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  • 1
    Electronic Resource
    Electronic Resource
    Bounds for bounded motion around a perturbed fixed point (1988)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 39 (1988), S. 813-825 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We consider a dissipative map of the plane with a bounded perturbation term. This perturbation represents e.g. an extra time dependent term, a coupling to another system or noise. The unperturbed map has a spiral attracting fixed point. We derive an analytical/numerical method to determine the effect of the additional term on the phase portrait of the original map, as a function of the boundδ on the perturbation. This method yields a valueδ c such that forδ〈δ c the orbits about the attractor are certainly bounded. In that case we obtain a largest region in which all orbits remain bounded and a smallest region in which these bounded orbits are captured after some time (the analogue of “basin” and “attractor” respectively). The analysis is based on the Lyapunov function which exists for the unperturbed map.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00945120
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Complexes of block copolymers in solution: Tree approximation (1989)
    Springer
    Journal of statistical physics 57 (1989), S. 1069-1098 
    Details
    ISSN: 1572-9613
    Keywords: Block copolymers ; generating function ; Polya's theorem ; gelation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We determine the statistical properties of block copolymer complexes in solution. These complexes are assumed to have the topological structure of (i) a tree or of (ii) a line-dressed tree. In case the structure is that of a tree, the system is shown to undergo a gelation transition at sufficiently high polymer concentration. However, if the structure is that of a line-dressed tree, this transition is absent. Hence, we show the assumption about the topological structure to be relevant for the statistical properties of the system. We determine the average size of the complexes and calculate the viscosity of the system under the assumption that the complexes geometrically can be treated as porous spheres.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01020049
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Complexes of block copolymers in solution: A graph-theoretical approach (1989)
    Springer
    Journal of statistical physics 57 (1989), S. 1099-1122 
    Details
    ISSN: 1572-9613
    Keywords: Block copolymers ; generating function method ; Polya's theorem ; gelation ; nonnested structures
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We determine the statistical properties of block copolymers in solution. These complexes are assumed to have the topological structure of connected graphs with “nonnested” loops and cycles. The generating function method is used to determine the number of topologically different complexes containing a given number of block copolymers. It is shown that at sufficiently high concentration the system undergoes a transition to a gel phase. Furthermore, the average number of polymers per complex is calculated. Finally, the relative increase in viscosity is found under the assumption that the complexes can be treated as porous spheres.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01020050
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    An algorithm for determining the approximation orders of multivariate periodic spline spaces (1993)
    Springer
    Numerical algorithms 5 (1993), S. 71-81 
    Details
    ISSN: 1572-9265
    Keywords: Approximation order ; multivariate splines ; polynomial splines ; 41A15 ; 65D07
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We give an algorithm which computes the approximation order of spaces of periodic piece-wise polynomial functions, given the degree, the smoothness and tesselation. The algorithm consists of two steps. The first gives an upper bound and the second a lower bound on the approximation order. In all known cases the two bounds coincide.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02109285
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  • 5
    Electronic Resource
    Electronic Resource
    Degenerate polynomial patches of degree 11 for almostGC 2 interpolation over triangles (1993)
    Springer
    Numerical algorithms 5 (1993), S. 557-568 
    Details
    ISSN: 1572-9265
    Keywords: Approximation by polynomials ; interpolation ; degenerate patches ; 41A05 ; 41A10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We consider the problem of interpolating scattered data in ℝ3 by analmost geometrically smoothGC 2 surface, where almostGC 2 meansGC 2 except in a finite number of points (the vertices), where the surface isGC 1. A local method is proposed, based on employing so-called degenerate triangular Bernstein-Bézier patches. We give an analysis of quintic patches forGC 1 and patches of degree eleven for almostGC 2 interpolation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02113891
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    Paper (German National Licenses)
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