Uniformization of Riemann surfaces revisited

Annals of Global Analysis and Geometry - We give an elementary and self-contained proof of the uniformization theorem for noncompact simply connected Riemann surfaces.     

Construction and analytical applications of a liquid-state iodide-selective electrode with a metal complex as exchanging site

Summary A new type of liquid-membrane iodide-selective electrode based on a 0.001M solution of tris(l,10-phenanthroline)ruthenium(II) iodide in 1,2-dichlorobenzene is described. The electrode has Nernstian behaviour down to 7×1O^–6M iodide. It has good selectivity towards halide (k _{I, Cl}=5.3×10^–6 andk _{I, Br}=1.6×10^–4) and other inorganic ions, and a linear response to iodide at pH-values from 3 to 9. It can be used either in direct iodide analyses or in potentiometric titrations. Titration of halide mixtures or of pseudohalides is also possible. The method has been used for determining the free formaldehyde present in dispersing agents.

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Herstellung und analytische Anwendung einer jodid-spezifischen Elektrode mit Flüssigmembran mit einem Metallkomplex als Austauscher

Zusammenfassung Eine neue jodid-spezifische Flüssig-Membran-Elektrode auf der Basis einer 0,001 M Lösung von Tris(1,10-phenanthrolin)-Ruthenium(II)-jodid in 1,2-Dichlorbenzol wurde beschrieben. Sie zeigt Nernstsches Verhalten bis zu 7×10^–8 M Jodid, gute Selektivität gegenüber Halogeniden (k _{I, Cl}=5,3× 10^–6 undk _{I, Br}=1,6×10^–4) und anderen anorganischen Ionen und ein lineares Verhalten gegenüber Jodid bei pH 3–9. Die Elektrode läßt sich für direkte Jodidbestimmungen oder für potentiometrische Titrationen verwenden. Die Titration von Halogenidgemischen oder Pseudohalogeniden ist ebenfalls möglich. Das Verfahren wurde zur Bestimmung von freiem Formaldehyd in Dispersionsmitteln verwendet.

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Presented at the 8th International Microchemical Symposium, Graz, August 25–30, 1980.     

Phase behavior of water/oil/nonionic surfactants with normal distribution of the poly(ethylene oxide) chain length

The phase behavior of systems consisting of water/n-hexane/polyethoxylated nonionic surfactants with a normal distribution of ethylene oxide (EO) chain length has been investigated. The surfactants used were octylphenol ethoxylated with eight EO units and nonylphenol ethoxylated with seven and ten EO units. The oil/water weight ratio was keep constant at 1, whereas the amount of surfactant and the temperature were variables. The pseudobinary phase diagrams were used to find out the triphasic bodies on the temperature scale, the tricritical points and the effect of electrolyte on them. The presence of electrolyte and the increase in surfactant hydrophobicity promote the phase inversion.     

Clusters and fluctuations at mean-field critical points and spinodals

We show that the structure of the fluctuations close to spinodals and mean-field critical points is qualitatively different from the structure close to non-mean-field critical points. This difference has important implications for many areas including the formation of glasses in supercooled liquids. In particular, the divergence of the measured static structure function in near-mean-field systems close to the glass transition is suppressed relative to the mean-field prediction in systems for which a spatial symmetry is broken.     

Fractional exclusion statistics in general systems of interacting particles

I show that fractional exclusion statistics is manifested in general interacting systems and I calculate the exclusion statistics parameters. Most importantly, I prove that the mutual exclusion statistics parameters are proportional to the dimension of the Hilbert space on which they act [D.V. Anghel, J. Phys. A: Math. Theor. 40 (2007) F1013].     

Luminescent properties of cobalt-doped α-ZnAl2S4 spinel type single crystals

The absorption and luminescent properties of α-ZnAl₂S₄:Co spinel type crystals grown by chemical transport reactions method are investigated. The spectra are assigned to the electronic transitions of Co²⁺ ions located in tetrahedral sites. It is shown, that the revealed four radiative spectral components are caused by the ²A(²G)→⁴T₁(⁴F), ⁴T₁(⁴P)→⁴T₂(⁴F), ²E(²G)→ ⁴T₂(⁴F) and ²E(²G)→⁴T₁(⁴F) transitions.     

Radiative properties of α-ZnAl2S4:V spinel type single crystals

The absorption and luminescent properties of α-ZnAI₂S₄:V spinel type crystals in the temperature range 10-300 K are investigated. The spectra are assigned to the electronic transitions of trivalent vanadium ions located in octahedral sites. It is shown that at low temperatures the three main components of the revealed IR luminescence spectra are caused by the ¹A_1g(¹G)→¹E_g(¹D), ¹T_2g(¹D), ³T_2g(³F)→³T_1g(³F), and ¹E_g(¹D)→³T_1g(³F) transitions. The observed dependencies of the emission components intensities on temperature are explained assuming that there is a phonon assisted tunnelling between ³T_2g(³F) and ¹E_g(¹D) states. On temperature rise, the ³T_2g(³F)→³T_1g(³F) vibronic transitions suppress other emission channels, which leads to the enhancement of the integral luminescence intensity and to the broadening of the spectrum centred at λ=1.4 μm.     

A note on a Chern character on the circle

In this note we present a simple derivation of the Chern character of a certain finitely summable Fredholm module, associated to the algebra of pseudodifferential operators of order ≤0 on the unit circle S¹. Research supported in part by the Texas Advanced Research Program under Grant No. 003594-071