Orbits of Hurwitz action for coverings of a sphere with two special fibers

We consider finite, orientable, connected, branched coverings of a 2-sphere which have at most two nonsimple critical values. We prove that the equivalence class of a covering, up to a fiber preserving homeomorphism, is determined by its genus, the degree, the monodromy group and the branching data of the nonsimple critical values.     

Geometry of ammonia molecule in the lowest triplet state estimated theoretically

The geometrical parameters of the ammonia molecule in the lowest-lying triplet state have been estimated by means of the SCF method and by making an extrapolation to take into account electron correlation effects. The planar configuration has been obtained as the most probable geometrical arrangement (³ A₂″).     

Crystal and molecular structure of the meso-diastereoisomer of 1,12-dimethyl-2,11-dithia-5,8-dioxa[12](1,1′)ferrocenophane

The meso-diastereoisomer of 1,12-dimethyl-2,11-dithia-5,8-dioxa[12](1,1′)ferrocenophane crystallizes in space group P$\text{1}$ with a 8.879(2), b 10.135(2), c 12.030(2) Å, α 100.14(1), β 99.02(1), γ 103.93(1)°; the ferrocenyl moiety has an eclipsed conformation and the bridging chain a steric arrangement of the type aag⁺aag^?g⁺aag^?a.     

Reactivity of various four-coordinate aluminum alkyls towards dioxygen: evidence for spatial requirements in the insertion of an oxygen molecule into the AI-C bond

The interaction of dioxygen with various tetrahedral aluminum alkyls, (tBu)3Al.OEt2 (1), tBu2Al(mu-OtBu)2AltBu2 (6), (tBu)2Al(mesal) (2) [mesal=methyl salicylate anion], R2Al(mu-pz)2AlR2 [pz=deprotonated pyrazole, R= Me (3a), Et (3b), and tBu (3c)], R2Al(mu-3,5-Me2pz)2AIR2[3,5-Me2pz = deprotonated 3,5-dimethylpyrazole, R= Me (4a), and Et (4b)], and Et2B(mu-pz)2AlEt2 (5), has been investigated. We were particularly interested in the effect of steric hindrances both caused by the metal-bonded substituents and those that result from the nature of the bifunctional ligand used in the oxygenation reaction. In the reaction of 1 with O2, only the formation of the monoalkoxide compound6 was observed. The latter di-tert-butyl compound as well as all planar aluminapyrazoles, that is, the tert-butyl derivative 3c and lower alkylaluminum derivatives with the more demanding 3,5-dimethylpyrazoyl ligands 4a and 4b, are stable under an atmosphere of dry oxygen and ambient conditions. Inspection of the space-filling representation of these compounds has undoubtedly shown that the bulky tert-butyl groups or pyrazolyles ligands, respectively, provide steric protection for the metal center from the dioxygen attack. In contrast, the dialkylaluminum derivatives of pyrazole, 3a and 3b, and the diethylaluminum bis(1-pyrazolyl)borate complex 5, all with the metal center eclipsed with respect to the plane defined by the four nitrogen atoms, react smoothly with O2 to form the alkyl(alkoxy)aluminum complexes. In the reaction of 5 with O2 for example, the Et-B bonds remained intact, and the dimeric five-coordinate compound [Et2B(mu-pz)2 Al(mu-OEt)Et]2 (9) was isolated in good yield. The interaction of mononuclear di-tert-butyl chelate complex 2 with O2 at -15 degrees C gives (tBuOO)(tBuO)Al(mu-OtBu)2Al(mesal)2 (7) in high yield, and the presence of the alkylperoxo moiety is a particularly significant point in the resulting product. All the compounds have been characterized spectroscopically, and the structures of 3c, 4a, 6, 7, and 9 have been confirmed by X-ray crystallography. Structural features of 1-6 are discussed and are considered in relation to the possible approach pathways of the O2 molecule to the four-coordinate metal center. This analysis and the observed apparent dissimilarity in the reactions of model four-coordinate aluminum alkyls with O2 clearly show that the stereoelectronic prerequisites are responsible for the fundamentally different reactivity.     

