A new method has been developed for the synthesis of chiral 4-carboxyl oxazolidinones by the catalytic asymmetric aldol reaction of an isocyanatomalonate diester with an aldehyde in the presence of a thiourea catalyst. The resulting chiral 4-carboxyl oxazolidinones are the equivalent of β-hydroxy-α-amino acids bearing a tri- or tetrasubstituted carbon center at their α position. With this in mind, this procedure was successfully applied to the first total synthesis of mycestericin C, which was completed in 12 steps and represents one of the shortest reported sequences for the construction of natural products of this type.
The Boltzmann equation is studied without the cutoff assumption. Under a perturbative setting, a unique global solution of the Cauchy problem of the equation is established in a critical Chemin-Lerner space. In order to analyse the collisional term of the equation, a Chemin-Lerner norm is combined with a non-isotropic norm with respect to a velocity variable, which yields an apriori estimate for an energy estimate. Together with local existence following from commutator estimates and the Hahn-Banach extension theorem, the desired solution is obtained. Also, the non-negativity of the solution is rigorously shown.
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