Enumeration ofQ-acyclic simplicial complexes

Let (n, k) be the class of all simplicial complexesC over a fixed set ofn vertices (2≦k≦n) such that: (1)C has a complete (k−1)-skeleton, (2)C has precisely ( _k ⁿ⁻¹ )k-faces, (3)H _k (C)=0. We prove that for ,H _k−1(C) is a finite group, and our main result is: . This formula extends to high dimensions Cayley’s formula for the number of trees onn labelled vertices. Its proof is based on a generalization of the matrix tree theorem.     

Alkyl Ammonium Ion Selectivity of Hexahomotrioxacalix[3]arene Triamide Derivative having the Intramolecular Hydrogen-Bonding Group

The lower rim functionalized hexahomotrioxacalix[3]arene triamide 4 with cone-conformation was synthesized from triol 1 by a stepwise reaction. The different extractability for alkali metal ions, transition metal ions, and alkyl ammonium ions from water into dichloromethane is discussed. Due to the strong intramolecular hydrogen bonding between the neighboring NH and CO groups in triamide 4, its affinity to metal cations was weakened. Triamide 4 shows a single selectivity to n-BuNH₃⁺. The anion complexation of triamide 4 was also studied by ¹H NMR titration experiments. Triamide 4 binds halides through the intermolecular hydrogen bonding among the NH hydrogens of amide in a 1:1 fashion in CDCl₃. The association constants calculated from these changes in chemical shifts of the amide protons are K_a = 223 M⁻¹ for Cl⁻ and K_a = 71.7 M⁻¹ for Br⁻. Triamide 4 shows a preference for Cl⁻ complexation than Br⁻ complexation.     

Phase transitions in the tantalum-hydrogen system observed by PAC

The perturbation felt by¹⁸¹Hf probes in a¹⁸¹HfTa lattice loaded with 30 at% hydrogen was observed by PAC as a function of temperature. Three different interactions were identified: 1) Ν_Q1=433 (6) MHz, η=0.45 2) Ν_Q2=142 (9) MHz, η=0.9, and 3) Ν_Q?0, σ=4–14 Μ^?1 which are attributed to the Β^?, ε^? and α-phase in TaH system, respectively.     

Modular and Selective Arylation of Aryl Germanes (C−GeEt3) over C−Bpin,C−SiR3 and Halogens Enabled by Light-Activated Gold Catalysis

Selective C –C couplings are powerful strategies for the rapid and programmable construction of bi- or multiaryls. To this end, the next frontier of synthetic modularity will likely arise from harnessing the coupling space that is orthogonal to the powerful Pd-catalyzed coupling regime. This report details the realization of this concept and presents the fully selective arylation of aryl germanes (which are inert under Pd⁰/Pd^II catalysis) in the presence of the valuable functionalities C−BPin, C−SiMe₃, C−I, C−Br, C−Cl, which in turn offer versatile opportunities for diversification. The protocol makes use of visible light activation combined with gold catalysis, which facilitates the selective coupling of C−Ge with aryl diazonium salts. Contrary to previous light-/gold-catalyzed couplings of Ar–N₂⁺, which were specialized in Ar–N₂⁺ scope, we present conditions to efficiently couple electron-rich, electron-poor, heterocyclic and sterically hindered aryl diazonium salts. Our computational data suggest that while electron-poor Ar–N₂⁺ salts are readily activated by gold under blue-light irradiation, there is a competing dissociative deactivation pathway for excited electron-rich Ar–N₂⁺, which requires an alternative photo-redox approach to enable productive couplings.     

Steroids as chiral model compounds for selective reactions with metals

Our own work on steroid compounds with defined conformation as chiral model compounds for investigations of chemo-, regio- and stereoselectivity of metal-mediated new reactions is reviewed. Reactions with nickelacycles, (π-allyl)zirconoxycarbene complexes, iron tricarbonyl complexes of dienes and 1-azadienes, the Ru-catalyzed synthesis of 1,3-dihydropyrrol-2-ones from 1-azadienes, the Pd-catalyzed cyclopropanation of 1-azadienes, syntheses with cuprio steroids, copper complexes of amino alcohol derivatives and the copper-mediated hydroxylation of nonactivated C-H bonds with molecular oxygen are discussed.     

