Modelling and Optimization of Stability Constants of Cadmium or Zinc with Biological Buffers (DIPSO or TAPS) in Aqueous Solutions by Electrochemical Techniques

The complexation behavior of four systems involving cadmium(II) or zinc(II) in aqueous solutions with the biological buffers 3-[N,N-bis(2-hydroxyethyl)amino]-2-hydroxypropanesulfonic acid (DIPSO), and [(2-hydroxy-1,1-bis(hydroxymethyl)ethyl)amino]-1-propanesulfonic acid (TAPS) was studied by direct current polarography (DCP) and glass electrode potentiometry (GEP), at 25.0 ± 0.1 °C and ionic strength 0.1 mol·dm^?3 KNO₃. Except for the Cd–TAPS system, for which full characterization of the system was possible either by DCP or GEP, full characterization of the other metal-buffer systems (Zn–DIPSO, Zn–TAPS and Cd–DIPSO) was only possible using DCP. For Zn-buffers systems, ZnL⁺ and $ {\text{ZnL(OH)}}_{2}^{ - } $ ZnL(OH) 2 ? (where L stands for buffer) were identified. For the Zn–DIPSO system, the overall stability constant values (as log₁₀ β) are 2.1 ± 0.2 and 13.4 ± 0.2, respectively. For the Zn–TAPS system, the overall stability constants values (as log₁₀ β) are 2.4 ± 0.1 and 12.9 ± 0.3, respectively. For the Cd–DIPSO system, the overall stability constants values (as log₁₀ β) of CdL⁺ and CdL(OH) are 2.9 ± 0.1 and 6.9 ± 0.3, respectively. For the Cd–TAPS system, only the species CdL⁺ was identified with log₁₀ β = 2.5 ± 0.1.     

How to approximate the solutions of certain free boundary problems for the Laplace equation by using the contraction principle

We show how the free boundary of an ideal fluid, subject to a generalized Bernoulli condition, can (under appropriate circumstances) be approximated. Our method is based on a class of free-boundary perturbation operatorsT , 0<<1, which are all contracting relative to a suitable norm and class of boundaries, and whose fixed points converge to the desired free boundary solution as 0+.

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Zusammenfassung Wir zeigen, wie der freie Rand einer idealen Flüssigkeit, welcher einer verallgemeinerten Bernoulli-Bedingung genügt, unter geeigneten Umständen approximiert werden kann. Unsere Methode stützt sich auf eine Klasse freier RandperturbationsoperatorenT , 0<<1, welche relativ zu einer geeigneten Norm und Ränderklasse kontrahierend sind und deren Fixpunkte gegen die gewünschte Lösung der freien Randaufgabe mit 0+ konvergieren.

     

On the geometric form of free boundaries satisfying a bernoulli condition

In the x–y plane, let Ω denote an annular domain bounded by the simple closed curves ? and ?^*, such that the capacity potential U in Ω satisfies ∣ ▽ U∣ = 1 on ?. Assuming ?^* to be known, we obtain qualitative properties of ?. For example, the number of local maxima or minima of the y-co-ordinate relative to ? cannot exceed the corresponding number for ?^*.