A correlational inequality for linear extensions of a poset

Suppose 1, 2, and 3 are pairwise incomparable points in a poset onn≥3 points. LetN (ijk) be the number of linear extensions of the poset in whichi precedesj andj precedesk. Define λ by $$\lambda = \frac{{N(213)N(312)}}{{\left[ {N(123) + N(132)} \right]\left[ {N(231) + N(321)} \right]}}$$ Two applications of the Ahlswede-Daykin evaluation theorem for distributive lattices are used to prove that λ?(n?1)²/(n+1)² for oddn, and λ?(n?2)/(n+2) for evenn. Simple examples show that these bounds are best-possible. Shepp (Annals of Probability, 1982) proved thatP(12)?P(12/13), the so-calledxyz inequality, whereP(ij) is the probability thati precedesj in a randomly chosen linear extension of the poset, thus settling a conjecture of I. Rival and B. Sands. The preceding bounds on λ yield a simple proof ofP(12)<P(12/13), which had also been conjectured by Rival and Sands.     

Comparing Intrinsic Reactivities of the First‐ and Second‐Generation Ruthenium Metathesis Catalysts in the Gas Phase

An experimental comparison of the gas‐phase reactivity of the 14‐electron reactive intermediates produced by phosphine dissociation from the first‐ and second‐generation ruthenium metathesis catalysts, (L)Cl₂Ru?CHR (L=PCy₃ or NHC), supports Grubbs's contention that the second‐generation catalysts show hundred‐fold higher phenomenological activity despite a slower phosphine dissociation because of a much more‐favorable partitioning of the 14‐electron active species towards product‐forming steps. The gas‐phase study finds, in ring‐opening metathesis of norbornene as well as acyclic metathesis of ethyl vinyl ether, that the first‐generation systems display evidence for a higher barrier above that for phosphine dissociation; the second‐generation systems, on the other hand, behave as if there is no significantly higher barrier.     

Ab initio calculations on the interaction of oxygen containing ligands with alkali cations. The system H2CO/Li+

Ab initio calculations on formaldehyde/Li⁺ complexes are presented. The most stable arrangement is characterized by an energy of interaction of 43.2 kcal/mole, C_2v symmetry and an oxygen—lithium distance of R_OLi = 1.77 Å. A detailed analysis of the electron density function gives proof of the electrostatic nature of the complexes H₂O/Li⁺ and H₂Co/Li⁺ and shows extensive mutual polarization. The failure of the semi-empirical method to predict the changes in electron density at the Li⁺ cation correctly is explained.     

Molecular orbital theoretical prediction of the isomeric products formed from reactions of arene oxides and related metabolites of polycyclic aromatic hydrocarbons

MO theoretical calculations based on the perturbational method of Dewar provide good correlation between predicted and observed structures of products formed during: (1) isomerization of arene oxides to phenols; (2) hydration and nucleophilic addition to arene oxides; and (3) dehydration of arene dihydrodiols. The method is equally applicable to the arene oxides, dihydrodiols, etc. derived from carcinogenic and noncarcinogenic polycyclic hydrocarbons. Extension to the related enzymatic reactions occurring during metabolism of carcinogenic hydrocarbons and to the reactions of the biologically active arene diolepoxides and aryloxirenes suggests the potential utility of this approach in predicting (a) metabolite structure and (b) the structural requirements for carcinogenic and mutagenic activity.     

“Deuterated” Raney nickel: deuteration (reduction) of alkenes,carbonyl compounds and aromatic rings. Proton-deuterium exchange of “activated” aliphatic and aromatic ring hydrogens.

In the absence of deuterium gas, the reaction of deuterated Raney nickel with benzene derivatives, carbonyl compounds, alkenes and activated methylene groups gave either fully deuterated (reduced) products or led to hydrogen-deuterium exchange.     

Monitoring of ethanol during fermentation using a microbial biosensor with enhanced selectivity

The present study is concerning the construction of ferricyanide-mediated Gluconobacter oxydans cell ethanol biosensor. The size exclusion effect of a cellulose acetate membrane was used for elimination of glucose interferences during ethanol assays in real samples. A typical response time of the biosensor was 13 s with a high sensitivity of 3.5 microA mM(-1). The microbial biosensor exhibits a very low detection limit of 0.85 microM and a wide linear range from 2 to 270 microM. The operational stability was excellent. During 8.5 h of repetitive ethanol assays, no decrease in the sensor sensitivity was observed. The biosensor was successfully used in the off-line monitoring of ethanol fermentation with a good agreement with HPLC measurements (R(2)=0.998).     

Spektroskopische und theoretische Untersuchungen am Borazolmolekül und seinen Bortrihalogenoderivaten

Zusammenfassung Es werden Hückel-MO-Rechnungen am Borazol und den B-Trihalogenoborazolen durchgeführt und die entsprechenden Parameter an den teils bekannten und teils gemessenen UV-Spektren geeicht. Die für diese Verbindungen bestimmten chemischen Verschiebungen der ¹¹B- und ¹⁴N-Kernresonanz lassen sich mit den berechneten -Elektronendichten erklären.

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Hückel-MO calculations are performed for Borazine and the B-Trihalogenoborazines; the parameters used are calibrated with the UV-spectra, which had either been measured here or obtained from the literature. The calculated -electron densities compare favorably well with the ¹¹B- and ¹⁴N-nuclear magnetic resonances determined for the above mentioned compounds.

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Résumé Le borazole et les B-trihalogenoborazoles sont calculés par la méthode de Hückel en utilisant des paramètres calibrés sur les spectres U.V. mesurés ou obtenus dans la littérature. Les densités électroniques sont en bon accord avec le déplacement chimique de N.M.R. de ¹¹B et ¹⁴N déterminé pour les composés cidessus.

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Herrn Professor Dr. H. Hartmann danken wir für sein stetes Interesse und die wohlwollende Förderung dieser Arbeit. Für die Hilfe bei der Aufnahme des Vakuum-UV-Spektrums von Fluoroborazol danken wir Herrn Diplom-Physiker E. Mohler.     

Carbophile Additionen von Organocupraten mit 1,3-Thiazol-5(4H)-thionen

Carbophilic Additions of Organocuprates and 1,3-Thiazole-5(4H)-thiones Organocuprates and 1,3-thiazole-5(4H)-thiones 1 react in THF at 0° via carbophilic addition onto the C? S bond to give 4,5-dihydro-1,3-thiazole-5-thiols 3 (Scheme 3). This observation is in marked contrast to the previously described reaction of organolithium compounds and 1 , which undergo a thiophilic addition onto the exocyclic S-atom. As an exception, treatment of the 1,3-thiazole-5(4H)-thione 1a with tert-butyl cuprate leads to 7a (Scheme 3).