Eigenvalue bounds for elliptic operators

Lower bounds for the real parts of the points in the spectrum of elliptic equations are derived. These bounds, depending only on the diameter L of the domain G and on the maximum norm M of the coefficients a, b, are optimal. They are always positive and thus the spectrum is bounded away from the imaginary axis. This result is then used to prove an “anti-dynamo theorem” for magnetic fields with plane symmetry in the case of a compressible steady flow surrounded by a perfect conductor.     

Polyhedral clathrate hydrates of a strong base: Phase relations and crystal structures in the system tetramethylammonium hydroxide-water

The tetramethylammonium hydroxide-water system has been studied by low-temperature differential thermal analysis and X-ray powder diffraction. The melting diagram was constructed for concentrations between 66.7 and 100 mol% H₂O. It shows the existence and stability ranges of as many as eight crystalline hydrate phases:- and-Me₄NOH·2H₂O (phase transition at –85°C, decomposition atca. 105°C), Me₄NOH·4 H₂O (melting point 44°C, incongruent), and-Me₄NOH·5 H₂O (phase transition at 42°C, melting point 68°C, congruent),- and-Me₄NOH·7.5 H₂O (phase transition at 6°C, melting point 16°C, incongruent), and Me₄NOH·10 H₂O (melting point –20°C, incongruent). The structures of all these phases, except the already known one of-Me₄NOH·5 H₂O, were determined from single-crystal MoK diffractometer data. The decahydrate and the high-temperature forms of the 7.5-hydrate and the pentahydrate are genuinepolyhedral clathrate hydrates, the first ones reported of a strong base. Their mostly novel three-dimensional anionic host structures, formed by the hydrogen-bonded OH^– ions and H₂O molecules, arefour-connected throughout, in spite of their proton deficiency which is apparently leveled by disorder. Disorder also affects the enclosed cationic Me₄N⁺ guest species. Like the low-temperature form of the pentahydrate, that of the 7.5-hydrate has a clathrate-related, but not fully polyhedral structure, some of the oxygen atoms being three-connected only. The tetrahydrate presents the rare case of both a hydrogen bond of the type OH^–...OH₂ and a (deprotonated) water-channel structure. This is fully ordered and apart from that can be derived from the polyhedral one of the-pentahydrate just by removing the appropriate number of water molecules from certain positions. The structures of- and-Me₄NOH·2 H₂O contain identical one-dimensionalspiro chains [HO^–(HOH)_/42] with the hydroxide protonnot participating in the hydrogen bonding. The Me₄N⁺ ion is ordered in the and disordered in the phase.Supplementary Data relating to this article are deposited with the British Library as Supplementary Publication No. SUP 82076 (66 pages).Dedicated to Dr D. W. Davidson in honor of his great contributions to the sciences of inclusion phenomena.     

Reaction of N,N-diarylamidines with 3,4,5,6-tetrachloro-1,2-benzoquinone

A synthesis of 5,11b-dihydro-1H-dibenzo[d,f][1,3]diazepin-1-ones was found in the reaction of nitro-substituted N¹,N²-diarylamidines with 3,4,5,6-tetrachloro-1,2-benzoquinone. In contrast, 6,7,8,9-tetrachlorodibenzodioxins were obtained from reaction of N¹,N²-diphenylpropionamidine and N¹,N²-di-(4-tert-butylphenyl)acetamidine with 3,4,5,6-tetrachloro-1,2-benzoquinone.     

Alkoxylierung von bis(trimethylsilyl)-aminofluorsilanen,sowie siloxanbildung unter äthereliminierung

The reaction of bis(trimethylsilyl)aminofluorsilanes, (Me₃Si)₂NSiF₂R (R = CH₃ or F), with sodium alcoholates or sodium phenylate yields under elimination of NaF alkoxy- and aryloxy-aminofluorosilanes of the composition (Me₃Si)₂NSiF(R)OR′(R′ = CH₃, C₂H₅, C₃H₇, C₆H₅). A disiloxane is formed by thermal elimination of diethyl ether from bis(trimethylsilyl)aminomethylfluoroethoxysilane. The IR, mass, ¹H and ¹⁹F NMR spectra of the above-mentioned compounds are reported. ab]Die Reaktion von Bis(trimethylsilyl)-aminofluorsilanen des Typs (Me₃Si)₂NSiF₂R (R = F, CH₃) mit Natriumalkoholaten und Natriumphenolat führt unter NaF-Abspaltung zu Alkyl- und Aryloxyaminofluorsilanen der Zusammensetzung: (Me₃Si)₂NSiF(R)OR′ (R′ = CH₃, C₂H₇, C₆H₅, C₆H₅). Ein Disiloxan könnte durch die thermische Eliminierung von Diäthyläther aus Bis(trimethylsilyl)aminomethyl-fluor-äthoxy-silylarnin erhalten werden.Die IR-, Massen-, ¹H- und ¹⁹F-NMR-Spektren der dargestellten Verbindungen werden mitgeteilt.     

