Exotic differentiable structures and general relativity

We review recent developments in differential topology with special concern for their possible significance to physical theories, especially general relativity. In particular we are concerned here with the discovery of the existence of non-standard (fake or exotic) differentiable structures on topologically simple manifolds such asS ⁷, ⁴ andS ³ X ¹. Because of the technical difficulties involved in the smooth case, we begin with an easily understood toy example looking at the role which the choice of complex structures plays in the formulation of two-dimensional vacuum electrostatics. We then briefly review the mathematical formalisms involved with differentiable structures on topological manifolds, diffeomorphisms and their significance for physics. We summarize the important work of Milnor, Freedman, Donaldson, and others in developing exotic differentiable structures on well known topological manifolds. Finally, we discuss some of the geometric implications of these results and propose some conjectures on possible physical implications of these new manifolds which have never before been considered as physical models.     

An algebraic approach to the planar coloring problem

We point out a general relationship between the planar coloring problem withQ colors and the Temperley-Lieb algebra with parameter . This allows us to give a complete algebraic reformulation of the four color result, and to give algebraic interpretations of various other aspects of planar colorings.Work supported in part by NSF Grant #DMS-882602, the program for Mathematics and Molecular Biology, UC Berkeley, and a visiting fellowship of the Japan Society for the promotion of science at Kyoto University, Kyoto, JapanWork supported in part by DOE Contact #DE-AC02-76ERO3075 and by a Packard Fellowship for Science and Engineering     

Substituent effects in the fragmentation reactions of acetanilides and phenyl acetates

The mass spectra of a group of m- and p-substituted acetanilides were measured to determine the effect of the substituents, if any, on the rate of C₂H₂O expulsion (rearrangement) vs. the rate of [CH₃CO]⁺ formation (simple cleavage). Our results agree with observations of others in that substituents which raise the ionization potential of the aromatic ring appear to localize, on the average, less charge density on this locus, and conversely. The atomic composition of the substituent, however, irrespective of its position, seems to determine the relative rates of the competing reaction. Although in several cases Z_m/Z_p values were close to unity, rearrangement of isomeric molecular ions to a common species is shown not to occur.     

Die Verbindungen Ta3Ga2 und IrGa

Ohne Zusammenfassung     

Technetium-99m-diethyl-IDA instant kit: Labelling kinetics and biological properties

A formulation of stannous-diethyl-IDA freeze-dried kit, containing 50 mg diethyl-IDA and 0.4 mg hydrated stannous chloride, to be labelled with technetium has been developed for hepatobiliary scintigraphy. Gel chromatography column scanning technique has been applied for determination of technetium fractions in the preapration. The optimal pH value of the preparation with a high hepatobiliary specificity was found between 5.5 to 6.0. Effect of ligand to metal ratio on the stability of the prepared Sn-diethyl-IDA solution prior mixing with technetium has been investigated. The reaction conditions (initial pH) between the ligand and stannous ion affects the percent hydrolysis of the labelled compund, i.e. the formation rate of the complex. The organ distribution data of^99mTc-diethyl-IDA in mice for 60 minutes post injection were satisfactory. The radiopharmaceutical exhibits rapid blood clearance, great hepatic clearance and very short hepatocyte transit time. Uptake of the radiopharmaceutical in various organs of mouse at 5 minute post injection showed that the greater part of the injected radioactivity has distributed between liver and intestine. However, about 12% and 60% of the injected dose has been found in liver and intestine respectively. The renal uptake of the HB agent in mice is relatively low and decreases with time to become about 0.3% at 60 minutes post injection. Blood clearance data of the radiopharmaceutical kit in rabbits showed that the HB agent is-rapidly cleared, since the initial decrease was very fast with a half-time of 1.5 minutes.