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.     

A Simple Bi-directional Mode Expansion Propagation Algorithm Based on Modes of a Parallel-plate Waveguide

The bi-directional mode expansion propagation algorithm (BEP) is known to be an accurate and efficient method for modelling field distribution in high-index contrast waveguide structures with strong back-reflections like Bragg gratings and photonic crystals. The main difficulty of this method is that for lossy structures, the propagation constants of modes are to be searched in the complex plane. To speed-up this procedure, a two-step algorithm for eigenmode calculation based on the expansion into the modes of an empty metallic waveguide has recently been proposed. Proper truncation rules possessing good convergence of the expansion method for both TE and TM modes have also been recently published. In this contribution, both these approaches are combined in the development of an extremely simple version of the two-dimensional BEP method that makes use of the field expansion into the eigenmodes of a parallel-plate waveguide. The method is strictly reciprocal and appeared to be computationally reliable also for strongly lossy structures. High numerical stability is ensured using the scattering matrix formalism, and an efficient method of calculating Bloch modes for symmetric as well as asymmetric periodic waveguide structures is adopted. A wide range of applicability of the method is demonstrated by a few examples.     

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.     

Fractional Hamiltonian Monodromy

We introduce fractional monodromy in order to characterize certain non-isolated critical values of the energy–momentum map of integrable Hamiltonian dynamical systems represented by nonlinear resonant two-dimensional oscillators. We give the formal mathematical definition of fractional monodromy, which is a generalization of the definition of monodromy used by other authors before. We prove that the 1:( − 2) resonant oscillator system has monodromy matrix with half-integer coefficients and discuss manifestations of this monodromy in quantum systems. Communicated by Eduard Zehnder Submitted: February 25, 2005; Accepted: November 17, 2005     

Scientist up to the highest level

Dr. Miroslav Kyrš, DrSc. passed away prematurely and unexpectedly in August 2006 at age of 75. He was a leading person of the Czech radiochemistry during the second half of the 20th century and his results have of world-wide impact. His diligence, intelligence and permanent activity led him to be at first a laboratory chief and subsequently for about 25 years to be a chief of the Radiochemical Department of Czech Nuclear Research Institute (NRI) at Řež near Prague.     

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.