Interaction of Ytterbium Trifluoride with Zirconium in a NaF-ZrF4 Molten Mixture

The interaction of ytterbium trifluoride with zirconium in a molten mixture of sodium and zirconium fluorides have been studied by differential thermal analysis, X-ray diffraction, and electronic and IR spectroscopy. In the temperature range 440–640°C, zirconium reduces YbF₃ to ytterbium. The reaction products also contain low-valence zirconium and ytterbium compounds.     

Ultrasonic amplification semiconductors subjected to deformation

It is shown that in semiconductors with inherent piezo-effect or high relative dielectric permittivity (?_rel ? 10³) which have undergone uniaxial deformation an additional electron-phonon interaction is possible, this being conditioned by the non-linear deformation piezo-effect or electrostriction. The non-linear piezo-module in CdS and the electrostriction constant of the second order in SrTiO₃ have been experimentally investigated.Additional ultrasound amplification conditioned by deformation can exceed the amplification in a non-deformed semiconductor by one order.     

Uniform stability of the inverse Sturm-Liouville problem with respect to the spectral function in the scale of Sobolev spaces

We consider the inverse problem of recovering the potential for the Sturm-Liouville operator Ly = ?y″ + q(x)y on the interval [0, π] from the spectrum of the Dirichlet problem and norming constants (from the spectral function). For a fixed θ ≥ 0, with this problem we associate a map F: W ₂ ^θ → l _D ^θ , F(σ) = {s _k } ₁ ^∞ , where W ₂ ^θ = W ₂ ^θ [0, π] is the Sobolev space, σ = ∫ q is a primitive of the potential q ∈ W ₂ ^{θ ? 1} , and l _D ^θ is a specially constructed finite-dimensional extension of the weighted space l ₂ ^θ ; this extension contains the regularized spectral data s = {s _k } ₁ ^∞ for the problem of recovering the potential from the spectral function. The main result consists in proving both lower and upper uniform estimates for the norm of the difference ‖σ ? σ ₁‖ _θ in terms of the l _D ^θ norm of the difference of the regularized spectral data ‖s ? s₁‖ _θ . The result is new even for the classical case q ∈ L ₂, which corresponds to the case θ = 1.     

A mapping method in inverse Sturm-Liouville problems with singular potentials

In the space L ₂[0, π], the Sturm-Liouville operator L _D(y) = ?y″ + q(x)y with the Dirichlet boundary conditions y(0) = y(π) = 0 is analyzed. The potential q is assumed to be singular; namely, q = σ′, where σ ∈ L ₂[0, π], i.e., q ∈ W ₂ ^?1 [0, π]. The inverse problem of reconstructing the function σ from the spectrum of the operator L _D is solved in the subspace of odd real functions σ(π/2 ? x) = ?σ(π/2 + x). The existence and uniqueness of a solution to this inverse problem is proved. A method is proposed that allows one to solve this problem numerically.     

Ergodic decomposition of group actions on rooted trees

We prove a general result about the decomposition into ergodic components of group actions on boundaries of spherically homogeneous rooted trees. Namely, we identify the space of ergodic components with the boundary of the orbit tree associated with the action, and show that the canonical system of ergodic invariant probability measures coincides with the system of uniform measures on the boundaries of minimal invariant subtrees of the tree. Special attention is paid to the case of groups generated by finite automata. Few examples, including the lamplighter group, Sushchansky group, and so-called universal group, are considered in order to demonstrate applications of the theorem.     

Formation of nanobumps and nanoholes in thin metal films by strongly focused nanosecond laser pulses

Nanobumps and nanoholes have been formed in gold and silver films with various thicknesses on a dielectric substrate by strongly focused single nanosecond pulses of a Nd:YAG laser. An apertureless dielectric fiber probe and an aspherical lens with a numerical aperture of 0.5 were used to focus laser radiation into a diffraction-limited spot on the surface of gold and silver films, respectively. Atomic force and electron microscopy studies have demonstrated that the shape and dimension of nanostructures, as well as the threshold parameters of laser radiation for their formation, are determined by the thickness of a modified film (“size effect”) and by the duration of a laser pulse owing to the lateral heat conduction in films (nonlocal energy deposition effect). Mechanisms of the dynamic formation of such structures in metallic films by nanosecond laser pulses due to phase transformations of their material have been discussed.     

The Properties of Zr,Ti, Al and Si Nitride-Based Multilayer Coatings Obtained By Cathodic Arc Plasma Deposition

Russian Physics Journal - The paper investigates the cathodic arc plasma deposition of multilayer ZrTiN and ZrTiAlSiN coatings with the maximum hardness of 28 and 29 GPa, respectively. When the...