Discrete subgroups of <Emphasis Type="Italic">PU</Emphasis> (2, 1) acting on P<Stack><Subscript>ℂ</Subscript><Superscript>2</Superscript></Stack> and the Kobayashi metric

In this paper, we prove following: If G ⊂ PU (2, 1) is an infinite, discrete group, acting on P_ℂ² without complex invariant lines, then the component containing ℍP_ℂ² of the domain of discontinuity Ω(G) = PP_ℂ²∖ Λ (G), according to Kulkarni, is G-invariant complete Kobayashi hyperbolic. The authors were supported by the Universidad Autónoma de Yucatán and the Universidad Nacional Autónoma de México.     

Scattering of small solutions to generalized benjamin-bona-mahony equation in several space dimensions

We show that the supremum norm of solutions with small initial data of the generalized Benjamin-Bona-Mahony equation u_t-△u_t=(b,▽u)+u^p(a,▽u)in x?Rⁿ,n≥2, with integer p≥3 , decays to zero like t^-2/3 if n=2 and like t^-1+6, for any δ0, if n≥3, when t tends to infinity. The proofs of these results are based on an analysis of the linear equation u_t-△=(b,▽u)) and the associated oscillatory integral which may have nonisolated stationary points of the phase function.     

Direct electrochemistry of cytochrome c on nanotextured diamond surface

Nanotextured diamond surfaces with geometrical properties close to protein dimensions were used for the realization of direct electron transfer of cytochrome c (cyt c) without any covalent bonding. The peroxidase activity of native and denatured cyt c was also investigated. Cyclic voltammograms of native cyt c show quasi-reversible electron transfer reactions, while no heme redox activity is detected for denatured cyt c. Unfolding (denaturation) of cyt c can be achieved in the presence of hydrogen peroxide. Partially or fully denatured cyt c showed higher peroxidase activity than native cyt c. This is because denatured cyt c loses its tertiary structure and hydrogen peroxide is easier to access the heme redox center. The apparent Michaelis–Menten constant K_m for native and denatured cyt c has been determined to be 0.23 mM and 0.08 mM.     

Aminophosphinic Acids in a Pyridine Series: Cleavage of Pyridine-2- and Pyridine-4-methyl(amino)phosphinic Acids in Acidic Solutions

The synthesis of a series of new pyridine aminomethylphosphinic acids is described. These compounds were obtained in the reaction of the corresponding pyridine aldehydes with primary amines and with ethyl phenylphosphinate, or methylphosphinate, in the presence of bromotrimethylsilane. In aqueous, strong acid solutions, pyridine aminophosphinic acids were split, forming the phenyl-, or methylphosphonic, acid and the corresponding secondary pyridyl-alkylamines. The kinetics of some observed cleavages were measured, and a mechanism of the cleavage has been proposed.     

Static Headspace Sampling and Solid-Phase Microextraction for Assessment of Edible Oils Stability

Static headspace sampling and headspace solid-phase microextraction have been applied for the determination of the low molecular mass aldehydes—markers of edible oil oxidation. Preconcentration and determination conditions for the two procedures were optimized. LODs LOQs and repeatability of a standard mixture were established for all investigated compounds. Both methods of sampling were applied to the analysis of samples of rapeseed and sunflower oils. It appears that solid-phase microextraction is better than headspace sampling for the analysis of volatile oxidation products. Solid-phase microextraction can be conducted at a much lower temperature and has lower LOD values and better repeatability than headspace sampling.     

