From Brunn–Minkowski to sharp Sobolev inequalities

We present a simple direct proof of the classical Sobolev inequality in with best constant from the geometric Brunn–Minkowski–Lusternik inequality. Research supported in part by NSF Gr. No. 0405587 and B. Zegarlinski’s Pierre de Fermat Grant 2006 from the Région Midi-Pyrénées, France.     

AFM investigation of the mechanism for microwave effect on ferroelectric triglycine sulfate

Relation between the microwave effect on ferroelectric triglycine sulfate and the crystal structure dynamics is studied within the concept of ferroactive medium evolution. It is shown that the effect is most distinct in defect-free samples and correlates with the domain structure dynamics. Domain walls are considered to be responsible for structure-sensitive characteristics of triglycine sulfate.     

Solvolysis of 8-bromotheophylline by acetic anhydride in the presence of potassium fluoride

Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 5, p. 699, May, 1991.     

The flow pattern in a liquid layer and the spectrum of the boundary-value problem when the surface tension depends non-linearly on the temperature

The flow of a liquid in a plane channel on the bottom of which a specified temperature distribution is maintained while the free surface is thermally isolated is considered. The surface tension of the liquid depends quadratically on the temperature. The system of Navier-Stokes and heat conduction equations possess a self-similar solution which leads to the non-linear eigenvalue problem of finding the flow temperature fields in the channel. The spectrum of this problem is investigated analytically for low Marangoni numbers (the second approximation) and numerically in the limiting case of an ideally heat conducting liquid for any Marangoni number. The pattern of the thermocapillary flow in the layer is analysed as a function of the parameter values. The non-uniqueness of the solution, which is typical for problems of this kind, is established. The results are compared with those obtained previously in the first approximation with respect to the Marangoni number.     

Variations of random processes with independent increments

In the paper one considers random processes _{s ost} with independent increments, continuous in the mean (_P<). One establishes relations among multiple integrals, variations, i.e., the limits of sums of the form , and the Itô stochastic integrals.Translated from Zapiski Nauchnykh Seminarov Leningradskago Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 130, pp. 25–35, 1983.     

Disaccharide nucleosides: The crystal and molecular structure of 2′-<Emphasis Type="Italic">O</Emphasis>-β-<Emphasis Type="Italic">D</Emphasis>-ribopyranosylcytidine

The crystal structure of a disaccharide nucleoside, 2′-O-β-D-ribopyranosylcytidine, is studied using X-ray diffraction (space group P2₁, a = 6.827(2) Å, b = 12.813(3) Å, c = 9.532(2) Å, β = 92.934(5)°, V = 832.7(4) ų, Z = 2). The stereochemical features of the molecular structure of 2′-O-β-D-ribopyranosylcytidine are analyzed, and the structural data are compared with those obtained for the previously studied disaccharide nucleoside 2′-O-β-D-ribofuranosyluridine.     

The use of carbonaceous materials as field-emission cathodes

The advantages and disadvantages of carbon fibers and graphite plates with a developed surface as field-emission cathode materials are discussed. Experimental data for the chemical composition of the materials and the effect of thermal annealing on their structure and emission properties are presented. A correlation between the work function and the amount of cesium implant is studied. The feasibility of preparing planar cold cathodes with a developed surface by means of radiation technologies is considered, and the evolution of the emitting surface during bombardment by low-energy residual gas ions is traced. Cold cathode designs for various applications are recommended.     

Ion-photon emission of metal-containing organic dyes

The main parameters of ion-photon emission are investigated under ionic bombardment of metal-containing organic dyes and their mixtures with cholesterol. The spectral composition, quantum yield, and spatial distribution of emission from knocked-out excited particles have been determined. Several assumptions about the processes inherent to organic compounds under consideration have been made on the basis of the received data.