On Discrete Zariski-Dense Subgroups of Algebraic Groups

We investigate under which conditions an algebraic group G defined over a locally compact field k admitr a subgroup Γ? G(k) which is dense in the Zariski topology, but discerte in the topology induced by the locally compact topology on k. For non—solvable groups we provide a complete answer.     

Preparation and Properties of Novel Cationically Active Oligo-p-Methoxystyryl-Silica Composites

Abstract

The preparation of cationically active oligo-p-methoxystyrene-silica composites by cationic interfacial polymerization is described. In addition to the effective preparation of the interfacial initiator, p-methoxybenzylium-hydrogen sulfate-silica, and p-methoxybenzylium-trifluoroacetate-silica, a procedure to yield new kinds of composites is reported. The outstanding properties of the “living” oligo-p-methoxy-styryl-hydrogen sulfate-silica is demonstrated by means of zeta potential measurements, solid-state ¹³C-NMR spectroscopy, UV/Vis spectroscopy, and electron scanning microscopy.     

Determination of benzotrifluoride derivative compounds in groundwater

Two simple analytical methods for the simultaneous determination and quantification of benzotrifluoride and eight chlorinated, amino and nitro benzotrifluoride derivatives in groundwater are proposed. Benzotrifluoride, 4-chlorobenzotrifluoride, 2,4-dichlorobenzotrifluoride and 3,4-dichlorobenzotrifluoride, were extracted by Purge-and-Trap on the basis of their volatile properties, while 3-aminobenzotrifluoride, 4-nitrobenzotrifluoride, 3-amino-4-chlorobenzotrifluoride, 3-nitro-4-chlorobenzotrifluoride and 4-chloro-3,5-dinitrobenzotrifluoride extractions were done with an automated SPE system. The analytical separations and detections were performed with two different GC systems, both equipped with single quadrupole mass spectrometer as detector. The LOD ranges for the two methods were 0.002–0.005 μg L⁻¹ and 0.01–0.07 μg L⁻¹, respectively. Both extraction methods were developed using spiked Milli-Q water and were then demonstrated with groundwater samples collected during autumn 2008. The areas of groundwater collection were polluted due to an episode of improper industrial soil disposal and consequent leakage of aliphatic and aromatic, fluorinated chemicals into the groundwater. This work eventually revealed the presence of several benzotrifluoride compounds most of them, like dichloro- and amino-derivatives, never been reported as environmental contaminants.     

Zur theorie polarer multikomponentsysteme

A fluid mixture consisting of molecules with permanent electric dipole moment and scalar polarizability is described by means of correlation functions. To analyse the two-particle correlation functions we extend the graph-theoretical conception developed by Wertheim in the case of multicomponent systems by using graphs with colored points. In order to carry out a topological reduction of these sets of colored graphs the corresponding functions are found to be matrices or tensors. By the aid of a new connecting formalism the tensor notation preserves the structure of the equations in the analysis of correlation functions. These functions can be separated with respect to the range of interactions involved. Then, in applying the results to the case of a polar multicomponent mixture we can derive equations for the dielectric constant of systems consisting of both rigid and polarizable dipoles. These equations involve a correlation factor matrix which is the multicomponent equivalence of the Kirkwood factor. The dielectric expressions are used to obtain dipolar contributions to the Helmholtz free energy of mixing.     

On Manifolds with Trivial Logarithmic Tangent Bundle: The Non-Kähler Case

We study non-Kähler manifolds with trivial logarithmic tangent bundle. We show that each such manifold arises as a fibre bundle with a compact complex parallelizable manifold as basis and a compactficiation of a semi-torus as fibre.     

Competing polarization mechanisms in the heavy-fermion paramagnet CeCu<Subscript><Emphasis Type="Bold">6</Emphasis></Subscript>

Nuclear magnetic resonance (NMR) and relaxation of ⁶³Cu and ⁶⁵Cu in a powder sample of the heavy-fermion paramagnet CeCu₆ is measured and analysed quantitatively. Five different Cu sites are accessible to a detailed analysis. We derive quadrupolar splitting frequencies, Ce to Cu transferred hyperfine field coupling constants, and transversal as well as longitudinal relaxation behaviour. Only small relaxation anomalies are observed at the orthorhombic to monoclinic structural phase transition of CeCu₆. We point to the different importance of transferred hyperfine interaction and local conduction electron density for static or dynamic part, respectively, of Cu hyperfine interaction. The different sign of the transferred hyperfine interaction from Ce³⁺ to different Cu neighbours reveals the different competing interaction mechanisms, giving rise to the heavy-fermion paramagnetic behavior of CeCu₆. Received 20 November 2001