Norm inequalities for spherical means

The regularity and integrability of spherical means of functions inL ^p ( ⁿ ,n2, are studied. Sharp results are obtained.     

High-resolution mass spectra of two α,β-unssaturated γ-dilactones

The fragmentations of two α,β-unsaturated γ-dilactones in a mass spectrometer are studied. The main feature is conecutive carbon monoxide expulsions. Strong indication of ejection of a fragment C₂O₂ is presented, however. Masses were determined by the high resolution rechnique and metastable transitions were detected by defocusing. Corresponding deuterated dilactones were also studied to verify the fragmentation mechanism.     

Construction of orbital angular momentum eigenfunctions for many-particle systems by harmonic projection

Formulas are derived which allow the direct construction of total orbital angular momentum eigenfunctions for many-particle systems without the use of Clebsch–Gordan coefficients. One of the equations is closely analogous to Dirac' identity for the total spin operator. This equation describes the action of L² on a function of the particle coordinates in terms of a class operator of the symmetric group and a "contraction operator." A general projection operator for constructing symmetric eigenfunctions of L² is presented.     

Field desorption mass spectrometry of 1-methylpyridinium salts

Quaternary pyridinium salts were investigated by field desorption, field ionization and electron impact mass spectrometry. Thermal decomposition of the salts under field desorption conditions was found to give very abundant volatile products, identified as the dihydro analogues and the ‘methides’ of the cations. The formation of the volatile compounds, especially those with molecular weights corresponding to those of the (cation ?1), (cation +1) and (cation +13) was studied in detail by deuterium and ¹³C labelling experiments.     

Selective Halogen-Lithium Exchange Reaction of Bromine-Substituted 25,26,27,28-Tetrapropoxycalix[4]arene

Methods are described for the selective bromine-lithium exchange reaction of bromine-substituted calix[4]arenes with either n-BuLi or t-BuLi in THF. Quenching of the lithiated calix[4]arenes with MeOH, D(2)O, CH(3)SSCH(3), B(OCH(3))(3), DMF, or CO(2) as electrophiles resulted in 5-monosubstituted, 5,17-disubstituted, or 5,11,17,23-tetrasubstituted calix[4]arenes with H, D, SCH(3), B(OH)(2), CHO, or COOH functionalities.     

Resistivity of positive-J spin glasses: Study ofLaGd under hydrostatic pressure

Results of a new calculation of the resistivity in the noise model of spin glasses, based on the –J S interaction forpositive J, are compared with measurements of the resistivity in an fcc La-8at% Gd alloy under hydrostatic pressures up to 12 kbar, the first positive-J resistivity investigations under pressure. A positive value ofJ that decreases with increasing pressure, in accord with other experiments, leads to quantitative agreement between theory and experiment if one uses a large electronic density of states at the Fermi energy, in accord with specific heat measurements and electronic band structure calculations in fcc La. Impurity potential scattering is found to contribute significantly to the resistivity. Its size and pressure variation is determined.This work is supported in part by the Deutsche Forschungs-gemeinschaft.     

Reactions of polystyryl anions with carbon dioxide and oxygen. Analysis of products by silica gel chromatography

Polystyryllithium was prepared by anionic polymerization. This “living polymer” and the polystyrylmagnesium bromide derived from it were treated with carbon dioxide (solid or gas). The highest yields of carboxylic acid were obtained when solid carbon dioxide was used with polystyryllithium or by treatment of polystyrylmagnesium bromide with gaseous carbon dioxide. The products from the reaction of polystyryllithium with oxygen were polymeric ketone X, the alcohols IXa and IXb, and coupling products (e. g., XI). The various functionalized and unfunctionalized polystyrene products were isolated by chromatography on silica gel and were characterized by gel permeation chromatography (GPC), thin layer chromatography (TLC), and high-performance liquid chromatography (HPLC) in combination with chemical transformations.     

Field ionization mass spectrometry as a facile method for the study of the thermal formation of radicals

Electron impact spectra of thermolysis products of organic salts heated in the ion source of a mass spectrometer may give rise to organic ions corresponding to the cation of the salt. Field ionization mass spectrometry has been used as a facile method for detemining whether such an ion is due to ionization of the corresponding radical present in the gas phase, or to an electron impact induced fragmentation of a reaction product of higher mass. By comparison of the electron impact and field ionization spectra of a series of N-methyl pyridinium, tropylium and 1,2-dithiolylium salts it has been found possible to identify the radicals formed thermolytically, when present.