Unbounded Jacobi Matrices with a Few Gaps in the Essential Spectrum: Constructive Examples

We give explicit examples of unbounded Jacobi operators with a few gaps in their essential spectrum. More precisely a class of Jacobi matrices whose absolutely continuous spectrum fills any finite number of bounded intervals is considered. Their point spectrum accumulates to +?? and ???. The asymptotics of large eigenvalues is also found.     

Fast folding of RNA pseudoknots initiated by laser temperature-jump

RNA pseudoknots are examples of minimal structural motifs in RNA with tertiary interactions that stabilize the structures of many ribozymes. They also play an essential role in a variety of biological functions that are modulated by their structure, stability, and dynamics. Therefore, understanding the global principles that determine the thermodynamics and folding pathways of RNA pseudoknots is an important problem in biology, both for elucidating the folding mechanisms of larger ribozymes as well as addressing issues of possible kinetic control of the biological functions of pseudoknots. We report on the folding/unfolding kinetics of a hairpin-type pseudoknot obtained with microsecond time-resolution in response to a laser temperature-jump perturbation. The kinetics are monitored using UV absorbance as well as fluorescence of extrinsically attached labels as spectroscopic probes of the transiently populated RNA conformations. We measure folding times of 1-6 ms at 37 °C, which are at least 100-fold faster than previous observations of very slow folding pseudoknots that were trapped in misfolded conformations. The measured relaxation times are remarkably similar to predictions of a computational study by Thirumalai and co-workers (Cho, S. S.; Pincus, D.L.; Thirumalai, D. Proc. Natl. Acad. Sci. U. S. A. 2009, 106, 17349-17354). Thus, these studies provide the first observation of a fast-folding pseudoknot and present a benchmark against which computational models can be refined.     

Localization for a Random Walk in Slowly Decreasing Random Potential

We consider a continuous time random walk X in a random environment on ?⁺ such that its potential can be approximated by the function V:?⁺→? given by $V(x)=\sigma W(x) -\frac {b}{1-\alpha}x^{1-\alpha}$ where σW a Brownian motion with diffusion coefficient σ>0 and parameters b, α are such that b>0 and 0<α<1/2. We show that P-a.s. (where P is the averaged law) $\lim_{t\to\infty} \frac{X_{t}}{(C^{*}(\ln\ln t)^{-1}\ln t)^{\frac{1}{\alpha}}}=1$ with $C^{*}=\frac{2\alpha b}{\sigma^{2}(1-2\alpha)}$ . In fact, we prove that by showing that there is a trap located around $(C^{*}(\ln\ln t)^{-1}\ln t)^{\frac{1}{\alpha}}$ (with corrections of smaller order) where the particle typically stays up to time t. This is in sharp contrast to what happens in the “pure” Sinai’s regime, where the location of this trap is random on the scale ln² t.     

Superprism effect in 1D photonic crystal

It is shown that superprism effect can be observed not only in 2D and 3D photonic crystal but also in 1D photonic crystal. To observe the effect a diffraction grating should be put on the top of the 1D PC. It is shown that the band gap more dramatically appears in 1D PC than in 2D PC. This effect makes all PBG effects including superprism effect more pronounced and also weakens the influence of losses.     

Acoustic emission during heterogeneous and homogeneous plastic flow of a metallic glass

Measurements have been made of the acoustic emission that occurs during the plastic deformation of metallic glass subjected to various heat treatments. It is shown that for the same temperature and deformation rate it is possible to have either homogeneous flow with no acoustic emission or localized flow accompanied by intense discrete acoustic emission, depending on the preliminary annealing conditions. From an analysis of the experimental results, it is deduced that the nature of the plastic flow of metallic glasses is determined by the structural relaxation rate at the experimental temperature and the conditions of intense structural relaxation, that plastic flow is homogeneous viscoelastic, and, under the conditions of kinetically inhibited structural relaxation, that it is localized and occurs by a dislocation-like mechanism. Fiz. Tverd. Tela (St. Petersburg) 39, 885–888 (May 1997)     

Application of Acoustic Spectroscopy to Investigation of Microinhomogeneous Media

Main mechanisms of absorption and dispersion of sound velocity in microinhomogeneous media are considered. Existing formulas for the velocity and absorption of sound in dispersion media is generalized to the case of continuos dispersed phase particle size distribution. The obtained relations were used for the analysis of the acoustic spectra of dodecane-based magnetic fluid measured in the 12–2000 MHz frequency range at temperatures varied from 0 to 80°C. The distribution of the volume fraction over particle sites in the examined magnetic fluid was described by a lognormal function. Parameters characterizing particle size distribution were determined. The analysis of the results of processing of the acoustic spectra of magnetic fluid indicated that the main contribution to the additional absorption (compared to absorption in the dispersion medium) originates from the friction and heat exchange between the particles and dispersion liquid. Absorption of sound due to scattering by the particles was negligibly small.     

New class of non-carbon AlP nanotubes: Structure and electronic properties

A new class of non-carbon nanotubes based on Group III and Group V elements (aluminum and phosphorus, respectively) is considered. The equilibrium geometry, energy characteristics, and electronic structure of the AlP nanotubes were calculated using the density functional theory. These calculations demonstrated that the AlP nanotubes are energetically stable structures. It was found that a low strain energy (approximately 0.01–0.07 eV) is required for rolling a two-dimensional hexagonal AlP structure into a tube. The AlP nanotubes are found to be wide-band-gap semiconductors with a band gap of 2.05–3.73 eV with direct (for the zigzag type) or indirect (for the armchair type) transitions between the top of the valence band and the bottom of the conduction band. The band gap of these nanotubes increases with the tube diameter, approaching the band gap of a two-dimensional hexagonal AlP layer.     

Some analogs of the Carleson embedding theorem for certain Hilbetr spaces of analytic functions

The embedding theorems mentioned in the title are proved for Hilbert spaces of holomorphic and harmonic functions satisfying slow growth conditions near the boundary. Bibliography: 3 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 206, 1993. pp. 40–54. Translated by V. I. Vasyunin.