Coverings of topological loops

In this paper, we show that in some cases, no proper covering of a locally compact group topologically generated by left translations of a topological loop can occur as the group topologically generated by left translations of a topological loop. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 22, Algebra and Geometry, 2004.     

Relativistic shift of the linear Zeeman effect

The efficiency with which a magnetic field acts on sublevels of the first and second doublets of a hydrogen-like atom is shown to vary because of relativistic effects by a factor of 1 ? 2γ(l + 1)/(2l + 3) and 1 ? 2γl/(2l ? 1), respectively, where γ is the ratio of the electron binding energy to the rest energy and l is the quantum number of the orbital angular momentum.     

A method for calculating invariant subspaces of symmetric hyperbolic equations

An algorithm is constructed for calculating invariant subspaces of symmetric hyperbolic systems arising in electromagnetic, acoustic, and elasticity problems. Discrete approximations are calculated for subspaces that correspond to minimal eigenvalues and smooth eigenfunctions. Difficulties related to the presence of an infinite-dimensional kernel in the differential operator are successfully handled. The efficiency of the algorithm is demonstrated using acoustics equations.     

A simple electronic speckle shearing interferometer

A new speckle shearing interferometer with simple setup is proposed. The interferometer can be converted easily from a speckle referenced speckle pattern interferometer into a speckle shearing interferometer and vice versa. A beamsplitter and a mirror are used to generate the shear. The amount of shear can be adjusted by simply rotating the mirror. The costs involved are low and it is particularly useful for fast inspection in non-destructive testing of structural integrity. Both the theoretical studies of the method of measurement and the experimental results are presented.     

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.     

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.     

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.     

Temperature and junction-type dependency of Andreev reflection in MgB2

We studied the voltage and temperature dependency of the dynamic conductance of normal metal-MgB₂ junctions obtained either with the point-contact technique (with Au and Pt tips) or by making Ag-paint spots on the surface of MgB₂ samples. The fit of the conductance curves with the generalized BTK model gives evidence of pure s-wave gap symmetry. The temperature dependency of the gap, measured in Ag-paint junctions (dirty limit), follows the standard BCS curve with 2Δ/k_BT_c=3.3. In out-of-plane, high-pressure point-contacts we obtained almost ideal Andreev reflection characteristics showing a single small s-wave gap Δ=2.6±0.2 meV (clean limit).