Dynamical symmetries in relativistic kinetic theory

This paper is part of a program investigating symmetries that are defined at a physical or observational level rather than purely geometrically. Here we generalize previous work on dynamical matter symmetries of relativistic gases. If the matter symmetry vector is surface-forming with the dynamical Liouville vector, then Einstein's equations reduce it to a Killing symmetry of the metric. We show that this conclusion is unaltered if the gas particles are subject to a nongravitational force (including the electromagnetic force on charged particles) or if the gravitational field obeys higher-order field equations. In the Brans-Dicke theory, the matter symmetry reduces to a homothetic symmetry of the metric. This is also the case for a generalized conformal symmetry in Einstein's theory. We consider the problem of relaxing the surface-forming assumption in an attempt to determine whether there are dynamical symmetries that do not necessarily reduce to geometrical symmetries of the metric.     

Single crystal X-ray structure of tetrahedral C60F36: the most aromatic and distorted fullerene

Tetrahedral C60F36 is shown by its single-crystal X-ray structure to be the most aromatic (and distorted) fullerene derivative, having four planar hexagons with almost equal bond lengths, the average of which (1.373 A) is the same as in C60F18; one exceptionally long FC-CF bond (1.665 A) corresponds to the similarly long bond in C60F18 (a motif of T C60F36) and is likely to be the site of oxygen insertion in C60F36O.     

Supercritical Fluid Chromatography of polyphenolic compounds in grape seed extract

Summary Supercritical Fluid Chromatography with a packed column on a mixture of eight polyphenols has been optimized. Carbon dioxide which was modified with methanol which contained less than 1% (w/w) citric acid as a secondary additive served as the mobile phase. Two tandem diol columns were used sequentially. The optimized method was applied to a supercritical fluid grape seed extract. Various components in the extract could be identified by retention time and ultraviolet spectral comparison with our synthetic mixture of polyphenols.     

Microwave spectrum,dipole moment,and a proposed structure for 1-cyanobicyclo[1.1.0]butane

The microwave spectra of the normal and the 2-¹³C isotopic species of 1-cyanobicyclo[1.1.0]butane have been observed and assigned, leading to the following rotational constants: (normal), A=8807.202 ± 0.004, B=2924.334 ± 0.002, C=2509.322 ± 0.002 and (isotope), A=8608.85 ± 0.85, B=2902.88 ± 0.02, and C=2478.56 ± 0.02 MHz. Measurements of the second-order Stark effect led to _T=4.08 ± 0.01 D. Based on the available microwave data coupled with geometryoptimizedab initio molecular orbital structures for cyanocyclopropane and 1-cyanobicyclo[1.1.0]-butane, a molecular structure for the latter molecule is proposed. Analysis of the dipole moments of these molecules and of bicyclo[1.1.0]butane has led to the conclusion that the bicyclobutyl group is a better electron donor than is cyclopropyl. In addition, a simple frontier molecular orbital model is not sufficient for explaining all of the structural changes that occur on substituting cyano at the bridgehead of bicyclo[1.1.0]butane.     

Preparation and characterisation of synthetic mixtures of lithium isotopes

Re-certification of the absolute isotopic composition of the natural lithium isotopic reference material (IRM), IRMM-016, requires measurements calibrated by means of synthetic mixtures of highly enriched lithium isotopes. Ten such mixtures were prepared by weighing and mixing of two well characterised, isotopically enriched, Li₂CO₃ compounds. The starting materials, 99.9981% enriched ⁶Li, and 99.9937% enriched ⁷Li, were purified by ion exchange, and the purified materials converted from LiOH to Li₂CO₃ by reaction with CO₂. Ten new mixtures were prepared by mixing different weighed amounts of these dissolved Li₂CO₃ carrier compounds. The compounds had an estimated level of impurities of 100 ± 100 μg · g^–1 (expanded uncertainty with a coverage factor of 2). In the ten mixtures, the n(⁶Li)/n(⁷Li) ratio varies from 0.025 to 14 and the achieved expanded relative uncertainty on the amount ratio prepared is typically 2 · 10^–4. These mixtures were then used to determine the correction factor, K, for mass discrimination of the measurement procedure and instrument concerned.     

Optimization of photodynamic therapy light dose distribution and treatment volume by multi-fiber insertions

Abstract The development of a methodology which optimizes the light dosage in tissue and improves the tailoring of the light with consequent sparing of normal adjacent tissue, will enhance the possibility for routine clinical photodynamic therapy. Specific, important goals for the clinical use of PDT are (a) efficient distribution of light flux to all parts of the tumor at sufficient level to effect eradication. (b) avoidance of the destruction of adjacent normal tissue, and (c) ability to tailor the treatment field, taking into account the varied shapes of tumors. Dividing the available power among several fibers is a promising method of achieving these goals. This is accomplished by (1) extending the volume, and by (2) increasing the flux spatial uniformity. This latter defocussing of the flux field is especially important because it may help to avoid concentrating a high intensity field from an implanted fiber near an essential structure of the normal tissue. The question arises how best to orient these multiple fibers for maximum coverage and uniformity. Hence, theoretical and experimental investigations were made to determine optimal fiber placements. A series of intensity distributions were generated using two and three fibers positioned at various separations within a postulated tumor volume. A criterion for uniformity was defined. Iterative computation produced optimal fiber separation for the given constraints. In the two fiber case, for small values of attenuation coefficient (μ. ≦ 0.2 mm^?1), optimal fiber separation ranged from 0.6 to 0.7 times the diameter of the defined volume. For large values of attenuation coefficient (μ. ≧ 0.8), fiber separation was about 0.5 to 0.55 times the region diameter. The effects of fiber separation on volume of treatment were also determined. Maximal treatment volume was found to be dependent on the attenuation coefficient. With μ, = 0.50, a 40% increase in treatment volume over single fiber insertion of equivalent energy input was shown to be obtainable with a dual fiber configuration of 24 mm separation. Experiments using two fibers in vitro in mammalian tissue were performed to substantiate these results. The multiple fiber system is a promising method for delivering optimum light dosage to targeted PDT tissue.     

Efficient synthesis of 5-substituted-4,5-dihydro-1,2,4-triazin-6-ones and 5-substituted-1,2,4-triazin-6-ones

Treatment of methyl α-(dimethylarninomethyleneamino)carboxylates 1 (from α-amino acids and dimethylformamide dimethylacetal) with hydrazine gives 5-substituted-4,5-dihydro-1,2,4-triazin-6-ones 2 , which are smoothly dehydrogenated to 5-substituted-1,2,4-triazin-6-ones 3 with potassium permanganate in acetone/acetic acid.     

Total syntheses of spiroviolene and spirograterpene A: a structural reassignment with biosynthetic implications

The recent natural product isolates spiroviolene and spirograterpene A are two relatively non-functionalized linear triquinane terpenes with a large number of structural homologies. Nevertheless, three significant areas of structural disparity exist based on their original assignments, one of which implies a key stereochemical divergence early in their respective biosyntheses. Herein, using two known bicyclic ketone intermediates, a core Pd-catalyzed Heck cyclization sequence, and several chemoselective transformations, we describe concise total syntheses of both natural product targets and propose that the structure of spiroviolene should be reassigned. As a result, these natural products possess greater homology than previously anticipated.

Concise syntheses of spiroviolene and spirograterpene A have been achieved from a common intermediate, indicating a structure revision of one is necessary along with implications for its biosynthesis.