Best approximation of periodic functions by trigonometric polynomials in L2

Estimates are gotten for the best approximations in L₂ (0, 2) of a periodic function by trigonometric polynomials in terms of its m-th continuity modulus or in terms of the continuity modulus of its r-th derivative. The inequality E_n–1(f)L₂<(C _2m ^m _m(2/n;f)L₂(1 const) is proved, where the constant (C _2m ^m )^–1/2 is unimprovable for the whole space L₂ (0, 2). Two titles are cited in the bibliography.Translated from Matematicheskie Zametki, Vol. 2, No. 5, pp. 513–522, November, 1967.     

Unusual field dependence of the Hall effect in Ni3Mn films

An anomalous behavior of the Hall emf E_h in disordered Ni₃Mn vacuum condensates is discovered. As the magnetic field H is increased from zero, E_h first increases in absolute value, its sign being negative. At a certain field, E_h then begins to decrease, passes through zero, and subsequently approaches saturation in the normal manner, its sign being positive. This behavior can be explained by assuming the presence in the condensate of several magnetic phases with emf values of different signs and with different saturation fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 101–104, December, 1976.     

SEM diagnostics of the surface of MK-40 and MA-40 heterogeneous ion-exchange membranes in the swollen state after thermal treatment

The morphology of the surface of MK-40 and MA-40 ion-exchange membranes in the swollen state after chemical and thermal treatment is studied using scanning electron microscopy. The distribution of portions of the ion exchanger on the surface of heterogeneous membranes is found to be of a complex stochastic nature; their sizes for the MK-40 and MA-40 membranes are 5–30 and 8–40 μm, respectively, while the sizes typical for the secondary porous structure are 2–8 μm. An increase in the share of the ion-exchange component of the surface (by 20–40%), the sizes of the ion-exchange portions (by 20%), and the surface porosity (by two-three times) in the samples subjected to thermal treatment is revealed.     

Imaging properties of a 2D crossed holographic grating on silver halide photoemulsions

A technique is proposed for photochemical processing of photoemulsions, which makes it possible to form lens-shaped focusing elements at the nodes of crossed 2D holographic gratings (2DHGs). The results of experiments on 2DHG recording performed on PFG-01 material using this technique show considerable improvement of imaging properties of 2DHG.     

Laser-induced fluorescence spectroscopy of the secondary cataract

Excitation–emission matrices of laser-induced fluorescence of lens capsule epithelium, the lens nucleus, and the lens capsule are investigated. A solid-state laser in combination with an optical parametric generator tunable in the range from 210 to 350 nm was used for excitation of fluorescence. The spectra of fluorescence of all three types of tissues exhibit typical features that are specific to them and drastically differ from one another. This effect can be used for intrasurgical control of presence of residual lens capsule epithelium cells in the capsular bag after surgical treatment of a cataract.     

Numerical modeling of three-dimensional convection in the upper mantle of the earth beneath Eurasia lithosphere

We constructed a three-dimensional numerical model of thermal convection in the upper mantle of the Earth in spherical variables using an artificial compressibility method. Results of three-dimensional modeling of convection beneath the Eurasia cratons are presented. The calculation results illustrate the structure of convective flows.