A sequential sorting network analogous to the batcher merge

We present a network of delay log₂N, whose comparators have only log₂N different lengths with maximum length N/2. This network is log-sequential in that it will sort N data items when they are passed through it log₂Ntimes. The design, which is related to the Batcher odd-even merge, is distinctly different from the first known example of a log-delay log-sequential network, due to Dowd, Perl, Rudolf, and Saks. It is quite probably the best possible sorting network.     

Properties of a representation of a basis for the null space

Given a rectangular matrixA(x) that depends on the independent variablesx, many constrained optimization methods involve computations withZ(x), a matrix whose columns form a basis for the null space ofA ^T(x). WhenA is evaluated at a given point, it is well known that a suitableZ (satisfyingA ^T Z = 0) can be obtained from standard matrix factorizations. However, Coleman and Sorensen have recently shown that standard orthogonal factorization methods may produce orthogonal bases that do not vary continuously withx; they also suggest several techniques for adapting these schemes so as to ensure continuity ofZ in the neighborhood of a given point.This paper is an extension of an earlier note that defines the procedure for computingZ. Here, we first describe howZ can be obtained byupdating an explicit QR factorization with Householder transformations. The properties of this representation ofZ with respect to perturbations inA are discussed, including explicit bounds on the change inZ. We then introduceregularized Householder transformations, and show that their use implies continuity of the full matrixQ. The convergence ofZ andQ under appropriate assumptions is then proved. Finally, we indicate why the chosen form ofZ is convenient in certain methods for nonlinearly constrained optimization.The research of the Stanford authors was supported by the U.S. Department of Energy Contract DE-AM03-76SF00326, PA No. DE-AT03-76ER72018; the National Science Foundation Grants MCS-7926009 and ECS-8312142; the Office of Naval Research Contract N00014-75-C-0267; and the U.S. Army Research Office Contract DAAG29-84-K-0156.The research of G.W. Stewart was supported by the Air Force Office of Scientific Research Contract AFOSR-82-0078.     

Inhibition of bacterial ice nucleators by fish antifreeze glycoproteins

Certain bacteria promote the formation of ice in super-cooled water by means of ice nucleators which contain a unique protein associated with the cell membrane. Ice nucleators in general are believed to act by mimicking the structure of an ice crystal surface, thus imposing an ice-like arrangement on the water molecules in contact with the nucleating surface and lowering the energy necessary for the initiation of ice formation. Quantitative investigation of the bacterial ice-nucleating process has recently been made possible by the discovery of certain bacteria that shed stable membrane vesicles with ice nucleating activity. The opposite effect, inhibition of ice formation, has been described for a group of glycoproteins found in different fish and insect species. This group of substances, termed antifreeze glycoproteins (AFGPs), promotes the supercooling of water with no appreciable effect on the equilibrium freezing point or melting temperature. Substantial evidence now indicates that AFGPs act by binding to a growing ice crystal and slowing crystal growth. As the ice-nucleating protein surface is believed to have a structure similar to an embryonic ice crystal, AFGPs might be predicted to interact directly with a bacterial ice-nucleating site. We report here that AFGPs from the antarctic fish Dissostichus mawsoni inhibit the ice-nucleating activity of membrane vesicles from the bacterium Erwinia herbicola. The inhibition effect shows saturation at high concentration of AFGP and conforms to a simple binding reaction between the AFGP and the nucleation centre.     

New tetrahydroanthraquinones from the genus Cortinarius

Austrocortirubin and austrocortilutein the first hydroxylated tetrahydro-anthraquinones from Basidiomycetes, have been isolated from an Australian toadstool belonging to the subgenus Dermocybe of Cortinarius.     

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.