Justification of Averaging Method for Multifrequency Impulsive Systems

We prove new theorems on the justification of the averaging method for multifrequency oscillation systems with pulse influence at fixed times.     

Mechanism of the D’yakonov-Perel’ spin relaxation in frequent electron-electron collisions in a quantum well with a finite width

A precession mechanism of spin relaxation of conduction electrons in a square quantum well is analyzed. The dependence of the spin relaxation time on the width of a quantum well and the height of its barriers is calculated under the assumption that the electron-electron collisions dominate over other processes of carrier scattering.     

A study of the atmospheric lead pollution in Seville, Spain. Influence of meteorology and traffic, and relationship with other traffic-generated pollutants

A study of the atmospheric pollution by suspended particulate lead in the city of Seville, Spain, was carried out during the period between March 1983 and February 1984. The results obtained from seven sampling stations allowed us to study the site to site variations; there are two locations with average annual concentrations higher than 2 micrograms X m-3. In one station, the meteorological and traffic effects and relationship with other traffic-related pollutants, were investigated. The regression analyses performed on the average monthly data have shown an inverse correlation with wind speed and temperature and a direct correlation with carbon monoxide and smoke concentrations, but no significant correlation was found with the lead deposition levels.     

A microspectroscopic study of the electronic homogeneity of ordered and disordered Sr2FeMoO6

Disordered Sr₂FeMoO₆ shows a drastic reduction in saturation magnetization compared to highly ordered samples, moreover magnetization as a function of the temperature for different disordered samples shows qualitatively different behaviours. We investigate the origin of such diversity by performing spatially resolved photoemission spectroscopy on various disordered samples. Our results establish that e_xtensive electronic inhomogeneity, arising most probably from an underlying chemical inhomogeneity in disordered samples, is responsible for the observed magnetic inhomogeneity. It is further pointed out that these inhomogeneities are connected with composition fluctuations of the type Sr₂Fe_1+x Mo_1-x O₆ with Fe-rich (x > 0) and Mo-rich (x < 0) regions. Dedicated to Prof J Gopalakrishnan on his 62nd birthday.     

Synthesis and characterization of isotopically enriched methylmercury (CH3201Hg+)

A simple procedure for the synthesis of an important standard, isotopically enriched methylmercury, which is not commercially available, has been established successfully. The isotopically enriched standard synthesized is utilized in conventional isotope dilution mass spectrometry (IDMS), as well as in speciated IDMS (SIDMS), for determination of the true concentration of methylmercury in environmental samples. The CH₃²⁰¹Hg⁺ standard has been synthesized from commercially available ²⁰¹HgO and tetramethyltin. The synthesis time required is 1 h at 60°C. The product is highly pure, yielding more than 90% as ²⁰¹Hg in CH₃²⁰¹Hg⁺. Hazardous dimethylmercury does not occur during this synthesis procedure. The product synthesized was analyzed using high‐performance liquid chromatography coupled with inductively coupled plasma mass spectrometry (ICP‐MS) and ICP‐MS alone in order to determine its concentration, isotopic composition and purity. The stability of the product was also evaluated for over 6 months and found to be stable at 4°C in the dark. The isotopically enriched methylmercury synthesized can be used in SIDMS and IDMS analyses as a standard. Copyright © 2003 John Wiley & Sons, Ltd.     

Elastoplastic torsion theory for whisker crystals

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 127–134, March–April, 1991.     

20-relative neighborhood graphs are hamiltonian

For any two points p and q in the Euclidean plane, define LUN_pq = { v | v ∈ R², d_pv < d_pq and d_qv < d_pq}, where d_uv is the Euclidean distance between two points u and v . Given a set of points V in the plane, let LUN_pq(V) = V ∩ LUN_pq. Toussaint defined the relative neighborhood graph of V, denoted by RNG(V) or simply RNG, to be the undirected graph with vertices V such that for each pair p,q ∈ V, (p,q) is an edge of RNG(V) if and only if LUN_pq (V) = ?. The relative neighborhood graph has several applications in pattern recognition that have been studied by Toussaint. We shall generalize the idea of RNG to define the k-relative neighborhood graph of V, denoted by kRNG(V) or simply kRNG, to be the undirected graph with vertices V such that for each pair p,q ∈ V, (p,q) is an edge of kRNG(V) if and only if | LUN_pq(V) | < k, for some fixed positive number k. It can be shown that the number of edges of a kRNG is less than O(kn). Also, a kRNG can be constructed in O(kn₂) time. Let E_c = {e_pq| p ∈ V and q ∈ V}. Then G_c = (V,E_c) is a complete graph. For any subset F of E_c, define the maximum distance of F as max_epq∈Fd_pq. A Euclidean bottleneck Hamiltonian cycle is a Hamiltonian cycle in graph G_c whose maximum distance is the minimum among all Hamiltonian cycles in graph G_c. We shall prove that there exists a Euclidean bottleneck Hamiltonian cycle which is a subgraph of 20RNG(V). Hence, 20RNGs are Hamiltonian.     

Reduction of nonholonomic variation problems to isoperimetric ones and connections in principal bundles

Translated from Matematicheskie Zametki, Vol. 49, No. 5, pp. 37–44, May, 1991.