On the properties of the identically singular Lagrange problem

We consider the identically singular Lagrange problem of the calculus of variations. It is investigated how the conjugate points and the Jacobi equation index are related to the solvability conditions of the appropriate matrix Riccati equation and the reducibility of the functional to a perfect square. The criterion of the trajectory variation smallness at a small variation of the functional in the neighborhood of the extremal is obtained.     

Synthesis of the nitrogen-fixing enzyme system in oligonitrophilic bacteria

Oligonitrophilic bacteria were cultivated on a medium containing only 2.5--10.0 mg/litre of nitrogen compounds. They assimilated elementary nitrogen only after utilization of these nitrogen compounds during growth and formation of nitrogen-fixing enzyme system. Their cells grown on a medium containing high concentrations of bound nitrogen did not fix nitrogen during further incubation in the atmosphere of 15N; therefore, the enzymes involved in nitrogen fixation were induced. These organisms are characterized by diauxia during their growth on media containing "start" doses of nitrogen. Enzymes catalysing nitrogen fixation in azotobacter are also induced. But, contrary to oligonitrophilic bacteria, the azotobacter does not require nitrogen compounds in the medium in order to adapt to molecular nitrogen, and its growth curve is not of a biphasal character. These data and the evidence of other authors suggest that all nitrogen-fixing microorganisms are characterized by the induced, not constitutive, enzymes involved in reduction of molecular nitrogen.     

Biogenesis of cellulolytic enzymes by Trichoderma ligorum on media with "inductor"

Identical distribution of C2- and Cx-cellulase activities of enzyme complexes produced by Trichoderma lignorum on a medium with lactose, a soluble "inductor", and on a medium with cellulose was found by means of disc elestrophoresis in polyacrylamide gel. The maximum rate of synthesis of cellulases on the medium with lactose was registered during the highest deceleration, and even complete cessation, of the fungal growth. During this phase, only one electrophoretically homogeneous cellulase component with Rf of 0.44 possessing all types of the cellulase activity is present in the cultural broth. In the course of growth of the fungus on cellulose after 48 hours, also only one electrophoretically homogeneous component with Rf of 0.44 was found in the cultural broth when the rate of the substrate degradation was highest. The appearance of minor protein components with the activity of cellulase at later stages of cultivation after cessation of the fungal growth is supposed to be caused by modification of the main cellulase component with Rf of 0.44 by the growth medium.     

Influence of the dentate fascia on the sensory responses of neurons in hippocampal field CA3

In experiments with unanaesthetized rabbits the influences of electric stimulation of the dentate fascia (DF) on the extracellularly recorded spontaneous and evoked activity of the CA3 neurones were investigated. Stimulation of a fixed locus in the DF during recording in the CA3 by a microelectrode, shifted along the longitudinal axis of the hippocampus, supported the notion of the topical, "segmental" organization of connections between the DF and CA3. A relatively narrow "active zone" (approximately 700 nm) appeared in the CA3 during the threshold DF stimulation: it was bordered by zones with predominantly inhibitory responses to stimulation. The CA3 neurones in the "active zone" rapidly lost their reactivity to sensory stimuli. In the "inhibitory" and "zero" zones the normal level of reactivity to sensory stimuli was preserved.     

Serial measurements of body composition in obese subjects during a very-low-energy diet (VLED) comparing bioelectrical impedance with hydrodensitometry

Bioelectrical impedance analysis (BIA) is a convenient, inexpensive, and noninvasive technique for measuring body composition. BIA has been strongly correlated with total body water (TBW) and also has been validated against hydrodensitometry (HD). The accuracy and clinical utility of BIA and HD during periods of substantial weight loss remain controversial. We measured body composition in moderately and severely obese patients serially using both methods during a very-low-energy diet (VLED). Mean initial weight in these patients was 116 (+/-30) kg (range, 74-196 kg). Mean weight loss was 24 (+/-13) kg with a decrease in fat mass (FM) by HD of kg (p < 0.001) and a decrease in fat-free mass (FFM) of 3.6 kg (p < 0.05). Loss of FFM is best predicted by the rate (kg/wk) of weight loss (r2 = 0.86, p < 0.0001). FFM, as predicted from BIA equations, was highly correlated with FFM as estimated by HD during all testing sessions (r = 0.92-0.98). Although highly correlated, BIA overestimated FFM relative to HD and this difference appeared to be more pronounced for taller patients with greater truncal obesity. Although the discrepancy was no greater during weight-loss treatment, the level of disagreement was considerable. Therefore, the two methods cannot be used interchangeably to monitor relative changes in body composition in patients with obesity during treatment with VLED. The discrepancy between BIA and HD may be caused by body mass distribution considerations and by perturbations in TBW which affect the hydration quotient for FFM (BIA) and/or which affect the density constants for FFM and FM (HD).     

The Influence of the Annealing Regime on the Properties of Terahertz Antennas Based on Low-Temperature-Grown Gallium Arsenide

Low-temperature gallium arsenide (LT-GaAs) films were grown by the method of molecularbeam epitaxy (MBE) at a reduced temperature (230°C) on GaAs(100) substrates and subjected to postgrowth annealing in various regimes. Photoconductive antennas (PCAs) with flag geometry formed on the film surface were characterized by terahertz (THz) response power at various bias voltages. The method of THz spectroscopy was used to study the characteristics of PCAs based on LT-GaAs films annealed in various regimes and the optimum interval of postgrowth annealing temperatures (670–720°C) was established.     

Energy-Band Structure Features of Some Crimped-Shape Nanotubes

Abstract

Energy spectra of four stereoregular carbon quasi-1D-macromolecules with polyhedral elementary units containing 60 or 58 atoms were calculated by the crystalline orbital method in the valence approach. The EHT (see R. Hoffmann, J. Chem. Phys. 1963, 39, 1397) with standardized weighted non-diagonal elements of the matrix Hamiltonian was used. Atomic coordinates of the elementary units of carbon systems under consideraton were determined as a result of energy optimization of conforming trimers by the MNDO/PM3 methods. Geometries of inner monomers were used for modeling macromolecule structures. It was found that the widths of energy gaps of three systems [C₆₀]_n under consideration are located in the interval from 1.3 to 1.5 eV. Besides, quasi-localized energy levels were found in the spectrum gaps of these carbon quasi-1D-systems.     

Adaptive modified alternating triangular iterative method for solving grid equations with a non-self-adjoint operator

Adaptive methods for solving convection-diffusion problems are developed. A variant of the adaptive modified alternating triangular method of minimal corrections is constructed and its convergence rate is estimated given that the grid Peclet number is bounded, which holds for monotone difference approximations of diffusion-convection problems. Results of the numerical calculation of spatial three-dimensional currents in the Sea of Azov are given; a parallel implementation of this method performed on a supercomputer at the Taganrog Institute of Technology is considered.     

Kinetic description of rapeseed oil conversion into aromatic hydrocarbons on promoted MFI zeolite

An approach to the construction of a kinetic model for the reactions of rapeseed oil hydroconversion to aromatic hydrocarbons has been proposed, which is based on analysis of experimental data obtained using a MFI zeolite promoted with zinc and chromium ions. An empirical mathematical model describing the dynamic behavior of the main products of the decomposition reaction of rapeseed oil as a model feedstock has been developed. It has been shown that an increase in the space time and temperature in the examined range of reaction conditions increase the yield of aromatic hydrocarbons. The influence of hydrogen pressure on the yield of aromatics is nonmonotonic in character, passing through a maximum, with the optimum yield being in the middle of the hydrogen pressure range of 10–20 atm.