Die Spannungsfunktionen des dreidimensionalen Kontinuums; statische Deutung und Randwerte

Ohne Zusammenfassung     

A metric variant of Frobenius's theorem and some other remarks on positive matrices

The theory of positive (=nonnegative) finite square matrices continues, three quarters of a century after the pioneering and well-known papers of Perron and Frobenius [4], to present a multitude of different aspects. This is evidenced, for example, by the recent papers [1] and [2], as well as by the vast literature concerned with extensions to operators on infinite dimensional spaces (see [5]). Supposing A to be a positive n × n matrix with spectral radius r(A) = 1, the main purpose of this note is to display the role of λ = 1 as a root of the minimal polynomial of A (or equivalently, of certain norm conditions on A, for the lattice structure of the space M spanned by the unimodular eigenvectors of A as well as for the permutational character of A on M. Proposition 1 can thus be viewed as a variant of Frobenius's theorem on the peripheral spectrum of indecomposable square matrices, and we hope that the proof of Proposition 2 will clarify to what extent indecomposability is responsible for the main results available in that special case. The remaining remarks (Propositions 3 and 4) are concerned with the spectral characterization of permutation matrices and with finite groups of positive matrices. Some of that material is undoubtedly known, but we give simple, transparent proofs.     

A nuclear magnetic resonance determination of the barrier to internal rotation in phenylethane

The long-range nuclear spin-spin coupling constant between the methylene protons and the ring protons at the para position in 3,5-dibromo-phenylethane in benzene solution is consistent with a two-fold barrier of 1.2 ± 0.1 kcal/mole to rotation about the sp²-sp³ carbon-carbon bond, in agreement with thermodynamic data on phenylethane and with deductions based on hyperfine interactions in related radical anions. The low-energy conformation has a plane of symmetry, the methyl group being situated out of the aromatic plane, in disagreement with Raman depolarization data interpretations and with deductions based on proton chemical shifts.     

Preparation and analysis of heart and skeletal muscle specimens with LAMMA

Summary A technique is described to obtain shockfrozen tissue specimens from a beating heart in situ using liquid propane as cooling agent. The method allows to take up to 8 samples from the ischemic area of the left ventricle of a pig heart following acute coronary artery occlusion.A freeze-drying apparatus was developed in which, under a vacuum of 10^–6 mm Hg, the specimens remain for 10 days with the temperature slowly rising from initially –100 C to room temperature. Freezing damages in the tissues samples due to the formation of ice crystals either during shock-freezing or freeze-drying are usually below the spatial resolution of the microscope system employed in the LAMMA instrument. Already after a few minutes of ischemia, a considerable decrease of the intracellular K/Na relation was measured. LAMMA spectra from skeletal muscle were taken to check for possible ion redistribution which had eventually occurred during the various steps of the preparation procedure employed.Supported by Deutsche Forschungsgemeinschaft, SFB 68, A 10     

Direct measurement of Fano-effect on Rb at 266 nm

Polarization of photoelectrons from Rb produced by circularly polarized light (λ = 266 nm) was measured to be 68 ± 5%. This value agrees with earlier indirect measurements of the Fano effect on Rb.