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Best simultaneous diophantine approximations of some cubic algebraic numbers

Nicolas Chevallier (2002)

Journal de théorie des nombres de Bordeaux

Let α be a real algebraic number of degree 3 over whose conjugates are not real. There exists an unit ζ of the ring of integer of K = ( α ) for which it is possible to describe the set of all best approximation vectors of θ = ( ζ , ζ 2 ) .’

Binary and ternary relations

Vítězslav Novák, Miroslav Novotný (1992)

Mathematica Bohemica

Two operators are constructed which make it possible to transform ternary relations into binary relations defined on binary relations and vice versa. A possible graphical representation of ternary relations is described.

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