Height in splittings of relatively hyperbolic groups

Geometriae Dedicata - Given a finite graph of relatively hyperbolic groups with its fundamental group relatively hyperbolic and edge groups quasi-isometrically embedded and relatively quasiconvex...     

Equivariant Spectral Triples on the Quantum SU(2) Group

We characterize all equivariant odd spectral triples for the quantum SU(2) group acting on its L ₂-space and having a nontrivial Chern character. It is shown that the dimension of an equivariant spectral triple is at least three, and given any element of the K-homology group of SU_q(2), there is an equivariant odd spectral triple of dimension 3 inducing that element. The method employed to get equivariant spectral triples in the quantum case is then used for classical SU(2), and we prove that for p < 4, there does not exist any equivariant spectral triple with nontrivial K-homology class and dimension p acting on the L ₂-space.The first author would like to acknowledge support from the National Board of Higher Mathematics, India.     

Use of ultrafine-dispersed nanodiamond for selective deposition of boron-doped diamond films

A suspension of ultrafine-dispersed nanodiamond was used for introducing (in particular, selectively) high-density centers of diamond nucleation on various substrates. High-quality doped diamond films to be used as electrochemistry electrodes were deposited from the gas phase in a microwave discharge on certain substrates treated using ultrafine-dispersed nanodiamond. A uniform distribution of nucleation centers with concentrations greater than 10¹⁰ cm^-2 on silicon substrates was obtained. Electrochemical current-potential curves were measured for continuous films. Diamond meshes of different transparency were grown using selective nucleation. Successful production of high-quality doped diamond meshes gives grounds to consider them the most promising electrodes for use in electrochemistry.     

Microstructure and mechanical characteristics of nanodiamond-SiC compacts

Superhard nanodiamond-SiC ceramics are prepared by infiltrating liquid Si into porous nanodiamond compacts under pressure. Synthesized samples are 2.2 mm thick and 3–4 mm in diameter. The effect of particle size of dynamically synthesized nanodiamond powders on silicon infiltration and SiC phase formation is studied. It is established that silicon does not penetrate into the pores of nanodiamond powders if the original particle size is smaller than 0.5–1.0 μm. The critical pore size for infiltration is 100–200 nm. A study of the microstructure of the samples showed the presence of the nanometer-and submicron-scale SiC phase. The ultrasound velocities are measured in the prepared compacts, and the elastic moduli are calculated. __________ Translated from Fizika Tverdogo Tela, Vol. 46, No. 4, 2004, pp. 734–736. Original Russian Text Copyright ? 2004 by Ekimov, Gromnitskaya, Mazalov, Pal’, Pichugin, Gierlotka, Palosz, Kozubowski.     

Asymptotic Expansions of Posterior Distributions in Nonregular Cases

We study the asymptotic behaviour of the posterior distributions for a one-parameter family of discontinuous densities. It is shown that a suitably centered and normalized posterior converges almost surely to an exponential limit in the total variation norm. Further, asymptotic expansions for the density, distribution function, moments and quantiles of the posterior are also obtained. It is to be noted that, in view of the results of Ghosh et al. (1994, Statistical Decision Theory and Related Topics V, 183-199, Springer, New York) and Ghosal et al. (1995, Ann. Statist., 23, 2145-2152), the nonregular cases considered here are essentially the only ones for which the posterior distributions converge. The results obtained here are also supported by a simulation experiment.     

Low-temperature specific heat of crystalline and amorphous Eu2(MoO4)3

The specific heat C _total of crystalline and amorphous Eu₂(MoO₄)₃ is measured in the temperature interval 4.5–30 K. The amorphous state is obtained by applying pressure ∼7 GPa at room temperature. It is found that the specific heat of the crystal at T⩽7.5 K is described by a cubic function of temperature, while the specific heat of the amorphous sample has a strongly non-Debye character in the entire experimental temperature interval. The curve of C _total for amorphous europium molybdate is analyzed in a model of soft atomic potentials, and it is shown that it agrees well with universal low-temperature anomalies of the specific heat of classical glasses obtained by quenching from the liquid. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 8, 623–627 (25 October 1998)     

Olefinic-ester cyclizations using Takai-Utimoto reduced titanium alkylidenes

The scope and limitations of the Takai-Utimoto reagent to induce the cyclization of olefinic-esters is described. Critical is the steric environment about both the ester and the olefin. Mechanistically, these results support the hypothesis that cyclized product comes from an olefin metathesis, carbonyl-olefination sequence.     

Study of the peak effect phenomenon in single crystals of 2H-NbSe2

The weakly pinned single crystals of the hexagonal 2H-NbSe₂ compound have emerged as prototypes for determining and characterizing the phase boundaries of the possible order-disorder transformations in the vortex matter. We present here a status report based on the ac and dc magnetization measurements of the peak effect phenomenon in three crystals of 2H-NbSe₂, in which the critical current densities vary over two orders of magnitude. We sketch the generic vortex phase diagram of a weakly pinned superconductor, which also utilizes theoretical proposals. We also establish the connection between the metastability effects and pinning.