Doping of KDP single crystals with cerium: Growth and optical properties

The features of doping of KDP crystals with cerium ions and organocerium complexes with alizarin complexon and arsenazo III have been investigated. It is established that “direct” doping by introducing cerium salts into the initial solution cannot be implemented. The effect of organometallic complexes of cerium on the crystal growth has been studied. Organocerium complexes predominantly enter the prismatic or pyramidal growth sectors. It is shown that the complex arsenazo III + Ce blocks the growth of the prismatic sector. Cerium-doped KDP crystals exhibit a photoluminescence band peaking at the wavelength λ_max= 350 nm.     

The transition of spontaneous polymerization of acrylamide to “explosive” regime

Experimental results related to the transition of spontaneous polymerization of acrylamide complexes with metal nitrates to the “explosive” regime at room temperature are presented. It is suggested that the “explosion” has a thermal nature. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 859–861, April, 1997.     

On the optimization of approximate integration by Monte Carlo methods

We solve the problem of optimization of monte Carlo methods for approximate integration over an arbitrary absolutely continuous measure. We propose a convenient model of Monte Carlo methods which uses the notion of transition probability.     

Widths and optimal quadrature formulas for convolution classes

We compute Kolmogorov widths in the space L₁ for classes of periodic functions representable in the form of a kernel convolution that does not increase the number of sign changes with values in a given transposition invariant set of functions, and solve the optimization problem for quadrature formulas in these classes.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 9, pp. 1135–1148, September, 1991.     

Transport properties of separating membranes MF-4SK during alkaline electrolysis of water

The transport properties of separating membranes MF-4SK are studied during electrolysis of H₂O in solutions of KOH. The effective diffusion coefficients of molecules of KOH and H₂O and the transfer coefficients of ions K⁺ and OH^? and molecules of H₂O are measured at KOH concentrations reaching 11 M, currents reaching 0.31 A cm^?2, at ambient temperature and at 80°C. In contact with a KOH solution in the concentration interval 0.1 to 11 M, the membranes that initially swelled in H₂O lose a considerable fraction of water that was present in them and the overall volume of clusters and solution-filled channels in them noticeably decreases. The coefficients of transfer by current of ions K⁺ out of anodic compartment into cathodic and the OH^? ions in the reverse direction, respectively, happen to be equal to about 0.6 and 0.4 at ambient temperature and 0.8 and 0.2 at 80°C. The coefficients of transfer of water molecules out of the anodic volume into the cathodic volume in the process of electrolysis happen to be in the limits 1.6–1.9 at ambient temperature and in the limits 2.2–2.8 at 80°C. The effective diffusion coefficients of molecules of KOH and H₂O at moderate concentrations of KOH (5.6 M) amount to ～2.6 × 10^?7 and 30 × 10^?7 cm²s^?1 at ambient temperature and ～4 × 10^?7 and 61 × 10^?7 cm²s^?1 at 80°C, respectively. At a high concentration of KOH (～10 M) these quantities substantially diminish.     

Inequalities of Bernstein type for polynomial splines in L2

For 2-periodic polynomial splines of order r, of minimal defect, with nodes at the points k/n, n , there are established the sharp inequalities