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.     

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.     

Semi-wet growth and characterization of multi-functional nano-engineered mixed metal oxides for industrial application

This review paper covers the low temperature wet growth of nano-engineered particles of ZnO-based mixed metal oxides, their growth mechanism, and characterization using X-ray diffraction, SEM, TEM and IR, UV–visible, and XPS spectral techniques. Main focus of this article is centered on low temperature semi-wet methods of synthesis that are suitable for large scale production of zinc oxide-based systems mixed with iron oxide, copper oxide, nickel oxide and cobalt oxide. These mixed metal oxides have broad industrial applications as catalyst, semiconductors, adsorbents, superconductors, electro-ceramics, and antifungal agents in addition to extensive applications in medicines. This paper discusses the low-cost and environment friendly synthesis of these mixed metal oxides, measurement of properties and applicability of these materials systems.     

A 1H MRS study of probable Alzheimer's disease and normal aging: implications for longitudinal monitoring of dementia progression

In order to evaluate the capability of 1H MRS to monitor longitudinal changes in subjects with probable Alzheimer's disease (AD), the temporal stability of the metabolite measures N-acetylaspartate and N-acetylaspartylglutamate (NA), total Creatine (Cr), myo-Inositol (mI), total Choline (Chol), NA/Cr, mI/Cr, Chol/Cr and NA/mI were investigated in a cohort of normal older adults. Only the metabolite measures NA, mI, Cr, NA/Cr, mI/Cr, and NA/mI were found to be stable after a mean interval of 260 days. Relative and absolute metabolite measures from a cohort of patients with probable AD were subsequently compared with data from a sample of normal older adult control subjects, and correlated with mental status and the degree of atrophy in the localized voxel. Concentrations of NA, NA/Cr, and NA/mI were significantly reduced in the AD group with concomitant significant increases in mI and mI/Cr. There were no differences between the two groups in measures of Cr, Chol, or Chol/Cr. Significant correlations between mental status as measured by the Mini-Mental State Examination and NA/mI, mI/Cr and NA were found. These metabolite measures were also significantly correlated with the extent of atrophy (as measured by CSF and GM composition) in the spectroscopy voxel.     

On the Geometry and Mass of Static,Asymptotically AdS Spacetimes,and the Uniqueness of the AdS Soliton

We prove two theorems, announced in [6], for static spacetimes that solve Einstein's equation with negative cosmological constant. The first is a general structure theorem for spacetimes obeying a certain convexity condition near infinity, analogous to the structure theorems of Cheeger and Gromoll for manifolds of non-negative Ricci curvature. For spacetimes with Ricci-flat conformal boundary, the convexity condition is associated with negative mass. The second theorem is a uniqueness theorem for the negative mass AdS soliton spacetime. This result lends support to the new positive mass conjecture due to Horowitz and Myers which states that the unique lowest mass solution which asymptotes to the AdS soliton is the soliton itself. This conjecture was motivated by a nonsupersymmetric version of the AdS/CFT correspondence. Our results add to the growing body of rigorous mathematical results inspired by the AdS/CFT correspondence conjecture. Our techniques exploit a special geometric feature which the universal cover of the soliton spacetime shares with familiar ``ground state' spacetimes such as Minkowski spacetime, namely, the presence of a null line, or complete achronal null geodesic, and the totally geodesic null hypersurface that it determines. En route, we provide an analysis of the boundary data at conformal infinity for the Lorentzian signature static Einstein equations, in the spirit of the Fefferman-Graham analysis for the Riemannian signature case. This leads us to generalize to arbitrary dimension a mass definition for static asymptotically AdS spacetimes given by Chruciel and Simon. We prove equivalence of this mass definition with those of Ashtekar-Magnon and Hawking-Horowitz.