O -posunutiach
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Anton Kotzig (1946)
Časopis pro pěstování matematiky a fysiky
Christine Bachoc, Gabriele Nebe, Boris Venkov (2002)
Acta Arithmetica
Iskander Aliev (2002)
Acta Arithmetica
Gilbert Muraz, Jean-Louis Verger-Gaugry (2005)
Journal de Théorie des Nombres de Bordeaux
The set of point sets of , having the property that their minimal interpoint distance is greater than a given strictly positive constant is shown to be equippable by a metric for which it is a compact topological space and such that the Hausdorff metric on the subset of the finite point sets is compatible with the restriction of this topology to . We show that its subsets of Delone sets of given constants in , are compact. Three (classes of) metrics, whose one of crystallographic nature,...
Kołodziejczyk, Krzysztof (1999)
Beiträge zur Algebra und Geometrie
Frédéric Guérin (1991)
Monatshefte für Mathematik
Johannes Schleischitz (2020)
Communications in Mathematics
Following a suggestion of W.M. Schmidt and L. Summerer, we construct a proper -system with the property . In fact, our method generalizes to provide -systems with , for arbitrary . We visualize our constructions with graphics. We further present explicit examples of numbers that induce the -systems in question.
Sukumar Das Adhikari, Yong-Gao Chen (1999)
Acta Arithmetica
Watanabe, Takao (2000)
Journal of Lie Theory
Maxim Skriganov (1993)
Annales de l'institut Fourier
The phenomenon of anomaly small error terms in the lattice point problem is considered in detail in two dimensions. For irrational polygons the errors are expressed in terms of diophantine properties of the side slopes. As a result, for the -dilatation, , of certain classes of irrational polygons the error terms are bounded as with some , or as with arbitrarily small .
N.M. Korneenko, N.N. Metelskij (1993)
Discrete & computational geometry
J.M. Wills, J. Zaks, M.A. Perles (1982)
Elemente der Mathematik
Arnold Neumaier (1983)
Mathematische Zeitschrift
Masami Fujimori (2003)
Bulletin de la Société Mathématique de France
We show in detail that the category of general Roth systems or the category of semi-stable systems of linear inequalities of slope zero is a neutral Tannakian category. On the way, we present a new proof of the semi-stability of the tensor product of semi-stable systems. The proof is based on a numerical criterion for a system of linear inequalities to be semi-stable.
Smirnov, Yu.A. (2005)
Journal of Mathematical Sciences (New York)
B. Diviš, B. Novák (1974)
Acta Arithmetica
Werner Georg Nowak (1991)
Czechoslovak Mathematical Journal
Volker Kessler (1991)
Journal de théorie des nombres de Bordeaux
I. Bárány, A.M. Vershik (1992)
Geometric and functional analysis
H. Fast, S. Świerczkowski (1958)
Colloquium Mathematicae
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