Theory of oscillation type viscometers IV: A thick disk

The viscous drag exerted by a fluid on an oscillating disk is determined by methods similar to those used in Part III. The present paper differs from Part III in that the boundary layer thickness is assumed here to be small compared with both the thickness and the radius of the disk. An extrapolation of the formulae derived here agree sufficiently well, however, with those derived for the thin disk (boundary layer thickness large compared with the thickness but small compared with the radius) that it is possible to make an interpolation between the present formulae and those of Part III that will permit the evaluation of the drag for arbitrary shape disks provided the boundary layer thickness is small compared with the radius.

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Zusammenfassung Der Einfluss der Zähigkeitskräfte auf eine in einer Flüssigkeit schwingende Scheibe wird nach den gleichen Methoden wie in Tiel III behandelt. Jedoch wird im Unterschied dazu vorausgesetzt, dass die Grenzschichtdicke klein ist im Verhältnis zur Dicke und zum Radius der Scheibe. Die abgeleiteten Formeln lassen sich mit gutem Ergebnis für die dünne Scheibe extrapolieren (hier ist die Grenzschichtdicke jedoch gross, verglichen mit der Scheibendicke, aber klein gegenüber dem Radius), so dass es möglich ist, zwischen diesen Formeln und denen des Teils III zu interpolieren. Damit wird die Berechnung des Reibungsmomentes für Scheiben unterschiedlichster Form ermöglicht, vorausgesetzt, dass die Grenzschichtdicke klein ist gegenüber dem Radius der Scheibe.

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This research was supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command, under contract No. AF 18 (600) 1548. Reproduction in whole or in part is permitted for any purpose of the United States Government. Part of the work was done while one of the authors (G. F. N.) was being supported by a grant from the Alfred P. Sloan Foundation.     

A study of the γ-ray decays from single particle states in 91Zr and 93Mo

Lifetimes have been measured in ⁹¹Zr and ⁹³Mo by the Doppler shift attenuation method through the ⁹⁰Zr(¹³C, ¹²C)⁹¹Zr and the ⁹²Mo(¹³C, ¹²C)⁹³Mo reactions. Gamma rays were observed in coincidence with the back scattered particles and the reactions took place at sub-Coulomb energies. The lifetimes measured in ⁹¹Zr are τ(1205) = 250⁺⁹⁰_?70 fs, τ(1467) = 280⁺¹⁶⁰_?110 fs, τ(2042) < 30 fs, τ(2558) = 180⁺⁹⁰_?60 fs. The lifetimes measured in ⁹³Mo are τ(1361) = 170⁺⁸⁰_?40 fs, τ(1494) = 60 ± 40 fs, τ(1697) = 440⁺²³⁰_?130 fs, τ(2705)=160⁺⁸⁰_?60fs These results are compared with the expectations of the shell model and the $\text{3}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{→ 2}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{E}\text{2}$ transition is shown to be very enhanced.     

Elucidation of the structure of a highly efficient blue emitting lithium boron 2-(2-hydroxyphenyl) benzoxazole

We have studied the new blue electroluminescent material (compound 1) synthesized from the reaction of 2-(2-hydroxyphenyl)benzoxazole with LiBH₄ according to Tao's procedure [J. Am. Chem. Soc. 121 (1999) 9447; Appl. Phys. Lett. 75 (1999) 1665] Compound 1 showed the UV and the PL peak at 366 and 432 nm, respectively. The manufactured device (ITO/compound 1(600 Å)/Al) showed the EL peak at 412 nm. However, the structure of compound 1 was not fully identified as examined by experiment. In order to disclose the structure of compound 1, we proposed several possible compounds and calculated each compound, using the following methods. Hartree–Fock with the 3-21G(d) basis set was used for energy calculation and geometry optimizations of those compounds. Excitation energies were obtained from time-dependent density functional theory (TD-DFT) using the B3LYP functional with the 3-21G(d) basis set. As a result, [(box)(boxH)Li]₂ was found to be one of the possible compounds which had the most stable geometry structure. Its optical properties showed remarkably good agreement with the characterization data of compound 1. In addition, the structure of [(box)(boxH)Li]₂ was also compared well with that of LiBq₄ which was reported by the groups of Tao and was argumentatively asserted by Radu and coworkers [J. Am. Chem. Soc. 125 (2003) 880].     

Menus of kuratowski subgraphs

Motivated by heuristic embedding algorithms, this paper is concerned with the organization of potentially large lists of Kuratowski subgraphs of an arbitrary nonpianar graph. A graphical structure called a "nearly Hamiltonian" graph is defined. It is shown that lists of Kuralowski subgraphs can be lexicographically organized in such structures. It is shown that any nonpianar graph contains such structures and at least one such structure with a nonempty list of Kuratowski subgraphs can be located in linear time in ihe edges of the graph.     

Assessment of noise from “quiet” pile drivers

This paper summarizes the results of a study aimed at defining the basic characteristics of noise from a range of pile driving devices which were either adapted or designed specifically to generate noise levels below those normally expected. The parameters studied were noise levels, spectra and waveform shapes. In addition, the noise reduction techniques employed by each manufacturer are described in detail.     

Numerically stable methods for quadratic programming

Numerically stable algorithms for quadratic programming are discussed. A new algorithm is described for indefinite quadratic programming which utilizes methods for updating positivedefinite factorizations only. Consequently all the updating procedures required are common to algorithms for linearly-constrained optimization. The new algorithm can be used for the positive-definite case without loss of efficiency.