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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 71 (1991), S. 549-568 
    ISSN: 1573-2878
    Keywords: Dubovitskii-Milyutin method ; Euler-Lagrange equation ; equality constraints ; nonregular operators ; Lusternik theorem ; Pareto optimality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An optimization problem with inequality and equality constraints in Banach spaces is considered in the case when the operators which determine the equality constraints are nonregular. In this case, the classical Euler-Lagrange equation has the degenerate form, i.e., does not depend on the functional to be minimized. Applying some generalization of the Lusternik theorem to the Dubovitskii-Milyutin method, the family of Euler-Lagrange equations is obtained in the nondegenerate form under the assumption of twice Fréchet differentiability of the operators. The Pareto-optimal problem is also considered.
    Type of Medium: Electronic Resource
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  • 2
    Publication Date: 1991-12-01
    Print ISSN: 0022-3239
    Electronic ISSN: 1573-2878
    Topics: Mathematics
    Published by Springer
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  • 3
    Publication Date: 2024-02-06
    Description: Pit lakes in the ‘anthropogenic lake district’ in the Muskau Arch (western Poland; central Europe) are strongly affected by acid mine drainage (AMD). The studied acidic pit lake, ŁK-61 (pH 〈3), is also exposed to floods due to its location in the flood hazard area, which may significantly influence the geochemical behavior of elements. The elemental compositions of water and lake sediment samples were measured with ICP–OES and ICP–MS. The sediment profile was also examined for 137Cs and 210Po activity concentrations using gamma and alpha spectrometry, respectively. Grain size distribution, mineralogical composition, diatoms, and organic matter content in the collected core were also determined. The key factors responsible for the distribution of selected heavy metals (e.g., Cu, Ni, Pb, Zn) and radioisotopes (137Cs and 210Po) in the bottom sediments of Lake ŁK-61 are their coprecipitation/precipitation with Fe and Al secondary minerals and their sorption onto authigenic and allogenic phases. These processes are likely driven by the lake tributary, which is an important source of dissolved elements. The data also showed that the physiochemical parameters of Lake ŁK-61 water changed during an episodic depositional event, i.e., the flood of the Nysa Łużycka River in the summer of 2010. The flood caused an increase in the water pH, as interpreted from the subfossil diatom studies. The down-core profiles of the studied heavy metal and radionuclide (HMRs) contents were probably affected by this depositional event, which prevented a detailed age determination of the collected lake sediments with 137Cs and 210Pb dating methods. Geochemical modeling indicates that the flood-related shift in the physicochemical parameters of the lake water could have caused the scavenging of dissolved elements by the precipitation of fresh secondary minerals. Moreover, particles contaminated with HMRs have also possibly been delivered by the river, along with the nutrients (e.g., phosphorus and nitrogen).
    Language: English
    Type: info:eu-repo/semantics/article
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