Kristallstrukturen von Säurehydraten und Oxoniumsalzen. XX. Die Oxoniumtetrafluoroborate H3OBF4, [H5O2]BF4 und [H(CH3OH)2]BF4

Crystal Structures of Acid Hydrates and Oxonium Salts. XX. Oxonium Tetrafluoroborates H₃OBF₄, [H₅O₂]BF₄, and [H(CH₃OH)₂]BF₄ The crystal structures of three oxonium tetrafluoroborates were determined. H₃OBF₄, oxonium tetrafluoroborate proper, is triclinic with space group P1 , Z = 2 and the unit cell dimensions a = 4.758, b = 6.047, c = 6.352 Å and α = 80.40, β = 79.48, γ = 88.25° at ?26°C. Cations H₃O⁺ and anions BF₄^? are linked by hydrogen bonds O? H…?F into ribbons of condensed rings. In [H₅O₂]BF₄ (diaquohydrogen tetrafluoroborate, monoclinic, P2₁/c, Z = 4, a = 6.584, b = 9.725, c = 7.084 Å, β = 95.15° at ?100°C) the hydrogen bond in the cation H₅O₂⁺ is 2.412 Å short, asymmetric and approximately centered and the linking of cations and anions three-dimensional. In [H(CH₃OH)₂]BF₄ (Bis(methanol)hydrogen tetrafluoroborate, monoclinic, P2₁/c, Z = 4, a = 5.197, b = 14.458, c = 9.318 Å, β = 94.61° at ?50°C) the cation [H(CH₃OH)₂]⁺ is characterized for the first time in a crystal structure with an again very short (2.394 Å), asymmetric and effectively centered hydrogen bond. By further hydrogen bonds cations and anions form only dimers of the formula unit of centrosymmetric cyclic structure.     

Capillary array scanner for time-resolved detection and identification of fluorescently labelled DNA fragments

The first capillary array scanner for time-resolved fluorescence detection in parallel capillary electrophoresis based on semiconductor technology is described. The system consists essentially of a confocal fluorescence microscope and a x,y-microscope scanning stage. Fluorescence of the labelled probe molecules was excited using a short-pulse diode laser emitting at 640 nm with a repetition rate of 50 MHz. Using a single filter system the fluorescence decays of different labels were detected by an avalanche photodiode in combination with a PC plug-in card for time-correlated single-photon counting (TCSPC). The time-resolved fluorescence signals were analyzed and identified by a maximum likelihood estimator (MLE). The x,y-microscope scanning stage allows for discontinuous, bidirectional scanning of up to 16 capillaries in an array, resulting in longer fluorescence collection times per capillary compared to scanners working in a continuous mode. Synchronization of the alignment and measurement process were developed to allow for data acquisition without overhead. Detection limits in the subzeptomol range for different dye molecules separated in parallel capillaries have been achieved. In addition, we report on parallel time-resolved detection and separation of more than 400 bases of single base extension DNA fragments in capillary array electrophoresis. Using only semiconductor technology the presented technique represents a low-cost alternative for high throughput DNA sequencing in parallel capillaries.     

SCF-Xα-SW model calculations for metal clusters of nickel,copper, and silver and for the oxygen chemisorption on these metals

The oxygen chemisorption on Ni, Cu and Ag is studied by comparing PE spectra of these systems and SCF-Xα scattered-wave cluster models. Consideration of octahedral clusters M₆ (M = Ni, Cu, Ag) shows that they are large enough to reproduce trends in energy differences, such as the width of the d-bands and the distance from the top of the d-bands to the Fermi level, as found in experiment and in bulk energy band calculations. Substrate model clusters for the interaction of oxygen with different metal surfaces are derived from an octahedron by removing one ((100) face) or two adjacent metal atoms ((110) face). Comparing the UPS difference spectrum for O/Ag (110) with several Ag₄O cluster models makes it possible to interpret the peaks above the Ag d-band as O-Ag anti-bonding levels. These peaks are caused by O 2p-Ag 4d and O 2p-Ag 5s interaction. The corresponding bonding levels fall in the Ag d-bands and cannot therefore be identified with confidence in the spectra. The decreasing intensity of the oxygen derived peak below the metal d-band in the UPS spectra when going from Ni to Cu to Ag, and the simultaneously increasing O peaks above the d-band correlate with the changes of the localization of the corresponding bonding and anti-bonding levels in the oxygen sphere and the decreasing strength of the chemisorption bond.     

Soliton concept in general relativity

Soliton physics has made considerable progress in solving nonlinear problems. This paper is meant to relate the soliten concept to the stationary axisymmetric vacuum fields in general relativity. We present a functional transformation which, working as a nonlinear creation operator, generates gravitational fields of isolated sources. When applied to flat space-time (gravitational vacuum) this operation leads to a nonlinear superposition of an arbitrary number of Kerr particles. This superposition also includes the Tomimatsu-Sato fields. The functional transformations form an infinite-parameter group which contains the Kinnersley-Geroch group as a subgroup.This essay received the second award from the Gravity Research Foundation for the year 1980.-Ed.