The matrix equation AX-YB=C and related problems

The main result of the paper is a theorem, using which a new proof of Roth’s theorem is obtained, a new solvability criterion for the matrix equation AX-YB = C is proved, a formula for a particular solution of the latter is derived, and the least of the orders of square nonsingular matrices containing a given rectangular matrix as a submatrix is determined. Bibliography: 5 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 323, 2005, pp. 15–23.     

Tensile behaviour of corroded and hydrogen embrittled 2024 T351 aluminum alloy specimen

The synergetic effect of corrosion and corrosion induced hydrogen embrittlement damage processes which occur at local scale has been found to result in a dramatic macroscopic tensile ductility loss of the 2024 aluminum alloy. In the present work, the tensile behaviour of corroded 2024 T351 specimens has been estimated on the basis of FE analysis by taking into account the local material properties in the damaged areas. A parametric study is involved to account for the effect of thickness in the results. Calculated tensile properties obtained with the analysis agree well with experimental data.     

Spin dynamics investigated by EPR in the paramagnetic regime of La2/3Ca1/3Mn1−x Me x O3 (Me = Al, In) manganites

We report an electron paramagnetic resonance (EPR) investigation of the spin dynamics in the paramagnetic regime of the colossal magnetoresistive manganites La_2/3Ca_1/3Mn_1?x Me _x O₃ (Me=Al, In;x≤0.05). The temperature dependences of the EPR linewidth and integral intensity have been analyzed in terms of the bottleneck spin relaxation and small-polaron hopping models. The exchange coupling integral between Mn³⁺ and Mn⁴⁺ ions and the polaron activation energy decrease with increasing doping level. A discussion is given concerning the factors which could explain the observed changes.     

Semi-implicit complementary volume scheme for solving level set like equations in image processing and curve evolution

Summary. We introduce linear semi-implicit complementary volume numerical scheme for solving level set like nonlinear degenerate diffusion equations arising in image processing and curve evolution problems. We study discretization of image selective smoothing equation of mean curvature flow type given by Alvarez, Lions and Morel ([3]). Solution of the level set equation of Osher and Sethian ([26], \[30]) is also included in the study. We prove and estimates for the proposed scheme and give existence of its (generalized) solution in every discrete time-scale step. Efficiency of the scheme is given by its linearity and stability. Preconditioned iterative solvers are used for computing arising linear systems. We present computational results related to image processing and plane curve evolution. Received April 25, 2000 / Revised version received June 11, 2001 / Published online November 15, 2001     

Families of Line-Graphs and Their Quantization

Any directed graph G with N vertices and J edges has an associated line-graph L(G) where the J edges form the vertices of L(G). We show that the non-zero eigenvalues of the adjacency matrices are the same for all graphs of such a family L ⁿ (G). We give necessary and sufficient conditions for a line-graph to be quantisable and demonstrate that the spectra of associated quantum propagators follow the predictions of random matrices under very general conditions. Line-graphs may therefore serve as models to study the semiclassical limit (of large matrix size) of a quantum dynamics on graphs with fixed classical behaviour.     

Uncharged encapsulated iron(II) complexes: transfer chemical potentials and solvation in water-methanol and water-t-butanol mixtures

Summary Transfer chemical potentials have been determined from measured solubilities for four uncharged encapsulated iron(II) complexes containing three diimine ligating moieties and O₃BOBu-n and O₃BF capping groups, in H₂O–MeOH andt-BuOH–H₂O solvent mixtures, The trends in transfer chemical potentials are discussed in terms of the natures of the encapsulating ligands, and are compared with those for a selection of other iron(II)-diimine complexes.