RESULTS OF STATIC TESTS OF PROTECTIVE STRUCTURES OF AGRICULTURAL TRACTORS CABINS

The purpose of research is determination of cabin deformation indicators using standardized methods and developed technical means. Research methods. The tests were performed according to the methods described in [DSTU ISO 5700, 2019] using a loading bench, pressure and displacement sensors, digital measuring amplifier Spider 8 and laptop Panasonic CF-19 Touchbook, model: CF-19KHR88PE. Research results. The protective structure AI.209.45.011.00 of the cab of tractors type C25 "Slobozhanets" was provided for testing. Before the tests, the dimensions of the cab structure were measured and recorded. During the first longitudinal loading from front to right, the load was applied to the upper transverse element of the protective structure. The point of application of the load was at a distance of 260 mm from the outer corner of the edge of the protective structure. An even load distribution in the direction perpendicular to the direction of action and along the loading beam was ensured using a sealing element. The value of the energy absorbed by the protective structure was 13100 J (required energy - 12586 J) with a maximum applied force of 82 kN and a displacement of 340 mm. During the first and second compression tests, the structure was loaded vertically with a force of 180 kN along the front and rear upper transverse elements of the protective structure with a holding of the specified force for 5 s. The side load was applied horizontally to the upper right longitudinal element of the protective structure at a distance of 85 mm forward from the control point of the driver's seat. The length of the loading beam was 600 mm. The value of the energy absorbed by the protective structure of 17000 J (required energy - 15732 J) at a maximum applied force of 80 kN and a displacement of 290 mm was achieved. After all test stages, the frontmost point of the protective structure was 70 mm and the front left point was 35 mm. The rear end points were also shifted backwards by 45 mm - right and 30 mm - left. In the lateral direction, the front right extreme point moved forward by 15 mm. After the tests, the free space area was not violated. Conclusions. The methods and technical means used during the tests allow determine the magnitude of the applied forces and deformation with the necessary accuracy and reliability. During the compression tests, the values of the test force (180 kN) were achieved, and during the application of horizontal loads - the energy absorbed by the protective structure (13100 J - longitudinal load and 17000 J - lateral load). The greatest final deformation was suffered by the protective structure at the front extreme point - 70 mm, while the violation of the zone of free space of the driver by the elements of the protective structure is not observed. Therefore, the protective structure AI.209.45.011.00 cab of tractors type C25 "Slobozhanets" withstood static tests for compliance with DSTU ISO 5700.

STUDY OF VOLTAGE MODE IN THE LONG-DISTANCE AC TRANSMISSION LINE

The charging currents of EHV transmission lines cause the Ferranti effect, which causes an increase in voltage at intermediate points transmission line. The work aims to study the laws of the voltage distribution along the line route and to develop a method for determining the coordinates of a point with extreme voltage. Methodology. Mathematical modeling of long-distance transmission lines in Wolfram Mathematica allowed to form the laws of the voltage distribution along the line and determine the coordinate of the extreme point on the voltage. Results. It is shown that the application of the traditional model of idealized power transmission causes high modeling accuracy only in the modes of unloaded line and low loads. In the range of medium and high loads, the simulation error reaches unacceptably large values. The paper proposes more accurate models for determining the coordinate of an extreme voltage point: linearized and second- and third-order models. It is shown that the proposed models are characterized by higher accuracy in a wide range of loads. Increasing the degree of the model results in higher accuracy, but is associated with an increase in the cumbersomeness of the mathematical model. It is shown that first and second-order models provide sufficient accuracy for typical designs of 750 kV power transmission lines. It is shown that neglecting the losses on the corona has almost no effect on the accuracy of calculating the coordinates of the extreme point on the voltage, which simplifies the linear calculation model and models of the second and third-order. Originality. Mathematical models of the first, second and third orders have been developed for high-precision determination of the coordinate of a voltage-extreme point along a long-distance transmission line. Practical significance. The offered mathematical models are intended for application in problems of regulation and adjustment of parameters of flexible power transmissions. Ref. 12, figure, tables 4.

Review of the genus Lemaireia Nässig & Holloway, 1988 from China, with description of a new species (Lepidoptera: Saturniidae)

A new species of the genus Lemaireia Nässig & Holloway, 1988 (Lepidoptera: Saturniidae: Saturniinae: Saturniini), L. daparo sp. n., is described from evergreen broad-leaf forests in Panzhihua (Sichuan), Qujing (Yunnan) and Dali (Yunnan) of China. The new species resembles L. luteopeplus aureopeplus Nässig & Holloway, 1988 and L. hainana Nässig & Wang, 2006 from China, but can be easily separated from them by the male genitalia. In addition, the genus Lemaireia is reported here for the first time from Sichuan Province, and now its distribution range reached the northeastern extreme point. The habitus, diagnostic characters and distribution map of the three species of the genus Lemaireia from China are provided. A list of all Lemaireia species presently known worldwide is also given.

