On the problem of stochastic differential inclusions

In this paper we study a stochastic differential equation with multivalued maximally monotone drift operator. Under certain assumptions on the growth of the multivalued operator we prove a theorem on the existence and uniqueness of the solution of such an equation.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 54–59, 1987.     

Surface analytical characterization of oxide-free Si(100) wafer surfaces

Summary Wet-chemical cleaning procedures of Si(100) wafers are surface analytically characterized and compared. Hydrophobic surfaces show considerably less native oxides in comparison to hydrophilic surfaces.The growth of the oxide is determined as a function of exposure to air by means of XPS measurements. The chemically shifted Si2p XPS signal is utilized for the quantification of the growth kinetics.One hour after cleaning no chemically shifted Si2p XPS peak is discernible on the hydrophobic surfaces. Assuming homogeneous oxide growth, the detection limit of native oxides is estimated to be below 0.05 nm using an emission angle of 18° with respect to the wafer surface. The calculation of the oxide thickness from the chemically shifted and nonchemically shifted Si2p XPS peak intensities is carried out according to Finster and Schulze [1]. For more than a day after cleaning no surface oxides can be identified on the hydrophobic surfaces. The oxide growth kinetics is logarithmic. The very slow oxidation rate cannot be attributed to fluorine residues since no fluorine is seen by XPS. We explain the slow oxidation rate by a homogeneous hydrogen saturated Si(100) wafer surface.

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Oberflächenanalytische Charakterisierung oxidfreier Si(100)-Waferoberflächen

     

Molecular orbital momentum distributions and binding energies for nitric oxide

Binding energy spectra of the valence electrons of the open shell molecule NO have been obtained up to 55 eV at azimuthal angles of 0° and 7° using binary (e, 2e) spectroscopy at an impact energy of 1200 eV. The momentum distribution has been obtained for the least tightly bound (unpaired) electron, removal of which leads to formation of the X ¹Σ⁺ ground state of NO⁺. Momentum distributions have also been measured at 21.0 and 40.5 eV. The measured momentum distributions are compared with several literature wavefunctions of varying complexity. They are found to be in excellent agreement with those calculated using the natural spin orbital wavefunctions of Kouba and Ohrn.     

Estimate for the Gradient of the Solution to the Neumann Problem for (p,q)-Nonlinear Equations

We consider the Neumann boundary value problem for the class of (p,q)-nonlinear elliptic equations. The numbers p and q, 2 ⩽ p < q, characterize the power growth with respect to the gradient of eigenvalues of the leading matrix of the equation. An a priori estimate for the maximum of the modulus of the gradient of the solution is obtained in a neighborhood of the boundary of the domain for some interval of p and q. Bibliography: 5 titles. __________ Translated from Problemy Matematicheskogo Analiza, No. 31, 2005, pp. 47–57.     

Free nonassociative supercommutative algebras

In the present work, we prove that homogeneous subalgebras of free nonassociative supercommutative algebras are free. As a consequence, we show that the group of automorphisms of a free nonassociative supercommutative algebra of finite rank is generated by elementary automorphisms. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 3, pp. 103–109, 2003.     

Reaction of 2-formyl-1,3-cyclohexanediones with cyanoacetamide

Chemistry of Heterocyclic Compounds -     

Convergence of the method of partition of regions for second-order elliptic conjugation problems

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 8, pp. 1137–1141, August, 1989.