Associated functions of a nonlinear spectral problem for a system of ordinary differential equations

We study the notion of associated functions of a nonlinear spectral problem for a linear system of ordinary differential equations supplemented with nonlocal conditions given by a Stieltjes integral. We establish the relationship of this problem with the corresponding problem in a finite-dimensional linear space. We consider a numerical method for finding associated functions and justify its stability.     

Rate of localized gas discharge etching of silicon

The dependence of the etching rate of silicon on the technological, design, and electrophysical parameters that characterize the glowing conditions and the properties of a localized gas discharge is studied. Experiments are performed at a gas pressure of 104–105 Pa and a discharge gap of 50–500 μm. Emission spectroscopy is shown to be an efficient method for controlling the beginning and the end of localized gas discharge etching of different materials.     

The multidimensional moment-constrained maximum entropy problem: A BFGS algorithm with constraint scaling

In a recent paper we developed a new algorithm for the moment-constrained maximum entropy problem in a multidimensional setting, using a multidimensional orthogonal polynomial basis in the dual space of Lagrange multipliers to achieve numerical stability and rapid convergence of the Newton iterations. Here we introduce two new improvements for the existing algorithm, adding significant computational speedup in situations with many moment constraints, where the original algorithm is known to converge slowly. The first improvement is the use of the BFGS iterations to progress between successive polynomial reorthogonalizations rather than single Newton steps, typically reducing the total number of computationally expensive polynomial reorthogonalizations for the same maximum entropy problem. The second improvement is a constraint rescaling, aimed to reduce relative difference in the order of magnitude between different moment constraints, improving numerical stability of iterations due to reduced sensitivity of different constraints to changes in Lagrange multipliers. We observe that these two improvements can yield an average wall clock time speedup of 5–6 times compared to the original algorithm.     

Nonlinear spectral problem for a singular system of ordinary differential equations with a nonlocal condition

We consider a nonlinear spectral problem for a system of ordinary differential equations defined on an unbounded half-line and supplemented with a nonlocal condition specified by a Stieltjes integral. We suggest a numerically stable method for finding the number of eigenvalues lying in a given bounded domain of the complex plane and for the computation of these eigenvalues and the corresponding eigenfunctions. Our approach uses a simpler (with uncoupled boundary conditions) auxiliary boundary value problem for the same equation.     

Nonlinear spectral problem for a self-adjoint vector differential equation

We consider a spectral problem that is nonlinear in the spectral parameter for a self-adjoint vector differential equation of order 2n. The boundary conditions depend on the spectral parameter and are self-adjoint as well. Under some conditions of monotonicity of the input data with respect to the spectral parameter, we present a method for counting the eigenvalues of the problem in a given interval. If the boundary conditions are independent of the spectral parameter, then we define the notion of number of an eigenvalue and give a method for computing this number as well as the set of numbers of all eigenvalues in a given interval. For an equation considered on an unbounded interval, under some additional assumptions, we present a method for approximating the original singular problem by a problem on a finite interval.     

4-(2-Hydroxyaryl)-1,2,3-selenadiazoles as Precursors of Benzofuran-2-selenolates

The reaction of selenium dioxide with o-hydroxyacetophenone semicarbazones gives 4-(2-hydroxyaryl)-1,2,3-selenadiazoles which undergo ready decomposition by the action of potassium carbonate to form benzofuran-2-selenolates. The latter can be alkylated with methyl iodide and benzyl chloride and arylated with 2,4-dinitrochlorobenzene. Intermediate formation of 2-(o-hydroxyphenyl)ethyneselenolate during decomposition of 1,2,3-selenadiazoles was proved by the isolation of methyl o-methoxyphenylethynyl selenide when the substrate was treated with potassium carbonate in the presence of methyl iodide.     

A novel polybromide complex of bismuth – (Et4N)3{[Bi2Br9](Br2)}: synthesis and structural features

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Specific features of the combustion of hydrogen-oxygen mixtures near the lower concentration flammability limit

The combustion of hydrogen-air mixtures near the lower composition flammability limit in cylindrical reactors of various diameters is studied. The speed of flame propagation in the horizontal direction is lower than that in the upward direction. Chromatographic analysis showed that, during the combustion of these mixtures, hydrogen is consumed only partially. That the flame propagates despite a low adiabatic temperature can be explained by the formation of the well-known cellular structure.     

Geminate Pairs and Their Role in Radiation-Induced Conductivity of Poly(methyl methacrylate)

Non-steady-state radiation-induced conductivity of poly(methyl methacrylate) was studied at room and elevated temperatures. It was shown that the conductivity is due to electric polarization of geminate pairs. The evolution of geminate pairs was rationalized in terms of the Rose–Fowler–Weisberg generalized model. The conclusions by the model were compared with the results of previous studies on the kinetics of formation and decay of geminate pairs upon pulse radiolysis or flash photolysis of doped poly(methyl methacrylate).