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An algebraic model for the relation between a certain classical particle system and the quantum environment is proposed. The quantum environment is described by the category of possible quantum states. The initial particle system is represented by an associative algebra in the category of states. The key new observation is that particle interactions with the quantum environment can be described in terms of Hopf-Galois theory. This opens up a possibility to use quantum groups in our model of particle...

Quartic exercises.

Knus, Max-Albert, Tignol, Jean-Pierre (2003)

International Journal of Mathematics and Mathematical Sciences

Quasi-additive functions.

J. Tabor (1990)

Aequationes mathematicae

Quasi-Fibonacci numbers of order 11.

Wituła, Roman, Słota, Damian (2007)

Journal of Integer Sequences [electronic only]

Quasilineary Properties of Differentiable Functions in a Field with a Non-Archimedean Valuation.

Ruben Schramm (1974)

Mathematische Zeitschrift

Quasi-permutation polynomials

Vichian Laohakosol, Suphawan Janphaisaeng (2010)

Czechoslovak Mathematical Journal

A quasi-permutation polynomial is a polynomial which is a bijection from one subset of a finite field onto another with the same number of elements. This is a natural generalization of the familiar permutation polynomials. Basic properties of quasi-permutation polynomials are derived. General criteria for a quasi-permutation polynomial extending the well-known Hermite's criterion for permutation polynomials as well as a number of other criteria depending on the permuted domain and range are established....

Quaternion Extensions of Order 16

Michailov, Ivo (2005)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 12F12We describe several types of Galois extensions having as Galois group the quaternion group Q16 of order 16.This work is partially supported by project of Shumen University.

Quaternion extensions with restricted ramification

Peter Schmid (2014)

Acta Arithmetica

In any normal number field having Q₈, the quaternion group of order 8, as Galois group over the rationals, at least two finite primes must ramify. The classical example by Dedekind of such a field is extraordinary in that it is totally real and only the primes 2 and 3 are ramified. In this note we describe in detail all Q₈-fields over the rationals where only two (finite) primes are ramified. We also show that, for any integer n>3 and any prime $p \equiv 1 (m o d 2^{n - 1})$ , there exist unique real and complex normal number...

Quelques généralisations du 17e problème de Hilbert.

Danielle GONDARD (1973/1974)

Seminaire de Théorie des Nombres de Bordeaux

Quelques propriétés d’approximation reliées à la cohomologie galoisienne d’un groupe algébrique fini

David Harari (2007)

Bulletin de la Société Mathématique de France

On étudie différentes propriétés d’approximation pour des espaces homogènes $X$ (à stabilisateur fini) de ${GL}_{n}$ sur un corps de nombres. On discute également du lien avec le problème de Galois inverse et on établit une formule pour le groupe de Brauer non ramifié de $X$ .

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