Parabolic target space and primal-dual interior-point methods

In this paper we develop new primal-dual interior-point methods for linear programming problems, which are based on the concept of parabolic target space. We show that such schemes work in the infinity-neighborhood of the primal-dual central path. Nevertheless, these methods possess the best known complexity estimate. We demonstrate that the adaptive-step path-following strategies can be naturally incorporated in such schemes.     

Effect of stock dispersity on properties of ceramic materials

Powdered ceramic piezoelectric phases of fixed chemical composition and prescribed particle size in the range from 15 to 350 nm were obtained using a unified synthesis technique. The dependence of their electrical parameters on the granulometric composition of the stock was studied.     

Dependence of the natural frequencies and mode shapes of vibrations of an ideal gas on the acoustic resonance parameters

The problem of plane wave propagation through a circular hole is studied in the framework of long-wave approximation. The constructive notion of “apparent mass of holes” (Rayleigh; Fok) is used to construct a mathematical model of gas vibrations in an acoustic resonator and determine and analyze the natural frequencies and mode shapes for the velocity potential depending on the relative geometric parameters of the system. The high-precision calculations of the boundary value problem for the natural frequencies and mode shapes in the parametric approximation to the cross-section are based on a numerical-analytical accelerated convergence method. Two models are analyzed and compared, and the basic qualitative properties of gas vibrations are revealed depending on the basic parameters such as the mode number, relative size of the hole, and the dividing wall location.     

Parametric vibrations of a mechanical system and their stability for an arbitrary modulation coefficient

The natural frequencies and modes of parametric vibrations of a mechanical system are studied, by way of example, for a pendulum of variable length with modulation coefficient varying from arbitrarily small to maximum admissible values. Analytic and numerical methods are used to construct and study the boundaries of the resonance domains for the first four vibration modes, and the main qualitative properties of higher modes are found. The complete degeneration of modes with even numbers, i.e., the coincidence of the frequencies of symmetric and nonsymmetric naturalmodes for admissible values of the modulation parameter, is proved. The global picture of boundaries of stability domains for the lower equilibriumis constructed, and a significant difference from the Ince-Strutt diagram is shown. Specific properties of the natural modes are established.     

