Operatorenkalkül über freien Monoiden II: Binomialsysteme

In this part starting from a generalization of the binomial theorem a development of Rota's theory of polynomial sequences of binomial type to the case of countably many noncommuting variables is given. Translation invariance of operators gives the relation to the formal power series considered inI. For a special class of binomial systems there are given a number of characterizations, such as a generalized Rodrigues formula. In the case of an analogue of the Newton polynomials those are used for a study of generalized Stirling numbers. (In III the theory of binomial systems of diagonal type will be continued until an analogue of Lagrange inversion and a short development of the theory of generalized Sheffer polynomials will be given.)     

Supernovae and the nuclear equation of state at high densities

An extensive study of the shock-explosive mechanism for generating type II supernovae is made. The nuclear high-density equation of state plays an important role, moderate softening of the equation of state leading to a considerable increase in shock strength. A definition of shock energy which can be used throughout the life of the shock is introduced.     

Acetobacter cellulosic biofilms search for new modulators of cellulogenesis and native membrane treatments

Since natural substances like pseudoxanthins exert a positive effect on the cellulogenic ability ofAcetobacter xylinum when producing cellulosic pellicles suitable for skin burn therapy, new defined and complex modulators were sought. Ca²⁺ and Mg²⁺ (4 mM) were strongly stimulatory. Na⁺ had no effect and K⁺ was inhibitory. Ammonium dihydrogen phosphate (0.12 g/L) ensured the same nitrogen supply as the same concentration of yeast extract as measured by cellomembrane dry wt./yield albeit higher yeast extract supplies produced thicker membranes. Corn steep liquor (CSL) was also progressively beneficial from 0.125 to 0.5 mL/L, and this yield could be further improved by the combination of CSL with a tea infusion (source of caffeine). Uridine (precursor for UDP-Glc, sugar donor in cellulose biosynthesis), guanine, guanosine, and its butirylated derivatives (precursors for the positive modulator of cellulose synthetase, di-cGMP) resulted in only moderate stimulation. Sodium phytate and betaine were also slightly stimulatory. The fibrilar product from a newAcetobacter isolate (Ax-M) was characterized as cellulose by comparison with the solid-state¹³C-NMR of algal cellulose. Its X-ray diffractogram was a confirmatory analysis. After incorporation of tamarind xyloglucan to previously air-dried cellulosic pellicles, diffractometry displayed only slight differences. Mercerized (5M NaOH) fresh cellulosic biofilms underwent drastic size reduction (3.5-fold), turning compact nut still flexible if maintained wet.     

Diastereoselective Manipulations of Bicyclo[m.1.0]alkane Derivatives. 4. Reactions of Nucleophiles with Bicyclo[m.1.0]alk-3-en-2-ones

Enantiomerically enriched bicyclo[m.1.0]alk-3-en-2-ones possessing 8-, 12-, and 15-membered rings were prepared and subjected to additions of nucleophiles. 1,2-Additions of n-butyllithium were highly diastereoselective for all cyclopropyl enones examined. Reactions of (Z)-bicyclo[6.1.0]non-3-en-2-one and (E)-bicyclo[13.1.0]hexadec-3-en-2-one with dimethyloxosulfonium methylide were highly diastereoselective, while reaction of (E)-bicyclo[10.1.0]tridec-3-en-2-one with this reagent was not diastereoselective. In contrast, 1,4-additions of lithium diorganocuprates were highly diastereoselective for the 8- and 12-membered enones but were not diastereoselective for the 15-membered enone. All reactions were chemically efficient. The diastereoselectivities observed for 1,2-additions, which are thought to involve early transition states, can be rationalized by consideration of the low-energy conformations of each cyclopropyl enone. The diastereoselectivities observed for 1,4-additions, which may involve late transition states, do not correlate simply with the lowest energy conformations of these enones.