Results 11 to 20 of about 582 (179)
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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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\
Anand Pillay
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A Novel Cipher-Based Data Encryption with Galois Field Theory [PDF]
Sensors, 2023 Both the act of keeping information secret and the research on how to achieve it are included in the broad category of cryptography. When people refer to “information security,” they are referring to the study and use of methods that make data transfers ...
Mohammad Mazyad Hazzazi +3 more
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Noncyclic BCH and Srivastava codes over the subgroup of the groups of units of Galois rings $${G}{R}({{q}}^{{u}},{m})$$ for advanced error control [PDF]
Scientific ReportsThis paper presents a systematic algebraic construction of noncyclic generalizations of BCH and Srivastava codes over Galois rings $$GR\left({q}^{u},m\right).$$ The proposed codes are defined via parity-check matrices whose entries are carefully chosen ...
Muhammad Sajjad +4 more
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DIFFERENTIAL GALOIS THEORY AND INTEGRABILITY [PDF]
International Journal of Geometric Methods in Modern Physics, 2009 This paper is an overview of our works that are related to investigations of the integrability of natural Hamiltonian systems with homogeneous potentials and Newton's equations with homogeneous velocity independent forces. The two types of integrability obstructions for these systems are presented.
Maciejewski, Andrzej J. +1 more
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Galois Theory for Finite Algebras of Operations and Multioperations of Rank 2
Известия Иркутского государственного университета: Серия "Математика", 2019 The construction of Galois theory for the algebras of operations and relations is a popular topic for investigation. It finds numerous applications in both algebra and discrete mathematics – especially for the perfect Galois connection, since if such a ...
N.A. Peryazev
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Generation modulo the action of a permutation group [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 Originally motivated by algebraic invariant theory, we present an algorithm to enumerate integer vectors modulo the action of a permutation group. This problem generalizes the generation of unlabeled graph up to an isomorphism.
Nicolas Borie
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Probabilistic Galois theory [PDF]
Bulletin of the London Mathematical Society, 2012 We show that there are at most $O_{n,ε}(H^{n-2+\sqrt{2}+ε})$ monic integer polynomials of degree $n$ having height at most $H$ and Galois group different from the full symmetric group $S_n$, improving on the previous 1973 world record $O_{n}(H^{n-1/2}\log H)$.
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SERRE WEIGHTS AND WILD RAMIFICATION IN TWO-DIMENSIONAL GALOIS REPRESENTATIONS
Forum of Mathematics, Sigma, 2016 A generalization of Serre’s Conjecture asserts that if $F$ is a totally real field, then certain characteristic
LASSINA DEMBÉLÉ +2 more
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Advanced Engineering Research, 2018 Introduction. Polynomials in several variables over Galois fields provide the basis for the Reed-Muller coding theory, and are also used in a number of cryptographic problems.
V. M. Deundyak, N. S. Mogilevskaya
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