Accuracy-enhancement scheme for the Sturm-Liouville equation

Enhanced-accuracy spline-difference schemes are constructed and analyzed for the one-dimensional Sturm-Liouville problem with piecewise-constant coefficients. Uniformmetric bounds are obtained for eigenvalues, eigenfunctions, and their derivatives. The results of numerical experiments using a test problem are reported.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 61, pp. 3–8, 1987.     

Optimization of solutions of one class of problems in seepage theory

Optimal control of prevention of groundwater flooding is considered. Optimization is performed by construction and operating costs of the protective structures. The seepage problem is solved for homogeneous Isotropic regions protected by perfect vertical drain ditches. A computer program is developed to solve the problem. Numerical results are reported.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 59, pp. 84–89, 1986.     

Statistics of random compacts in euclidean space

The article describes and studies two methods of statistical estimation of various geometrical characteristics of convex compact random subsets in the Euclidean space. Estimation accuracy using a finite number of measurements is considered. A theorem characterizing Gaussian random sets is given, which states that all these sets are of the form A=M+ξ, where M has a degenerate distribution and ξ is a normal random vector.     

Addition reactions of linear siloxanes to allylamine

Russian Chemical Bulletin -     

Dioxomolybdenum(VI) and dioxotungsten(VI) complexes supported by an amido ligand

Stepwise addition of one equivalent of n-butyllithium and trimethylsilyl chloride to 2-tert-butylmercaptoaniline affords the new ligand 1-(Me3SiNH)-2-(t-BuS)C6H4 (LH), that reacts with one equivalent of butyllithium to its lithium salt LLi. Dioxodichloromolybdenum [MoO2Cl2] and dioxodichlorotungsten dimethoxyethane [WO2Cl2(dme)] react in tetrahydrofuran solution at low temperature with two equivalents LLi to monomeric dioxomolybdenum(VI) [MoO2L2] (1) and dioxotungsten(VI) complex [WO2L2] (2) employing two bidentate amido thioether ligands. The crystallographic determination of the molecular structures of 1 and 2 show evidence for M...S contacts. The reaction of [MoO2Cl2] with LLi in tetrahydrofuran solution at room temperature leads next to 1 to two compounds where silyl group migration from nitrogen to oxygen atoms occurs forming [Mo(=NL')2(OSiMe)2] (3) and [Mo(=NL')2(OSiMe3)L] (4, L' = N-2-t-BuSC6H4) as determined by NMR spectroscopy. Compound 4 was isolated in low yield and its molecular structure determined by X-ray crystallography. Higher yields of a bisimido complex can be obtained by the direct reaction of one equivalent of LLi with [Mo(NAr)2Cl2(dme)] (Ar = 2,6-Me2C6H4) forming [Mo(NAr)2LCl] (5).