Wilson's functional equations on groups

We study properties of solutionsf, g, h C(G) of the functional equation

Large deviations for martingales with some applications

Let(X _i ) be a martingale difference sequence. LetY be a standard normal random variable. We investigate the rate of uniform convergence

Titantetrafluorid – Eine überraschend einfache Kolumnarstruktur

Titanium Tetrafluoride – a Surprising Simple Column Structure For the first time single crystals of TiF₄ have been obtained by solvothermal decomposition of (O₂)₂Ti₇F₃₀ in anhydrous HF. The colourless, transparent needles crystallize orthorhombic in spacegroup Pnma–D (No. 62) with a = 2 281.1, b = 384.8, c = 956.8 pm, Z = 12. The new type of structure is dominated by isolated columns of corner-linked TiF₆-octahedra.     

(Z)-1-[2-(Triarylstannyl)vinyl]-1-cycloheptanols: Synthesis, characterization, halodemetallation and crystal structures

The synthesis and characterization by ¹H, ¹³C, ¹¹⁹Sn NMR and ¹¹⁹Sn Mössbauer spectroscopy of (Z)-1-[2-(triphenylstannyl)vinyl]-1-cycloheptanol,

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(1), and (Z)-1-[2-tri-p-tolylstannyl)vinyl-1-cycloheptanol,

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(2), are described, together with their halodemetallation by I₂, Br₂ and ICIl to yield derivatives of the types

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(Ar = phenyl or p-tolyl, N = 1, 2; X = I, Br, Cl, respectively). The solid-state structures of four compounds have been determined by X-ray diffraction analysis. In the crystals of

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(1) and

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(2) the Sn atom has a tetrahedral geometry distorted towards trigonal bipyramid as a consequence of a close intramolecular contact with the hydroxyl O(1) atom of 2.742(3) Å and 2.768(3) Å, respectively. A trigonal bipyramidal geometry is found in

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(12) and

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(4), in which significant Sn---O(1) interactions are noted [2.437(8) Å and 2.407(8) Å, respectively].     

Structure-based identification and clustering of protein families and superfamilies

Summary We describe an approach to protein structure comparison designed to detect distantly related proteins of similar fold, where the procedure must be sufficiently flexible to take into account the elasticity of protein folds without losing specificity. Protein structures are represented as a series of secondary structure elements, where for each element a local environment describes its relations with the elements that surround it. Secondary structures are then aligned by comparing their features and local environments. The procedure is illustrated with searches of a database of 468 protein structures in order to identify proteins of similar topology to porcine pepsin, porphobilinogen deaminase and serum amyloid P-component. In all cases the searches correctly identify protein structures of similar fold as the search proteins. Multiple cross-comparisons of protein structures allow the clustering of proteins of similar fold. This is exemplified with a clustering of /- and -class protein structures. We discuss applications of the comparison and clustering of three-dimensional protein structures to comparative modelling and structure-based protein design.     

Kerr constants and dipole moments of aminobenzoic acids in dioxane

Aminobenzoic acids in dioxane have been investigated by dipole moment and Kerr effect methods.m-Aminobenzoic acid exists in a solution mainly (60 %) in thesyn-form. Inp-aminobenzoic acid, conjugation flattens the pyramidal configuration of the nitrogen atom, which is even more flattened ino-aminobenzoic acid owing to an intramolecular hydrogen bond.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 859–861, May, 1994.     

On Lipschitz property of solutions of functional equations

In this work it is proved that under certain conditions the continuous vector-valued solutionsf of the functional equation

Ein Beitrag über Ba3Pt4HgO11: Das erste Erdkalimetall-Oxoplatinat(II,V)/Oxomercurat

A Contribution on Ba₃Pt₄HgO₁₁: The First Alkaline-Earth Oxoplatinate(II,V)/Oxomercurate Single crystals of Ba₃Pt₄HgO₁₁ were prepared by oxygen high pressure technique (4 200–3 600 bar) and investigated by X-ray methods. It crystallizes with hexagonal symmetry, space group D? P6 2c, a = 6.021, c = 17.374 Å, Z = 2. Ba₃Pt₄HgO₁₁ represents a new structure type, showing structural relationships to Ba₂Hg₃Pd₇O₁₄ and to the precious metal 6L-perovskites. The Hg²⁺ ions show dumb-bell like coordination, Pt²⁺ a square-planar surrounding and Pt⁵⁺ face shared double octahedra.     

CdHgO2: Ein Oxomercurat mit Verwandtschaft zur Crednerit-Struktur

CdHgO₂: An Oxomercurate related to the Crednerite Structure Single crystals of CdHgO₂ were prepared by oxygen high pressure technique (600°C, 3900 bar) and investigated by X-ray technique. It crystallizes with monoclinic symmetry, space group C–C2/m; a = 5.933, b = 3.452, c = 5.875 Å, β = 91.26°; Z = 2. The Hg²⁺ ions show dumb-bell like coordination, Cd²⁺ an octahedral one. CdHgO₂ shows strong relationship to the Crednerite structure. The orientation of the O? Hg? O dump-bells to the CdO₆ octahedra layers is discussed with respect to related oxomercurates.