In the paper the mathematical models describing connection between two time series are researched. At first each of them is investigated separately, and the ARIMA(p, d, q) model is constructed. These models are based on the time series characteristics obtained during the analysis stage. The connection between two time series is confirmed with the aid of cointegration statistical tests. Then the mathematical model of the connection between series is constructed. The ADL(p, q) model describes this dependence. It’s shown that for the time series under investigation the orders p, q of the ADL(p, q) model are connected with the ARIMA(p, d, q) orders of the  describing each series separately. This step makes the set of the investigated ADL(p, q) models much smaller. In the previous papers it was also shown that the ARIMA(p, d, q) automatical fitting functions in popular packages use limitations on the p, q orders of the time series process: q ≤ 5, p ≤ 5. The wish to use the simplest models is also built in the structure of the Akaike (AIC) and Bayes (BIC) informational criteria. In the paper the maximal values of the ADL(p, q) model orders are supposed to be the orders of the appropriate ARIMA(p, d, q) series. In the previous work it was shown that using high order ARIMA(p, d, q) it is possible to fit the models better. In this paper the experiments on the ADL(p, q) models construction are presented. The wage index and money income index time series pair is researched, and also the gas, water and energy production and consumption index/real agricultural production index pair is investigated. The data in the 2000–2018 time period is taken from the dynamic series of macroeconomic statistics of the Russian Federation.

This article discusses the issues of ensuring the effectiveness of monitoring for correct estimates of parameter manifestations (start time, intensity and severity) of catastrophic natural (earthquakes, floods and others) and man-made (water and air pollution) processes. Organizational structure of monitoring with reasonable time and address of the measurement mode taking into account the main features and stages of forming controlled natural and technogenic processes should ensure the acquisition of data needed for further calculations of the start time of earthquakes, territorial distribution and levels of water or air pollution, etc. Besides, the article outlines requirements for the relevant qualification of engaged staff capable of correctly interpreting the results of monitoring measurements and performing the necessary calculation of numerous parameters, for example, in the case of pollution evaluation. As a result, all this allows to ensure the compliance of obtained assessments with the real condition of monitored object, which is the basis for informed decisions on a set of actions to further ensure technosphere security. Along with this, the proposed monitoring approach allows to optimize the measuring base in order to achieve the necessary efficiency in assessing the status of controlled objects and the layout of the base in terms of the characteristics of buildings and their intrinsic properties, as well as the specificity of technogenic impact and natural processes on technosphere objects.

This article discusses the application of complex methods for detecting, recognizing, distinguishing borders and measuring various parameters of noisy, low-contrast, difficult-to-see images of space, air or ground objects. The problem of detecting, recognizing, distinguishing and measuring parameters of objects images (space or air objects, aircraft, ship, ground transport, people, coasts, etc.) is still among the very complex, completely unsolved radio engineering and telecommunications (“connected”) tasks. Currently, infrared (IR) direction finding, optical (laser location) direction finding and radar are used to detect, recognize, distinguish boundaries and measure the parameters of unknown objects against the background of external natural or artificial interference and noise. These methods have their own advantages and disadvantages, which do not always coincide. Therefore, it is of theoretical and practical interest to use them jointly, multifunctionally, or integrationally to identify objects against the background of external natural or deliberate interference and noise. When applying multifunctional methods for detecting, recognizing, distinguishing borders and measuring parameters of noisy, low-contrast images of objects against the background of external natural or artificial interference and noise. Digital processing of objects is mainly used now, which can be defined as a process during which an image is: modified to obtain a new one, which will be more convenient for research by a computer, or by the human eye; it is transformed into a certain set of characteristics and parameters visible and related to the observation area that are automatically analyzed by the computer, or directly presented to a person, taking into account pre-established criteria for developing a final conclusion about the studied object. Typically, the result of digital processing of the received signals is a new image that can be easily converted to analog form and directly observed on a computer display.

Prototype filters have wide usage for the design of filters with required quality indexes (QI) of gain-frequency response (GFR). The designed filter is obtained from a prototype filter b means of frequency transformation, which preserves these QI. But most of employed frequency transformations result in variations of QI of phase-frequency response (PFR). In this paper we proposed to use prototype filters that are Pareto-optimal for QI of GFR and PFR. Transfer functions of these filters may be found by means of heuristic optimization algorithms. This method will be efficient if the frequency transformation preserves the optimality of filters. It was shown that frequency transformation has this feature if it preserves the result of QI comparison (more or less) for filters with equal orders. Compliance of this criterion was checked for bilinear transformation of analog low pass filters (LPF) into digital LPF and for Konstantinidis transformation of digital LPF into other digital LPF. The analysis showed that Pareto-optimality for QI of GFR and PFR is preserved if the delay-frequency characteristic of the filter has a minimum at zero frequency and has a maximum at the upper boundary of the pass band. These conditions are complied for LPF with sufficiently small unevenness of GFR in the pass band and sufficiently fast decline of GFR at higher frequencies. Examples confirming these conclusions are given.

