Absolute frequency measurement of the In+ clock transition with a mode-locked laser

The absolute frequency of the In(+) 5s(2) (1)S(0)5s5p (3)P(0) clock transition at 237 nm was measured with an accuracy of 1.8 parts in 10(13). Using a phase-coherent frequency chain, we compared the (1)S(0)(3)P(0) transition with a methane-stabilized HeNe laser at 3.39 mum, which was calibrated against an atomic cesium fountain clock. A frequency gap of 37 THz at the fourth harmonic of the HeNe standard was bridged by a frequency comb generated by a mode-locked femtosecond laser. The frequency of the In(+) clock transition was found to be 1 267 402 452 899.92 (0.23) kHz, the accuracy being limited by the uncertainty of the HeNe laser reference. This result represents an improvement in accuracy of more than 2 orders of magnitude over previous measurements of the line and now stands as what is to our knowledge the most accurate measurement of an optical transition in a single ion.s.     

Negative compressibility and nonequivalence of two statistical ensembles in the escape transition of a polymer chain

An end-tethered polymer chain compressed between two pistons undergoes an abrupt transition from a confined coil state to an inhomogeneous flowerlike conformation partially escaped from the gap. This phase transition is first order in the thermodynamic limit of infinitely long chains. A rigorous analytical theory is presented for a Gaussian chain in two ensembles: (a) the H-ensemble, in which the distance H between the pistons plays the role of the independent control parameter, and (b) the conjugate f-ensemble, in which the external compression force f is the independent parameter. Details about the metastable chain configurations are analyzed by introducing the Landau free energy as a function of the chain stretching order parameter. The binodal and spinodal lines, as well as the barrier heights between the stable and metastable states in the free energy landscape, are presented in both ensembles. In the loop region for the average force with dependence on the distance H (i.e., in the H-ensemble) a negative compressibility exists, whereas in the f-ensemble the average distance as a function of the force is strictly monotonic. The average fraction of imprisoned segments and the lateral force, taken as functions of the distance H or the average H, respectively, have different behaviors in the two ensembles. These results demonstrate a clear counterexample of a main principle of statistical mechanics, stating that all ensembles are equivalent in the thermodynamic limit. The authors show that the negative compressibility in the escape transition is a purely equilibrium result and analyze in detail the origin of the nonequivalence of the ensembles. It is argued that it should be possible to employ the escape transition and its anomalous behavior in macroscopically homogeneous, but microscopically inhomogeneous, materials.     

Reactions of silicon hydrides catalyzed by rhodium(III) sulfoxide complexes

Russian Journal of General Chemistry - Dehydrocondensation reactions of silicon hydrides catalyzed by the rhodium(III) complex [RhCl3(Me2SO)3] in the absence of the second substrate were studied....     

Synthesis and cytotoxicity of novel dispiro derivatives of 5-arylidenoxazolones,potential inhibitors of p53—MDM2 protein-protein interaction

Russian Chemical Bulletin - Regioselective synthesis of new dispiro indolinones combining both an indolinone and an oxazolone fragment in their structure comprised the 1,3-dipolar cycloaddition of...     

Universal properties of a single polymer chain in slit: Scaling versus molecular dynamics simulations

We revisit the classical problem of a polymer confined in a slit in both of its static and dynamic aspects. We confirm a number of well known scaling predictions and analyze their range of validity by means of comprehensive molecular dynamics simulations using a coarse-grained bead-spring model of a flexible polymer chain. The normal and parallel components of the average end-to-end distance, mean radius of gyration and their distributions, the density profile, the force exerted on the slit walls, and the local bond orientation characteristics are obtained in slits of width D=4/10 (in units of the bead diameter) and for chain lengths N=50/300. We demonstrate that a wide range of static chain properties in normal direction can be described quantitatively by analytic model-independent expressions in perfect agreement with computer experiment. In particular, the observed profile of confinement-induced bond orientation is shown to closely match theory predictions. The anisotropy of confinement is found to be manifested most dramatically in the dynamic behavior of the polymer chain. We examine the relation between characteristic times for translational diffusion and lateral relaxation. It is demonstrated that the scaling predictions for lateral and normal relaxation times are in good agreement with our observations. A novel feature is the observed coupling of normal and lateral modes with two vastly different relaxation times. We show that the impact of grafting on lateral relaxation is equivalent to doubling the chain length.     

Henstock type integral in compact zero-dimensional metric space and quasi-measures representations

Properties of a Henstock type integral defined on a compact zero-dimensional metric space are studied. Theorems on integral representation of so-called quasi-measures, i.e., linear functionals on the space of ??polynomials?? defined on the space of the above mentioned type, are obtained.     

Integration of Banach-valued functions and Haar series with Banach-valued coefficients

It is proved that for any Banach space each everywhere convergent Haar series with coefficients from this space is the Fourier–Haar series in the sense of Henstock type integral with respect to a dyadic differential basis. At the same time, the almost everywhere convergence of a Fourier–Henstock–Haar series of a Banach-space-valued function essentially depends on properties of the space.     

Proximity-induced superconductivity in graphene

We propose a way of making graphene superconductive by putting on it small superconductive islands which cover a tiny fraction of graphene area. We show that the critical temperature, T _c , can reach several Kelvins at the experimentally accessible range of parameters. At low temperatures, T T _c , and zero magnetic field, the density of states is characterized by a small gap E _g ≤ T _c resulting from the collective proximity effect. Transverse magnetic field H _g (T) ∝ E _g is expected to destroy the spectral gap driving graphene layer to a kind of a superconductive glass state. Melting of the glass state into a metal occurs at a higher field H _g2(T). The article is published in the original.