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  • 1
    Electronic Resource
    Electronic Resource
    Structure of the vapor–liquid interface near the critical point (1993)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 99 (1993), S. 582-589 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We measured the thicknesses of the vapor–liquid interfaces near the critical points of carbon dioxide (CO2), sulfur hexafluoride (SF6), and trifluoromethane (CHF3) using ellipsometry. The data (when scaled by the refractive index difference Δn and the correlation length ξ) are in agreement with other ellipticity data for binary and pseudobinary mixtures at low pressures. Fully constrained theories of the interface correctly predict the temperature dependence and scaling of the thickness but systematically overestimate the thickness itself by 15%–20%. The theory can be brought into agreement with experiment when an intrinsic interfacial stiffness is added to the theory. A novel feature of the present measurements is that the effects from pressure-induced window strain were measured and mitigated by using a cylindrically-symmetric pressure cell with floating seals.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.465784
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  • 2
    Electronic Resource
    Electronic Resource
    A stabilized vapor liquid interface in deuterated cyclohexane–methanol mixtures (1986)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 85 (1986), S. 3631-3635 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The ellipticity of the vapor–liquid interface above mixtures of methanol (CH3OH) and deuterated cyclohexane (C6D12) has been measured in the vicinity of the consolute point. The data above and below Tc are consistent with models for the structure of the interface adapted from the theory of Widom and Ramos-Gomez and Widom. As three-phase coexistence is approached, the quantity of methanol adsorbed at the interface increases whether ordinary or deuterated cyclohexane is used in the mixture. If ordinary cyclohexane were used for studies within the three-phase region below Tc, thick, unstable, lenticular films of the methanol-rich liquid phase would form at the interface and lead to nonreproducible data. In the present measurements lenticular films do not form when deuterated cyclohexane is used in the mixture. (The entire methanol-rich phase then forms on top.) The gravitationally stable interface above the deuterated mixture can be studied reliably in the three-phase region below Tc even though the liquid phases are nearly density matched.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.450934
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  • 3
    Electronic Resource
    Electronic Resource
    STUDIES OF THIN FILMS IN BINARY FLUID MIXTURES USING ELLIPSOMETRY (1983)
    Oxford, UK : Blackwell Publishing Ltd
    Annals of the New York Academy of Sciences 404 (1983), S. 0 
    Details
    ISSN: 1749-6632
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Natural Sciences in General
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1749-6632.1983.tb19495.x
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  • 4
    Electronic Resource
    Electronic Resource
    Unconstrained duals to partially separable constrained programs (1992)
    Springer
    Mathematical programming 56 (1992), S. 337-341 
    Details
    ISSN: 1436-4646
    Keywords: 90C25 ; 65K05 ; Lagrange dualization ; existence theorems ; numerical aspects
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this note partially separable convex programs are dualized in such a way that, under certain assumptions, unconstrained concave duals arise. A return formula is given by which the solution of the primal is directly computed if a solution of the dual is known. Further, the solvability of both the primal and the dual is shown to depend essentially on the behaviour of the lower dimensional programs for determining the Fenchel conjugates.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580906
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  • 5
    Electronic Resource
    Electronic Resource
    Über Verfahren zur zweiseitigen Approximation inverser Elemente (1976)
    Springer
    Computing 17 (1976), S. 59-67 
    Details
    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Abstract In a partially ordered ring, a set of iterative methods is constructed in order to approximate the inverse of a given element, not necessarily positive or inverse-positive. Two sequences are generated both converging to the inverse. In addition the inverse is monotonously enclosed. The method of order four has the maximal efficiency index.
    Notes: Zusammenfassung Anknüpfend an Arbeiten von G. Alefeld und J. Herzberger und von J. W. Schmidt werden in einem halbgeordneten RingR Iterationsverfahren untersucht, welche geeignet sind, die Inverse eines nicht notwendig positiven oder inverspositiven Elementesa∈R zu approximieren. Es werden jeweils zwei Folgen (X n ) und (y n ) konstruiert, welche beide gegen die Inversea −1 konvergieren und diese zusätzlich im Sinne vonX n−1 ≦X n ≦a −1 ≦y n ≦y n−1 monoton einschließen. Von den betrachteten Verfahren hat das vierter Ordnung den größten Effektivitätsindex.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02252260
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  • 6
    Electronic Resource
    Electronic Resource
    Monotone Einschließung von Inversen positiver Elemente durch Verfahren vom Schulz-Typ (1976)
    Springer
    Computing 16 (1976), S. 211-219 
    Details
    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Abstract The conditional iterationx n+1 =sup (x n ,x n +x n (e−ax n )),y n−1 =inf (y n ,x n +y n (e−ax n )) generating sequences (x n ) and (y n ) is considered in partially ordered spaces. Under certain conditions it is shown, that the inversea −1 of a positive elementa≧0 is monotonously enclosed in the sensex n ≦x n+1 ≦a −1 ≦y n+1 ≦y n and that (x n ) and (y n ) converge toa −1 quadratically.