This paper discusses the effect of the distribution of the granules size in nanocomposites on physical properties within the framework of the quasi-classical size effect. Methods of effective medium for describing nanocomposites are discussed. This paper also notes and discusses the contribution of various mechanisms that affect the optical and magneto-optical properties of such structures, especially in the IR region of the spectrum, where the quasi-classical dimensional effect is most pronounced. The Droude-Lorentz mode describes the contribution of the dimensional effect to the diagonal and non-diagonal components of the effective medium's permittivity tensor. The lognormal distribution of the granule size characteristic of many nanostructures is considered. Based on this approach, the dependences of the standard deviation on the value of the integral as a function of the average size of the granules were obtained. Based on the normalization condition, the numerical value of the standard deviation of the r values and the average particle size were analytically determined. This paper also discusses the fundamental significance of the results obtained – the possibility of applying this approach to all possible distributions. The found value of the average size of nanocomposite granules makes it possible to model various properties of nanocomposite structures, first of all, optical and magneto-optical properties, with the help of known methods within the framework of the effective medium approximation. This is especially important for describing the percolation transition in nanocomposites. The problem being solved is important and relevant, since many interesting and important effects are realized in such magnetic nanocomposites, such as the magneto-optical Kerr effect, the anomalous Hall effect, the giant magnetoresistance, and many others. The results obtained allow us to better describe materials that are widely used in modern electronics and nanoelectronics.

The study aims to assess the impact of violation of the assumption about normality of the investment portfolio returns on its risk measures. The article is focused on the Value at Risk (VaR) metric required by major regulatory authorities for bank risk assessment. Using historical share prices of several Russian companies it is shown that the assumption about returns normality is not supported by statistical tests. It is also shown that the empirical distribution of the assets returns is described by Johnson’s distribution. The Kolmogorov-Smirnov test supports the obtained results. The tests proposed by the authors allow estimating the loss in accuracy in parameters calibration of the autoregressive model, obtained by using the maximum likelihood method when the asset returns have non-gaussian distribution. It was found that the loss in the accuracy lies in the range [22%, 26%] for absolute returns and in the range [33%, 38%] for relative returns depending on the autoregression parameter which varies in the range [–0.9, 0.9]. The error of ten-day VaR estimation was calculated for 1% (99%) and 5% (95%) significance levels. At a significance level of 5% (95%) the VaR metric obtained under the assumption that the asset returns have normal distribution is lower than the true value by 7% (6%) for absolute returns and 4% (13%) for relative returns, which indicates strong underestimation of the portfolio risk. At a significance level of 1% the metric is conservative exceeding the true value by 12.5%.

This article is devoted to mathematical models of thermal shock in terms of dynamic thermoelasticity and their application to the specific conditions of intensive heating and cooling of solids. A scheme is proposed for deriving the compatibility equation in voltages for dynamic problems, which generalizes the well-known Beltrami-Mitchell relation for quasistatic cases. The proposed relation can be used to consider numerous special cases in the theory of thermal shock in Cartesian coordinates for both bounded canonical bodies and partially bounded ones. As a detailed study, the latter case was considered under conditions of abrupt temperature heating and cooling, thermal heating and cooling, and medium heating and cooling. Numerical experiments were carried out, and the wave nature of the propagation of thermoelastic waves was described. The effect of relaxation of the solid boundary on sudden heating and sudden cooling, which has been little studied in thermomechanics, is described. It is established that this effect influences maximum of internal temperature stresses, which depend on the parameters characterizing the elastic and thermal properties of materials, as well as the heating time and cooling time. A “compatibility equation” in displacements was proposed to study the problem of thermal shock in cylindrical and spherical coordinate systems in bodies with a radial heat flow and central symmetry. The formulation of a generalized problem in the theory of thermal shock is formulated, which is of practical and theoretical interests for many areas of science and technology.

The article analyzes the modern concept of responsible design, its components and main provisions. The main components of responsible design are the systems of universal and unpleasant design, the history of the origin and development of these components, as well as their modern extended understanding. The basic principles and areas of application of universal and unpleasant design are given. Features of formation of responsible approach to design as a basis of world view of future designers as exemplified by training students specializing in "Design" and "Technology for the decorative processing of materials", both at the level of bachelors and at the level of masters are shown. A set of knowledge, skills abilities necessary for the designer to understand the concept of responsible design ensure such a design process is determined. The arising problems are considered, and the approaches to their solution on the basis of modern competence approach are offered. The authors formulated tasks and exercises that help the teacher to form the responsibility of the designer, as well as test questions and topics of tasks, up to the final state certification, allowing to check and consolidate the understanding and application of the concept of responsible design. Examples of developments made by students using the concept of responsible design are given.