One cannot hear orbifold isotropy type

We show that the isotropy types of the singularities of Riemannian orbifolds are not determined by the Laplace spectrum. Indeed, we construct arbitrarily large families of mutually isospectral orbifolds with different isotropy types. Finally, we show that the corresponding singular strata of two isospectral orbifolds may not be homeomorphic. Received: 6 October 2005     

Conformations of 1,3,3,5,7,7-Hexamethyl-1,5-diazacyclooctane and Its Bis-BH(3) Adduct. Mono- and Bis-BH(3) Adducts of Di-Tertiary Amines

A variable-temperature (1)H- and (13)C-NMR study revealed a conformational equilibrium for 1,3,3,5,7,7-hexamethyl-1,5-diazacyclooctane (4) having DeltaG() = 8.8 +/- 0.6 kcal/mol at 184 K. This activation barrier connects a major and a minor form of 4. Molecular mechanics calculations on 4 led to the conclusion that the major form is a set of twist-chair-chairs interconverting rapidly via the chair-chair and that the minor form is most likely a set of twist-boat-boats interconverting rapidly via the boat-boat. The proximity of the two nitrogen lone pairs in the major form of 4 made plausible the expectation that 4, as well as a related diamine with apposed nitrogens, 3,7-dimethyl-3,7-diazabicyclo[3.3.1]nonane (3), might bind a Lewis acid, namely BH(3), using both lone pairs simultaneously and equally. This proved not to be the case: for 3 only the bis-BH(3) adduct was found and for 4 the mono-BH(3) adduct utilized only one nitrogen lone pair. The structure of the bis-BH(3) adduct of 4 (12) was determined by X-ray crystallography to be a twist-boat-boat with BH(3)s cis. Molecular mechanics calculations on 12 were consistent with the solid state conformation found.     

Functionalization of the 4(5)methyl group of imidazoles: A novel synthesis of substituted imidazoles

Acyl vinyl phosphonium salts react with amidines to form imidazolyl phosphonium salts. These imidazolyl salts can be readily converted to multifunctional imidazoles with quantitative recovery of triphenyl phosphine.     

Nuclear magnetic resonance coupled microseparations

The increased separation efficiency afforded by reducing the size of the separation column has resulted in 'microseparations' becoming an important component in many chemical and biochemical applications. The coupling of microseparations with NMR detection is an area of increasing interest owing to the high structural information of NMR. In order to couple efficiently with the separation, the NMR detector must be reduced in size to correspond to that of the separation peak. This paper summarizes some of the approaches used in coupling NMR detection with pressure-driven and electrophoretic microseparations, the design of small NMR detectors and applications of this technology.     

An electronic aid for line selection for scanning inductively coupled plasma atomic emission spectrometers

This article is an electronic publication in Spectrochimica Acta Electronica (SAE), the electronic section of Spectrochimica Acta Part B (SAB). Accompanying this hard copy text is a disk containing the program, source flies, data files and a brief manual along with a few programming notes. The main article discusses the purpose of this work, and the Appendix provides brief instruction on the use of the program, manipulation of the data, and source code. An automatic file selection system for the control of a rapid scanning spectrometer performing atomic emission spectrometry has been developed using the PROLOG language. The system can be “taught” the elemental composition of a given sample type. It uses this information (when available) to generate a linear search strategy which minimizes the number of lines that need to be measured. The rules used by the system can be observed during system operation to allow a trace of the logic. Reading of the initial data base takes no more than 6 s and then decisions are made in less than 1 s per line.