On the topology of black holes

We establish from local hypotheses some results concerning the final state topology of black holes. We show that the surface of a black hole must have 2-sphere topology and that the topology of space in its vicinity is simple.Dedicated to Ted FrankelThis work has been partially supported by NSF grants DMS-8802877 and DMS-9006678     

Cobalt(II) halide complexes ofN-2-(4-picolyl)-,N-2-(6-picolyl)-andN-2-(4,6-lutidyl)-N′-phenylthioureas

Summary Co^II complexes of various stoichiometries have been isolated from reactions of the metal chlorides and bromides withN-2-(4-picolyl)-,N-2-(6-picolyl)- andN-2-(4,6-lutidyl)-N-phenylthioureas.     

Characterizing the "shell phase" formed from amphiphilic picolinates

The shell phase forms when certain picolinates are subjected to energy input (via sonication or vortexing) while exposed to a water/toluene mixture. A shell, about 600 A thick and containing the picolinate and (very likely) toluene, surround the water droplets that are always produced during the mixing process. Solubility in either phase appears to be deleterious to shell formation. The shells, stable for months, are not easily distorted but can be punctured, even skewered, with a syringe needle without destroying the sphere, yet there is enough mobility among the molecules to repair the physical damage after the needle is removed. This, plus the absence of evidence for crystallinity, suggests a solid or semisolid film forms when picolinates, with the aid of an aromatic solvent, are provided the energy to rearrange themselves on water droplet surfaces. Structure-activity comparisons among the 10 compounds studied indicate that chain-chain association and intermolecular hydrogen bonding are dominant forces in a side-by-side self-assembly of the molecules within the shells.     

Approximate methods for the fast computation of EPR and ST-EPR spectra. III. Extension of the perturbation approximation to conditions of overmodulatio

The electron paramagnetic resonance (EPR) and saturation transfer electron paramagnetic resonance (ST-EPR) spectra typical of nitroxide spin labels obeying an isotropic, brownian diffusion model are theoretically investigated. The derivative approximation discussed in the first paper of this series (I) is examined and generalized to consider large modulation amplitudes. The approximation considers both molecular and applied modulation effects with the Zeeman modulation frequency acting as a perturbation parameter. The application of the approximation to first and second harmonic simulations is discussed. The observations of I are preserved for first harmonic spectra. The approximation is able to accurately reproduce the in-phase absorption and in-phase-quadrature dispersion signals. In-phase dispersion signals are reproducible at low microwave powers while in-phase-quadrature signals may be reproduced at higher powers. The approximation is of limited utility for second harmonic simulations and is particularly unable to reproduce the in-phase-quadrature absorption signal at this harmonic. The approximation enables a marked reduction in both the core and CPU time required for simulations. Factors of 3 and 4.2 respectively were realized in the simulations of slow isotropic brownian diffusion.     

Narrow band quantitative and multivariate electroencephalogram analysis of peri-adolescent period

ABSTRACT: BACKGROUND: The peri-adolescent period is a crucial developmental moment of transition from childhood to emergent adulthood. The present report analyses the differences in Power Spectrum (PS) of the Electroencephalogram (EEG) between late childhood (24 children between 8 and 13 years old) and young adulthood (24 young adults between 18 and 23 years old). RESULTS: The narrow band analysis of the Electroencephalogram was computed in the frequency range of 0--20 Hz. The analysis of mean and variance suggested that six frequency ranges presented a different rate of maturation at these ages, namely: low delta, delta-theta, low alpha, high alpha, low beta and high beta. For most of these bands the maturation seems to occur later in anterior sites than posterior sites. Correlational analysis showed a lower pattern of correlation between different frequencies in children than in young adults, suggesting a certain asynchrony in the maturation of different rhythms. The topographical analysis revealed similar topographies of the different rhythms in children and young adults. Principal Component Analysis (PCA) demonstrated the same internal structure for the Electroencephalogram of both age groups. Principal Component Analysis allowed to separate four subcomponents in the alpha range. All these subcomponents peaked at a lower frequency in children than in young adults. CONCLUSIONS: The present approaches complement and solve some of the incertitudes when the classical brain broad rhythm analysis is applied. Children have a higher absolute power than young adults for frequency ranges between 0-20 Hz, the correlation of Power Spectrum (PS) with age and the variance age comparison showed that there are six ranges of frequencies that can distinguish the level of EEG maturation in children and adults. The establishment of maturational order of different frequencies and its possible maturational interdependence would require a complete series including all the different ages.     

Mild and Efficient Synthesis of Benzo-Fused Seven- and Eight-membered Ring Lactams: A Convenient Approach to Biologically Interesting Chemotypes

A general and efficient method for the synthesis of benzo-fused 7- and 8-membered ring lactams via the Beckmann rearrangement of cyclic oximes is presented.

Supplemental materials are available for this article. Go to the publisher's online edition of Synthetic Communications® to view the free supplemental file.     

Biomimetic Synthesis of Materials for Technology

In a world with ever decreasing natural reserves, researchers are striving to find sustainable methods of producing components for technology. Bioinspired, biokleptic and biomimetic materials can be used to form a wide range of technologically relevant materials under environmentally friendly conditions. Here we investigate a range of biotemplated and bioinspired materials that can be used to develop components for devices, such as optics, photonics, photovoltaics, circuits and data storage.