Orbits and Invariants Associated with a Pair of Spherical Varieties: Some Examples

Let H and K be spherical subgroups of a reductive complex group G. In many cases, detailed knowledge of the double coset space H\G/K is of fundamental importance in group theory and representation theory. If H or K is parabolic, then H\G/K is finite, and we recall the classification of the double cosets in several important cases. If H=K is a symmetric subgroup of G, then the double coset space K\G/K (and the corresponding invariant theoretic quotient) are no longer finite, but several nice properties hold, including an analogue of the Chevalley restriction theorem. These properties were generalized by Helminck and Schwarz (Duke Math. J. 106(2) (2001), pp. 237–279) to the case where H and K are fixed point groups of commuting involutions. We recall Helminck and Schwarz's main results. We also give examples to show the difficulty in extending these results if we allow H=K to be a reductive spherical (nonsymmetric) subgroup or if we have H symmetric and K spherical reductive.     

Venus atmospheric waves: A challenge for nonlinear dynamics

Planetary-scale cloud patterns seen in ultraviolet images of Venus are produced by atmospheric waves traveling slowly with respect to the cloud-top winds. The cloud features often combine to produce a dark horizontal “Y” shape that encircles the planet. Linear wave theory and detailed observations of the waves show that the “Y” is a combination of two components-a midlatitude wave traveling somewhat slower than the winds and an equatorial wave moving slightly faster. However, nonlinear effects must be invoked in order to couple the two modes in such a way as to reproduce the observations.     

Boron-doped diamond: Investigation of the stability of surface-doping versus bulk-doping using cyclic cluster model calculations

Boron-doped bulk diamond and the boron-doped hydrogen terminated (001) surface of diamond were investigated using the cyclic cluster model. Structure and stability of the hydrogen-terminated (001) surface were calculated and compared with experimental and other theoretical results from the literature. Boron-doping was modeled by substitution of a carbon atom by a boron atom in different positions with increasing distance from the surface up to boron-doped bulk diamond. In agreement with experiments on nanoclusters, boron is most stable in the first surface layers. (c) 2008 Wiley Periodicals, Inc. J Comput Chem, 2008.     

Synthese und Strukturen der ersten mehrkernigen Mangan‐Guanidin‐Komplexe und der ersten Mangan‐Komplexe mit mono‐protonierten Bis‐Guanidinliganden

Syntheses and Structures of the First Polynuclear Manganese Guanidine Complexes and of the First Manganese Complexes Containing Mono‐Protonated Bis‐Guanidine Ligands Metallation of two differently alkylated bis‐guanidine ligands containing a central pyridine functionality, namely N²,N⁶‐bis(1,3‐dimethylimidazolidin‐2‐ylidene)pyridine‐2,6‐diamine (DMEG₂py {N₇C₁₅H₂₃}, L¹ ) and N²,N⁶‐bis(1,1,3,3‐tetramethyl‐guanidine)pyridine‐2,6‐diamine (TMG₂py {N₇C₁₅H₂₇}, L² ), with manganese(II) bromide and chloride leads to the formation of the novel complexes [MnBr₃(TMG₂pyH)] ([MnBr₃(N₇C₁₅H₂₈)], ( 1 )), [MnBr₂(DMEG₂pyH)₂]²⁺ ([MnBr₂(N₇C₁₅H₂₄)₂]²⁺, ( 2 )), and [Mn₂X₃(DMEG₂py)₂]⁺ ([Mn₂X₃(N₇C₁₅H₂₃)₂]⁺; ( 3a ): X = Cl; ( 3b ): X = Br). 2 and 3 have been isolated as tetrahalomanganate salts. Single crystal X‐ray analyses show that all of them contain the manganese atoms in unusual pseudo‐tetrahedral coordination environments. 3a· 1/2[MnCl₄] and 3b· 1/2[MnBr₄] are isostructural and crystallize in the monoclinic space group C2c. The complex cations 3 exhibit a binuclear structure with two terminal and one bridging halide ion, respectively. The compounds 1 and 2 are mononuclear species crystallizing in the orthorhombic space group P2₁2₁2₁ in the case of 1 and in the triclinic space group in the case of 2· [MnBr₄]. The ability of L¹ and L² to bind either two manganese ions naked or only one of them in the mono‐protonated stage is the most remarkable property of these ligands. Further striking features are the spatial arrangements of the pyridine‐to‐manganese bonds which deviate significantly from the situation expected for nitrogen donor functions in sp² hybridized stages. Moreover, regarding each chelating ligand portion as a component which occupies one coordination site of the metal atom, a pseudo‐tetrahedral metal coordination is identified. To our knowledge, 1 and 2 are the first manganese complexes containing mono‐protonated bis‐guanidine ligands, whereas 3a and 3b are the first polynuclear manganese‐guanidine compounds known so far.     

The influence of X-ray resonant Raman scattering effects on the detection of copper(II) tetrasulphonated phthalocyanine (CuTSPc) thin-films deposited on gold electrodes

The influence of X-ray resonant Raman scattering on the detection capabilities of copper(II) tetrasulphonated phthalocyanine (CuTSPc) thin-films on gold electrodes has been investigated by means of synchrotron radiation X-ray fluorescence. In particular the paper focuses on the influence of the excitation energy in the relative narrow energy region of 9.2 to 11.7 keV on the detection limits and the peak-to-background ratios of copper.     

Biotinylated nanodiamond: simple and efficient functionalization of detonation diamond

We have developed a simple and efficient method for the covalent functionalization of detonation nanodiamond. After homogenization of the surface by borane reduction, the surface was modified with (3-aminopropyl)trimethoxysilane. Subsequent grafting of biotin yielded covalently biotinylated nanodiamond, which was characterized by FTIR spectroscopy, X-ray powder diffractometry, thermogravimetry, and elemental analysis. The activity was tested with horseradish peroxidase-labeled streptavidin. The surface loading of biotin was found to be 1.45 mmol g-1. The new material opens the way to covalently bonded diamond bioconjugates for labeling, drug delivery, and other applications.     

Structural importance of secondary interactions in molecules: origin of unconventional conformations of phosphine-borane adducts

The series of phosphine-borane adducts, Ph2(H3C--C[triple chemical bond]C)P--B(C6F5)3 (8 c), Ph(H3C--C[triple chemical bond]C)2P--B(C6F5)3 (8 b) and (H3C--C[triple chemical bond]C)3P--B(C6F5)3 (8 a), was prepared. The X-ray crystal structure analyses revealed close to eclipsed conformations for all members of this series with average dihedral angles theta(C-P-B-C) of 8.1 degrees (8 c), 12.3 degrees (8 b) and 20.3 degrees (8 a). Quantum chemical analysis of these compounds revealed the importance of a subtle interplay between competing attractive and repulsive secondary interactions, causing the surprising eclipsed conformational preference for systems of this degree of complexity. Some cyclic phosphine-borane adducts were studied for comparison.