The Markov power moment problem in problems of controllability and frequency extinguishing for the wave equation on a half-axis

In this paper necessary and sufficient conditions of null-controllability and approximate null-controllability are obtained for the wave equation on a half-axis. Controls solving these problems are found explicitly. Moreover, bang-bang controls solving the approximate null-controllability problem are constructed with the aid of solutions of a frequency extinguishing problem in the restricted band (−a,a) for this equation and the Markov power moment problem.     

Non-linear Stability of Modulated Fronts¶for the Swift–Hohenberg Equation

We consider front solutions of the Swift–Hohenberg equation ∂ _t u= -(1+ ∂ _x ²)² u + ɛ² u -u ³. These are traveling waves which leave in their wake a periodic pattern in the laboratory frame. Using renormalization techniques and a decomposition into Bloch waves, we show the non-linear stability of these solutions. It turns out that this problem is closely related to the question of stability of the trivial solution for the model problem ∂ _t u(x,t) = ∂ _x ² u (x,t)+(1+tanh(x-ct))u(x,t)+u(x,t) ^p with p>3. In particular, we show that the instability of the perturbation ahead of the front is entirely compensated by a diffusive stabilization which sets in once the perturbation has hit the bulk behind the front. Received: 23 February 2001 / Accepted: 27 August 2001     

On c‐Bhaskar Rao designs with block size 4

Several new families of c‐Bhaskar Rao designs with block size 4 are constructed. The necessary conditions for the existence of a c‐BRD (υ,4,λ) are that: (1)λ_min=?λ/3 ≤ c ≤ λ and (2a) c≡λ (mod 2), if υ > 4 or (2b) c≡ λ (mod 4), if υ = 4 or (2c) c≠ λ ? 2, if υ = 5. It is proved that these conditions are necessary, and are sufficient for most pairs of c and λ; in particular, they are sufficient whenever λ?c ≠ 2 for c > 0 and whenever c ? λ_min≠ 2 for c < 0. For c < 0, the necessary conditions are sufficient for υ> 101; for the classic Bhaskar Rao designs, i.e., c = 0, we show the necessary conditions are sufficient with the possible exception of 0‐BRD (υ,4,2)'s for υ≡ 4 (mod 6). © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 361–386, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10009     

The study and applications of photochemical-dynamical gravity wave model II

A nonlinear, compressible, non-isothermal gravity wave model that involves photochemistry is used to study the effects of gravity wave on atmospheric chemical species distributions in this paper. The changes in the distributions of oxygen compound and hydrogen compound density induced by gravity wave propagation are simulated. The results indicate that when a gravity wave propagates through a mesopause region, even if it does not break, it can influence the background distributions of chemical species. The effect of gravity wave on chemical species at night is larger than in daytime.     

Raman spectroscopy of topotecan, an inhibitor of DNA topoisomerase I

Topotecan (TPT), a water-soluble derivative of camptothecin (inhibitor of human DNA topoiomerase I), has found wide application in cancer chemotherapy. The central problem in using topotecan is the presence of lactone rings in its molecules, which undergo hydrolysis at a physiological pH yielding an inactive and even toxic form of the drug. The analysis of Raman spectra of TPT in H₂O and D₂O solutions made it possible to assign the spectral bands to the vibrations of particular molecular groups. Spectral features indicative of the opening of the lactone rings of the TPT molecules, deprotonation of the hydroxyl groups in their quinoline fragments, and of possible participation of the hydroxyl and carbonyl groups in H bonding are found. The data obtained are necessary to study the molecular mechanisms of TPT-DNA interaction and the formation of ternary complexes between TPT, DNA, and DNA topoisomerase I.     

Black-hole horizon and metric singularity at the brane separating two sliding superfluids

An analogue of a black hole can be realized in the low-temperature laboratory. The horizon can be constructed for “relativistic” ripplons (surface waves) living on the brane. The brane is represented by the interface between two superfluid liquids, ³He-A and ³He-B, sliding along each other without friction. A similar experimental arrangement was recently used for the observation and investigation of the Kelvin-Helmholtz type of instability in superfluids [1]. The shear-flow instability in superfluids is characterized by two critical velocities. The lowest threshold measured in recent experiments [1] corresponds to the appearance of the ergoregion for ripplons. In the modified geometry, this will give rise to the black-hole event horizon in the effective metric experienced by ripplons. In the region behind the horizon, the brane vacuum is unstable due to interaction with the higher-dimensional world of bulk superfluids. The time of the development of instability can be made very long at low temperature. This will allow us to reach and investigate the second critical velocity—the proper Kelvin-Helmholtz instability threshold. The latter corresponds to the singularity inside the black hole, where the determinant of the effective metric becomes infinite.     

Linear nonstationary optical dimensional resonances in atomic nanostructures

The existence of linear nonstationary optical resonances in a diatomic nanostructural object with a dipole-dipole atomic interaction has been proved. A new solution to the joint system of modified Bloch optical equations and nonlocal field equations is obtained for time intervals much shorter than the times of phase and energy relaxation. Formulas for effective polarizabilities of the object’s atoms, which have a set of dimensional resonances, are derived. The frequencies of these resonances significantly differ from the eigenfrequencies of the object’s atoms, and their properties depend on the interatomic distance, light-pulse duration, initial atomic inversions, and the orientation of the object’s axis relative to the direction of incidence of the external light wave.     

Laser induced copper electroless plating on polyimide with Q-switch Nd:YAG laser

The results of laser induced deposition of copper on polyimide substrate from copper electrolyte solution are reported. Unlike most work reported in the literatures where CW Ar⁺ lasers were used, a second harmonic (532 nm wavelength) Q-switch Nd:YAG laser was used for our experiments. The deposition process was conducted by laser-catalyzing of the polyimide surface and subsequent photothermal-accelerated reduction of copper-complex ions in an alkaline reducing environment. The characteristics of the deposited copper line were investigated in terms of laser beam scanning speed, and the number of scans. The surface morphology and chemical composition of the deposited copper were analyzed using field emission scanning electron microscope (FESEM) and energy dispersive spectrometer (EDX). The optimum processing conditions have been identified. The copper deposit was found to adhere well to the substrate.     

Dynamical Characteristics of Traveling Wave Packets of Total Electron Content Disturbances

Using the COPHASE method and the GPS interferometry method for travelling ionospheric disturbances, we analyze in detail the spatio-temporal properties of travelling wave packets (TWP) of total electron content (TEC) disturbances. The analysis is performed on the example of a clearest TWP manifestation observed in California, USA, in October 18, 2001, using the GLOBDET technique, developed at the Institute of Solar-Terrestrial Physics of the Siberian Branch of RAS for global detection and monitoring of natural and technogenic ionospheric disturbances on the basis of TEC variations retrieved from the global network of GPS receivers. In the time domain, TWPs are quasi-periodic TEC oscillations of duration about 1 h, period of 10–20 min, and amplitude exceeding that of the background TEC fluctuations by at least one order of magnitude. The velocity and direction of TWP motion are similar to those of mid-latitude mesoscale travelling ionospheric disturbances, as obtained earlier from the analysis of phase parameters of HF radio signals and the signals of geostationary satellites and discrete space radio sources.