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Установлены следующ ие факты.1.Константы Лебегаλ n 0 интерполяционных многочленов Лагранж а на [−1,1] по системе узлов
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\left\{ { - \cos \frac{{(2k - 1)\pi }}{{2n + 1}}} \right\}_{k = 1}^{n + 1} ,n = 1,2,...$$ \end{document}
, представимы в виде ас имптотического ряда:
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\lambda _n^0 = \frac{2}{\pi }\ln n + \frac{2}{\pi }\left( {c + \ln \frac{8}{\pi }} \right) + \mathop \Sigma \limits_{v = 1}^\infty \frac{{a_{2v} }}{{n^{2v} }},$$ \end{document}
гдеc — постоянная Эйл ера; дляa 2v указаны явн ые выражения и для всехl
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\lambda _n^0 = \frac{2}{\pi }\ln n + \frac{2}{\pi }\left( {c + \ln \frac{8}{\pi }} \right) + \mathop \Sigma \limits_{v = 1}^\infty \frac{{a_{2v} }}{{n^{2v} }} + R_{n,\iota } ,\Gamma e|R_{n,\iota } |\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \leqslant } \frac{{0,15(2l + 1)!}}{{(2\pi )^{2\iota } n^{2\iota + 2} }}.$$ \end{document}
2.Если обозначить чере зλ n * константу Лебега по оптимальной на [−1,1] сис теме узлов {x j *}j=1 n, то для всехп:λ n *∈(λ n 0−0,42,λ n 0).
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Abstract  

The evolution of ion exchange processes for separation and purification of substances by use of the influence of temperature both on the equilibrium and the dynamic properties of some ion exchange resins is discussed. Significant improvement of some ion exchange separations, diminishing of reagents consumption and waste quantities is achieved. In the same way, environmentally non-hazardous reagentless ion exchange methods of divalent and monovalent ionic mixtures separation are developed. This report is based on experimental studies of the equilibrium, dynamic and some other properties of ion exchange resins.

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The thermal solid-state isomerizations of Copy2Cl2 (py=pyridine), Nien2(NO2)2 and Nien2(NCS)2 (en=ethylenediamine) were studied by thermal analysis, thermomicroscopy, X-ray diffraction and IR-spectroscopy. It was shown that the reactions proceed by nuclear formation and growth. The kinetic-morphological peculiarities of the processes suggest that the process-determining stage is a phase stage, i. e. structural transformation. The topography and kinetics of processes are therefore determined by the crystal structures of the initial material and the reaction product, and by the contact conditions at the interface. The stress relaxation processes affect the morphology of the products and the kinetics of the transformation.

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Abstract  

Diffusion coefficients of radionuclides237Np,239Pu and241Am in simulated alumina phosphate and alumina borosilicate glasses at temperatures lower than their transformation temperature were determined. Actinides are known to be the least mobile elements. In particular, the diffusion coefficients of actinides in alumina phosphate glasses at 673 K are about 10–18 m2·s–1, and in alumina borosilicate at 773 K about 10–19 m2·s–1. It is shown that crystallization of glasses leads to increasing237Np diffusion mobility. It is also shown that a rather small quantity of water absorbed by a crystallized alumina phosphate glass in tensifies low-temperature migration of237Np.

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Abstract  

Diffusion coefficients of22Na,90Sr and134Cs in some aluminoborosilicate and silicophosphate glasses and ceramics have been determined by the integral residual radioactivity method. The temperature dependence of22Na diffusion coefficients has also been found.

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Abstract  

The possibilities of using a computer to optimize the conditions of gamma-activation analysis are considered. Criteria of optimum conditions are formulated. The optimization program is constructed of the following operations being automatically performed: (1) determination of a list of isotopes and their gamma-lines formed during the interaction between the activating bremsstrahlung and the substance whose elemental composition elements to be analyzed plus matrix is preliminarily given; (2) optimization of the analysis time regimes and the value of the maximum energy of the activating bremsstrahlung; (3) choice of a gamma-line of the isotope of an element to be analyzed by which the quantitative determination of this element is expedient. For these purposes a catalogue of nuclear-physical constants (half-lives and energies which was compiled from published data tables of gamma-line outputs obtained experimentally under standardized conditions for different values of the maximum energy of the bremsstrahlung as well as mathematical models of the monoenergetic gamma-ray spectra) has been used.

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Abstract  

A mathematical model is suggested for the approximation of the monoenergetic gamma-ray spectra obtained by a Ge(Li) detector. Some features of the instrumentation monoline spectra in the energy range upto 2 MeV are considered in detail. Computer program “APPROXIMATSIYA” is described. The program allows to determine the parameters of the mathematical model with the purpose to construct a making up standard spectrum library. The results of the monoline spectrum processing are discussed.

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By means of DSC, DTA, TG and NMR it was established that the process of cure of epoxy resins induced by aqueous solutions of heteropolyacids consists of two stages, the first one being connected with a catalytic interaction between oligomer and water, and the second one with epoxy-hydroxyl etherification. Analysis of kinetic data shows that the first reaction is diffusion controlled, the second process can be described by pseudo-first order kinetics with activation energy about 40 kJ/M.

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Abstract  

Perovskite SrCo0.6Fe0.2Nb0.2O3-z attracts attention as a promising material with high oxygen conductivity. The sample was investigated by means of high-temperature X-ray powder diffraction and thermogravimetry. Phase transition was detected near 400 °C and accompanied with significant mass loss. The phase transition affects oxygen mobility, important for the synthesis of oxygen permeable membranes. The unit cell parameters are proved to change with temperature after two effects (1) reversible conventional thermal expansion and (2) irreversible contraction-expansion due to the changes in the oxygen content. In situ high-temperature X-ray diffraction experiments allowed us to separate the contributions and to measure them as a function of temperature.

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Journal of Radioanalytical and Nuclear Chemistry
Authors: N. Shilo, E. Ippolitov, V. Ivanenko, B. Kustov, V. Zheleznov, G. Aristov, A. Shtan, I. Ivanov, V. Kovalenko, and N. Kondrat’ev

Abstract  

A facility using a californium neutron source and a method for the neutron activation analysis of gold were developed. The sensitivity of the determination is 0.1 g/t. The sources of random and systematic errors have been studied. It has been concluded that in prospection and evaluation of gold ore deposits, the traditional test tube analysis for gold may be replaced with the developed method.

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