Computational formulas of the semiempirical theory of intensities in harmonic spectroscopy

A procedure is presented for obtaining computational formulas of the semiempirical theory of intensities within the framework of the vibrational-rotational model of a rigid polyatomic molecule, using the natural vibrational coordinates to describe the nuclear subsystem. An analysis is made of the contribution of the mechanical, kinematic, and electrooptical anharmonicity and vibrational-rotational interaction to the computational formula of harmonic spectroscopy. The mathematical tools of tensor analysis were used to describe the intramolecular dynamics. Saratov State Technical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, p. 59–64, February, 1998.     

On the 4-rank of class groups of quadratic number fields

We prove that the 4-rank of class groups of quadratic number fields behaves as predicted in an extension due to Gerth of the Cohen–Lenstra heuristics. Mathematics Subject Classification (2000)  11R29, 11R11, 11R45     

Convective motion of a conducting liquid carrying a current in a transverse magnetic field

The convective instability of a layer of conducting liquid carrying a current and lying in a magnetic field perpendicular to the current is considered. The problem of the nonconductive approximation in a linear setting is solved. The relationships between the Rayleigh number and the Hartmann number (determining the neutral stability) are derived.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza. No. 2, pp. 20–26, March–April, 1971.     

Approximate calculation of the effect of the walls on a model of a cavity modelled in accordance with the Éfros or Ryabushinskii schemes

The article sets forth an approximate method for calculating the effect of the walls on the area of the midsection of a plane or axisymmetric cavity, modelled in accordance with the Éfros or Ryabushinskii schemes. For the plane problem, a comparison with the results of an exact solution is given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 161–163, November–December, 1975.The author takes the occasion to thank A. G. Terent'ev for kindly furnishing his calculations.     

Propagation of nonlinear waves in a porous medium with two-phase saturation by a liquid and a gas

The propagation of nonlinear waves through a porous medium saturated with a viscous liquid and a gas is investigated with allowance for the capillary pressure. Numerical solutions of the traveling-wave type are constructed for the generalized Korteweg-de Vries-Burgers equation for the wave amplitudes. Three types of regimes of longitudinal wave propagation, including soliton-like regimes, are found.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 86–95, July–August, 1996.     

The motion of snow avalanches in the conditions of limiting friction

We investigate the equations of motion of large snow avalanches, and in contrast with [1–3] we take into account the fact that the dry friction can reach a critical value above which the snow in the avalanche or the underlaying material cannot sustain the friction. We find asymptotic solutions for long times after the beginning of motion. These solutions describe the avalanche motion in which a part of the snow moves in the conditions of limiting friction over a tilted plane with a uniform layer of snow. The equations which are used to find these asymptotic solutions have the property that for certain depths the flow velocity of small perturbations decreases with increasing depth. This is related to a number of unusual features (from the hydraulic point of view) of the solutions. In particular, on relatively gentle slopes two zones are formed in the avalanche: the forward part, with a large velocity and thickness of the moving layer, and the rear part, which is significantly slower and thinner. The two parts are separated by a narrow region characterized by a sharp decline in velocity and thickness of the moving layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 30–37, September–October, 1977.     

STABILIZATION OF LIPID BILAYERS ON SURFACES THROUGH CHARGED POLYMERS

ABSTRACT

It is our concept to use a polymer as a hydrophilic cushion to stabilize a lipid bilayer on a solid support. This can be accomplished by using polyacrylamides with disulfides and DMPE anchors as a hydrophilic cushion. These polymers have the additional functionalities to chemisorb on gold surfaces through the disulfides and to bind a lipid bilayer on it through the insertion of the lipid anchors into the lipid bilayer. This paper shows that a polymer with the additional functionality of charged groups increases the attraction of vesicles to form a tethered supported lipid bilayer. By varying the amount of charged groups in the polymer, we are able to control the hydrophilic behavior of the polymer and therefore are able to change the wetting on a surface. This was examined by measuring the contact angles. Using the technique of the surface plasmon spectroscopy, we are able to monitor the process of vesicle fusion on the polymer support.     

Unprecedented Kinetic Inertness for a Mn2+-Bispidine Chelate: A Novel Structural Entry for Mn2+-Based Imaging Agents

The search for more biocompatible alternatives to Gd³⁺-based MRI agents, and the interest in ⁵²Mn for PET imaging call for ligands that form inert Mn²⁺ chelates. Given the labile nature of Mn²⁺, high inertness is challenging to achieve. The strongly preorganized structure of the 2,4-pyridyl-disubstituted bispidol ligand L₁ endows its Mn²⁺ complex with exceptional kinetic inertness. Indeed, MnL₁ did not show any dissociation for 140 days in the presence of 50 equiv. of Zn²⁺ (37 °C, pH 6), while recently reported potential MRI agents MnPyC3A and MnPC2A-EA have dissociation half-lives of 0.285 h and 54.4 h under similar conditions. In addition, the relaxivity of MnL₁ (4.28 mm ⁻¹ s⁻¹ at 25 °C, 20 MHz) is remarkable for a monohydrated, small Mn²⁺ chelate. In vivo MRI experiments in mice and determination of the tissue Mn content evidence rapid renal clearance of MnL₁. Additionally, L₁ could be radiolabeled with ⁵²Mn and the complex revealed good stability in biological media.     

Evidence of Noncentrosymmetry of Human Tooth Hydroxyapatite Crystals

Herein, we investigate human single hydroxyapatite crystals (enamel and dentine) by convergent‐beam electron diffraction (CBED) and automated electron‐diffraction tomography (ADT). The CBED pattern shows the absence of the mirror plane perpendicular to the c axis leading to the P6₃ space group instead of the P6₃/m space group considered for larger‐scale crystals, this is confirmed by ADT. This experimental evidence is of prime importance for understanding the morphogenesis and the architectural organization of calcified tissues.