Estimate for the Best Approximation of Summable Functions of Several Variables with a Certain Symmetry of Fourier Coefficients

An upper bound for the best approximation of summable functions of several variables by trigonometric polynomials in the metric of L is determined in terms of Fourier coefficients. We consider functions representable by trigonometric series with certain symmetry of coefficients satisfying a multiple analog of the Sidon–Telyakovskii conditions.     

An analysis of migration paths of Li+ cations in ternary oxygen-containing compounds Li p X q O r

A new method was developed for studying voids and channels in crystal structures based on the Voronoi-Dirichlet partition of crystal space, and 822 structurally characterized ternary compounds Li ^p X ^q O ^r were analyzed for the first time. For these compounds, the dimensionality was determined and the migration patterns of channel systems capable of providing lithium-ion transport were constructed. The calculated coordinates of lithium atoms in the centers of the voids are consistent (within 0.4 ?) with the known structural data. Among these compounds, 113 compounds have infinite channel systems, 60 compounds (18 structural types, STs) have been described earlier in the literature as solid electrolytes, and 53 compounds (23 STs) can be considered as potential one-, two-, or three-dimensional ionic conductors (13, 3, and 7 STs, respectively). Original Russian Text ? N.A. Anurova, V.A. Blatov, G.D. Ilyushin, O.A. Blatova, A.K. Ivanov-Shitz, L.N. Dem’yanets, 2008, published in Kristallografiya, 2008, Vol. 53, No. 6, pp. 987–993.     

Dislocation model of a nanotwin

We propose a dislocation model of a nanotwin, which is used to calculate the stress fields in the nanotwin. We consider the role of these stresses in the process of interdislocation interaction and nanotwin growth.     

A quality criterion for visual tracking during nystagmus

The aim of this study is to construct a quantitative characteristic for the degree of gaze stabilization on a visual target with consideration of physiological constraints. A quality criterion for visual tracking during optokinetic vestibulocervical nystagmus is proposed. The index of imaginary tracking during rotation in the dark allows one to speak of a difference in the image stabilization quality between a healthy person and a patient. Experimental nystagmus data are used to calculate the quality index of visual tracking and the index of imaginary tracking.     

LES of turbulent heat transfer: proper convection numerical schemes for temperature transport

Large eddy simulations of two basic configurations (decay of isotropic turbulence, and the academic plane channel flow) with heat transfer have been performed comparing several convection numerical schemes, in order to discuss their ability to evaluate temperature fluctuations properly. Results are compared with the available incompressible heat transfer direct numerical simulation data. It is shown that the use of regularizing schemes (such as high order upwind type schemes) for the temperature transport equation in combination with centered schemes for momentum transport equation gives better results than the use of centred schemes for both equations. Copyright © 2004 John Wiley & Sons, Ltd.     

Attenuation of electromagnetic waves in a semiconductor superlattice in a magnetic field

Magnetoplasma waves and inhomogeneous (complex) waves in an infinite semiconductor superlattice in a magnetic field are studied, and dispersion curves are obtained. It is shown analytically and numerically that, in periodic structures, among inhomogeneous waves, there are many complex waves for which the imaginary part of the wave vector is greater than the real part. The effect of dissipation in a medium on the dispersion curves of magnetoplasma waves is examined. The dependence of the minimum phase velocity on the collision frequency and the magnetic field strength is studied.     

Structure and properties of the mesophase of syndiotactic polystyrene. VIII. Solvent sorption behavior of syndiotactic polystyrene/p‐chlorotoluene mesophase membranes

A crystalline δ form of a syndiotactic polystyrene (sPS) membrane was prepared from a solution of sPS (1 wt %) and p‐chlorotoluene (p‐CT) by a solution‐casting method. The mesophase (δ empty form) of sPS was obtained by the extraction of the guest solvent from the δ form of sPS by a stepwise solvent‐extraction method. The sPS/p‐CT mesophase membrane [p‐CT (A‐M)] was used for the sorption of 1 mol % p‐CT for different times and for the sorption of different concentrations of p‐CT, chlorobenzene (CB), p‐xylene (p‐X), toluene, and chloroform for 48 h. The presence of solvents in the sPS membrane was confirmed by IR analysis. A thermal study revealed that the sorption amount of 1 mol % p‐CT increased with increasing immersion time, and the sorption amounts of different solvents increased with increasing solvent concentration. Differential scanning calorimetry results showed that the desorption peak temperature increased as the amount of the solvent increased in the clathrated sPS membrane. Wide‐angle X‐ray diffraction results showed that 2θ at 8.25° was slightly shifted toward 8°, and there was no change in the peak position at 10° for p‐CT (A‐M), which was immersed in different solvents (1 mol %); however, the intensity of 2θ at 10° was not similar for all the samples. Among the solvents used for the sorption studies at 1 mol %, p‐CT (A‐M) could sorb more p‐CT and CB than p‐X, toluene, and chloroform. The solvent sorption isotherm was the Langmuir sorption mechanism. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3439–3446, 2004