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  • 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
    A multiplicative barrier function method for linear programming (1986)
    Springer
    Algorithmica 1 (1986), S. 455-482 
    Details
    ISSN: 1432-0541
    Keywords: Linear programming ; Interior method ; Barrier function ; Newton method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A simple Newton-like descent algorithm for linear programming is proposed together with results of preliminary computational experiments on small- and medium-size problems. The proposed algorithm gives local superlinear convergence to the optimum and, experimentally, shows global linear convergence. It is similar to Karmarkar's algorithm in that it is an interior feasible direction method and self-correcting, while it is quite different from Karmarkar's in that it gives superlinear convergence and that no artificial extra constraint is introduced nor is protective geometry needed, but only affine geometry suffices.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01840457
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Mechanical control of foaming in a bubble column (1984)
    New York, NY [u.a.] : Wiley-Blackwell
    Biotechnology and Bioengineering 26 (1984), S. 702-713 
    Details
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: This study was performed to evaluate the effects of the air sparge rate, working liquid volume, liquid feed rate onto the disk, and disk diameter on the foam-breaking performance of foam-breaking apparatus with a rotating disk (FARD) installed in the bubble column. Experimental results showed that the smaller the air sparge rate and working liquid volume were, and the larger the liquid feed rate and disk diameter, the lower the critical disk rotational speed required for reduced foam-breaking. The presence of the effective ranges of the disk diameter and liquid feed rate for foam breaking was also confirmed. Furthermore, the quantitative predictions of the upper limits of the liquid feed rate, foam-breaking regions, and the required foam-breaking power were carried out, based on the results obtained above. Comparison of the FARD with two conventional mechanical foam-breaking spray-type apparati also demonstrated the highest level of the FARD in respect not only to foam-breaking performance but also to power requirements.
    Additional Material: 21 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/bit.260260712
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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)
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  • 5
    Electronic Resource
    Electronic Resource
    Simulation of citric acid production by rotating disk contactor (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Biotechnology and Bioengineering 56 (1997), S. 689-696 
    Details
    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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    Paper (German National Licenses)
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