Diagonally implicit Runge-Kutta methods for stiff problems

Diagonally implicit Runge-Kutta methods are examined. It is shown that, for stiff problems, the methods based on the minimization of certain error functions have advantages over other methods; these functions are determined in terms of the errors for simplest model equations. Methods of orders three, four, five, and six are considered.     

Study of the correlation between the structure and critical temperatureT c of sputtered Nb-Ge films

Nb-Ge layers with continuous change of chemical and phase composition were prepared by the d.c. sputtering method. The dependence of critical temperatureT _c on phase composition, Ge-content, lattice imperfections and composition irregularities were studied. Films with highT _c contain beside the A-15 Nb₃Ge phase also the hexagonal and tetragonal modification of the Nb₅Ge₃ phase. Correlation betweenT _c and Nb₃Ge phase composition determined from the lattice parameter was found. In samples with highestT _c the lattice parametera ₀=0·5135 nm corresponding to 22–23 at.% of germanium was determined.     

Method of Mössbauer spectrochronograms employing the principle of modulation of the magnetic hyperfine interaction

The possibilities of the method of Mössbauer spectrochronograms (MSCs) for studying dynamical processes in magnets under conditions of RF remagnetization of the magnets are studied theoretically. It is shown that unlike the standard Mössbauer spectra MCSs contain more detailed information about the character of the modulation of the hyperfine interaction and therefore about the behavior of the local magnetization. The region in which the method of MSCs is effective is determined by means of calculations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 24–29, November, 1989.     

Behavior of 4-hydroxy-4-methyl-2-pentynonitrile in water in the presence of lithium hydroxide

Conclusions 4-Hydroxy-4-methyl-2-pentynonitrile is transformed by the action of LiOH in water to 2,2,4,4-tetramethyl-5-cyanomethylene-1,3-dioxolane and 5-amino-2,2-dimethyl-2,3-dihydro-3-furanone.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 6, pp. 1421–1422, June, 1989.     

Estimation of the hate of flow in porous media

In a number of problems of the theory of flow in porous media it is particularly important to find the integral characteristics of the flow for regions that constitute extended stream tubes. (Such a region can be imagined as the result of the continuous deformation of a cylinder whose lateral surfaces are impermeable while the bases are surfaces of constant pressure, the inlet and outlet of the flow. In the plane case the cylinder becomes a rectangle.) Usually, the flow rate Q is to be found from the difference of head H. In some cases it possible to obtain upper and lower bounds for the flow rate by varying the flow region, the flow resistance field or the form of the flow law [1–4]. The aim of the present study is to find the shape of the region of fixed volume (in the plane case area) which for given constraints realizes an extremum of the steady-state flow rate. It is shown that the extremality requirement leads to an additional local condition on the unknown part of the boundary. A class of plane problems for which the resulting boundary-value problem with an unknown boundary is effectively solved is identified. Examples are given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 80–87, March–April, 1986.     

Enthalpies of Dissolution of Crystalline Naproxen Sodium in Water and Potassium Hydroxide Aqueous Solutions at 298 K

The enthalpies of dissolution of crystalline naproxen sodium in water and aqueous solutions of KOH at 298.15 K are measured by direct calorimetric means in a wide range of concentrations. The acid–base properties of naproxen sodium at ionic strength I ~ 0 and I = 0.1 (KNO₃) and a temperature of 298.15 K are studied by spectrophotometric means. The concentration and thermodynamic dissociation constants are determined. The standard enthalpies of the formation of naproxen sodium and the products of its dissociation in aqueous solution are calculated.     

Direct observation of the second-order Stark effect of theX-B transition in molecular iodine

The second-order Stark shift of the components of the hyperfine structure of the transition¹ _g ⁺ ( = 0,j = 13, 15) ³ _ou ⁺ ( = 43,j = 12, 16) (of molecular iodine have been studied by means of saturated absorption spectroscopy in an external cell with the I₂ vapour located in an electric field. The anisotropic polarizabilities of the upper and lower levels together with the difference between the isotropic polarizabilities of the levels of the transition have been obtained.     

Development of methods of ligand control in Pd-catalyzed hydrosilylation of 1,3-alkadienes

The catalytic activity of palladium(II) complexes in trichlorosilane reactions with 1,3-alkadienes (isoprene and 2,3-dimethyl-1,3-butadiene) is strongly affected by the nature of the phosphorus-containing ligand.Translated from Zhurnal Obshchei Khimii, Vol. 74, No. 10, 2004, pp. 1639–1643.Original Russian Text Copyright © 2004 by Reznikov, Skvortsov.This revised version was published online in April 2005 with a corrected cover date.