The basic stratum of some simple Shimura varieties

Under simplifying hypotheses we prove a relation between the $\ell $ -adic cohomology of the basic stratum of a Shimura variety of PEL-type modulo a prime of good reduction of the reflex field and the cohomology of the complex Shimura variety. In particular we obtain explicit formulas for the number of points in the basic stratum over finite fields. We obtain our results using the trace formula and truncation of the formula of Kottwitz for the number of points on a Shimura variety over a finite fields.     

A rapid non-acidolytic method for deprotection and removal of peptides from solid phase resins - applications of ammonium formate catalytic transfer hydrogenation

Ammonium formate aided catalytic transfer hydrogenation has been employed in the cleavage, and concommitant deprotection, of the pentapeptide leucine enkephalin from the Merrifield peptide resin under ambient conditions of temperature and pressure in a neutral medium.     

On multiple roots in Descartes’ Rule and their distance to roots of higher derivatives

If an open interval I contains a k  -fold root α$\alpha$ of a real polynomial f, then, after transforming I   to (0,∞)$(0,\infty )$, Descartes’ Rule of Signs counts exactly k roots of f in I, provided I is such that Descartes’ Rule counts no roots of the kth derivative of f. We give a simple proof using the Bernstein basis.     

Advantages of synthesizing trans-1,2-cyclohexanediol in a continuous flow microreactor over a standard glass apparatus

Comparison is made between the preparation of trans-1,2-cyclohexanediol in standard glassware (conventional batch production) and in a microreactor (continuous flow production). The reaction sequence involved two exothermic steps where the standard procedure demands slow reagent addition and careful temperature control. In the microreactor, the reaction could be carried out safely with up to 3 times higher reagent concentration. Synthetic benefits were a faster reaction rate and a higher purity product free of colored impurities (a feature of the batch procedure).