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  • Articles  (340)
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  • 11
    Publication Date: 2018-03-06
    Description: We study local piecewise conjugacy of the quantized dynamics arising from factorial languages. We show that it induces a bijection between allowable words of same length and thus it preserves entropy. In the case of sofic factorial languages we prove that local piecewise conjugacy translates to unlabeled graph isomorphism of the follower set graphs. Moreover, it induces an unlabeled graph isomorphism between the Fischer covers of irreducible subshifts. We verify that local piecewise conjugacy does not preserve finite type nor irreducibility; but it preserves soficity. Moreover, it implies identification (up to a permutation) for factorial languages of type 1 if, and only if, the follower set function is one-to-one on the symbol set.
    Print ISSN: 0033-5606
    Electronic ISSN: 1464-3847
    Topics: Mathematics
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  • 12
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    Oxford University Press
    Publication Date: 2018-03-06
    Description: Let λ be a large enough cardinal number (assuming the Generalized Continuum Hypothesis it suffices to let λ=ℵω). If X is a Banach space with dens(X)≥λ, which admits a coarse (or uniform) embedding into any c0(Γ), then X fails to have non-trivial cotype, i.e. X contains ℓ∞n C -uniformly for every C〉1. In the special case when X has a symmetric basis, we may even conclude that it is linearly isomorphic with c0(densX).
    Print ISSN: 0033-5606
    Electronic ISSN: 1464-3847
    Topics: Mathematics
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  • 13
    Publication Date: 2018-03-06
    Description: We prove a normal form result for the groupoid of germs generated by PSL(2,ℂ) and the exponential map. We discuss three consequences of this result: (1) a generalization of a result of Cohen about the group of translations and powers, which gives a positive answer to a problem posed by Higman; (2) as proof that the subgroup of Homeo(ℝ,+∞) generated by the positive affine maps and the exponential map is isomorphic to an HNN-extension; (3) a finitary version of the immiscibility conjecture of Ecalle–Martinet–Moussu–Ramis.
    Print ISSN: 0033-5606
    Electronic ISSN: 1464-3847
    Topics: Mathematics
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  • 14
    Publication Date: 2016-12-01
    Description: The finite Steinhaus problem asks whether every finite set AR2 with |A|=n 〉 1 there cannot exist a set SR2 such that |(A)S|=1 for every isometric copy (A) of A . It is easy to see that it holds for n=2,3 and a recent theorem of Xuan (extending results of Miller–Weiss and Gao) shows the result for n = 4. We make some connections between this problem and certain algebraic concepts, and show the result for n=5,7 .
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    Electronic ISSN: 1464-3847
    Topics: Mathematics
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  • 15
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    Oxford University Press
    Publication Date: 2016-12-01
    Description: We describe how to represent Rosen continued fractions by paths in a class of graphs that arise naturally in hyperbolic geometry. This representation gives insight into Rosen's original work about words in Hecke groups, and it also helps us to identify Rosen continued fraction expansions of shortest length.
    Print ISSN: 0033-5606
    Electronic ISSN: 1464-3847
    Topics: Mathematics
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  • 16
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    Oxford University Press
    Publication Date: 2016-12-01
    Description: A Lie algebra L over a field F is said to be finitary if it is isomorphic to a subalgebra of the Lie algebra of finite rank linear transformations of a vector space over F . A non-zero element aL is said to be extremal if ada2L=Fa By using Baranov's classification, it is not difficult to verify that any simple finitary Lie algebra over an algebraically closed field of characteristic 0 is spanned by extremal elements. In this note, we provide a classification-free proof of this result by using Jordan theory instead of representation theory.
    Print ISSN: 0033-5606
    Electronic ISSN: 1464-3847
    Topics: Mathematics
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  • 17
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    Oxford University Press
    Publication Date: 2016-12-01
    Description: We prove that the quartic 3-folds defined by i=05xi=i=05xi4–t(i=05xi2)2=0 in P5 are rational for t=16 and t=710 .
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    Electronic ISSN: 1464-3847
    Topics: Mathematics
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  • 18
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    Oxford University Press
    Publication Date: 2016-12-01
    Description: We establish the equality of two definitions of a Euler class in algebraic geometry: the first definition is as a ‘characteristic class’ with values in Chow–Witt theory, while the second definition is as an ‘obstruction class.’ Along the way, we refine Morel's relative Hurewicz theorem in A1 -homotopy theory, and show how to define (twisted) Chow–Witt groups for geometric classifying spaces.
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    Electronic ISSN: 1464-3847
    Topics: Mathematics
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  • 19
    Publication Date: 2016-12-01
    Description: In 1951, Pólya and Szegö expressed a lower bound for the torsional rigidity of a convex plane domain in terms of the area and inradius of the domain. On the other hand, in 1995 Avkhadiev showed that the torsional rigidity and the Euclidean moment of inertia are comparable quantities for simply connected domains. In this paper, for the p -order Euclidean moments of a convex plane domain, we prove inequalities similar to that of Pólya and Szegö. These geometrical inequalities allow us to obtain upper bounds for the torsional rigidity of a convex plane domain in terms of the p -order Euclidean moment of the domain.
    Print ISSN: 0033-5606
    Electronic ISSN: 1464-3847
    Topics: Mathematics
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  • 20
    Publication Date: 2016-12-01
    Description: We explore new implications of the M(r,s) and M*(r,s) properties for Banach spaces. We show that a Banach space X satisfying property M(1,s) for some 0 〈 s≤1 , admitting a point x 0 in its unit sphere at which the relative weak and norm topologies agree, satisfies the generalized Gossez–Lami Dozo property. We establish sufficient conditions, in terms of the (r,s) -Lipschitz weak * Kadec-Klee property on a Banach space X , to guarantee that its dual space satisfies the uniform Kadec-Klee property in the weak * topology. We determine appropriate conditions to assure that a Banach space X satisfies the (r,s) -Lipschitz weak * KKP. These results are applied to prove that every spin factor satisfies the UKK property, and consequently, the KKP and the UKK property are equivalent for real and complex JB * -triples.
    Print ISSN: 0033-5606
    Electronic ISSN: 1464-3847
    Topics: Mathematics
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