Universal finite group extensions and a non-splitting theorem

LetG andK be finite groups whose orders have a common prime divisor. Then there is a groupK ^* closely related toK for which there is a non-split extension ofK ^* byG. I wish to express thanks to the Mathematics Institute of the Hebrew University of Jerusalem for its hospitality from September to December 1972, and to Dr. Avinoam Mann for his helpful comments.     

Study of cylindrical stress waves generated by exploding wires

An experimental technique utilizing high-pressure gas from an exploding wire is used to load long, hollow, thick-walled cylinders from the inside. Resulting plane-strain cylindrical stress waves are one-dimensional in nature. Asimultaneity of impact is studied with methods of high-speed photography and dynamic photoelasticity.     

The absence of surface dipole contributions to metal work functions

A simple model, derived from a linear approximation to the ionization potentials of atoms, is used to compute the work functions of some 43 metals, mostly within their experimental uncertainties. The computation does not make use of a surface dipole contribution. In this respect, it departs from the current literature of many-body theoretical calculations in which the surface dipole plays a major role. Even without the use of surface dipoles, the model can still count for small differences observed on different crystal faces. The model also accounts for the experimental correlations of work functions with half the ionization potential and yields a simple formalism for computing the work functions of metallic clusters. Finally, the model yields the work functions of ions in terms of the same parameter used for the work functions of electrons.     

Analysis of nitrogen-influenced surface near zones of ferrous materials by glow discharge spectroscopy (GDOS)

Glow discharge spectroscopy (GDOS) will be shown to be a quick, informative and simple method for quantitative depth profile analysis of elements of nitrided layers well suited for their quality control. By systematic variation of all glow discharge determining parameters it is possible to get an excellent depth resolution in the order of sub-m corresponding to a comparatively large analytical activated area (50 mm²). In this paper the behaviour of a number of important parameters related to sputtering of the activated area will be discussed. Some quantitative GDOS depth profiles of carbon and nitrogen of pure iron samples nitrided by different procedures will be shown as examples for application.     

Errors in two-point sound reproduction

This paper deals with the problem of reproducing two signals at two points in space by using two acoustic sources. While much is now known about the techniques available for the design of matrices of inverse filters that enable this objective to be achieved in practice, it is still the basic physics of the sound field produced that controls the effectiveness of such systems and which ultimately dictates their design. The basic physical processes involved in producing the cross-talk cancellation that enables the reproduction of the desired signals is revisited here by using a simple two source/two field point free field model. The singular value decomposition is used to identify those frequencies where the inversion problem becomes ill-conditioned and to explain physically the origin of the ill-conditioning. As observed previously, it is found that cross-talk cancellation becomes problematic when the path length difference between the two sources and one of the field points becomes equal to one half the acoustic wavelength. The ill-conditioned frequencies are also found to be associated with a limited spatial region of cross-talk cancellation and with large source outputs manifested in the time domain by responses of long duration.     

A new nucleophilic addition/ring-closure sequence. Enantioselective synthesis of 3-deoxy-8-oxatropanes

[reaction: see text] A study of new nucleophilic addition/ring-closure (NARC) sequences has resulted in the development of a stereoselective synthetic route to 3-deoxy-8-oxatropanes. The new sequences consisted of either a syn or anti aldol addition, employing an omega-alkenoyl sultam, followed by two-step bicyclic ring construction involving, consecutively, ring-closing metathesis and intramolecular oxymercuration.     

Investigations into a free radical-mediated 1,2-imino migration

The radical reactions of a series of bromides 9a-c and selenides 12-15 have been investigated to determine the factors that are important for a successful radical-mediated 1,2-imino migration.