variance

Mathematical modeling of impurity diffusion process under given statistics of a point mass sources system. II

Modeling of the impurity diffusion process in a layer under the action of a system of random point sources is carried out.  Mass sources of different power are uniformly distributed in a certain internal interval, that may also coincide with the entire region of the layer.  The statistics of random sources is given.  The solution of the initial-boundary value problem is found as the sum of the homogeneous problem solution and the convolution of the Green's function with the system of the random point sources.  Averaging of the solution is performed on the internal subinterval and in the ent

Адаптивна фільтрація параметрів руху об‘єкта у горизонтальній площині

Реалізована процедура використання алгоритму класичного фільтра Калмана для оцінки параметрів руху об’єкта, що маневрує. Застосування фільтра Калмана мотивовано необхідністю мінімізувати дисперсію оцінки вектора випадкового процесу. Результати оцінки параметрів руху обробляють згладжуючим алгоритмом Рауч–Тюнга– Штрібеля також з метою мінімізації дисперсії. Алгоритми Калмана та Рауча–Тюнга– Штрібеля можна застосовувати для використання в оцінці параметрів руху автомобіля, повітряного судна, бойового снаряду.

Simulation of statistical mean and variance of normally distributed data $N_X(m_X,\sigma_X)$ transformed by nonlinear functions $g(X)=\cos X$, $e^X$ and their inverse functions $g^{-1}(X)=\arccos X$, $\ln X$

This paper presents analytical relationships for calculating statistical mean and variances of functions $g(X)=\cos X$, $e^X$, $g^{-1}(X)=\arccos X$, $\ln X$ of transformation of a normally $N_X(m_X,\sigma_X)$ distributed random variable.

Simulation of statistical mean and variance of normally distributed random values, transformed by nonlinear functions $\sqrt{|X|}$ and $\sqrt{X}$

This paper presents theoretical studies of formation regularities for the statistical mean and variance of normally distributed random values with the unlimited argument values subjected to nonlinear transformations of functions $\sqrt{|X|}$ and  $\sqrt{X}$.  It is shown that for nonlinear square root transformation of a normally distributed random variable, the integrals of higher order mean $n>1$ satisfy the inequality $\overline{(y-\overline{Y})^n}\neq 0$.  On the basis of the theoretical research, the correct boundaries $m,\sigma \to \infty$ of error transfer for

Formation of gender linguistics term system

In the article the gender linguistics term system is considered. Some of the problems in the terminology formation, including difficulties in identifying its composition, the presence of a significant number of synonyms and variations, differences regarding definitions and spelling of certain terms are outlined. It’s emphasized that the analyzed term system while in its infancy requires a comprehensive study, normalization and standardization.

An estimation of cross-spectral components for periodically non-stationary random processes

Correlations between harmonic components of random processes is a feature of signal non-stationarity. In the case of periodically non-stationary random processes (PNRP) correlate harmonics distant one from another on frequencies, what multiple to value T, T - period of non-stationarity [1, 2]. Since faults appearance in rotating elements of mechanical systems leads to periodical non-stationarity of vibration signals when searching of correlations between harmonic components can lay in the base for defects detection [1, 3-5].

Methods of evaluating investment risks

The approaches to the formation of the investment risks essence, their classifying features and the methods of their assessment are summarized. The basic constituents of the investment risk nature as an economic category are substantiated. The main methods of evaluating investment risks are analyzed. Particular attention is paid to the intuitive part of the process of making investment decisions. The major factors affecting the choice of the investment risks analyzing methods are singled out.