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  • 1
    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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    Paper (German National Licenses)
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  • 2
    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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    Paper (German National Licenses)
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  • 3
    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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  • 4
    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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  • 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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    Paper (German National Licenses)
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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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    Paper (German National Licenses)
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  • 7
    Electronic Resource
    Electronic Resource
    Characterization of minimal elements in minimization problems with constraints (1978)
    Springer
    Journal of optimization theory and applications 24 (1978), S. 549-567 
    Details
    ISSN: 1573-2878
    Keywords: Minimization with constraints ; generalized weight function ; characterization theorems ; critical point ; extremal signature
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract LetX be a compact Hausdorff space andC(X) be the set of all continuous functions defined onX. LetV⊂C(X), and consider the problem of minimizing sup x∈X W[x,v(x)], withv∈V. The functionW is a generalized weight function and can be chosen such that certain constraints are included. The notions of critical point and extremal signature are used to formulate characterization theorems for a minimal element inV. It is shown that these theorems hold only under certain conditions ofV andW. The results obtained are applied to the problem of the Chebyshev approximation with constraints and to the problem of optimization with strictly quasiconvex constraints.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935299
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  • 8
    Electronic Resource
    Electronic Resource
    Differentiable dependence upon the data in a one-phase Stefan problem (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 73-90 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: It is well known that the free boundary of the one-phase Stefan problem (1.1-5) depends continuously on the boundary data [1]. In this paper we prove that, in addition, the solution operator S which, to each g. assigns the corresponding free boundary, is continuously Frechet differentiable and we give the defining formulas of the Frechet derivative.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670020108
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    Paper (German National Licenses)
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  • 9
    Electronic Resource
    Electronic Resource
    Admissibility and uniqueness of weak solutions to hyperbolic systems of balance laws (1989)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 253-269 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A system of quasi-linear first-order equations written in the divergence form and constrained by the unilateral differential inequality (the second law of thermodynamics) with a strictly concave entropy function is analysed. In the class BV, i.e. a subset of regular distributions represented by functions of bounded variation in the sense of Tonelli-Cesari, a weak solution to the system is defined. The parabolized version of the system is also discussed in order to define an admissible weak solution as a limit of a sequence of Lipschitz continuous solutions to the parabolic problem. It is proved that an admissible weak solution of the Cauchy problem is unique in the class BV.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670110206
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  • 10
    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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    Paper (German National Licenses)
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