Comparison of agarose and cross-linked protein gels as magnetic resonance imaging phantoms

Measurements of the magnetic field dependence of spin-lattice relaxation rates and the response of the water-proton signal intensity to off-resonance radio frequency fields show that the commonly used agarose phantom provides a less faithful representation for the magnetic response of tissue than does a cross-linked protein system. The origin of these differences lies in the structure and intramolecular dynamics of the macromolecular system used to make the gel. These distinctions will also cause differences in the magnetic response of the water spin system when paramagnetic relaxation agents or contrast agents are incorporated. Use of a thermally cross-linked bovine serum albumin phantom is suggested.     

Casimir self-stress on a perfectly conducting spherical shell

The Casimir stress on a perfectly conducting uncharged sphere, due to occurrence of fluctuations in the electromagnetic field, is calculated using a source theory formulation. Two independent methods are employed: we compute (1) the total Casimir energy inside and outside the sphere, and (2) the radial component of the stress tensor on the surface. It is necessary to exercise care in allowing the field points to overlap; a correct limiting procedure supplies a “cutoff” in the frequency integration. In spite of numerous technical improvements, the result of Boyer, that the self-stress is repulsive (and not attractive as Casimir hoped), is confirmed unambiguously. The magnitude of the Casimir energy of a sphere of radius a is found, by numerical and analytic techniques, to be $\text{E = (}\text{h}\text{?}\text{c}\text{2a}\text{)(0.09235)}$, also in agreement with the very recent result of Balian and Duplantier.     

Inverse vibrational distributions of photofragments

X-ray diffraction data from a Cr₂(SO₄)₃ solution were examined. A peak at 3.25 Å in the correlation function reveals the formation of inner chromium-sulphate complexes. Least-squares refinements of the i(s) curve are consistent with a structural unit in which the CrOS angle is 136°. Each sulphate ion interacts with approximately eight water molecules.     

A study of nitric oxide adsorbed on nickel oxide,cobalt oxide,and graphite by X-ray photoelectron spectroscopy

The nitrogen 1s binding energy of nitric oxide adsorbed on nickel oxide, cobalt oxide and graphite was measured at several temperatures by X-ray photoelectron spectroscopy. For the oxides, a temperature dependent range of binding energies was observed, but for graphite the nitrogen 1s binding energy was independent of temperature. The values obtained suggest that significant back donation of electrons occurs from the oxides to the adsorbed nitric oxides, but no back donation occurs from graphite to adsorbed nitric oxide. However, adsorption did not cause changes in the binding energy of substrate core electrons. It is believed that unless the mean free path of electrons is short, the total photoelectron signal will not reveal changes in binding energy of electrons from substrate atoms at the surface.     

Triangles II: Complex triangle coordinates

Summary This paper is the second in a series of three examining Euclidean triangle geometry via complex cross ratios. In the first paper of the series, we examined triangle shapes. In this paper, we coordinatize the Euclidean plane using cross ratios, and use these triangle coordinates to prove theorems about triangles. We develop a complex version of Ceva's theorem, and apply it to proofs of several new theorems. The remaining paper of this series will deal with complex triangle functions.     

A note on the stress singularity at a penny-shaped crack in three-dimensional electrostriction

Zusammenfassung Diese Mitteilung behandelt eine vollständige Bewertung der Spannungs-Singularität am Rande eines flachen kreisförmigen Spaltes unter der Einwirkung von Elektrostriktion. Die Ergebnisse bestätigen die Schlussfolgerungen, welche früher bei zweidimensionalen Problemen gezogen wurden.Die der Elektrostriktion zuzuschreibende Singularität zeitigt eine rein radiale Spannung, welche nicht dazu neigt, die schon bestehenden Spalten ihrer Ausdehnungs-Oberfläche entlang auszubreiten.

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Research supported by the National Science Foundation under grant NSF GP 22567.

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Research supported by the United States Atomic Energy Commission.