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  • Computational geometry  (2)
  • Modified pruning technique  (1)
  • Polymer and Materials Science  (1)
  • Potential function  (1)
  • Shortest path  (1)
  • Visibility  (1)
Source
Material
Years
Keywords
  • 1
    Electronic Resource
    Electronic Resource
    On the convexity of the multiplicative version of Karmarkar's potential function (1988)
    Springer
    Mathematical programming 40 (1988), S. 29-32 
    Details
    ISSN: 1436-4646
    Keywords: Potential function ; multiplicative penalty function ; convexity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Karmarkar's potential function is quasi-convex, but not convex. This note investigates the multiplicative version of the potential function, and shows that it is not necessarily convex in general, but is strictly convex when the corresponding feasible region is bounded. This implies that the multiplicative version of the potential function in Karmarkar's algorithm is convex, since it works on a simplex.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580721
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Visibility of disjoint polygons (1986)
    Springer
    Algorithmica 1 (1986), S. 49-63 
    Details
    ISSN: 1432-0541
    Keywords: Computational geometry ; Computer graphics ; Robotics ; Visibility ; Hidden-line Elimination ; Visibility graph ; Shortest path
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Consider a collection of disjoint polygons in the plane containing a total ofn edges. We show how to build, inO(n 2) time and space, a data structure from which inO(n) time we can compute the visibility polygon of a given point with respect to the polygon collection. As an application of this structure, the visibility graph of the given polygons can be constructed inO(n 2) time and space. This implies that the shortest path that connects two points in the plane and avoids the polygons in our collection can be computed inO(n 2) time, improving earlierO(n 2 logn) results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01840436
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    A linear-time algorithm for linearL 1 approximation of points (1989)
    Springer
    Algorithmica 4 (1989), S. 77-96 
    Details
    ISSN: 1432-0541
    Keywords: Computational geometry ; Modified pruning technique ; LinearL 1 approximation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we present a linear-time algorithm for approximating a set ofn points by a linear function, or a line, that minimizes theL 1 norm. The algorithmic complexity of this problem appears not to have been investigated, although anO(n 3) naive algorithm can be easily obtained based on some simple characteristics of an optimumL 1 solution. Our linear-time algorithm is optimal within a constant factor and enables us to use linearL 1 approximation of many points in practice. The complexity ofL 1 linear approximation of a piecewise linear function is also touched upon.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01553880
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Synthesis and ion-coupling reactions of telechelic polystyrene having cyclic onium salt groupsThis paper is dedicated to Professor Teiji Tsuruta in honor of his 75th birthday (1997)
    Weinheim : Wiley-Blackwell
    Macromolecular Chemistry and Physics 198 (1997), S. 627-641 
    Details
    ISSN: 1022-1352
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: A series of mono- and bifunctional polystyrenes (1 c and 1′c) having 1-methylpyrrolidinium salt end groups were prepared through sequential derivatization, i.e., tosylation and quaternization reactions, of prepolymers having 3-hydroxypropyl groups (1 a and 1′a) produced by end-capping reactions of the relevant living polymers. The 1-methylpyrrolidinium salt end group was found to undergo a selective ring-opening reaction at 100°C by nucleophilic attack of a benzoate counter anion introduced by ion-exchange reaction. The ion-coupling reaction of 1 c and 1′c with poly(styrene-co-acrylate salt) was found to take place upon coprecipitation of an equimolar mixture into methanol to afford ionically linked pseudo-graft and network products, respectively. The subsequent heat treatment, converting the ionic bond into a covalent one, results in branched and crosslinked polystyrene with predetermined structural parameters.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/macp.1997.021980234
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    Paper (German National Licenses)
    Fulltext
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