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.     

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.     

On the possible connection between renormalization-groups and nonlinear semi-groups

Some algebraic properties of the renormalization-group (RNG) are studied using the nonlinear semi-group theory. The RNG is defined in an axiomatic manner as a bounded nonlinear semi-group on an abstract Banach space. Perturbations of the fixed point of RNG and the problem of marginality are investigated using a hierarchy of nonlinear semi-groups.     

Biophysical changes induced by cholesterol on phosphatidylcholine artificial biomembranes containing alamethicin oligomers

Cholesterol is an important constituent of eukaryotic cell membranes, whose interaction with phospholipids leads to a broad range of biological roles, such as: maintenance of proper fluidity, formation of raft domains, reduction of passive permeability of various chemical species through the bilayer (e.g., glucose, glycerol, K⁺, Na⁺ and Cl⁻ ions), and increased mechanical strength of the membrane. In this work we studied an interesting paradigm, as to whether cholesterol-containing phosphatidylcholine biomembranes influence the kinetics and transport features of alamethicin oligomers embedded into it. We demonstrate that moderate relative amounts of cholesterol increase the electrical conductance of various sub-conductance states of the alamethicin oligomer, caused probably by a non-monotonic change in the lumped dipole moment of the biomembrane. Our data suggest that biomembrane stiffness caused by cholesterol, visibly modifies the association-dissociation rates of alamethicin oligomerization in the biomembrane. Moreover, increasing concentrations of cholesterol seem to lead to more stable intermediate alamethicin oligomers. We show that in the presence of cholesterol, as the diameter of the alamethicin oligomer increases, so does the time of another monomer to get picked up. These results brings into focus the interesting issue of how oligomerization of proteins affects their interaction affinities for membrane-based lipids.     

From fractional exclusion statistics back to Bose and Fermi distributions

Fractional exclusion statistics (FES) is a generalization of the Bose and Fermi statistics. Typically, systems of interacting particles are described as ideal FES systems and the properties of the FES systems are calculated from the properties of the interacting systems. In this Letter I reverse the process and I show that a FES system may be described in general as a gas of quasiparticles which obey Bose or Fermi distributions; the energies of the newly defined quasiparticles are calculated starting from the FES equations for the equilibrium particle distribution. In the end I use a system in the effective mass approximation as an example to show how the procedure works.     

Comparative first-principle analysis of un-doped and V3+-doped α-ZnAl2S4 spinel

The experimental and theoretical studies of the optical properties of pure α-ZnAl₂S₄ and α-ZnAl₂S₄:V³⁺ crystals were carried out. The ab initio and crystal field calculations of the structural and optical properties of α-ZnAl₂S₄:V³⁺ were compared with the corresponding experimental data. It was shown that the lowest vanadium 3d states are located at about 1.36 eV above the valence band's top. The complete energy level scheme of the α-ZnAl₂S₄:V³⁺ system, which includes the host's electronic band structure and impurity ion's energy levels, was suggested on the basis of the performed calculations.