Computation of the Morse Spectrum

The Morse spectrum is a limit set of Lyapunov exponents of periodic pseudo-trajectories. This notion is especially important in the case where a dynamical system has infinitely many periodic trajectories of large period. A method for estimating the Morse spectrum was suggested by the first author in J. Math. Anal. Appl., 252 (2000). This method is based on ideas of symbolic dynamics which reduces the study of a dynamical system to the study of a certain graph, called a symbolic image. Within the framework of this method, the computation of the Morse spectrum is connected with searching simple closed paths and extracting contours with suitable characteristics. However, under iterations of the symbolic image, the number of such paths sharply increases, which leads to huge expenses of memory and time. We suggest an algorithm for constructing contours with the maximal and minimal mean values. This algorithm is based on a special version of the simplex method. Numerical tests are also described. Bibliography: 13 titles. Illustrations: 3 figures.     

Complementarity methodology as applied for solution of the inverse problem for solid-phase reaction kinetics III

Mathematical analysis has shown that invariant kinetic parameters (IKP) correspond to the real kinetic curve even in the case when the equation prescribing this curve is not used for the calculation of parameters. It has been proved that IKP values coincide with those obtained for isothermal conditions. The theory is verified by calculations using model experimental data. The IKP stability to random experimental errors is studied.     

Catalytic properties of Pd-containing systems based on SBA-15 molecular sieve modified with imidazolium ionic liquid

Palladium(II) ions were incorporated in SBA-15 molecular sieve modified with imidazolium-based ionic liquids. The synthesized materials were characterized using differential thermic analysis, low-temperature nitrogen adsorption, transmission electron spectroscopy and elemental analysis. The materials obtained basing on a grafted ion liquid, in 1-hexene hydrogenetion were shown to exhibit the catalytic activity significanly higher than those prepared via ion liquid adsorption on supports.     

Study of K^ - \to \pi ^0 e^ - \overline \nu _e \gamma decay with ISTRA+ setup

Results of study of the $K^ - \to \pi ^0 e^ - \overline \nu \gamma $ decay at the ISTRA+ setup are presented. We observed 4476 events of this decay. The branching ratio is found to be $R = \frac{{Br(K^ - \to \pi ^0 e^ - \overline \nu _e \gamma )}}{{Br(K^ - \to \pi ^0 e^ - \overline \nu _e )}}$ = (1.81±0.03(stat.)±0.07(syst.)) × 10^?2 for E*_γ > 10 MeV and θ*_eγ > 10°. For comparison with the previous experiment the branching ratio with cuts E*_γ > 10 MeV, 0.6 < cos θ*_eγ < 0.9 is calculated: R = $\frac{{Br(K^ - \to \pi ^0 e^ - \overline \nu _e \gamma )}}{{Br(K^ - \to \pi ^0 e^ - \overline \nu _e )}}$ = (0.47±0.02(stat.) ± 0.03(syst.)) × 10^?2. For the cuts E*_γ > 30 MeV and θ*_eγ > 20°, used in most theoretical papers, Br = (3.06 ± 0.09(stat.) ± 0.14(syst.)) × 10^?4. For the asymmetry we get A _ξ = ?0.015 ± 0.021. At present it is the best estimate of this asymmetry.     

Phase-controlled force and magnetization oscillations in superconducting ballistic nanowires

The emergence of superconductivity-induced phase-controlled forces in the (10(-2)-10(-1)) nN range and of magnetization oscillations in nanowire junctions is discussed. A giant magnetic response to applied weak magnetic fields is predicted in the ballistic Josephson junction formed by a superconducting tip and a surface, bridged by a normal-metal nanowire where Andreev states form.     

Ultrasound-assisted synthesis of nanostructured transition metal oxides

Ultrasound pretreatment of aqueous solutions of cetyltrimethylammonium bromide as a structure- directing agent has been applied to prepare nanostructured mesoporous Mn, Fe, and Ni oxides. After removal of the template by triple extraction with a water–ethanol solution of sodium acetate or ammonium chloride, air-calcined samples of oxide materials prepared in such a way possess surface areas of about 300–450 m²/g and are thermally stable up to 300°C.     

Analysis of the single-particle energies of 1<Emphasis Type="Italic">f</Emphasis> and 2<Emphasis Type="Italic">p</Emphasis> proton states in <Superscript>64,66,68</Superscript>Zn nuclei by the mean field model with dispersive optical potential

Single-particle proton energies near the Fermi energy in ^64,66,68Zn are analyzed using the mean field model with dispersive optical potential. Good agreement is obtained between the calculated energies and experimental data. The set of parameters of the dispersive optical potential is compared with the set found for neighboring ^58,60,62,64Ni with the magic number Z = 28.     

Investigation of special features of the neutron and proton shell structure of the isotopes 90,92,94,96Zr

The neutron and proton single-particle energies and the occupation probabilities for the valence states of the even-even isotopes ^90,92,94,96Zr are determined by matching data on nucleon-stripping and nucleon-pickup reactions on the same nucleus. The data obtained in this way suggest the magicity of the number N = 56 for Z = 40. The single-particle energies of all bound neutron and proton states in the ^90,92,94,96Zr nuclei are described within the experimental errors on the basis of the dispersive optical model.     

Models of active Brownian motors based on internal oscillations

We analyze the dynamics of driven translations or rotations based on models with internal oscillations. In particular we discuss several new mechanisms of motors driven by chemical energy. First we study the simple depot model and give analytical solutions including efficiency and stochastic effects. Then we introduce internal oscillations based on inertia including variable friction functions. Further we replace inertia by delay effects and study motors in trigger regime. As possible applications we consider a model of ATP-driven motors operating on angle and elasticity variables. We develop a model of F₁-ATPase motors with three β-subunits which drive the rotation of the central γ-shaft.