    Notes: Zusammenfassung Es wird gezeigt, daß die bedingte Iterationx n+1 =sup (x n ,x n +x n (e−ax n )),y n+1 =inf (y n ,x n +y n (e−ax n )) unter bestimmten Voraussetzungen die Inversea −1 eines positiven Elementsa≧0 gemäßx n ≦x n+1 ≦a −1 ≦y n+1 ≦y n monoton einschließt und daß die Folgen (x n ) und (y n ) quadratisch gegena −1 konvergieren.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02280880
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  • 7
    Electronic Resource
    Electronic Resource
    On the R-order of coupled sequences (1981)
    Springer
    Computing 26 (1981), S. 333-342 
    Details
    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Für Folgen aus einem iterativen Näherungsverfahren, die einem mit Hilfe von Potenzfunktionen beschreibbaren System von Ungleichungen genügen, wird gezeigt, daß ihre R-Ordnung mindestens gleich dem Spektralradius der Matrix aus den Exponenten ist, sofern ein zum Spektralradius gehörender Eigenvektor mit ausschließlich positiven Komponenten existiert.
    Notes: Abstract The R-order of sequences, coupled by a system (1) of difference inequalities, is shown to be at least equal to the spectral radius of the matrix of the exponents if a positive eigenvector belonging to the spectral radius exists.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02237952
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  • 8
    Electronic Resource
    Electronic Resource
    A criterion for the positivity of rational cubicC 2-spline interpolants (1990)
    Springer
    Computing 44 (1990), S. 365-368 
    Details
    ISSN: 1436-5057
    Keywords: 65D07 ; 41A15 ; Positive spline interpolation ; sufficient and necessary existence condition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es wird eine hinreichend und notwendige Bedingung für die Positivität von rational-kubischen Splines angegeben, welche sich leicht überprüfen läßt. Sie ist bei Interpolationsdaten mit positiven Ordinaten durch hinreichend große Rationalitätsparameter stets erfüllbar.
    Notes: Abstract By means of a finite set of inequalities a sufficient and necessary condition for the positivity of rational cubic splines is given which holds true whenever the rationality parameters are sufficiently large.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02241274
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  • 9
    Electronic Resource
    Electronic Resource
    Ableitungsfreie Verfahren ohne Auflösung linearer Gleichungen (1970)
    Springer
    Computing 5 (1970), S. 71-81 
    Details
    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Summary Iteration methods are given for the solution of nonlinear equations in normed spaces requiring functionvalues and first-order divided differences. The latter may be replaced by derivations. The linear equations of each iteration step are solved only approximatively but this does not diminish the order of convergence.
    Notes: Zusammenfassung Zur Lösung von nichtlinearen Gleichungen in normierten Räumen werden Iterationsverfahren angegeben, die Funktionswerte und Steigungen erster Ordnung benutzen. Es ist möglich, die Steigungen durch Ableitungen zu ersetzen. Die linearen Gleichungen, die in jedem Iterationsschritt auftreten, werden nur näherungsweise gelöst. Dabei ist es wichtig, daß hierdurch keine Verringerung der Konvergenzgeschwindigkeit eintritt.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02234251
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  • 10
    Electronic Resource
    Electronic Resource
    Extremwertermittlung mit Funktionswerten bei Funktionen von mehreren Veränderlichen (1966)
    Springer
    Computing 1 (1966), S. 224-232 
    Details
    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Summary The idea of regula falsi to use only function-values is extended to the computing of extreme-values by differentiable functions of several variables. Iterative methods of this kind will be found by approximating the function by an interpolation polynomial and by taking its extreme-value. The interpolation polynomial being appropriately chosen, the methods converge if the initial values approximate the solution sufficiently well. The speed of convergence is better than linear.
    Notes: Zusammenfassung Es wird die Idee der Regula falsi, allein mit Funktionswerten zu arbeiten, auf die Extremwertbestimmung bei differenzierbaren Funktionen von mehreren Veränderlichen übertragen. Derartige Iterationsverfahren lassen sich angeben, indem man die Funktion durch ein Interpolationspolynom ersetzt und als Näherung seine Extremwerte ermittelt. Bei geeigneter Wahl des Interpolationspolynoms erhält man Verfahren, die bei hinreichend guten Anfangsnäherungen stets konvergieren. Die Konvergenzgeschwindigkeit ist überlinear.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02234365
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