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  • 1
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Comparative Biochemistry and Physiology -- Part B: Biochemistry and 101 (1992), S. 591-594 
    ISSN: 0305-0491
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Biology , Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 0368-1874
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Journal of Electroanalytical Chemistry 189 (1985), S. 203-218 
    ISSN: 0368-1874
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 38 (1982), S. 111-135 
    ISSN: 1573-2878
    Keywords: Minimax problems ; minimax function ; minimax function depending on the state ; minimax function depending on the control ; optimal control ; minimax optimal control ; numerical methods ; computing methods ; transformation techniques ; gradient-restoration algorithms ; sequential gradient-restoration algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In a previous paper (Part 1), we presented general transformation techniques useful to convert minimax problems of optimal control into the Mayer-Bolza problem of the calculus of variations [Problem (P)]. We considered two types of minimax problems: minimax problems of Type (Q), in which the minimax function depends on the state and does not depend on the control; and minimax problems of Type (R), in which the minimax function depends on both the state and the control. Both Problem (Q) and Problem (R) can be reduced to Problem (P). In this paper, the transformation techniques presented in Part 1 are employed in conjunction with the sequential gradient-restoration algorithm for solving optimal control problems on a digital computer. Both the single-subarc approach and the multiple-subarc approach are employed. Three test problems characterized by known analytical solutions are solved numerically. It is found that the combination of transformation techniques and sequential gradient-restoration algorithm yields numerical solutions which are quite close to the analytical solutions from the point of view of the minimax performance index. The relative differences between the numerical values and the analytical values of the minimax performance index are of order 10−3 if the single-subarc approach is employed. These relative differences are of order 10−4 or better if the multiple-subarc approach is employed.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 38 (1982), S. 97-109 
    ISSN: 1573-2878
    Keywords: Minimax problems ; minimax function ; minimax function depending on the state ; minimax function depending on the control ; optimal control ; minimax optimal control ; numerical methods ; computing methods ; transformation techniques ; gradient-restoration algorithms ; sequential gradient-restoration algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper contains general transformation techniques useful to convert minimax problems of optimal control into the Mayer-Bolza problem of the calculus of variations [Problem (P)]. We consider two types of minimax problems: minimax problems of Type (Q), in which the minimax function depends on the state and does not depend on the control; and minimax problems of Type (R), in which the minimax function depends on both the state and the control. Both Problem (Q) and Problem (R) can be reduced to Problem (P). For Problem (Q), we exploit the analogy with a bounded-state problem in combination with a transformation of the Jacobson type. This requires the proper augmentation of the state vectorx(t), the control vectoru(t), and the parameter vector π, as well as the proper augmentation of the constraining relations. As a result of the transformation, the unknown minimax value of the performance index becomes a component of the parameter vector being optimized. For Problem (R), we exploit the analogy with a bounded-control problem in combination with a transformation of the Valentine type. This requires the proper augmentation of the control vectoru(t) and the parameter vector π, as well as the proper augmentation of the constraining relations. As a result of the transformation, the unknown minimax value of the performance index becomes a component of the parameter vector being optimized. In a subsequent paper (Part 2), the transformation techniques presented here are employed in conjunction with the sequential gradient-restoration algorithm for solving optimal control problems on a digital computer; both the single-subarc approach and the multiple-subarc approach are discussed.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 57 (1995), S. 1005-1011 
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: We have successfully prepared Congo Red-based polyurethane ionomers at our lab, and these ionomer structures have been proven by infrared (IR) spectra. For a dye-based polyurethane ionomer molecule solution, the surface tension was found to decrease, but the number-average particle size was found to increase with increasing concentration of Congo Red employed to prepare this ionomer molecule. Interestingly, the number-average particle size of dye-based polyurethane ionomer molecules decreases with increasing concentration of Congo Red in the presence of other dyes (i.e., Remajol Brilliant Blue R and Amaranth), as a result of Congo Red intramolecular interaction. It is important to point out that the addition of a fixed concentration of Amaranth to prepare Congo Red-based polyurethane ionomer molecules will significantly enhance the tensile strength but will decrease the elongation of this ionomer molecule. © 1995 John Wiley & Sons, Inc.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 52 (1994), S. 1165-1173 
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Red#170 (pigment) polyurea microcapsules have been successfully prepared at our laboratory. Both core and shell of these microcapsules are demonstrated to be red#170 pigment and polyurea, respectively, by infrared (IR) spectra. The number-average particle sizes of these microcapsules are seen to decrease with increasing concentration and the ethylene oxide chain length of nonylphenylpolyoxyethylene ether (NPn; n = 6, 8, 10, 12, 16) as an emulsifier in the water phase used for making microcapsules. Experimental results indicate that the average particle sizes of red#170 polyurea microcapsules are smaller for the system with NP16 than for the system with NP4 (in the oil phase) and/or NP16 (in the water phase) and that, in the presence of NPn, these particle sizes are seen to be slightly smaller for use of methylcellulose than for use of sodium carboxymethylcellulose as a protective colloid. It is also interesting to note that the released amounts of red#170 pigment from polyurea microcapsules in di-n-butylphthalate solvent is lower for a system with NP16 than for a system with methylcellulose, as a result of good emulsification leading to decrease the interaction between toluene diisocyanate and water molecules. This may further cause more crosslinkage to take place at the urea groups, resulting in a decrease in the porosity of the capsules. © 1994 John Wiley & Sons, Inc.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
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