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  • Articles: DFG German National Licenses  (3)
  • Aspergillus niger  (1)
  • LinearL 1 approximation  (1)
  • Potential function  (1)
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  • Articles: DFG German National Licenses  (3)
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Years
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical programming 40 (1988), S. 29-32 
    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
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Algorithmica 4 (1989), S. 77-96 
    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
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  • 3
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Biotechnology and Bioengineering 56 (1997), S. 689-696 
    ISSN: 0006-3592
    Keywords: citric acid ; Aspergillus niger ; rotating disk contactor ; simulation ; biofilm ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A simple model was presented to describe the time courses of citric acid production by a rotating disc contactor (RDC) using Aspergillus niger. The model is expressed by Monod-type cell growth, Luedeking-Piret-type citric acid production rate equations, and the diffusion equation for oxygen in the biofilm. The model contains five parameters which were determined by the nonlinear least squares method by fitting the numerical solution to the experimental data. In solving the equations, the cell density of the biofilm was estimated from the value of cellular mass per unit of biofilm area using an empirical equation. The experimental time courses in citric acid production period were well simulated with this model. The relation between the specific biofilm surface area and the rate of citric acid production was also explained by the simulation using the average values of five parameters of twelve runs. © 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 56: 689-696, 1997.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
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