Primeness of the enveloping algebra of a Cartan type Lie superalgebra

We show that a primeness criterion for enveloping algebras of Lie superalgebras discovered by Bell is applicable to the Cartan type Lie superalgebras , even. Other algebras are considered but there are no definitive answers in these cases.

     

The coefficients of the Laurent series expansions of real analytic functions

Letf be a real analytic function of a real variable such that 0 is an isolated (possibly essential) singularity off. In the existing literature the coefficients of the Laurent series expansion off around 0 are obtained by applying Cauchy's integral formula to the analytic continuation off on the complex plane. Here by means of a conformal mapping we derive a formula which determines the Laurent coefficients off solely in terms of the values off and the derivatives off at a real point of analyticity off. Using a more complicated mapping, we similarly determine the coefficients of the Laurent expansion off around 0 where now 0 is a singularity off which is not necessarily isolated.     

New solid state NMR techniques in coal analysis

Nuclear magnetic resonance (NMR) spectroscopy has become a valuable technique for the determination of the aromaticity of fossil fuels. Now, by exploiting ¹³C relaxation, intimate details of the structure of coal may be determined. This article briefly describes these new applications.     

Proton-ionizable crown compounds. 4. New macrocyclic polyether ligands containing a triazole subcyclic unit

A series of macrocyclic polyether (crown) ligands containing the proton-ionizable s-triazole subcyclic unit were prepared by reacting the 1-THP blocked 3,5-bis(chloromethyl)-1H-1,2,4-triazole with various oligoethylene glycols. The starting bis(chloromethyl)triazole is a vessicant and must be used with caution. Triazolo-18-crown-6 ( 5 ) formed stable complexes with barium, strontium, copper and benzylammonium cations but not with potassium or lithium. The crystal structure of 5 showed the triazole proton to be on nitrogen 3 which is outside the macroring cavity.