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  • 1
    Electronic Resource
    Electronic Resource
    Über Tschebyscheffsche Approximationen durch asymptotisch konvexe Funktionenfamilien (1966)
    Springer
    Computing 1 (1966), S. 214-223 
    Details
    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Summary In this paper we investigateTschebyscheff-Approximations for realvalued continuous functions by asymptotic convex familiesV of functions, which depend on a finite-dimensional set of real parameters. To obtain a characterization of best approximation extremal signatures are defined. We derive necessary and sufficient conditions for a subset ofV to be a set of best approximations for a given continuous functionf and for the dimension of the set of all best approximations forf to be bounded by a constant independent off. Finally we consider approximations by familiesV, which are differentiable in the parameters.
    Notes: Zusammenfassung In dieser Arbeit untersuchen wirTschebyscheffsche Approximationen an reellwertige stetige Funktionen durch asymptotisch konvexe FunktionenfamilienV, die von endlich vielen reellen Parametern abhängen. Zur Charakterisierung der besten Approximation werden Extremalsignaturen definiert. Wir leiten notwendige und hinreichende Bedingungen dafür her, daß eine Teilmenge vonV eine Menge von besten Approximationen für eine gegebene stetige Funktionf ist und daß die Dimension der Menge aller Minimallösungen fürf unter einer vonf unabhängigen Schranke bleibt. Schließlich betrachten wir Approximationen durch Funktionenfamilien, die nach den Parametern differenzierbar sind.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02234364
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  • 2
    Electronic Resource
    Electronic Resource
    Über eine Fixpunkteigenschaft der metrischen Projektion (1970)
    Springer
    Computing 5 (1970), S. 295-302 
    Details
    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Summary The generalizedKolmogoroff-criterion is always sufficient, but, in general, not necessary for a best approximation. With the aid of a fixed-point property of the metric projection, we give a characterization of certain subsets of a linear normed vector spaceR, for which, for every elementf inR, there is a best approximationv 0 off such thatv 0 satisfies theKolmogoroff-criterion.
    Notes: Zusammenfassung DasKolmogoroff-Kriterium ist stets eine hinreichende jedoch im allgemeinen nicht notwendige Bedingung für eine beste Approximation. Mit Hilfe einer Fixpunkteigenschaft der metrischen Projektion werden gewisse der Teilmengen eines normierten VektorraumesR charakterisiert, für die für jedes Elementf ausR mindestens eine beste Approximation fürf existiert, die demKolmogoroff-Kriterium genügt.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02248029
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  • 3
    Electronic Resource
    Electronic Resource
    Eine Variationsungleichung und Anwendungen (1974)
    Springer
    Numerische Mathematik 22 (1974), S. 137-147 
    Details
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper we prove a variational inequality which gives a necessary condition for a minimum of a certain in general non-differentiable function. This inequality is applied to problems of best approximation and optimization to deduce global conditions for a minimum.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01436728
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  • 4
    Electronic Resource
    Electronic Resource
    Chebychev sets which are not suns (1974)
    Springer
    Mathematische Annalen 212 (1974), S. 89-101 
    Details
    ISSN: 1432-1807
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01350779
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  • 5
    Electronic Resource
    Electronic Resource
    The interaction of the solar wind with a comet (1967)
    Springer
    Solar physics 1 (1967), S. 254-284 
    Details
    ISSN: 1573-093X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The flow of plasma on the sunward side of a comet is investigated by means of an axialsymmetric model based on hydrodynamics modified by source terms. The model assumes a given curvature of the isobaric surfaces, which corresponds to paraboloids around the nucleus of the comet. The flow on the axis can be represented by a solution of a system of seven ordinary differential equations (respectively five in case of pure photo-ionization). The flow pattern always contains a widely detached bow shock and a contact discontinuity separating a cavity with purely cometary plasma from the transition region containing also solar wind ions. The model is applied to the special case where the cometary gas is ionized by the solar UV radiation only. Numerical solutions are integrated for five levels of production of neutral gas by the comet and for seven typical situations in the undisturbed solar wind. The results imply standoff distances of the stagnation point from the nucleus of the order of 10 000 km or more, and distances of the bow shock of the order of 106–107 km.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00150860
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  • 6
    Electronic Resource
    Electronic Resource
    A refinement of an optimality criterion and its application to parametric programming (1984)
    Springer
    Journal of optimization theory and applications 42 (1984), S. 367-382 
    Details
    ISSN: 1573-2878
    Keywords: Semi-infinite optimization ; optimality criteria ; strong uniqueness ; parametric optimization ; numerical algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider semi-infinite linear minimization problems and prove a refinement of an optimality condition proved earlier by the author. This refinement is used to derive a sufficient condition for strong uniqueness of a minimal point. As an application, we show that these strongly unique minimal points depend (pointwise) Lipschitz-continuously on the parameter of the minimization problem. Finally, we consider numerical algorithms for semi-infinite optimization problems and we apply the above results to derive error estimates for these algorithms.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935322
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  • 7
    Electronic Resource
    Electronic Resource
    On the low wave number asymtotics for the two-dimensional exterior dirichlet problem for the reduced wave equationDedicated to E. Martensen on the occasion of his 60th birthday (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 335-341 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A new proof is given for the low wave number asymptotics for the solutions to the exterior Dirichlet problem for the reduced wave equation in two dimensions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670090126
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  • 8
    Electronic Resource
    Electronic Resource
    A penalty approximation for a unilateral contact problem in non-linear elasticity (1989)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 447-458 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Using Ball's approach to non-linear elasticity, and in particular his concept of polyconvexity, we treat a unilateral three-dimensional contact problem for a hyperelastic body under volume and surface forces. Here the unilateral constraint is described by a sublinear function which can model the contact with a rigid convex cone. We obtain a solution to this generally non-convex, semicoercive Signorinin problem as a limit of solutions of related energy minimization problems involving friction normal to the contact surface where the friction coefficient goes to infinity. Thus we extend an approximation result of Duvaut and Lions for linear-elastic unilateral contact problems to finite deformations and to a class of non-linear elastic materials including the material models of Ogden and of Mooney-Rivlin for rubberlike materials.Moreover, the underlying penalty method is shown to be exact, that is a sufficiently large friction coefficient in the auxiliary energy minimization problems suffices to produce a solution of the original unilateral problem, provided a Lagrange multiplier to the unilateral constraint exists.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670110403
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  • 9
    Electronic Resource
    Electronic Resource
    Variational derivatives and p-gradients of functionals on spaces of continuously differentiable functions (1983)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 5 (1983), S. 530-543 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The purpose of this paper is to introduce and study a new type of derivative - the variational gradient - for a functional on Cn[a, b]. Local and global versions of this concept are analyzed. This notion provides a natural approach to variational derivatives on Cn[a, b] under rather mild smoothness assumptions on the functional. When applied in the context of the Calculus of Variations, the notion of the variational gradient captures the natural boundary conditions (as well as the Euler-Lagrange equations) under weaker smoothness assumptions than those usually required using Gǎteaux variations.Conditions are established for the existence of the variational derivative and an integral representation for the Gǎteaux variation in terms of the variational derivative is derived. Conditions for the variational derivative to be differentiable are also established.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670050132
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  • 10
    Electronic Resource
    Electronic Resource
    An existence theorem for Poiseuille flow with surface tension in an open channel (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 23-30 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Poiseuille-type flow in an open channel is studied taking surface tension and wall adhesion into account. A proof is presented of the existence of a solution under certain conditions.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670130103
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