Random walks on almost connected locally compact groups: Boundary and convergence

We prove that, given an arbitrary spread out probability measure μ on an almost connected locally compact second countable groupG, there exists a homogeneous spaceG/H, called the μ-boundary, such that the space of bounded μ-harmonic functions can be identified withL ^∞ (G/H). The μ-boundary is an amenable contractive homogeneous space. We also establish that the canonical projection onto the μ-boundary of the right random walk of law μ always converges in probability and, whenG is amenable, it converges almost surely. The μ-boundary can be characterised as the largest homogeneous space among those homogeneous spaces in which the canonical projection of the random walk converges in probability.     

Activation enthalpy for ligand-bridged electroreduction of cobalt(III) complexes in mixtures of water with acetone

The activation enthalpy for the reduction of two pentaamminecobalt(III) complexes attached to a mercury electrode by thiophenecarboxylate ligands was evaluated from the temperature dependence of the unimolecular rate constants measured in a nonisothermal cell arrangement. The data obtained for the reactant with a bridge featuring uninterrupted conjugation support our previous opinion that the decrease of the rate constant on addition of acetone to the mixtures results from a decrease in the nuclear frequency factor owing to the overdamped solvent friction. The unimolecular frequency factors and the adiabaticity of the processes are discussed.     

Practical synthesis of fluorous oxazolidinone chiral auxiliaries from alpha-amino acids

[reaction: see text] A series of new fluorous-supported oxazolidinone chiral auxiliaries has been prepared using a versatile and general five-step pathway, starting from readily available chiral alpha-amino acids. The key feature of this synthesis is the efficient generation of a suitably active perfluoroalkyllithium species. By use of this protocol, the auxiliaries can be obtained in high enantiomeric purity and on multigram scales from L-phenylalanine and L-valine with overall yields as high as 55%. The new methodology also incorporates fluorous solid-phase extraction on the large scale, allowing bulk quantities (up to 25 g) of fluorous compounds to be purified from the crude reaction mixture.     

QZ1 and QZ2: rapid, reversible quinoline-derivatized fluoresceins for sensing biological Zn(II)

QZ1, 2-[2-chloro-6-hydroxy-3-oxo-5-(quinolin-8-ylaminomethyl)-3H-xanthen-9-yl]benzoic acid, and QZ2, 2-[6-hydroxy-3-oxo-4,5-bis-(quinolin-8-ylaminomethyl)-3H-xanthen-9-yl]benzoic acid, two fluorescein-based dyes derivatized with 8-aminoquinoline, have been prepared and their photophysical, thermodynamic, and zinc-binding kinetic properties determined. Because of their low background fluorescence and highly emissive Zn(II) complexes, QZ1 and QZ2 have a large dynamic range, with approximately 42- and approximately 150-fold fluorescence enhancements upon Zn(II) coordination, respectively. These dyes have micromolar K(d) values for Zn(II) and are selective for Zn(II) over biologically relevant concentrations of the alkali and alkaline earth metals. The Zn(II) complexes also fluoresce brightly in the presence of excess Mn(II), Fe(II), Co(II), Cd(II), and Hg(II), offering improved specificity for Zn(II) over di(2-picolyl)amine-based Zn(II) sensors. Stopped-flow kinetic investigations indicate that QZ1 and QZ2 bind Zn(II) with k(on) values of (3-4) x 10(6) M(-1) s(-1), compared to (6-8) x 10(5) M(-1) s(-1) for select ZP (Zinpyr) dyes, at 4.3 degrees C. Dissociation of Zn(II) from QZ1 and QZ2 occurs with k(off) values of 150 and 160 s(-1), over 5 orders of magnitude larger than those for ZP probes, achieving reversibility on the biological (millisecond) time scale. Laser scanning confocal and two-photon microscopy studies reveal that QZ2 is cell-permeable and Zn(II)-responsive in vivo. Because of its weaker affinity for Zn(II), QZ2 responds to higher concentrations of intracellular Zn(II) than members of the ZP family, illustrating that binding affinity is an important parameter for Zn(II) detection in vivo.     

Reaction entropy for the electroreduction of bis(biphenyl)chromium(I) in different solvents

The reaction entropy, ΔS_r°, for the electroreduction of bis(biphenyl)chromium(I) has been measured in eight solvents using a non-isothermal cell arrangement. A correlation between the solvent acceptor number and the ΔS_r° values has been observed. The measured reaction entropies are higher than those for ferrocene/ferricenium ion and bis(benzene)chromium(O)/bis(benzene)chromium(I) couples.     