Mechanism of an alcohol-trapping reaction in the direct and benzophenone-sensitized photodenitrogenation of a spiroepoxy-substituted azoalkane: solvent effects and stereochemical deuterium labeling

The spin-state-dependent reactivity, singlet versus triplet, of the 2-spiroepoxy-1,3-cyclopentane-1,3-diyl DR2 has been assessed through alcohol-trapping reactions for which the effect of solvent acidity on the product distribution of the alcohol trapping products 2 versus 3 + 4 and stereochemical deuterium-labeling studies have been performed. The proposed mechanism for the solvent effect on the product ratio (2/3 + 4) reveals the importance of the hydrogen-bonded intermediates I1 and I2 in the trapping reactions; the stereochemical deuterium-labeling results clarify the dipole structure trapped by the alcohol. The dipoles DP1 and DP2, in which the configuration between the epoxide oxygen and the deuterium atoms is retained, are inferred for the direct photodenitrogenation reactions (singlet state), whereas for the benzophenone-sensitized photoreactions (triplet state), after ISC, the ring-opened dipole DP3 is implied as the intermediate that is trapped by the alcohol.     

Intramolecular and intermolecular kinetic isotope effects (KIE) in the nitrosoarene ene reaction: experimental evidence for reversible intermediate formation

The intramolecular and intermolecular kinetic isotope effects (KIE) have been determined for the nitrosoarene ene reaction with deuterium-stereolabeled 2,3-dimethyl-2-butenes (TME). trans-TME-d(6) (k(H)/k(D) = 3.0) and gem-TME-d(6) (k(H)/k(D) = 4.0) show large intramolecular primary isotope effects. In contrast, the intramolecular competition in cis-TME-d(6) (k(H)/k(D) = 1.5) and the intermolecular competition for the TME-d(0)/TME-d(12) pair (k(H)/k(D) = 1.98) show considerably smaller, but mechanistically significant kinetic isotope effects. The latter fact is rationalized in terms of reversible formation of a three-membered-ring intermediate, namely the aziridine N-oxide, or a similar unsymmetrical, polarized diradical in the first step of the reaction. Such reversibility has also been implied earlier for triazolinedione (TAD) and singlet oxygen ((1)O(2)) with deuterium-stereolabeled 2-butenes, but of the three enophiles, ArNO is the most sensitive toward reversibility, which is due to its moderate reactivity and its high steric demand.     

Stereochemical memory in the temperature-dependent photodenitrogenation of bridgehead-substituted DBH-type azoalkanes: inhibition of inverted-housane formation in the diazenyl diradical through the mass effect (inertia) and steric hindrance

The photochemical denitrogenation of the cyclopentene-annelated DBH-type azoalkanes 1 has been examined in solution as a function of bridgehead substitution and temperature. For all derivatives, namely, the unsubstituted 1a(H/H), monomethyl 1b(Me/H) dimethyl 1c(Me/Me), monophenyl 1d(Ph/H), and diphenyl 1e(Ph/Ph), the temperature-dependent ratio of syn and anti housanes 2 provides experimental support for a competition between the singlet (high temperature) and triplet (low temperature) reaction channels in the direct photolysis. The syn/anti ratio of the housanes 2 depends on the extent and type of bridgehead substitution; the amount of the anti diastereomer (retention) follows the order Ph > Me > H, and double substitution is more effective than single. This stereochemical memory is interpreted in terms of the mass effect (inertia) of the substituents and steric interaction (size) between the substituents at the bridgehead and the methylene bridge during the deazetation step of the transient diazenyl diradical conformations (1)DZ (exo-ax) and (1)DZ (exo-eq). These conformers are impulsively generated upon decay of the (1)(n,pi)-excited azoalkane, a trajectory assessed through computational work. The new mechanistic feature disclosed by the unprecedented anti stereoselectivity (retention) is the intervention of a puckered 1,3-cyclopentanediyl singlet diradical (1)DR as product bifurcation step, whose conformational relaxation to the planar species (loss of stereochemical memory) is encumbered by bridgehead substitution.     

Chiral calixarene derived from resorcinol. Part 4: Diastereoselective closure of the oxazine ring

A method for the preparation of a single diastereomer of the oxazine derivative of calixresorc[4]arene 3 has been developed. Lewis acids were employed for opening of the oxazine ring.