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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 31 (1980), S. 331-342 
    ISSN: 1573-2878
    Keywords: Minimax theorems ; Kuhn-Tucker optimality conditions ; duality theorem ; converse duality theorem ; constraint qualifications
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For a convex-concave functionL(x, y), we define the functionf(x) which is obtained by maximizingL with respect toy over a specified set. The minimization problem with objective functionf is considered. We derive necessary conditions of optimality for this problem. Based upon these necessary conditions, we define its dual problem. Furthermore, a duality theorem and a converse duality theorem are obtained. It is made clear that these results are extensions of those derived in studies on a class of nondifferentiable mathematical programming problems.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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  • 2
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Bioelectromagnetics 9 (1988), S. 159-166 
    ISSN: 0197-8462
    Keywords: Lorentz force ; Maxwell stress ; threshold field strength ; Life and Medical Sciences ; Occupational Health and Environmental Toxicology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: Static magnetic fields affect the diffusion of biological particles in solutions through the Lorentz force and Maxwell stress. These effects were analyzed theoretically to estimate the threshold field strength for these effects. Our results show that the Lorentz force suppresses the diffusion of charged particles such as Na+, K+, Ca2+, Cl-, and plasma proteins. However, the threshold is so high, i.e., more than 104 T, that the Lorentz force does not affect the ion diffusion at typical field strengths (a few Tesla at most). Since the threshold of gradient fields for producing a change in ion diffusion through the Maxwell stress is more than 105 T2/m for paramagnetic molecules (FeCl3, O2) and plasma proteins, their diffusion would be unaffected by typical gradient fields (100 T2/m at most) and even by high gradient fields (less than 105 T2/m) used in magnetic separation techniques. In contrast, movement of deoxygenated erythrocytes and FeCl3 colloids (more than 103 molecules) is influenced by the usual gradient fields due to a volume effect.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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