Results 11 to 20 of about 2,240,617 (314)
Algebraic extensions in free groups [PDF]
, 2006 The aim of this paper is to unify the points of view of three recent and independent papers (Ventura 1997, Margolis, Sapir and Weil 2001 and Kapovich and Miasnikov 2002), where similar modern versions of a 1951 theorem of Takahasi were given.
Miasnikov, Alexei +2 more
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Algebraic extensions of Gaudin models [PDF]
, 2004 We perform a In\"on\"u--Wigner contraction on Gaudin models, showing how the integrability property is preserved by this algebraic procedure. Starting from Gaudin models we obtain new integrable chains, that we call Lagrange chains, associated to the ...
Musso, Fabio +2 more
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Analytic gradients in variational quantum algorithms: Algebraic extensions of the parameter-shift rule to general unitary transformations [PDF]
Physical Review A, 2021 Optimization of unitary transformations in Variational Quantum Algorithms benefits highly from efficient evaluation of cost function gradients with respect to amplitudes of unitary generators. We propose several extensions of the parametric-shift-rule to
A. Izmaylov +2 more
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On the implicit constant fields and key polynomials for valuation algebraic extensions [PDF]
Journal of Commutative Algebra, 2021 This article is a natural continuation of our previous works [7] and [6]. In this article, we employ similar ideas as in [4] to provide an estimate of IC(K(X)|K, v) when (K(X)|K, v) is a valuation algebraic extension. Our central result is an analogue of
Arpan Dutta
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Algebraic extensions of commutative Banach algebras [PDF]
Pacific Journal of Mathematics, 1964 J. A. Lindberg
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First-order decidability and definability of integers in infinite algebraic extensions of the rational numbers [PDF]
Israel Journal of Mathematics, 2013 We extend results of Videla and Fukuzaki to define algebraic integers in large classes of infinite algebraic extensions of Q and use these definitions for some of the fields to show the first-order undecidabilitv.
Alexandra Shlapentokh
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Stallings graphs, algebraic extensions and primitive elements in F2 [PDF]
Mathematical Proceedings of the Cambridge Philosophical Society, 2012 We study the free group of rank two from the point of view of Stallings core graphs. The first half of the paper examines primitive elements in this group, giving new and self-contained proofs for various known results about them.
Ori Parzanchevski, Doron Puder
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An extension for feature algebra [PDF]
Proceedings of the First International Workshop on Feature-Oriented Software Development, 2009 Feature, algebra was introduced as an abstract framework for feature oriented software development. One goal is to provide a common, clearly defined basis for the key ideas of feature orientation. We first present concrete models for the original axioms of feature algebra which represent the main features of feature oriented programs.
Höfner, Peter +1 more
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Onto extensions of free groups [PDF]
Groups, Complexity, Cryptology, 2021 An extension of subgroups $H\leqslant K\leqslant F_A$ of the free group of rank $|A|=r\geqslant 2$ is called onto when, for every ambient free basis $A'$, the Stallings graph $\Gamma_{A'}(K)$ is a quotient of $\Gamma_{A'}(H)$.
Sebastià Mijares, Enric Ventura
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Extension of Algebraic Theories [PDF]
Proceedings of the American Mathematical Society, 1972 The algebraic theories of Lawvere are extended in a natural way to small complete categories. These categories exhibit not only the operations and identities, but some of the homomorphisms, functions, objects and constructions which are encountered when working within the algebraic categories associated with the theories.
Peake, E. J., Peters, G. R.
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