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  • 1
    Electronic Resource
    Electronic Resource
    Laser fluorimetry studies of ionpair aggregation in ionomers derived from copolymers and polymer containing 2-vinylfluorene (1987)
    Springer
    Polymer bulletin 17 (1987), S. 375-381 
    Details
    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary Time resolved fluorescence technique was used to demonstrate physically the ionpair aggregation phenomena in the ionomers containing fluorenylsodium as the pendant group along the polymer chains in THF at 25°C. It was found that ionpairs in the ionomer with mole fraction of fluorenylsodium equal to 0.02 did not associate to form stable aggregate. However, the ionpairs would aggregate in those ionomers with higher fluorenylsodium contents. In the homopolymer of vinylfluorenylsodium, extensive aggregation of the ionpairs was observed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00955723
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Optimal control computation for parabolic systems with boundary conditions involving time delays (1987)
    Springer
    Journal of optimization theory and applications 53 (1987), S. 475-507 
    Details
    ISSN: 1573-2878
    Keywords: Parabolic differential equations ; second boundary-value problems ; time-delayed arguments ; distributed optimal control problems ; necessary and sufficient conditions ; existence theory ; algorithms ; convergence of algorithms ; Galerkin's scheme ; lumped-parameter systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we consider a class of optimal control problems involving a second-order, linear parabolic partial differential equation with Neumann boundary conditions. The time-delayed arguments are assumed to appear in the boundary conditions. A necessary and sufficient condition for optimality is derived, and an iterative method for solving this optimal control problem is proposed. The convergence property of this iterative method is also investigated. On the basis of a finite-element Galerkin's scheme, we convert the original distributed optimal control problem into a sequence of approximate problems involving only lumped-parameter systems. A computational algorithm is then developed for each of these approximate problems. For illustration, a one-dimensional example is solved.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00938951
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    A feasible directions algorithm for time-lag optimal control problems with control and terminal inequality constraints (1985)
    Springer
    Journal of optimization theory and applications 46 (1985), S. 295-317 
    Details
    ISSN: 1573-2878
    Keywords: Nonlinear time-lag systems ; linear control constraints ; nonlinear terminal inequality constraints ; conditional gradient methods ; feasible direction methods ; control parametrization ; initial feasible control ; computational schemes ; finite convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A computational algorithm for a class of time-lag optimal control problems involving control and terminal inequality constraints is presented. The convergence properties of the algorithm is also investigated. To test the algorithm, an example is solved.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00939286
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Optimal control computation for nonlinear time-lag systems (1985)
    Springer
    Journal of optimization theory and applications 47 (1985), S. 91-107 
    Details
    ISSN: 1573-2878
    Keywords: Control parameterization ; piecewise constant functions ; nonlinear hereditary systems ; linear control constraints ; computational schemes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, a computational scheme using the technique of control parameterization is developed for solving a class of optimal control problems involving nonlinear hereditary systems with linear control constraints. Several examples have been solved to test the efficiency of the technique.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00941318
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Convergence of a feasible directions algorithm for relaxed controls in time-lag systems (1987)
    Springer
    Journal of optimization theory and applications 53 (1987), S. 461-474 
    Details
    ISSN: 1573-2878
    Keywords: Nonlinear time-lag systems ; linear control constraints ; nonlinear terminal inequality constraints ; feasible direction methods ; accumulation points ; relaxed controls ; relaxed control problems ; necessary conditions for optimality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we consider a class of time-lag optimal control problems involving control and terminal inequality constraints. A feasible direction algorithm has been obtained by Teo, Wong, and Clements for solving this class of optimal control problems. It was shown that anyL ∞ accumulation points of the sequence of controls generated by the algorithm satisfy a necessary condition for optimality. However, suchL ∞ accumulation points need not exist. The aim of this paper is to prove a convergence result, which ensures that the sequence of controls generated by the algorithm always has accumulation points in the sense of control measure, and these accumulation points satisfy a necessary condition for optimality for the corresponding relaxed problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00938950
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    Paper (German National Licenses)
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