Non-extreme-Points Approach to Extreme Points of Integral Families of Analytic Functions

Non extreme points of compact, convex integral families of analytic functions are investigated. Knowledge about extreme points provides a valuable tool in the optimization of linear extremal problems. The functions studied are determined by a 2-parameter collection of kernel functions integrated against measures on the torus. Families from classical geometric function theory such as the closed convex hull of the derivatives of normalized close-to-convex functions, the ratio of starlike functions of different orders, as well as many others are included. However for these families of analytic functions, identifying “all” the extreme points remains a difficult challenge except in some special cases. Aharonov and Friedland [1] identified a band of points on the unit circle which corresponds to the set of extreme points for these 2-parameter collections of kernel functions. Later this band of extreme points was further extended by introducing a new technique by Dow and Wilken [3]. On the other hand, a technique to identify a non extreme point was not investigated much in the past probably because identifying non extreme points does not directly help solving the optimization of linear extremal problems. So far only one point on the unit circle has beenidentified which corresponds to a non extreme point for a 2-parameter collections of kernel functions. This leaves a big gap between the band of extreme points and one non extreme point. The author believes it is worth developing some techniques, and identifying non extreme points will shed a new light in the exact determination of the extreme points. The ultimate goal is to identify the point on the unit circle that separates the band of extreme points from non extreme points. The main result introduces a new class of non extreme points.

EXTREME POINT METHODS IN THE STUDY OF ISOMETRIES ON CERTAIN NONCOMMUTATIVE SPACES

In this paper, we characterize surjective isometries on certain classes of noncommutative spaces associated with semi-finite von Neumann algebras: the Lorentz spaces $L^{w,1}$ , as well as the spaces $L^1+L^\infty$ and $L^1\cap L^\infty$ . The technique used in all three cases relies on characterizations of the extreme points of the unit balls of these spaces. Of particular interest is that the representations of isometries obtained in this paper are global representations.

Perfect 3D-curve RMDPL-IPOs& Bresenham’s 3D-Curve Algorithm (Part 2 & 3)

<div>The paper presents three new 26-connected constant feedrate incremental step algorithms that can be used in practical situations in CNC machining tools. The 1st, the perfect 3D line IPO is 100% incremental, the word "perfect" means that the accuracy can be much better than the accuracy of Bresenham's 3D line (e.g. accuracy can be 37% worse). The simplified state diagram computes one perfect major axis points and possibly a perfect non-major axis point. The selection criterion uses the real 3D distance to the line. The 2nd, the perfect 3D curve IPO is a QSIC-algorithm (intersection of two quadrics). The selection criterion uses the "Relative Curve Measurement Theorem" extended to quadrics and QSICs. The consequences of this theorem are crucial, it means that one must not calculate the time-consuming distance to the 3D curve, but it suffices to calculate the RMDPL or the relative minimal distance of two candidate points to the polar line of the QSIC with respect to the midpoint of the candidate points. As the midpoints are close to the curve, the polar lines enclose and inclose the curve. Theoretical, the RMDPL is fundamental, it is the core of all the successful 2D incremental step algorithms and the paper proves that it is the core of the 3D incremental step algorithms or the 3D reference pulse IPOs. Thanks to the RMDPL, the paper represents QSICs in a unique way comparable with 3D-lines. The 3rd, Bresenham's imperfect 3D curve IPO is less accurate but super-fast and can be used in many practical situations as the maximum error (MaxErr) is bounded to 0.707. The curve algorithms can have singular points, but that problem is simple solved. Each curve is a sub-segment of a monotonic curve from the starting extreme point to the ending extreme point. All the extreme points and the singular points are offline precomputed as the intersection points of three quadrics. The constant feedrate of sampled-data curves is clear when the arc length is known, but the real time calculation of the arc length of incremental step curves was until now an open problem. The former paper used the super-fast PRM-cs algorithm for 3D-lines and 2D curves and the same constant feedrate algorithm (actually, a real time length algorithm) can be used even in integer form. The implementation of the constant feedrate algorithm to a 26-connected curve with high accuracy turns out to be piece of cake in contrast to the sampled-data curves. All IPOs can be converted to constant feedrate listSIM-IPOs which can be used in real time in rigid simplified CNC machine tools.</div>

Perfect 3D-curve RMDPL-IPOs& Bresenham’s 3D-Curve Algorithm (Part 2 & 3)

