Verification of the gauss’s law with the unknown parameters by the Kolmogorov criterion in the problems of railways electric supply

Abstract Traction currents and voltages in the overhead railroad contact line hypothetically obey the Gauss’s distribution law. An algorithm for statistical modeling of the Kolmogorov distribution for the unknown values of the Gaussian law parameters has been developed. For a large number of the modeling program implementations, it has been shown that testing the hypothesis about the distribution law without taking into account the number of unknown parameters leads to an unacceptable increase in the criterion significance and a decrease in its power. The distribution of the Kolmogorov criterion is calculated with sufficient accuracy for two unknown parameters, which allows its wide practical use.

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The laws of distribution of some parameters when organizing the movement of trains

Herald of the Ural State University of Railway Transport ◽

10.20291/2079-0392-2021-3-27-39 ◽

2021 ◽

pp. 27-39

Author(s):

M. V. Fufacheva ◽

Keyword(s):

Coefficient Of Variation ◽

Least Squares Method ◽

Erlang Distribution ◽

Key Factors ◽

Distribution Law ◽

Statistical Parameters ◽

Railway Stations ◽

Coefficients Of Variation ◽

Kolmogorov Criterion ◽

Laws Of Distribution

The article discusses the key factors for the organization of train traffic. The analysis of statistical parameters of the intervals of departure of freight trains from railway stations and the length of the freight train flow is carried out. Based on these train schedules, graphical dependences of the intervals of departure of trains from separate points on the volume of train traffic and the distribution of train lengths in even and odd directions are constructed. Polynomial dependencies with coefficients of variation are derived. The curve of the second-order Erlang distribution function for the departure intervals is constructed. It is determined that the average departure intensity in one hour is equal to three trains, and the average departure interval lies between the 25th and 35th minutes with a probability of 0.793. There is a correlation between the coefficient of variation (mean square deviation) of the departure interval and its average daily deviation. The power function of the analytical ratio of the coefficient of variation from the average interval of departure of freight trains from the technical stations of the Krasnoyarsk railway during the day is determined using the least squares method. The degrees of correspondence of theoretical and statistical distributions of the number of cars in trains are studied using the Kolmogorov criterion with the calculation of the probability value and confirmation that the distribution of the number of cars in trains obeys the binomial law. Using the Pearson agreement criterion, it is proved that the frequency of departure of freight trains from railway stations obeys the exponential distribution law.

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Defocus ramp correction in spot-scan imaging

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100121053 ◽

1992 ◽

Vol 50 (1) ◽

pp. 130-131

Author(s):

Kenneth H. Downing

Keyword(s):

Computer Control ◽

Three Dimensional ◽

Sufficient Accuracy ◽

Objective Lens ◽

Electron Crystallography ◽

Contrast Transfer Function ◽

Tilt Axis ◽

Specimen Height ◽

The Difference ◽

Envelope Functions

Three-dimensional structures of a number of samples have been determined by electron crystallography. The procedures used in this work include recording images of fairly large areas of a specimen at high tilt angles. There is then a large defocus ramp across the image, and parts of the image are far out of focus. In the regions where the defocus is large, the contrast transfer function (CTF) varies rapidly across the image, especially at high resolution. Not only is the CTF then difficult to determine with sufficient accuracy to correct properly, but the image contrast is reduced by envelope functions which tend toward a low value at high defocus.We have combined computer control of the electron microscope with spot-scan imaging in order to eliminate most of the defocus ramp and its effects in the images of tilted specimens. In recording the spot-scan image, the beam is scanned along rows that are parallel to the tilt axis, so that along each row of spots the focus is constant. Between scan rows, the objective lens current is changed to correct for the difference in specimen height from one scan to the next.

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