Were researched dependences of standard mean square errors of land parcel area determination as a function of area and elongation coefficients. Using investigated values was made an approximation of quadratic polynomial function for standard mean square errors of land parcel area in intervals 0,1-1 ha, 1-10 ha, 10-100 ha with evaluation of accuracy of approximated functions.
The algorithm of 1D density distribution approximation by Legendre polinomials is presented. Based on this approximation the internal gravity potential and potential gravity energy of ellipsoid waz estimated.
We consider the method of constructing the local gravity field using technique called spherical cap harmonic analysis (SCHA). This approach involves using of associated Legendre functions of integer degree and noninteger order. These functions form two sets of functions. They are mutually orthogonal over the spherical cap in each set. However, in general these functions are not orthogonal. Thus, for using both of these sets of functions it is traditionally used least squares method. However, for higher orders it is quite difficult to compute eigenvalues and norms of these functions.
Purpose. Digital-SEM image, due to various physical factors of scanning electron microscope inherent significant geometric distortion. The aim of this study is to establish and Effective consideration to improve the accuracy to obtain quantitative spatial parameters mikrosurface objects are investigated using SEM. This problem is extremely important, especially nowadays when needed control of technological processes for the production of micron and submicron levels, particularly in engineering, microelectronics and many others.
For measurements of digital SEM images of test grid with a resolution 1425 lin/mm taken on a digital SEM DSM-960A (Carl Zeiss, Germany), are defined by their scale and geometric distortion of the SEM magnification range from 1000h to 20000h. Found that the large-scale distortions of digital SEM images obtained in this type of SEM is systematic, regardless of the increase and is approximately -2 % along the x-axis image and -4 % along the y-axis with a picture.
The purpose of this article is the research of results of approximation of functions of calculation of the meansquare errors of land parcels areas to determine such approximation function, which would allow most accurately calculate the permissible values of mean square errors depending on the size and elongation of land parcel. Methods. To meet the goal an approximation of functions by the method of least squares was performed. Two functions were used for approximation – the natural logarithm and power, as well as the evaluation of the accuracy was done.