Singularities in cascade models of the Euler equation

The formation of singularities in the three-dimensional Euler equation is investigated. This is done by restricting the number of Fourier modes to a set which allows only for local interactions in wave number space. Starting from an initial large-scale energy distribution, the energy rushes towards smaller scales, forming a universal front independent of initial conditions. The front results in a singularity of the vorticity in finite time, and has scaling form as function of the time difference from the singularity. Using a simplified model, we compute the values of the exponents and the shape of the front analytically. The results are in good agreement with numerical simulations.     

An Analytic Zariski Structure Over a Field

Following the introduction and preliminary investigations of analytic Zariski structures in Peatfield and Zilber (Ann pure Appl Logic 132:125–180, 2005) an example of an analytic Zariski structure extending an algebraically closed field is provided. The example is constructed using Hrushovski’s method of free amalgamation, and a topology is introduced in which we can verify the analytic Zariski axioms.     

Characterisation of adsorbed layers on sulphide minerals by photoelectron spectroscopy

The systems galena/2-mercaptobenzothiazole (MBT) and pyrite/MBT have been studied using synchrotron radiation excited photoelectron spectroscopy (SRXPS). The chemisorption of MBT and the multilayer formation of 2,2′-dithiobis(benzothiazole) (BBTD) are evidenced by additional structures, observed beside the substrate signals, in the S2p-spectra of cleaved mineral surfaces after adsorption of MBT. The amount of the complex remains constant at concentrations as high as 10^–5 mol/L whereas the amount of BBTD increases. From the dependence of the adsorbate intensities on the excitation energy the conclusion can be drawn that an overlayer of BBTD on a chemisorbed layer of MBT is formed. The very weak adsorption of MBT on pyrite in alkaline solutions may explain the selective flotation of galena from pyrite in alkaline media.     

Comparison of localization and delocalization indices obtained with Hartree-Fock and conventional correlated methods: effect of Coulomb correlation

Atomic populations and localization [lambda(A)] and delocalization [delta(A,B)] indices (LIs and DIs) are calculated for a large set of molecules at the Hartree-Fock (HF), MP2, MP4(SDQ), CISD, and QCISD levels with the 6-311++G(2d,2p) basis set. The HF method and the conventional correlation methods [MP2, MP4(SDQ), CISD, and QCISD] yield distinct sets of LIs and DIs. Yet, within the four conventional correlation methods the differences in atomic populations and LIs and DIs are small. Relative to HF, the conventional correlation methods [MP2, MP4(SDQ), CISD, QCISD] yield virtually the same LIs and DIs for molecules with large charge separations while LIs and DIs that differ significantly from the HF values--the LIs are increased and DIs decreased--are obtained for bonds with no or small charge separations. Such is the case in the archetypal homopolar molecules HC(triple bond)CH, H2C=CH2, CH3-CH3, and "protonated cyclopropane" C(3)H(7) (+), in which case the bonding may be atypical. Relative to HF, the typical effect of the conventional correlation methods is to decrease the DI between atoms.     

Substituierte 2-(Thiazol-4-yl)-phenole als Liganden und potentielle Extraktionsmittel für Kupfer(II)

Substituted 2-(Thiazol-4-yl)-phenols as Ligands and Potential Extractants for Copper (II) Substituted 2-(thiazol-4-yl)-phenols are obtained by the HANTZSCH synthesis. Their solubility in toluene is higher than in n-octane depending on the position, the chain length, and the polarity of the substituents. From alcoholic solutions complexes of the type CuL₂ⁿ are precipitated. According to the substituents their structure is distorted octahedral (CuL₂², CuL₂³) or distorted tetrahedral (CuL₂⁸, CuL₂⁹). The new complexes are nearly insoluble in toluene and aliphatic hydrocarbons, but CuL₂⁸ and CuL₂⁹ are soluble in chloroform. Therefore copper(II) may be extracted by HL⁸ and HL⁹ using chloroform as a diluent.     

Extraktion von 3d-Metallionen mit zweizähligen Sulfonamiden. I. Liganden mit Schwefel bzw. heterocyclisch gebundenem Stickstoff als zweitem Haftatom

Extraction of 3d-Metal Ions by Bidendate Sulfonamides. I. Ligands with Sulfur or Heterocyclic Nitrogen as a Second Donor Atom The properties of 2-acetylpyridine-p-toluensulfonylhydrazone (APSH - H), arensulfonylthioureas (I), and the esters of arensulfonylmonothiocarbamic acid (II) or arensulfonyldithiocarbamic acid (III) as extractants for the late 3d-metal ions are proved. APSH-H is comparable to the proprietary extractant LIX 34. But, because of the special structure of the corresponding 1,2-chelates, the pH_1/2-values of nickel(II) and cobalt(II) are ≈2 units lower. The pK_s-values, measured in dioxane-water mixtures (75 per cent v/v), increase in the order III < II < I. In aqueous solutions compounds of type III are acids of medium strength. In the case of compounds of type I the substituents of the non-sulfonated nitrogen have a strong influence on the pK_s-values (ΔpK_s = 4.6). Among the late 3d-elements, the ligands II and III extract only copper(II) (pH_1/2 ～2.7 or ～1.6), the ligands I extract zinc(II), cobalt(II), and nickel(II) as well, but not iron(II) and iron(III). The reasons of this unique behaviour are discussed.     

Multifunctional redox catalysts as selective enhancers of oxidative stress

Certain cancer cells proliferate under conditions of oxidative stress (OS) and might therefore be selectively targeted by redox catalysts. Among these catalysts, compounds containing a chalcogen and a quinone redox centre are particularly well suited to respond to the presence of OS. These catalysts combine the specific electrochemical features of quinones and chalcogens. They exhibit high selectivity and efficiency against oxidatively stressed rat PC12, human Jurkat and human Daudi cells in cell culture, where their mode of action most likely involves the catalytic activation of existent and the generation of new reactive oxygen species. The high efficiency and selectivity shown by these catalysts makes them interesting for the development of anti-cancer drugs.