Asymmetric diosmium sawhorse complexes

Three asymmetric diosmium(I) carbonyl sawhorse complexes have been prepared by microwave heating. One of these complexes is of the type Os₂(μ‐O₂CR)(μ‐O₂CR′)(CO)₄L₂, with two different bridging carboxylate ligands, while the other two complexes are of the type Os₂(μ‐O₂CR)₂(CO)₅L, with one axial CO ligand and one axial phosphane ligand. The mixed carboxylate complex Os₂(μ‐acetate)(μ‐propionate)(CO)₄[P(p‐tolyl)₃]₂, ( 1 ), was prepared by heating Os₃(CO)₁₂ with a mixture of acetic and propionic acids, isolating Os₂(μ‐acetate)(μ‐propionate)(CO)₆, and then replacing two CO ligands with two phosphane ligands. This is the first example of an Os₂ sawhorse complex with two different carboxylate bridges. The syntheses of Os₂(μ‐acetate)₂(CO)₅[P(p‐tolyl)₃], ( 3 ), and Os₂(μ‐propionate)₂(CO)₅[P(p‐tolyl)₃], ( 6 ), involved the reaction of Os₃(CO)₁₂ with the appropriate carboxylic acid to initially produce Os₂(μ‐carboxylate)₂(CO)₆, followed by treatment with refluxing tetrahydrofuran (THF) to form Os₂(μ‐carboxylate)₂(CO)₅(THF), and finally addition of tri‐p‐tolylphosphane to replace the THF ligand with the P(p‐tolyl)₃ ligand. Neutral complexes of the type Os₂(μ‐O₂CR)₂(CO)₅L had not previously been subjected to X‐ray crystallographic analysis. The more symmetrical disubstituted complexes, i.e. Os₂(μ‐formate)₂(CO)₄[P(p‐tolyl)₃]₂, ( 8 ), Os₂(μ‐acetate)₂(CO)₄[P(p‐tolyl)₃]₂, ( 4 ), and Os₂(μ‐propionate)₂(CO)₄[P(p‐tolyl)₃]₂, ( 7 ), as well as the previously reported symmetrical unsubstituted complexes Os₂(μ‐acetate)₂(CO)₆, ( 2 ), and Os₂(μ‐propionate)₂(CO)₆, ( 5 ), were also prepared in order to examine the influence of axial ligand substitution on the Os—Os bond distance in these sawhorse molecules. Eight crystal structures have been determined and studied, namely μ‐acetato‐1κO:2κO′‐μ‐propanoato‐1κO:2κO′‐bis[tris(4‐methylphenyl)phosphane]‐1κP,2κP′‐bis(dicarbonylosmium)(Os—Os) dichloromethane monosolvate, [Os₂(C₂H₃O₂)(C₃H₅O₂)(C₂₁H₂₁P)₂(CO)₄]·CH₂Cl₂, ( 1 ), bis(μ‐acetato‐1κO:2κO′)bis(tricarbonylosmium)(Os—Os), [Os₂(C₂H₃O₂)₂(CO)₆], ( 2 ) (redetermined structure), bis(μ‐acetato‐1κO:2κO′)pentacarbonyl‐1κ²C,2κ³C‐[tris(4‐methylphenyl)phosphane‐1κP]diosmium(Os—Os), [Os₂(C₂H₃O₂)₂(C₂₁H₂₁P)(CO)₅], ( 3 ), bis(μ‐acetato‐1κO:2κO′)bis[tris(4‐methylphenyl)phosphane]‐1κP,2κP‐bis(dicarbonylosmium)(Os—Os) p‐xylene sesquisolvate, [Os₂(C₂H₃O₂)₂(C₂₁H₂₁P)₂(CO)₄]·1.5C₈H₁₀, ( 4 ), bis(μ‐propanoato‐1κO:2κO′)bis(tricarbonylosmium)(Os—Os), [Os₂(C₃H₅O₂)₂(CO)₆], ( 5 ), pentacarbonyl‐1κ²C,2κ³C‐bis(μ‐propanoato‐1κO:2κO′)[tris(4‐methylphenyl)phosphane‐1κP]diosmium(Os—Os), [Os₂(C₃H₅O₂)₂(C₂₁H₂₁P)(CO)₅], ( 6 ), bis(μ‐propanoato‐1κO:2κO′)bis[tris(4‐methylphenyl)phosphane]‐1κP,2κP‐bis(dicarbonylosmium)(Os—Os) dichloromethane monosolvate, [Os₂(C₃H₅O₂)₂(C₂₁H₂₁P)₂(CO)₄]·CH₂Cl₂, ( 7 ), and bis(μ‐formato‐1κO:2κO′)bis[tris(4‐methylphenyl)phosphane]‐1κP,2κP‐bis(dicarbonylosmium)(Os—Os), [Os₂(CHO₂)₂(C₂₁H₂₁P)₂(CO)₄], ( 8 ).     

Contact-free determination of the current-voltage law parameters for melt-textured YBCO superconductors in orthogonal magnetic field

A contact-free method to obtain the current-voltage characteristics (CVC) of hard superconductors by measuring the relaxation of the magnetization in a perpendicular magnetic field is developed. The relaxation curves obtained for melt-textured YBCO samples are well fitted by curves calculated within the electrodynamic model using a power-law CVC. This procedure uses only two fitting parameters, namely, the critical sheet current J_c and the exponent m of the power-law CVC.     

Unexpected dimeric products from the amidomethylation of pentasubstituted benzenes

An isomeric series of unexpected diarylmethane products with flexible substituents, isolated from amidomethylation reactions of p-dimethoxybenzene derivatives, was analyzed by X-ray crystallography to reveal novel solid-state structures, two of which have identical elemental cell parameters.