An Efficient Route to New 1,2,4,3-Triazaphosphole-3-Oxide Derivatives

The condensation of hexamethylphosphorotriamide and bis-(dimethylamino) methylphosphonate with amidrazones 1 constitutes a new route to the synthesis of 1,2,4,3-triazaphosphole-3-oxide derivatives 3. Structures of all the synthesized compounds have been established by NMR (¹H, ¹³C, ³¹P) and IR spectroscopy, as well as by elemental analysis and MS spectral data for some products.     

One-Pot Synthesis of Asymmetrically Difunctionalized Oligomaltosides by Cyclodextrin Ring Opening

The synthesis of pure difunctionalized hexa-, hepta- and octamaltosides was performed by one-pot chemical reaction from perbenzoylated cyclodextrin. Oligomaltosides with azide, propargyl or allyl on reducing end and an unprotected hydroxyl group on non-reducing end were obtained from perbenzoylated α-, β- and γ-cyclodextrin with 12 to 48 % yields.     

Carleman inequalities for the heat equation in singular domains

We consider the Cauchy problem associated to the heat equation firstly in a plane domain with a reentrant corner, then in a cracked domain. By constructing a weight function, we show a result of null controllability using Carleman estimates.