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  • 1
    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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    Paper (German National Licenses)
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  • 2
    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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    Paper (German National Licenses)
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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
    On theR-order of coupled sequences arising in single-step type methods (1988)
    Springer
    Numerische Mathematik 53 (1988), S. 653-661 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65H10 ; 15A48 ; CR: G1.5
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary As shown in preceding papers of the authors, the verification of anR-convergence order τ for sequences coupled by a system (1.1) of basic inequalities can be reduced to the positive solvability of system (3.3) of linear inequalities. Further, the bestR-order $$\bar \tau$$ implied by (1.1) is equal to the minimal spectral radius of certain matrices composed from the exponents occuring in (1.1). Now, these results are proven in a unified and essentially simpler way. Moreover, they are somewhat extended in order to facilitate applications to concrete methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01397134
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  • 5
    Electronic Resource
    Electronic Resource
    Ausgangsvektoren für monotone Iterationen bei linearen Gleichungssystemen (1964)
    Springer
    Numerische Mathematik 6 (1964), S. 78-88 
    Details
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01386057
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    Powell-Sabin splines in range restricted interpolation of scattered data (1994)
    Springer
    Computing 53 (1994), S. 137-154 
    Details
    ISSN: 1436-5057
    Keywords: 65D05 ; 65D07 ; 41A15 ; Shape preserving interpolation of scattered data ; range restrictions ; Powell-Sabin splines ; minimum norm modification ; thin plate functional
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Behandelt wird die Interpolation unregelmäßig verteilter Daten durch quadratische Powell-Sabin-Splines, wobei stückweise konstante obere und untere Schranken für die Funktionswerte der Interpolierenden vorgegeben sind. Die hergeleiteten hinreichenden Bedingungen für die Einhaltung der zweiseitigen Schranken ergeben ein lösbares lineares Ungleichungssytem für die Gradienten als Parameter, welches bezüglich der Datenpunkte separiert ist. Die Auswahl von visuell gefälligen Interpolierenden erfolgt durch die Minimierung geeigneter Funktionale.
    Notes: Abstract The construction of range restricted bivariateC 1 interpolants to scattered data is considered. In particular, we deal with quadratic spline interpolation on a Powell-Sabin refinement of a triangulation of the data sites subject to piecewise constant lower and upper bounds on the values of the interpolant. The derived sufficient conditions for the fulfillment of the range restrictions result in a solvable system of linear inequalities for the gradients as parameters, which is separated with respect to the data sites. Since there exists an infinite number of spline interpolants meeting the constraints, the selection of a visually pleasant solution is based on the minimum norm modification of a suitable initial interpolant or on the minimization of the thin plate functional. While the first proposal reduces to the solution of independent local quadratic programs, the second proposal results in a global quadratic optimization problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02252986
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  • 7
    Electronic Resource
    Electronic Resource
    Konvergenz von quadratischen Interpolations- und Flächenabgleichssplines (1978)
    Springer
    Computing 19 (1978), S. 351-363 
    Details
    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Abstract The purpose of this paper is to show that for continuous functions the related quadratic splines converge without any assumption on the spline grid. The points of the interpolatory grid can be chosen between the corresponding points of the spline grid with a division ratio from $$\frac{{\sqrt 2 }}{2}$$ to $$1 - \frac{{\sqrt 2 }}{2}$$ . In the case of continuously differentiable functions the division ratio can even be taken between 0 and 1; in addition, the order of convergence is increased. For twice differentiable functions the full order of convergence is obtained. Analogous results about the convergence of histo splines are proved.
    Notes: Zusammenfassung In der Hauptsache wird gezeigt, daß quadratische Interpolationssplines ohne zusätzliche Voraussetzungen an das Splinegitter gegen die erzeugende Funktion konvergieren, sofern diese stetig ist. Dabei kann das Interpolationsgitter mit einem zwischen $$1 - \frac{{\sqrt 2 }}{2}$$ und $$\frac{{\sqrt 2 }}{2}$$ gelegenen Teilungsverhältnis aus dem Splinegitter erzeugt werden. Im Falle von stetig differenzierbaren Funktionen, bei denen das Teilungsverhältnis sogar zwischen 0 und 1 gewählt werden kann, erhöht sich die Konvergenzordnung der zugehörigen Splines und wird bei zweimaliger Differenzierbarkeit voll ausgeschöpft. Analoge Resultate werden über die Konvergenz von Flächenabgleichssplines gewonnen.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02252032
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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
    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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