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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Computing 36 (1986), S. 335-342 
    ISSN: 1436-5057
    Keywords: 65D07 ; 41A15 ; 90C20 ; Convexity conditions ; weakly coupled system of inequalities ; numerical algorithms ; quadratic programming ; unconstrained dual program with tridiagonal Hessian
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Während die Aufgabe der konvexen Interpolation im Falle kubischer Splines im allgemeineen nicht lösbar ist, kann jetzt gezeigt werden, daß sie bei Verwendung von Exponentialsplines Lösungen besitzt sofern die vorkommenden Parameter hinreichend roß sind, und es werden konkrete hinreichende und notwendige Lösbarkeitsbedingungen hergeleitet. Da eindeutige Lösbarkeit in der Regel nicht vorliegt, wird eine Auswahlfunktion eingeführt und das entstehende quadratische Optimierungsproblem nach Dualisierung numerisch behandelt.
    Notes: Abstract Sufficient and necessary conditions are derived under which interpolating splines are convex if the data set is in convex position. In order to select one of the interpolants, by means of a well-known objective function a quadratic optimization problem is stated which can be solved effectively by passing to a dual program.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Computing 39 (1987), S. 133-140 
    ISSN: 1436-5057
    Keywords: 65D10 ; 41A15 ; 90C20 ; Specially structured optimization problem ; Fenchel dualization ; return-formula
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es wird die Aufgabe betrachtet, eine vorgegebene Datenmenge durch konvexe kubischeC 1-Splines zu approximieren. Zu diesem Problem wird eine zugehörige duale Optimierungsaufgabe konstruiert, welche den Vorteil hat, daß keine Nebenbedingungen auftreten, und welche sich daher effektiver als das Ausgangsproblem numerisch behandeln läßt.
    Notes: Abstract In the present paper the problem of approximating given data sets by convex cubicC 1-splines is considered. To this programming problem a dual program is constructed which is unconstrained. Therefore an efficient computational treatment is possible.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Computing 35 (1985), S. 219-229 
    ISSN: 1436-5057
    Keywords: 65K05 ; 65D07 ; 90C20 ; 41A15 ; Existence conditions ; quadratic programming ; dual optimization problem ; tridiagonal Hessian ; Newton's method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Das Problem, konvexe Interpolationssplines mit minimaler mittlerer Krümmung zu ermitteln, führt auf eine speziell strukturierte quadratische Optimierungsaufgabe. In der vorliegenden Note wird eine zugehörige duale Aufgabe aufgestellt, die ohne Nebenbedingungen auskommt, deren Zielfunktion stückweise quadratisch ist und die daher eine effektive numerische Behandlung erlaubt.
    Notes: Abstract The problem of finding convex spline interpolants with minimal mean curvature leads to a quadratic optimization problem of special structure. In the present note a corresponding dual problem without constraints is derived. Its objective function is piecewise quadratic and therefore admits an effective numerical treatment.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Chemie Ingenieur Technik - CIT 67 (1995), S. 1126-1127 
    ISSN: 0009-286X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 27 (1982), S. 1277-1291 
    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: Viscosity measurements were carried out as a function of pressure and temperature with solutions of polystyrene in eight (endothermal) θ-solvents at the respective critical composition by means of a Searle-type apparatus. A rolling-ball viscometer was used for the investigation of the pure solvents. In all cases the viscosity coefficient increases in a more or less exponential manner when the pressure is raised. For θ-conditions, the volumes of activation of the solutions exceed that of the pure solvent by typically 10-15%. The exact amount of this extra efffect stemming from the presence of the polymer and its variation with temperature can be qualitatively correlated with the heats of mixing. The ratio of the viscosity of the solution at 1000 and 1 bar, respectively, can be varied for a given solvent power (θ-temperature) by the choice of the solvent from ca. 2 (cyclopentane) to 4 (trans-decalin). Within a given system, the maximum effects that can be realized by a change of the solvent power via the variation of temperature ranges from ca. 3 to 6 (tert-butylacetate).
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    Journal of Polymer Science 45 (1960), S. 189-194 
    ISSN: 0022-3832
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Kinetic measurements have been made on the bulk polymerization of styrene at 30 and 60°C. in the redox system dimethylaniline-benzoyl peroxide. From these measurements it has been ascertained that the kinetic behavior of this system at higher temperatures is the same as that at lower temperatures. The decomposition rate constant and the efficiency in initiating polymerization were determined. It has also been shown that neither the amine nor the products of the amine-peroxide reaction affect the propagation of the polymerization.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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  • 7
    ISSN: 0009-286X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    Advances in Polymer Technology 2 (1993), S. 75-106 
    ISSN: 0730-6679
    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
    Notes: The design of extrusion lines deals with the extruder and the die as well as with the down stream equipment, especially the cooling section. This paper aids in the design of these three units, regarding different aspects. The scale-up of extruders by means of the model theory is demonstrated in its practical use with examples. Emphasis is laid on the design of series of single screw extruders with mixing-pins and of twin-screw extruders (scale-up). There the adequate selection of the necessary restrictions for the compilation of model laws is discussed in detail. This is an approach to the safe machine design on the basis of model theory.The present standard of the calculation of threedimensional flow patterns in extrusion dies by means of the finite-element-method (FEM) is shown in order to point out how design-aids for the die-designer are derived from these calculations. After a discussion of application-criteria for the FEM, examples will show possible ways of using FEM-results.For the shaping of Y-branches in twin-screw machines the FEM-results point to possible plate-out areas and to their avoidance by geometrical modifications. The calculation of a die for a T-profile helps to design the passages between entry and exit sections. Finally, flow coefficients for the calculation of pressure losses in different cross sections are given.The design and optimization of cooling sections, as it can be done with the aid of the actual cooling models, is shown for some important extrusion processes. Heat transfer coefficients for practical cases (film-sheet-, pipe- and parison extrusion) are presented. Examples show, how diagrams for the design and optimization of cooling sections (for example the reduction of internal stresses and warping) can be made, using a microcomputer.
    Additional Material: 31 Ill.
    Type of Medium: Electronic Resource
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