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  • Nonlinear control systems  (1)
  • data fitting  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 89 (1996), S. 293-310 
    ISSN: 1573-2878
    Keywords: Nonlinear control systems ; flow differentiability ; L p -controls
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper considers the study of the regularity of the flow of a nonautonomous nonlinear control process when the set of control maps is endowed with theL p -topology. Roughly speaking, it is proved that, if the norm of the mapf(t, x, u) defining the process together with its first derivatives goes to infinity, with the norm ofu not faster than⊥u⊥ p ,p〉1, then the flow isC 1 in theL p -topology. This property implies that, if the control maps are bounded, then the flow is differentiable in anyL p ,p〉1. Moreover, it is proved that the only systems for which the flow is differentiable inL 1 are the affine ones.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 0947-6539
    Keywords: azo dyes ; circular dichroism ; data fitting ; formation constants ; protein complexation ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Difference absorbance and circular dichroism techniques show that two complexes are formed between human serum albumin (HSA) and Methyl Orange (MO). The stoichiometries of the two HSA-MO complexes (1:1 (C1) and 1:2 (C2)), their association constants (K1, 1 = 2.32 (0.18) × 105 M-1 and K1, 2 = 1.12 (0.15) × 1011 M-2), and both absorbance and dichroic spectra have been determined by a computational approach. Nearly 900 experimental points, consisting of absorbance and CD measurements registered in the 340-550 nm interval and over a wide range of concentrations of protein and ligand, have been included in a unique fitting procedure. The Scatchard plot indicates the existence of a unique binding site which can accommodate up to two molecules of MO in a positive co-operative process. Calculation of the CD spectrum for the C2 complex according to the DeVoe method reproduces the fitted dichroic spectrum for the same complex. The shapes of the fitted absorbance and dichroic spectra, as well as the influence of concentrated NaCl or ethylene glycol on the absorbances of both free MO and HSA-MO mixtures are consistent with the presence of dominant electrostatic interactions in C1. The C2 complex can be envisaged as a unique chromophore, consisting of two MO units associated in a stacking process into the same binding site of HSA, leading to a well-defined chirality. The general validity of this multitechnique, multiwavelength approach in the investigation of protein-ligand complexes is discussed.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
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