On estimates of approximation characteristics of the Besov classes of periodic functions of many variables

We obtain order estimates for some approximate characteristics of the Besov classes B _p,ϑ ^r of periodic functions of many variables. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 9, pp. 1250–1261, September, 1997.     

Generalized moment representations of basis hypergeometric series

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 6, pp. 803–808, June, 1989.     

MEASUREMENT OF CONTACT ANGLE IN A CLEARANCE-FIT PIN-LOADED HOLE

A simple experimental technique using an instrumented pin was developed for the measurement of the load-contact variation in a clearance-fit, pin-loaded hole. The method is applicable to both conducting and nonconducting materials.     

On a new class of function systems of Faber-Schauder type

In this paper, we introduce a new class of function systems generalizing the classical Faber-Schauder system. Under the condition that the generating sequence is bounded, we show that systems of such a class constitute bases in the space of continuous functions and prove some properties of series expansions of functions in these systems.     

Estimates of the rate of convergence of a dynamic reconstruction algorithm under incomplete information about the phase state

In this paper, we study a dynamic reconstruction algorithm which reconstructs the unknown unbounded input and all unobservable phase coordinates from the results of measurements of part of the coordinates. An upper and a lower bound for the accuracy of the reconstruction is obtained. We determine the class of inputs for which the upper bound is uniform. We give a condition for optimally matching the algorithm parameters, ensuring the highest order of the upper bound and equating the orders of the upper and lower bounds. Thus, we establish the sharpness of the upper bound.     

Stereochemical aspects of the formation of toxisterols A

Mechanisms for the formation of toxisterol A are suggested. The connection between the conformation of the initial previtamin and the stereochemistry of the reaction products is discussed.Lensoviet Leningrad Technological Institute. Translated from Khimiya Prirodnykh Soedinenii, No. 2, pp. 225–229, March–April, 1989.     

Mg 2p shallow core-level and local atomic structure of i-ZnMgRE quasicrystals

We present a detailed analysis of the Mg 2p shallow core-levels measured on icosahedral single-grain ZnMgY, ZnMgHo, and ZnMgEr quasicrystals during a photoelectron microscopy study. The synchrotron radiation photoemission measurements were performed on in situ cleaved samples at a pressure of 10⁻¹⁰ mbar and at low temperature, typically 90-150 K. The Mg 2p photoemission lines are essentially broadened as compared to those of the Mg 2p spin-orbit doublet recorded on the Zn₂Mg crystalline Laves phase. The broadening is associated to the coordination shifts of the Mg 2p level due to the inequivalent magnesium sites in the quasicrystalline lattice. The coordination shifts are calculated on the basis of i-ZnMg(Ho, Y) atomic structure data, recently determined from the pair distribution function analysis. The coordination shifts obtained are up to 0.2 eV. The Mg 2p experimental spectral intensity is nicely reproduced by a superposition of coordination-shifted Mg 2p spin-orbit doublets.