Photooxidation of Methionine Derivatives by the 4-Carboxybenzophenone Triplet State in Aqueous Solution. Intracomplex Proton Transfer Involving the Amino Group

Abstract— Oxidation of the triplet state of 4-carboxybenzophenone (CB) by a series of five substituted methionines and three methionine-containing dipeptides was monitored under laser flash photolysis conditions in aqueous solution. Spectral resolution techniques were employed to follow the concentration profiles of the intermediates formed from the quenching events. From these concentration profiles, quantum yields for the intermediates were determined. Branching ratios were evaluated for the decay of the charge-transfer complex by the competing processes of back electron transfer, proton transfer and escape of radical ions. The relative prominence of these processes was discussed in terms of the proton-transfer tendencies of the nominal sulfur-radical-cationic species. A systematic decrease was observed in the quantum yields for the escape of radical ions along with a correlated increase in the proton-transfer yields. The enhanced propensity of the sulfur radical cations to depro-tonate is due to deprotonation at the carbons adjacent to the sulfur-cationic site and at the unsubstituted amino groups when present. This scheme was supported by an observed decrease in the yields of dimeric sulfur radical cations with an increase in the electron-withdrawing abilities of the substituents, making the radical-cationic species stronger acids. The involvement of protons on the amino groups was implicated by the correlation of the quantum yields of ketyl radical formation in the photochemistry experiments with the rate constants for the reaction of the CB radical anion with the sulfur-containing substrates in pulse radiolysis experiments.     

Separable quantizations of Stäckel systems

In this article we prove that many Hamiltonian systems that cannot be separably quantized in the classical approach of Robertson and Eisenhart can be separably quantized if we extend the class of admissible quantizations through a suitable choice of Riemann space adapted to the Poisson geometry of the system. Actually, in this article we prove that for every quadratic in momenta Stäckel system (defined on 2n$2n$ dimensional Poisson manifold) for which Stäckel matrix consists of monomials in position coordinates there exist infinitely many quantizations–parametrized by n$n$ arbitrary functions–that turn this system into a quantum separable Stäckel system.     

Phase equilibria and modeling of ammonium ionic liquid, C2NTf2, solutions

Novel quaternary ammonium ionic liquid, ethyl(2-hydroxyethyl)dimethylammonium bis(trifluomethylsulfonyl)imide (C2NTf2), has been prepared from N,N-dimethylethanolamine as a substrate. The paper includes a specific basic characterization of the synthesized compound by NMR and the basic thermophysical properties: the melting point, enthalpy of fusion, enthalpy of solid-solid phase transition, glass transition determined by the differential scanning calorimetry (DSC), temperature of decomposition, and water content. The density of the new compound was measured. The solid-liquid or liquid-liquid phase equilibria of binary mixtures containing {C2NTf2+water or an alcohol (propan-1-ol, butan-1-ol, hexan-1-ol, octan-1-ol, decan-1-ol), aromatic hydrocarbons (benzene, toluene), aliphatic hydrocarbons (n-hexane, n-octane), dimethylsulfoxide (DMSO), or tetrahydrofuran (THF)} have been measured by a dynamic method in a wide range of temperatures from 230 to 430 K. These data were correlated by means of the nonrandom two-liquid (NRTL) equation utilizing temperature-dependent parameters derived from the solid-liquid or liquid-liquid equilibrium. From the solubility results, the negative value of the partition coefficient of ionic liquid in binary system octan-1-ol/water (log P) at 298.15 K has been calculated.     

A simple presentation for the mapping class group of an orientable surface

LetF _n.k be an orientable compact surface of genusn withk boundary components. For a suitable choice of 2n + 1 simple closed curves onF _n,1 the corresponding Dehn twists generate bothM _n,o andM _n,1. A complete system of relations is determined for these generators and the presentations ofM _n,0 andM _n,1 obtained in this way are much simpler than the known presentations.     

4‐Chloro‐1‐naphthol

Molecules of the title compound, C₁₀H₇ClO, (I), are connected by a single strong O—H...O hydrogen bond into a simple C(2) chain, which runs parallel to the c axis and is additionally stabilized by intermolecular π–π stacking interactions. The significance of this study lies in the comparison drawn between the crystal structure of (I) and those of several of its simple analogues. This comparison shows a close similarity in the packing of the molecules that form π‐stacks along the shortest crystallographic axes. A substantial spatial overlap is observed between adjacent molecules in such a π‐stack, depending mainly on the kind of substituent.