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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 101 (1999), S. 475-495 
    ISSN: 1573-2878
    Keywords: Variational inequalities ; convex programming ; complementarity problems ; exceptional families ; existence theorems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper introduces the concept of exceptional family for nonlinear variational inequality problems. Among other things, we show that the nonexistence of an exceptional family is a sufficient condition for the existence of a solution to variational inequalities. This sufficient condition is weaker than many known solution conditions and it is also necessary for pseudomonotone variational inequalities. From the results in this paper, we believe that the concept of exceptional families of variational inequalities provides a new powerful tool for the study of the existence theory for variational inequalities.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Macromolecular Chemistry and Physics 196 (1995), S. 2443-2462 
    ISSN: 1022-1352
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: An electroactive material with remarkable solubility, processibility as well as mechanical properties has been developed by complexation (thermal doping) of polyaniline (PANi) emeraldine base with dodecylbenzenesulfonic acid (DBSA) in the solid state. Isothermal treatment of such a mixture was found to promote the complex formation. Optimum conditions of complexation were established with respect to the formation of layered structure, electrical conductivity and solubility. The optimal temperature for the doping process was found to be in a range of 100-120°C while the best ratio of DBSA to PANi was between 3:1 and 4:1 by weight, a nearly stoichiometric equivalence of aniline repeat units and DBSA molecules. The time of isothermal treatment should be controlled within 30 min. Thermal doping induced orientation to polymer chains in a layered structure, whereby the hydrophobic tails of the surfactants function as spacers between parallel stacks of the main chains. This anisotropy was achieved by the self-assembly during the thermal doping rather than ordinary drawing or stretching of the polymers. A unique liquid crystalline mesophase with a smectic-like optical texture was observed for the soluble portions of some specimens. The excess DBSA in the samples is considered to function as a solvent and to give rise to the liquid crystalline fluidity of the phase. The scanning tunneling microscopy (STM) image 5000 × 5000 Å on a submicrometer scale obtained from a PANi/DBSA thin film exhibits a surface morphology with a granular size of 200-300 Å. The image of 150 × 150 Å on a molecular scale obtained from multilayer PANi/DBSA deposited on a highly oriented pyrolytic graphite (HOPG) surface provides a direct observation of a self-assembled structure and close layer packing of the polymer backbone with dimensions in accord with the results found by X-ray diffraction. Our results indicate that the thermal doping process of polyaniline by DBSA offers new possibilities to obtain optimal structures through a self-assembly.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
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