Schatten properties,nuclearity and minimality of phase shift invariant spaces

We extend Feichtinger's minimality property on the smallest non-trivial time-frequency shift invariant Banach space, to the quasi-Banach case. Analogous properties are deduced for certain matrix spaces.We use these results to prove that the pseudo-differential operator $\mathrm{Op}(a)$ is a Schatten-q operator from $M^{\infty }$ to $M^p$ and r-nuclear operator from $M^{\infty }$ to $M^r$ when $a\in M^r$ for suitable p, q and r in $(0,\infty ]$.     

α-Diphenylphosphino-N-(pyrazin-2-yl)glycine as a ligand in Ni-catalyzed ethylene oligomerization

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The Reactivity of Hexafluorothioacetone and Hexafluoroacetone versus Phosphites

Abstract

The dimer of hexafluorothioacetone reacted with various phosphites to form thiophosphates and bis(trifluoromethyl)methylenphosphoranes, being unstable in the case of (Me₃SiO) P(OMe)_3-n, (n=1?3), where phosphonates (Me₃SiO)_n-1(MeO)_3-nP(O)[C(CF₃)=CF₂] (n=1-3) and Me₃SiF were observed. In general, cyclic phosphites behaved similar to acyclic ones. The resulting bis(trifluoromethyl)methylenphosphoranes were thermally stable except compound A, because of a new intramolecular fluorine transfer to phosphorus forming fluorophosphorane B.     

[1,3]-CARBANIONISCHE UMLAGERUNGEN—SYNTHESE VON 1,3-BENZOXASILOLENEN

Abstract

2-Bromoaryloxy-chloromethyldiorganosilanes react with sodium in a one-pot-reaction via metallation, [1,3]-carbanionic rearrangement and cyclization to give diorgano-1,3-benzoxasilolenes. The title compounds have been characterized by n.m.r. spectroscopic data and an alternative independent synthesis.