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.     

An optimization approach for planning daily drayage operations

Daily drayage operations involve moving loaded or empty equipment between customer locations and rail ramps. Our goal is to minimize the cost of daily drayage operations in a region on a given day. Drayage orders are generally pickup and delivery requests with time windows. The repositioning of empty equipment may also be required in order to facilitate loaded movements. The drayage orders are satisfied by a heterogeneous fleet of drivers. Driver routes must satisfy various operational constraints. We present an optimization methodology for finding cost-effective schedules for regional daily drayage operations. The core of the formulation is a set partitioning model whose columns represent routes. Routes are added to the formulation by column generation. We present numerical results for real-world data which demonstrate that our methodology produces low cost solutions in a reasonably short time.     

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.