Comparison of different methods of evaluation of the effective energy of a combined X ray beam generated under different conditions enabled us to derive a formula for assessing the error of calculation of the effective ener gy of the combined X ray beam and its dependence on X ray tube anode voltage U a and thickness of filter made of a certain material.The following expression for the effective energy E ef was obtained:where h is Planck's constant; с is the speed of light in vac uum; е is electron charge; U a is anode voltage; d f is thick ness of filter made of material with mass photoelectric extinction coefficient τ m and density ρ; d is thickness of an additional layer of the same material; α and n are con stants incorporated in equations for the dependence of the mass photoelectric extinction coefficient τ m on radia tion energy E in each material [2]:Equation (2) was approximated from tabular values of mass photoelectric extinction coefficient τ mi , X ray energy quanta E i for aluminum (ρ = 2.700 g/cm 3 ), and reference value reported in [3]. The following values of the coeffi cients were obtained: α = 14970 cm 2 /(g⋅cm 3 ), n = 3.053.The thickness of the additional layer of the attenuat ing material was chosen to be d = 10 -3 cm, because pre liminary calculations revealed that such a layer caused insignificant changes of the effective energy E ef (less than 10 -2 keV). Therefore, the radiation passed through the fil ter of such thickness is virtually uniform.If U a is in kV, α is in cm 2 /(g⋅cm 3 ), ρ is in g/cm 3 , d and d f are in cm, then effective energy E ef in keV is calculated from the following equation:The results of preliminary calculations of E ef using Eq. (3) and computer software are sufficiently consistent with the GOST R IEC 61267 2001: Medical Diagnostic X Ray Apparatuses. Exposure Conditions During Testing [1].The results of calculations using Eq. (3) are given in Table 1.Let us estimate the error of calculations of effective energy E ef . In calculations from Eq. (3), the value E ef is determined indirectly from α and n. There is no statisti cally significant correlation between measured values of α and n. The mean square deviation σ(E ef ) of calculated value E ef can be calculated from:where σ(α) and σ(n) are mean square deviations of cor responding values.Determination of σ(α) and σ(n) should be preceded by calculations of α i and n i from: α i = τ mi ⋅E i n /(h⋅c) n ; n i = log (h⋅c/E i ) (τ mi /α).

The study divides the analysis of monitoring and diagnostic information, leaving for monitoring the parameters of the stationary process, and for diagnostics -various transient regimes in the technological process. This, in turn, divides the algorithms of information processing into control of the output from the given boundaries for stationary parameters and the classification and prediction for dynamically changing parameters in a multidimensional space. In view of the large number of monitoring and diagnostic information, as well as due to different algorithms for processing it in an appropriate information system, it is necessary to apply multi-dimensional analysis methods. As diagnostic influences, various jumplike changes of a "natural character" are used, and the state of the equipment allows judging the apparatus of the influence functions. The abrupt changes in the technological process are reflected in the change in its parameters. The reaction to them is weakened as they are removed in accordance with the influence functions. The values of the parameters at the moment of the reaction define a point in the multidimensional parameter space and allow one to relate the state to one or another standard, and to relate the corresponding management algorithm to the standard. The experimental model includes five links simulating the operations of the technological process, a pulsed signal source simulating a step change and five links of propagation delay simulating the duration of operations. The results confirmed theoretical conclusions about the influence functions.

The study is devoted to the theoretical justification of procedures and algorithms for managing the quality of products. The methods to control the abstract object are used. Since the object itself, for example, quality is a reflection from the material carrier: products and the production process, control and disturbing influences are attached to them. Control actions are divided into three types: parametric, structural and organizational. The first two types are associated with the flow of technological processes, and due to the application of managing organizational influences, the necessary external and internal conditions are achieved that increase the quality of products. It is shown that even a simple linear formulation allows us to pose and solve the optimal control problem and obtain practically important results.

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The study is devoted to the development of an algorithm for the optimal management of the volumes of orders for various building structures and their stock in the warehouse of a construction site. The state of the warehouse is described by a first-order differential equation, the functional is compiled using Prof. Letov's method of analytical construction of optimal regulators (ACOR), the solution is carried out by the Euler-Lagrange method. Based on previous studies of the optimal number of links in the construction team, the optimal dependences of the volumes of orders and stocks on the time of installation of the panel building have been obtained. As a result, it was found that all the dependencies show a monotonous tendency to zero as they approach the end of installation, increasing the intensity of installation increases the volume of orders and reduces the concavity of the stock schedule, increasing the contribution of order quantities in the functional increases both of these parameters.