Stereoselective synthesis of new spirobenzodihydropyrancyclohexanes

A stereoselective synthesis of unknown spirobenzodihydropyrancyclohexanes is described starting from arylcyclohexenes alkylated and cyclized via a coumarin intermediate and leading to new amino derivatives which are rigid analogs of dopamine.     

Analyse de complexité pour un théorème de Hall sur les fractions continues

We give a polynomial time controlled version of a theorem of M. Hall: every real number can be written as the sum of two irrational numbers whose developments into a continued fraction contain only 1, 2, 3 or 4. Mathematics Subject Classification: 03D15, 03F60, 11A55, 68Q25.     

Hermite and Smith normal form algorithms over Dedekind domains

We show how the usual algorithms valid over Euclidean domains, such as the Hermite Normal Form, the modular Hermite Normal Form and the Smith Normal Form can be extended to Dedekind rings. In a sequel to this paper, we will explain the use of these algorithms for computing in relative extensions of number fields.

     

Hamiltonian Stationary Lagrangian Surfaces in Euclidean Four-Space and Related Minimization Problems. Part II: Some Minimization Results

We study some minimization problems for Hamiltonian stationaryLagrangian surfaces in R⁴. We show that the flat Lagrangian torusS ¹ × S ¹ minimizes the Willmore functional among Hamiltonianstationary tori of its isotopy class, which gives a new proof of thefact that it is area minimizing in the same class. Considering theLagrangian flat cylinder as a torus in some quotient space R⁴/v Z, we show that it is also area minimizing in its isotopy class.