Interpolation of rational functions by simple partial fractions

We study a generalized interpolation of a rational function at n nodes by a simple partial fraction of degree n and reduce the consideration to the solvability question for a special difference equation. We construct explicit interpolation formulas in the case where the equation order is equal to 1. We show that for functions A(x − a) ^m , m ? \mathbbN m \in \mathbb{N} , it is possible to reduce the consideration to a system of m + 1 independent first order equations and construct explicit interpolation formulas. Bibliography: 6 titles.     

Adsorption inhibition of the growth of CaSO4 · 2H2O crystals in aqueous solutions

Crystallography Reports - The growth of gypsum CaSO4 · 2H2O crystals in aqueous solutions has been investigated, both on individual crystals and on crystals in a homogeneous suspension in the...     

Formation of multilayer strained-layer heterostructures by liquid epitaxy. II. Simulation of the fabrication of heterostructures based on indium-arsenic-antimony-bismuth solid solutions

The formation of InAs_1−x−y Sb_xBi_y/InSb and InAs_1−x−y Sb_xBi_y/InSb_yBi_y strained-layer heterostructures by “capillary” LPE is simulated. The laws governing the dependence of the gap width E _g and the thickness d of the epilayers on the conditions of the process are revealed. It is shown that because of the sharp increase in the rate of epitaxial deposition as the LPE temperature is raised, the successful growth of epilayers of subcritical thickness is possible only up to T<550 K. The influence of the rate of laminar flow of the liquid in the growth channel in a relaxation regime and in a continuous pumping regime on the uniformity of the distribution of E _g and d in the epitaxial heterostructures is analyzed. Effective combinations of parameters for carrying out the process, which ensure the achievement of E _g ≈0.1 eV (77 K) in the active layers with variable-band-gap layers of minimal thickness, are established. Zh. Tekh. Fiz. 67, 50–56 (July 1997)