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  • 1980-1984  (4)
  • 1981  (4)
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  • 1980-1984  (4)
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  • 1
    Electronic Resource
    Electronic Resource
    A result from diophantine approximation which has applications in economics (1981)
    Springer
    Manuscripta mathematica 35 (1981), S. 271-276 
    Details
    ISSN: 1432-1785
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We say that a real number α allows “poor” approximations if we can find 0〈ɛ=ɛ(α)〈1 and a sequence of integers n1〈n2〈... such that for all rationals p/q with q≦n. we have |α−.p/q| 〉 Kn j −l−ε where K is a constant depending only on α. In this note we prove that the set of numbers which allow “poor” approximations are precisely the very well-approximable numbers. The existence of numbers with “poor” approximations has been used by Cheng [1] to show the existence of a dense set of economies whose cone converges to the Walras equilibrium as slowly as 0(n−1/2−ε) after n replications.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01263263
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Lifting-line theory of swept wings based on the full potential theory (1981)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 32 (1981), S. 481-496 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Zusammenfassung Die asymptotische Theorie von transonischen gepfeilten Flügeln mit hohem Seitenverhältnis (Ref. [2]–[5]) wird erweitert auf wirbelfreie kompressible Strömungen mit Verwendung der Gleichungen der vollständigen Potentialtheorie. Die Formulierung gestattet die Behandlung von eingeschlossenen superkritischen Gebieten mit Stößen; die Resultate sind für schiefe, rückwärts- und vorwärtsgepfeilte Flügel verwendbar, sind aber auf Flügelgrundrisse mit streckenweise geraden Mittellinien beschränkt. Die Anströmgeschwindigkeit liegt immer unterhalb der Schallgeschwindigkeit. Für Flügelgeometrien die durch ein einziges Profil erzeugt werden, gestattet ein reduziertes System in zwei Dimensionen Lösungen mit einer Ähnlichkeits-Struktur, die eine Lösung für alle Stationen entlang der Spannweite liefert. Betreffend der genauen Bestimmung von Widerstand und Auftrieb wird von der Theorie eine wesentliche Verbesserung gegenüber der Analyse von Pfeilflügeln erwartet, die auf der Theorie von kleinen Störungen basiert. Die Arbeit gibt auch die Grundlage für eine Untersuchung des Einflusses von abgehenden Wirbeln, die in bisherigen dreidimensionalen Computer-Programmen nur unvollständig berücksichtigt worden sind.
    Notes: Abstract The asymptotic theory of high-aspect-ratio transonic swept wings of Refs. [2–5] is extended to irrotational compressible flows based on equations of the full-potential theory. The formulation allows for imbedded supercritical flows with shocks; the results are applicable to oblique wings, swept-back as well as swept-forward wings, but restricted to planforms with centerlines composed of straight segments. The free-stream velocity is assumed to remain below the sonic speed. For a wing geometry generated from a single airfoil shape, the reduced system of 2-D equations admits solutions with similarity structures, permitting the problem to be solved only once for all span stations. The application of the theory is expected to lead to a substantial improvement over the earlier analysis of transonic swept wings based on the small-disturbance theory, concerning the accurate determination of inviscid drag and lift. The study provides also a basis for examining the influence of the trailing vortex sheet geometry, which are incompletely accounted for in current 3-D computer programs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00947016
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Synthetic membranes containing schardinger cyclodextrin additives (1981)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 26 (1981), S. 489-497 
    Details
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: The permeation characteristics of the isomers of such aromatics as dichlorobenzenes, nitrochlorobenzenes, xylenes, etc., through a Methocel HG membrane containing various amounts of Schardinger α-cyclodextrin and β-cyclodextrin additives were measured in liquid/liquid dialysis and pervaporation experiments. The results showed that the cyclodextrins are able to selectively mediate molecular transport through the Methocel HG membranes. In general, increased membrane selectivity and a decrease in permeation rates were observed. Permeation rates for some aromatic compounds were decreased several hundred times with only 25% amounts of additive cyclodextrins in the Methocel HG membranes. Concentration electrical potential and bi-ionic electrical potential in membranes containing the Schardinger cyclodextrin have been measured and also show that the cyclodextrins are able to induce ion transport selectively through nonionic membranes. Dynamic mechanical properties of Methocel HG membranes containing cyclodextrins suggest these additives to be antiplasticizing agents. A mechanism for the modification of the intrinsic membrane permeation properties by cyclodextrin additive involving antiplasticizing action by the additives plus induced tortuous diffusion, where the latter is a result of specific interactions between the cyclodextrin additive and the permeating molecules, is proposed.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/app.1981.070260209
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Tacticity of poly(N-vinyl pyrrolidone) (1981)
    New York : Wiley-Blackwell
    Journal of Polymer Science: Polymer Letters Edition 19 (1981), S. 29-31 
    Details
    ISSN: 0360-6384
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pol.1981.130190106
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    Paper (German National Licenses)
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