Diffusion coefficients of 2-fluoroanisole, 2-bromoanisole, allylbenzene and 1,3-divinylbenzene at infinite dilution in supercritical carbon dioxide

The Taylor–Aris chromatographic technique was employed for the determination of diffusion coefficients of 2-fluoroanisole, 2-bromoanisole, allylbenzene and 1,3-divinylbenzene at infinite dilution in supercritical carbon dioxide from 313.16 to 333.16 K and pressures between 15 and 35 MPa. As expected, the diffusivities rise when temperature increases and pressure decreases. Numerous predictive equations are compared with experimental data: Lai–Tan, Liu–Ruckenstein cluster formula, Woerlee, Hippler–Schubert–Troe, Catchpole–King, Eaton–Akgerman, He, He–Yu, Liu–Silva–Macedo, Funazukuri and coworkers, Dariva–Coelho–Oliveira, Zhu–Lu–Zhou–Wang–Shi and the Liu–Ruckenstein RHS formula. The equations of He, He–Yu and Catchpole–King are the best of all, but cannot be used in the whole range of temperatures and solvent densities.     

Determination of cadmium,aluminium, and copper in beer and products used in its manufacture by electrothermal atomic absorption spectrometry

Procedures were developed for determining cadmium, aluminium, and copper in beer and the products used in its manufacture by electrothermal atomic absorption spectrometry. Beer samples were injected into the furnace and solid samples were introduced as suspensions after preparation in a medium containing hydrogen peroxide, nitric acid, and ammonium dihydrogen phosphate for cadmium atomization. Calibration was performed with aqueous standards, and characteristic masses and detection limits were, respectively, 1 and 0.3 pg for cadmium, 18 and 5.4 pg for aluminium, and 5.6 and 6.8 pg for copper. Different samples of beer, wort, brewer's yeast, malt, raw grain, and hops were analyzed by the proposed procedures. Cadmium was found in low concentrations (0.001-0.08 microg/g and 0-1.3 ng/mL); copper (3-13 microg/g and 25-137 ng/mL) and aluminium (0.6-9 microg/g and 0.1-2 microg/mL) were found at higher levels. The reliability of the procedure was confirmed by comparing the results obtained with others based on microwave oven sample digestion, and by analyzing several certified reference materials.     

Formal total synthesis of β-pipitzol

(±)-$\text{O}$-methylperezone ($\text{1b}$) was obtained by selective oxidative demethylation of (±)-leucoperezone trimethyl ether ($\text{4a}$). Compound ($\text{4a}$) was prepared by condensation of 2,3,5-trimethoxytoluene ($\text{5e}$) with 6-methyl-5-hepten-2-one, followed by reductive removal of the tertiary alcohol. The aromatic precursor $\text{5e}$ was prepared in four steps from 2,3-dimethoxytoluene ($\text{5a}$) and, alternatively, in three steps from 5-bromoveratraldehyde ($\text{6a}$). Racemic $\text{1b}$ and $\text{4a}$ were directly compared with the optically active molecules prepared from natural R(-)-perezone ($\text{1a}$).     

Copper-assisted oxidation of catechols into quinone derivatives

Catechols are ubiquitous substances often acting as antioxidants, thus of importance in a variety of biological processes. The Fenton and Haber–Weiss processes are thought to transform these molecules into aggressive reactive oxygen species (ROS), a source of oxidative stress and possibly inducing degenerative diseases. Here, using model conditions (ultrahigh vacuum and single crystals), we unveil another process capable of converting catechols into ROSs, namely an intramolecular redox reaction catalysed by a Cu surface. We focus on a tri-catechol, the hexahydroxytriphenylene molecule, and show that this antioxidant is thereby transformed into a semiquinone, as an intermediate product, and then into an even stronger oxidant, a quinone, as final product. We argue that the transformations occur via two intramolecular redox reactions: since the Cu surface cannot oxidise the molecules, the starting catechol and the semiquinone forms each are, at the same time, self-oxidised and self-reduced. Thanks to these reactions, the quinone and semiquinone are able to interact with the substrate by readily accepting electrons donated by the substrate. Our combined experimental surface science and ab initio analysis highlights the key role played by metal nanoparticles in the development of degenerative diseases.

An antioxidant catechol transforms following intramolecular redox reactions into highly reactive oxygen species, a semiquinone and a quinone, on copper.