<div>The paper presents three new 26-connected constant feedrate incremental step algorithms that can be used in practical situations in CNC machining tools. The 1st, the perfect 3D line IPO is 100% incremental, the word "perfect" means that the accuracy can be much better than the accuracy of Bresenham's 3D line (e.g. accuracy can be 37% worse). The simplified state diagram computes one perfect major axis points and possibly a perfect non-major axis point. The selection criterion uses the real 3D distance to the line. The 2nd, the perfect 3D curve IPO is a QSIC-algorithm (intersection of two quadrics). The selection criterion uses the "Relative Curve Measurement Theorem" extended to quadrics and QSICs. The consequences of this theorem are crucial, it means that one must not calculate the time-consuming distance to the 3D curve, but it suffices to calculate the RMDPL or the relative minimal distance of two candidate points to the polar line of the QSIC with respect to the midpoint of the candidate points. As the midpoints are close to the curve, the polar lines enclose and inclose the curve. Theoretical, the RMDPL is fundamental, it is the core of all the successful 2D incremental step algorithms and the paper proves that it is the core of the 3D incremental step algorithms or the 3D reference pulse IPOs. Thanks to the RMDPL, the paper represents QSICs in a unique way comparable with 3D-lines. The 3rd, Bresenham's imperfect 3D curve IPO is less accurate but super-fast and can be used in many practical situations as the maximum error (MaxErr) is bounded to 0.707. The curve algorithms can have singular points, but that problem is simple solved. Each curve is a sub-segment of a monotonic curve from the starting extreme point to the ending extreme point. All the extreme points and the singular points are offline precomputed as the intersection points of three quadrics. The constant feedrate of sampled-data curves is clear when the arc length is known, but the real time calculation of the arc length of incremental step curves was until now an open problem. The former paper used the super-fast PRM-cs algorithm for 3D-lines and 2D curves and the same constant feedrate algorithm (actually, a real time length algorithm) can be used even in integer form. The implementation of the constant feedrate algorithm to a 26-connected curve with high accuracy turns out to be piece of cake in contrast to the sampled-data curves. All IPOs can be converted to constant feedrate listSIM-IPOs which can be used in real time in rigid simplified CNC machine tools.</div>

Extreme points of ${\mathcal L}_s(^2l_{\infty})$ and ${\mathcal P}(^2l_{\infty})$

For $n\geq 2,$ we show that every extreme point of the unit ball of ${\mathcal L}_s(^2l_{\infty}^n)$ is extreme in ${\mathcal L}_s(^2l_{\infty}^{n+1})$, which answers the question in [Period. Math. Hungar. 2018, 77 (2), 274-290]. As a corollary we show that every extreme point of the unit ball of ${\mathcal L}_s(^2l_{\infty}^n)$ is extreme in ${\mathcal L}_s(^2l_{\infty})$. We also show that every extreme point of the unit ball of ${\mathcal P}(^2l_{\infty}^2)$ is extreme in ${\mathcal P}(^2l_{\infty}^n).$ As a corollary we show that every extreme point of the unit ball of ${\mathcal P}(^2l_{\infty}^2)$ is extreme in ${\mathcal P}(^2l_{\infty})$.

Extreme-Point Symmetric Mode Decomposition to Define the Turbulence Characteristics of a Flume Flow

Turbulence is a key feature of solid-liquid two-phase flows, and the pulsating velocity is the basis for calculating turbulence characteristics. In general, the method of mathematical expectation is used to calculate pulsating velocity. However, this method does not reflect the fluctuating state of the instantaneous velocity. Therefore, the method of extreme-point symmetric mode decomposition (ESMD) is adopted to calculate pulsating velocity and turbulence characteristics. The ESMD involves two stages, namely, modal decomposition and time-frequency analysis. The optimal adaptive global mean (AGM), which is the result of modal decomposition, can accurately reflect the fluctuation state of the instantaneous velocity, and the theory of the pulsating velocity defined on this basis is reasonable. Moreover, the flow pattern and turbulence behaviour of a two-phase flow can be predicted using the calculated turbulence characteristics. The method is used to analyse the pulsating velocity of the flume, and its rationality in theoretically predicting the turbulence behaviour of flume flows is demonstrated.

Fault Diagnosis of Axial Piston Pump Based on Extreme-Point Symmetric Mode Decomposition and Random Forests

Aiming at fault diagnosis of axial piston pumps, a new fusion method based on the extreme-point symmetric mode decomposition method (ESMD) and random forests (RFs) was proposed. Firstly, the vibration signal of the axial piston pump was decomposed by ESMD to get several intrinsic mode functions (IMFs) and an adaptive global mean curve (AGMC) on the local side. Secondly, the total energy was selected as the data of feature extraction by analyzing the whole oscillation intensity of the signal. Thirdly, the data were preprocessed and the labels were set, and then, they were adopted as the training and testing set of machine learning samples. Lastly, the RFs model was created based on machine learning service (MLS) to diagnose the faults of the axial piston pump on the cloud. Using the test and verifying the data set for comparative testing, the fault diagnosis precision rates of the model are above 90.6%, the recall rates are more than 90.9%, the F1 score is higher than 90.7%, and the accuracy rate of this model reached 97.14%. A benchmark data simulation of mechanical transmission systems and an experimental data investigation of an axial piston pump are performed to manifest the superiority of the present method by comparing with classification and regression trees (CART) and support vector machine (SVM).