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The problem of mathematical support development is solved to automate the extraction knowledge as production rules from the training data samples. The object of study is the process of constructing models of non-destructive quality control. The subject of study are methods of production rules extraction for synthesis of quality control models. The purpose of the work is to improve the efficiency of the process of production rules extraction for constructing models of quality control based on training samples. The stochastic method for the decision trees synthesis is proposed, which uses information about the informativeness of features, the complexity of the synthesized tree, as well as the accuracy of its recognition, which allows to form on the initial stage a set of tree structures, characterized by a simple hierarchy and low error recognition, in the process of search to create a new set of solutions with taking into account information about the significance of the features and interpretability of generated trees, which, in turn, provides the possibility of constructing a decision tree with a small number of elements (nodes and branches between them), and an acceptable recognition accuracy and retrieval based on it the most valuable instances. The software implementing proposed method is developed. The experiments to study the properties of the proposed method are conducted. The experimental results allow to recommend the proposed method for use in practice. [ABSTRACT FROM AUTHOR]

Truncation-error bounds for the 1-periodic continued fraction of special form are established at the following conditions: if first element of the fraction belongs to complex plain with the cut (-∞;-1/4] and the sum of modules of other elements is limited by a certain number; if elements belong to their respective parabolic regions or union of that parabolic regions and all their modules, except of the first one, are limited. [ABSTRACT FROM AUTHOR]

In this paper, we study the method of center gravity for determining the characteristics of symmetric objects on digital images. Moreover, an estimate error is less than the size of one pixel (subpixel accuracy). We show that this method is not only more precise, but also more rapid than other methods. Specifically, the research results allow estimating an optimum size of the test objects for calibration of space scanners and parameters of defocusing for the star chambers of orientation sensors. [ABSTRACT FROM AUTHOR]

The paper considers the minimization of the forecasting variance error of stochastic autoregressive moving average process by separating it into two autoregressive processes. More precisely, two methods are developed: the first method - for AR parameters estimation based on the estimates of the ARMA parameters of the initial process, and the second one - for estimation of the process states utilized to make the forecasts. [ABSTRACT FROM AUTHOR]

The present study tackles the frequency error of RMS Voltage induced by the partial loss of the input signal spectrum because of the limitations in the amplitude-frequency characteristics of the conversion channel. We propose the estimation of such errors for typical signals and provide recommendations for their decrease. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the influence of the transformation error on inspection reliability. We illustrate that the results uncertainty and the character of erroneous decisions depend on parity additive and multiplicate components. In addition, we offer to normalize the limiting values of a probable error, as well as the limiting value of its components, for the measuring methods used in the inspection process. [ABSTRACT FROM AUTHOR]

Control system exposed to random external disturbance is considered. Control law structure containing inverse control object dynamic model and realizing disturbance estimation is established. Gross error prediction algorithm is suggested. Gross error prediction is assumed as a basis for adaptation algorithm that provides control system properties rebuilding under the external disturbance changes. Simulation data illustrated the adaptation algorithm efficiency for control system prescribed accuracy providing under random disturbance with unknown behaviour. [ABSTRACT FROM AUTHOR]