The paper addresses the problem of modeling a smooth contour interpolating a point series belonging to a curve containing no special points, which represents the original curve with specified accuracy. The contour is formed within the area of possible location of the parts of the interpolated curve along which the curvature values are monotonously increased or decreased. The absolute interpolation error of the point series is estimated by the width of the area of possible location of the curve. As a result of assigning each intermediate point, the location of two new sections of the curve that lie within the area of the corresponding output section is obtained. When the interpolation error becomes less than the given value, the area of location of the curve is considered to be formed, and the resulting point series is interpolated by a contour that lies within the area. The possibility to shape the contours with arcs of circles specified by characteristics is investigated.

The problem of modelling a smooth contour with a regular change in curvature representing a monotone curve with specified accuracy is solved in this article. The contour was formed within the area of the possible location of a convex curve, which can interpolate a point series. The assumption that if a sequence of points can be interpolated by a monotone curve, then the reference curve on which these points have been assigned is monotone, provides the opportunity to implement the proposed approach to estimate the interpolation error of a point series of arbitrary configuration. The proposed methods for forming a convex regular contour by arcs of ellipses and B-spline ensure the interpolation of any point series in parts that can be interpolated by a monotone curve. At the same time, the deflection of the contour from the boundaries of the area of the possible location of the monotone curve can be controlled. The possibilities of the developed methods are tested while solving problems of the interpolation of a point series belonging to monotone curves. The problems are solved in the CAD system of SolidWorks with the use of software application created based on the methods developed in the research work.

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The paper provided describes a mathematical model of calibration process of fruit-stone culture seeds of cherry, sweet cherry, cherry-plum, apricot and almond using flat sieves with impact shock ball cleaners oscillating in the horizontal plane. It has been defined that the mathematical expectation of time of knocking out the fruit-stone from the sieve opening T ⌢ \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over T} is the minimum value of ratio of average time of complete ball motion cycle in space under sieve to the probability of knocking out the stone by a ball with the kinetic energy level of 2 Mj. The dependences of energy distribution density of ball on impact on the sieve have been obtained, based on which the intervals of ball cleaner parameters have been determined, i.e. the ball diameter D belongs to the interval 25–35 mm; the space height H under sorting sieve belongs to the interval 1.2D–1.4D mm; the value range for distance between rods t belongs to the interval 0.5D–0.7D mm. Using the method of golden section, the following parameters of ball cleaner were obtained: D = 33 mm, t = 23 mm, H = 40 mm. The parameters obtained provide mathematical expectation of time of knocking out the fruit-stone from the sieve opening T ⌢ \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over T} = 0.03 s. Consequently, the average ball velocity v ⌢ \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over v} is = 0.4 m∙s-1, and the average ball path is L ⌢ \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over L} = 0.006 m.

This article deals with the problem of harvesting combed straw by mixing it with the soil and the process of combed straw decomposition in particular. The idea and purpose of the research are also analysed in terms of circular economy, which represents a closed cycle. Combed straw is seen as a by-product which is reused as fertilizer to increase soil fertility, thus reducing the negative impact on the environment and increasing the efficiency of organic matter use. To analyse the qualitative aspect of the process, the introduction of an indicator is proposed—the straw decomposition coefficient. Experimental studies of straw decomposition in the soil were carried out using the mathematical theory of experimental design, where the response function is represented by the functional dependence of the straw decomposition coefficient on the length of its cutting and nitrogen and phosphorus application doses. For experimental studies, Box–Behnken design was used, which made it possible to calculate the regression coefficients by known formulas. Verification of the obtained coefficients according to Student’s t-test showed that all of them were significant. According to Fisher’s test, it was established that the model is adequate and can be used for further research. As determined by the experimental study, shredded straw incorporation improves soil properties and increases its biological activity. Ultimately, this improves plant nutrition and increases crop yields. The experiment results showed that reduced amounts of nitrogen and phosphorus fertilizers can be applied, thus leading to a reduction in the direct production costs of growing cereals in the following year. The integration of several technological processes, such as straw cutting, shredding, and incorporating it into the soil with simultaneous application of nitrogen and phosphorus fertilizers, increases the economic efficiency of grain production and a shortens the payback period for investment.