, 2014 Hopf Galois theory expands the classical Galois theory by considering the Galois property in terms of the action of the group algebra k[G] on K/k and then replacing it by the action of a Hopf algebra.
Crespo, Teresa +2 more
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Comptes Rendus. MathématiqueLet $L/K$ be a cyclic extension of degree $n = 2m$. It is known that the space $\mathrm{Alt}_K(L)$ of alternating $K$-bilinear forms (skew-forms) on $L$ decomposes into a direct sum of $K$-subspaces $A^{\sigma ^i}$ indexed by the elements of $\mathrm{Gal}
Gupta, Ashish, Mandal, Sugata
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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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Advances in Mathematics, 2003 In Proposition I of "Memoire sur les conditions de resolubilite des equations par radicaux", Galois established that any intermediate extension of the splitting field of a polynomial with rational coefficients is the fixed field of its galois group. We first state and prove the (dual) categorical interpretation of of this statement, which is a theorem ...
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Finding Minimum‐Cost Explanations for Predictions Made by Tree Ensembles
Software: Practice and Experience, EarlyView.ABSTRACT The ability to reliably explain why a machine learning model arrives at a particular prediction is crucial when used as decision support by human operators of critical systems. The provided explanations must be provably correct, and preferably without redundant information, called minimal explanations.
John Törnblom +2 more
wiley +1 more source
Annals of Pure and Applied Logic, 1997 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\
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A Vulnerability Lens for Intuitive‐Logic Scenarios
FUTURES &FORESIGHT SCIENCE, Volume 8, Issue 1, April 2026.ABSTRACT Exploration of possibilities by means of intuitive logic is hampered by a large number of scenarios, which easily exceed the limits imposed by human bounded rationality. While many practitioners constrain their scenarios within a 2 × 2 $2\times 2$ matrix by design, more structured approaches point to rationales such as eliminating ...
Guido Fioretti
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Construction of q-ary(n,M,d)-codes in PG(2,16)
Wasit Journal for Pure Sciences, 2023 The goal of this paper was to study the applications of the projective plane PG (2, q) over a Galois field of order q in the projective q-ary (n, M, d) -code such that the parameters length of code n, the maximum value size code M, and the minimum ...
Dunya Fareeq Fendi +1 more
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Reduced group schemes as iterative differential Galois groups
, 2019 This article is on the inverse Galois problem in Galois theory of linear iterative differential equations in positive characteristic. We show that it has an affirmative answer for reduced algebraic group schemes over any iterative differential field ...
Maurischat, Andreas
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