One approach to constructing a minimal convex hull

The minimal convex hull of a subset of finite-dimensional space is constructed in a discrete fashion: at each step, we construct a new set that includes the inherited set. The procedure for finding the chain of sets involves geometrically evident constructions. This chain becomes stationary; i.e., from some number onward, all the sets of the chain being constructed coincide with the minimal convex hull. Our approach uses the principal result (Caratheodory’s theorem) underlying the conventional approach to constructing a minimal convex hull.     

Investigation of the formation of nanowires from silicon whiskers

Nanowires have been prepared by the high-temperature oxidation of Si whiskers. The dependences of the nanowire formation on the oxidation parameters have been investigated. The oxidation rate is shown to depend on the whisker diameter. Oxidation in dry oxygen at temperatures no higher than 950°C results in self-stopping; i.e., the nanowire diameter is stabilized. Stabilization is not observed at oxidation temperatures above 950°C or at oxidation in wet oxygen. Oxidation at higher temperatures made it possible to obtain nanowires ≤5 nm in diameter in relatively thick (up to 200 nm in diameter) whiskers.     

The volume characteristics of solution of naphthalene in heptane-ethanol mixtures at 298.15 K

The solubility of naphthalene was studied by the isothermal saturation method, and the density of naphthalene-heptane-ethanol solutions at 298.15 K was measured using an oscillating tube densimeter. The results were used to calculate the volume characteristics of naphthalene in the systems specified. The solubility of naphthalene in heptane was substantially higher than in ethanol. The composition dependences of apparent partial molar volumes contained extrema. The reason for such nonlinear dependences can be a sharp change in the contribution to the entropy of mixing related to the packing of molecules of different diameters (naphthalene and heptane). Another possible mechanism of these anomalies can be related to the stabilization of the structure of alkanols in the solvation sheath of alkanes noticed earlier.     

Overtone spectroscopy of some benzaldehyde derivatives

Overtone spectrum of o, m and p-nitrobenzaldehydes and p-chlorobenzaldehyde has been studied in 2000–12000 cm⁻¹ region. Vibrational frequencies and anharmonicity constants for aryl as well as alkyl CH stretch vibrations have been determined. We have also determined the internuclear distances for the aryl CH bond in the different molecules. The small variation observed in these distances is an indication of the substitution effect. It is observed that in the case of p-disubstituted benzens, the shift in aryl CH bond is proportional to sum of the Hammet σ of the substituents. However in the case of o-disubstituted benzenes it is only 80% of the para-substituted shift.     

Diffraction,Interference, and Depolarization of Elastic Waves. Caustic and Penumbra

A theoretical study of polarization-spectral anomalies of wave fields, or their deviations from the predictions based on simple plane-wave models, is presented. A simple unified method of numerical simulation of anomalies of nonstationary wave fields near a caustic and in the penumbra is described. It uses both the leading and correcting terms in asymptotic expansions. Examples of calculation of displacements and average polarization ellipses are given. Qualitative properties of wave fields are discussed. A review of earlier research on polarization anomalies of elastic waves is given. Bibliography: 38 titles.Dedicated to L. A. Molotkov on the occasion of his 70th birthday__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 297, 2003, pp. 136–153.     

Synthesis and physical properties of Tl-Ca-Ba-Cu-O high-temperature superconductors

We present results of an investigation of Ti-Ca-Ba-Cu-O, high-temperature superconductors obtained under various technological conditions. Data from electrical, magnetic, and ultra-high frequency (UHF) measurements are given. We discuss the possibilities of applying magnetic and UHF methods to analyze the quality of HTSC ceramics.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 18–22, September, 1990.     

A study on the fragmentation of space debris particles at high-speed collision

A mathematical model was previously proposed by the first author to evaluate the number of fragments and their mass distribution at high-speed collision of two space debris particles and to determine their velocities after collision. The constants used in this model are assumed to be temperature-independent. In this paper it is shown that the consideration of temperature effects due to high-speed collision of particles leads to the formation of smaller fragments and to a significant increase of their total number.     

Synthesis,structure, and optical properties of iridium(III) complex with 1-benzyl-2-phenylbenzimidazole and 4,4'-dicarboxy-2,2'-bipyridyne

A new cyclometalated iridium(III) complex [Ir(L)₂(Hdcbpy)] (1) has been synthesized, where L is 1-benzyl-2-phenylbenzimidazole and Hdcbpy is monoprotonated 4,4′-dicarboxy-2,2′-bipyridine. The structure of complex 1 has been determined by X-ray diffraction. The optical properties of complex 1 have been studied, and the quantum yield of luminescence has been measured.     

Source below the free surface of a heavy liquid

The problem of the motion of a source under the free surface of an infinitely deep heavy liquid has been studied by Keldysh [1] under the assumptions used in the theory of small amplitude waves. However, these assumptions are no longer valid [2] for large Froude numbers F.A method using only one of the four assumptions of small amplitude wave theory (the assumption that the absolute value of the velocity at the free surface is nearly constant) was described in [2], In the following, this method is used to construct a solution of the problem which becomes exact as F . When F is not large our results are close to those of Keldysh if the source intensity is low. For F=0, both methods lead to exact results.