Synthons for syntheses of spiro[2.4]heptane analogues of prostaglandins

Methods for the preparation of synthons for syntheses of spiro[2.4]heptane analogues of prostaglandins are described. Two of them (1a and1b) enable the syntheses of 11-deoxy-type compounds and were prepared from spiro[2.4]heptan-4-one (3) which after transformation into the 5-phenylthio-,-unsaturated ketone5 was subjected to conjugate addition of organocuprate reagent6. The third synthon (2)-a potential intermediate in syntheses of complete spiro[2.4]heptane analogues of prostaglandins-was prepared from the bicyclic ketone10 byBaeyer-Villiger oxidation followed by epoxidation.

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Ausgangsverbindungen für die Synthese von Prostaglandin-analogen Spiro[2.4]heptanen

Zusammenfassung Es werden Synthesewege für Spiro[2.4]hepane als Analoge zu Prostaglandinen beschrieben. Zwei davon (1a und1b) ermöglichen die Synthese von Verbindungen des 11-Deoxy-Typs; sie wurden aus Spiro[2.4]heptan-4-on (3) dargestellt, das nach der Umwandlung zum 5-phenylthio-,-ungesättigten Keton5 einer konjugierten Addition von Organocuprat-Reagens6 unterworfen wurde. Das dritte (2), ein potentielles Zwischenprodukt in der Synthese von vollständigen Spiro[2.4]heptan-Analogen zu Prostaglandinen, wurde aus dem bicyclischen Keton10 durchBaeyer-Villiger-Oxidation gefolgt von einer Epoxidierung dargestellt.

     

New renin inhibitors containing pseudodipeptidic units in P3-P2 and P1-P1' positions

A series of four non-peptidic renin inhibitors have been designed and synthesized. All of them contain in their molecule (3S,4S)-4-amino-5-cyclohexyl-3-hydroxypentanoic acid (ACHPA), a hydrophobic portion at the C-terminus and a second dipeptide-like transition state analog or unnatural dipeptidic fragment at the N-terminus. Inhibitory activity of the compounds was measured in vitro by high performance liquid chromatography (HPLC). Their IC50 (M/l) values were: <10(-3) (12), 1.0 x 10(-6) (19), 4.0 x 10(-4) (23) and 1.0 x 10(-6) (29), respectively. All the compounds are stable against chymotrypsin.     

Entropy of electrochemical formation ofp-semiquinones in dimethylformamide

Entropy of formation of anion radicals at the mercury electrode in dimethyl-formamide for 1,4-benzoquinone, 1,4-naphthoquinone, 9,10-anthraquinone, and 5,12-tetracenequinone has been determined from the temperature dependences of the reversible half-wave potentials using a nonisothermal cell. The linear relationship between the entropy and the calculated spin density at the oxygen atom of semiquinones was established. Similarly the linear correlation of the literature reaction entropy for electrooxidation of a few heteroaromatic compounds versus the experimental spin density at a heteroatom (N, S or Se) from ESR measurements was also observed.

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Die Entropie der elektrochemischen Bildung vonp-Semichinonen in Dimethylformamid

Zusammenfassung Die Bildungsentropie von Anionenradikalen an der Quecksilberelektrode wurde in Dimethylformamid für 1,4-Benzochinon, 1,4-Naphthochinon, 9,10-Anthrachinon und 5,12-Tetracenchinon aus der Temperaturabhängigkeit der reversiblen Halbwellenpotentiale unter Benutzung einer nichtisothermen Zelle bestimmt. Es wurde eine lineare Abhängigkeit zwischen der Entropie und der berechneten Spindichte am Sauerstoffatom der Semichinone festgestellt. Eine ähnliche lineare Korrelation konnte für die Literaturdaten von Reaktionsentropien der Elektrooxidation einiger heteroaromatischer Verbindungen gegenüber den experimentellen Spindichten am Heteroatom (N, S, Se; ESR-Messungen) beobachtet werden.

     

Distribution of critical values of miniversal deformations of parabolic singularities

Summary We consider, in this paper, the critical values mapping, which associates with any polynomial from underdiagonal miniversal deformation of the family of parabolic singularities, the set of its critical values. We showed that the restriction of this mapping to the subset of polynomials withk different critical values,k2, is a covering of the space of unorderedk-tuples of different complex numbers. In particular, it is proved that the connected components of such subsets areK(, 1) spaces.