On Sections of Power Series

A single program has been developed to ensure that the final result of the data processing of the measurement calibration protocol is obtained under normal conditions. The calibration result contains a calibration function or a correction function in the form of a continuous sedate series and a calibration chart based on typical additive error probabilities. Solved the problem of the statistical treatment of the calibration protocol measuring in normal conditions within a single program “MMI–calibration 3.0” that includes identification of the calibration function in a continuous power series of indications of a measuring instrument and chart calibration. An example of solving the problem of calibration of the thermometer by the working standard of the 3rd grade with the help of the “MMI-calibration 3.0” program.

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The Green's function of a ordinary differential operators and integral representation the sums of certain power series

Доклады Академии наук ◽

10.31857/s086956520002998-0 ◽

2018 ◽

Vol 482 (5) ◽

pp. 500-503 ◽

Cited By ~ 1

Author(s):

K. Mirzoyev ◽

◽

T. Safonova ◽

Keyword(s):

Power Series ◽

Integral Representation ◽

Green’S Function ◽

Green's Function ◽

Differential Operators ◽

Ordinary Differential Operators

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Identification of the string boundary conditions using natural frequencies

Proceedings of the Mavlyutov Institute of Mechanics ◽

10.21662/uim2016.1.007 ◽

2016 ◽

Vol 11 (1) ◽

pp. 38-52

Author(s):

I.M. Utyashev ◽

A.M. Akhtyamov

Keyword(s):

Inverse Problems ◽

Power Series ◽

Boundary Value Problem ◽

Boundary Conditions ◽

Natural Frequencies ◽

Boundary Value ◽

External Environment ◽

Direct And Inverse Problems ◽

Symmetric Potential ◽

Modified Method

The paper discusses direct and inverse problems of oscillations of the string taking into account symmetrical characteristics of the external environment. In particular, we propose a modified method of finding natural frequencies using power series, and also the problem of identification of the boundary conditions type and parameters for the boundary value problem describing the vibrations of a string is solved. It is shown that to identify the form and parameters of the boundary conditions the two natural frequencies is enough in the case of a symmetric potential q(x). The estimation of the convergence of the proposed methods is done.

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