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Cubical polyhedra and homotopy, III

Jósef BlassWłodzimierz Holsztyński — 1972

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

In questa Nota, che fa seguito ad altre due apparse con lo stesso titolo in questi Rendiconti [1], vengono discusse proprietà combinatorie di poliedri cubici, mostrando fra 1altro che ogni poliedro simpliciale risulta omeomorfo ad un poliedro cubico.

Linear forms in the logarithms of three positive rational numbers

Curtis D. BennettJosef BlassA. M. W. GlassDavid B. MeronkRay P. Steiner — 1997

Journal de théorie des nombres de Bordeaux

In this paper we prove a lower bound for the linear dependence of three positive rational numbers under certain weak linear independence conditions on the coefficients of the linear forms. Let Λ = b 2 log α 2 - b 1 log α 1 - b 3 log α 3 0 with b 1 , b 2 , b 3 positive integers and α 1 , α 2 , α 3 positive multiplicatively independent rational numbers greater than 1 . Let α j 1 = α j 1 / α j 2 with α j 1 , α j 2 coprime positive integers ( j = 1 , 2 , 3 ) . Let α j max { α j 1 , e } and assume that gcd ( b 1 , b 2 , b 3 ) = 1 . Let b ' = b 2 log α 1 + b 1 log α 2 b 2 log α 3 + b 3 log α 2 and assume that B max { 10 , log b ' } . We prove that either { b 1 , b 2 , b 3 } is c 4 , B -linearly dependent over (with respect to a 1 , a 2 , a 3 ) or ...

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