Cyclohexylcarbonitriles: Diastereoselective Arylations with TMPZnCl·LiCl

Deprotonating substituted cyclohexanecarbonitriles with TMPZnCl·LiCl affords zincated nitriles that diastereoselectively couple with aryl bromides in the presence of catalytic Pd(OAc)(2) and S-Phos. Steric and electronic effects influence the diastereoselectivity; 4-t-butyl-, 4-TBSO-, and 2-Me-cyclohexanecarbonitriles exert virtually complete diastereocontrol whereas modest diastereoselectivity is observed with 4-i-Pr-, 4-Me-, and 3-Me-cyclohexanecarbonitriles. The unusual diastereoselectivity trends should prove useful for synthesizing substituted cyclohexanecarbonitrile-containing pharmaceuticals.     

Real recursive functions and their hierarchy

In the last years, recursive functions over the reals (Theoret. Comput. Sci. 162 (1996) 23) have been considered, first as a model of analog computation, and second to obtain analog characterizations of classical computational complexity classes (Unconventional Models of Computation, UMC 2002, Lecture Notes in Computer Science, Vol. 2509, Springer, Berlin, pp. 1–14). However, one of the operators introduced in the seminal paper by Moore (1996), the minimalization operator, has not been considered: (a) although differential recursion (the analog counterpart of classical recurrence) is, in some extent, directly implementable in the General Purpose Analog Computer of Claude Shannon, analog minimalization is far from physical realizability, and (b) analog minimalization was borrowed from classical recursion theory and does not fit well the analytic realm of analog computation. In this paper, we show that a most natural operator captured from analysis—the operator of taking a limit—can be used properly to enhance the theory of recursion over the reals, providing good solutions to puzzling problems raised by the original model.     

A foundation for real recursive function theory

The class of recursive functions over the reals, denoted by , was introduced by Cristopher Moore in his seminal paper written in 1995. Since then many subsequent investigations brought new results: the class was put in relation with the class of functions generated by the General Purpose Analogue Computer of Claude Shannon; classical digital computation was embedded in several ways into the new model of computation; restrictions of were proved to represent different classes of recursive functions, e.g., recursive, primitive recursive and elementary functions, and structures such as the Ritchie and the Grzergorczyk hierarchies.The class of real recursive functions was then stratified in a natural way, and and the analytic hierarchy were recently recognised as two faces of the same mathematical concept.In this new article, we bring a strong foundational support to the Real Recursive Function Theory, rooted in Mathematical Analysis, in a way that the reader can easily recognise both its intrinsic mathematical beauty and its extreme simplicity. The new paradigm is now robust and smooth enough to be taught. To achieve such a result some concepts had to change and some new results were added.     

FTIR Emission Spectra, Molecular Constants, and Potential Curve of Ground State GeO

Extensive new high-temperature, high-resolution FTIR emission spectroscopy measurements for the five common isotopomers of GeO are combined with previous diode laser and microwave measurements in combined isotopomer analyses. New Dunham expansion parameters and an accurate analytical potential energy function are determined for the ground X1Sigma+ state. Copyright 1999 Academic Press.