Moderate Deviations for Longest Increasing Subsequences: The Lower Tail

We derive a moderate deviation principle for the lower tail probabilities of the length of a longest increasing subsequence in a random permutation. It refers to the regime between the lower tail large deviation regime and the central limit regime. The present article together with the upper tail moderate deviation principle in Ref. 12 yields a complete picture for the whole moderate deviation regime. Other than in Ref. 12, we can directly apply estimates by Baik, Deift, and Johansson, who obtained a (non-standard) Central Limit Theorem for the same quantity.     

Stochastic Arithmetic: s-spaces and Some Applications

It has been recently shown that computation with stochastic numbers as regard to addition and multiplication by scalars can be reduced to computation in familiar vector spaces. In this work we show how this can be used for the algebraic solution of linear systems of equations with stochastic right-hand sides. On several examples we compare the algebraic solution with the simulated solution using the CADNA package.     

Diastereomer-differentiating hydrolysis of 1,3-diol-acetonides: a simplified procedure for the separation of syn- and anti-1,3-diols

[reaction: see text] A new method to facilitate the separation of diastereomeric syn- and anti-1,3-diols is described. The method relies on the different hydrolysis rates of the corresponding diastereomeric acetonides. Treatment of a dichloromethane solution of syn- and anti-1,3-diol-acetonide with a catalytic amount of diluted aqueous hydrochloric acid leads to the selective cleavage of the anti diastereomer. The resulting anti-1,3-diol can be easily separated from the unchanged syn-1,3-diol-acetonide.     

Ein Beitrag zur ?nologie und ?kologie von Selen

Summary Little is known about selenium contents in alcoholic beverages, especially in wine, because no reliable determination method was available so far. A procedure for the detection of selenium in the pg- and low ng-range was developed, which uses the hydride-generation-condensation-AAS (HGC-AAS). Selenium contents in 103 German wines of the year vintages 1950 until 1985 were determined. In mean they range between 0.29 and 0.79 g/l Se and show a certain dependence from the geological soil formation and the wine species. Corresponding vineyard soils from Ingelheim (Rheinhessen, FRG) contain 0.18–0.44 mg/kg Se, mean 0.24 mg/kg Se, 10% of it is available for plants. The distribution of selenium in grape berries shows selenium-rich seeds and — with red wine species — selenium-rich skins. Higher selenium contents by contamination were observed near an industrial location. The behaviour of selenium in the vegetation cycle is pursued. The selenium depletion during fermentation may amount to 60%. All results are summarized in the so-called trace element vinogram. Selenium hence is a regular and natural constituent part of wine.

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Herrn Prof. Dr. R. Neeb zum 60. Geburtstag gewidmet     

Der Abbau des Insektizides GS 13005 in der Ratte. Strukturaufklärung der wichtigsten Metabolite [1]

The structures of the essential metabolites which are excreted by the rat after oral application of GS 13005 (O,O-dimethyl-S-[(2-methoxy-1,3,4-thiadiazole-5(4H)-one-4-yl)-methyl] dithiophosphate) have been elucidated. The product of final oxidation, CO₂, was found to be the main metabolite (up to 36% of the dose applied). Among the degradation products excreted in the urine (up to 45% of the dose applied) the two most important were isolated. They are 4-methylsulfinylmethyl and 4-methylsulfonylmethyl derivatives respectively of the intact 2-methoxy-1,3,4-thiadiazole-5-one heterocycle (metabolites III and II, in amounts of 20–25% and 5–7% of the dose applied, respectively). These metabolites originate by methylation and subsequent oxidation from the mercaptomethyl derivative liberated after hydrolysis of the P S bond of the dithiophosphoric acid ester.     

Metallocene complexes as homogeneous catalysts in olefin polymerization

Ansa metallocene dichloride complexes of titanium, zirconium, and hafnium can be activated by methyl aluminoxane (MAO) to give excellent catalysts for the homogeneous polymerization of ethylene and propylene. The symmetry of the corresponding metaliocene dichloride complexes is essential for the stereospecific polymerization of propylene (isotactic, syndiotactic or atactic). The application of fluorenyl groups instead of cyclopentadienyl groups greatly increases the activity of the catalysts. The first ansa bis(fluorenyl) complexes of zirconium and hafnium, (C₁₃H₈-C₂H₄-C₁₃Hs)MCl₂ (M = Zr, Hf), have been prepared. It was found that after the activation by MAO the zirconium derivative demonstrates a very high activity. Several model complexes are presented in order to discuss the mechanism of the polymerization.This paper was presented at the INEOS-94 Workshop The Modern Problems of Organometallic Chemistry (Moscow, May 21–27, 1994).Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 7–14, January, 1995.     

The Structure of Tetrakis(pentafluorophenyl)tellurium(IV), Te(C6F5)4

Tetrakis(pentafluorophenyl)tellurium(IV), Te(C₆F₅)₄, was prepared from the reaction of TeCl₄ and Mg(C₆F₅)Br. Crystallization of the crude product from n‐pentane at ?25 °C gave suitable single crystals. The title compound crystallizes in the monoclinic space group P2₁/c (Z = 8) with two independent molecules per unit cell.     

Anthracene Based Bulky Diol Hosts. Crystal Structures of a Free Host and of Inclusion Compounds with Dipolar Guests

X-ray crystal structures are reported of a free host compound 1, comprising two diphenylmethanol terminal groups attached to a central 9,10-ethynyl substituted anthracene unit, and of three inclusion compounds of a fluoren-9-ol substituted analogous host 2 with acetone, dimethyl sulphoxide (DMSO) and dimethylformamide (DMF) as guest, respectively. Despite the presence of two hydroxyl groups in 1, there is no O–H...O hydrogen bond between the molecules in the guest free crystal – only weaker C–H...O interactions and van der Waals' type connections. In the inclusion compounds of 2, H-bonded 1:2 host–guest associates are formed, where each of the host hydroxyl groups binds to a guest oxygen atom. The orientations of the host–guest connections in these complexes vary, being E for acetone and Z for both DMSO and DMF guests, relative to the host anthracene unit. The DMSO and DMF inclusion compounds of 2 proved to be isostructural.