The problems of continuous motion of a cylindrical body with a displaced center of mass along vibrating horizontal and inclined surfaces are considered.
The analytical solutions of the motion equations were obtained by the method of partial discretization of nonlinear differential equations [1] and graphs of changes in the rotation angles of a cylindrical body were constructed for various cases.
In this paper we introduce, analyze and apply persistent homology, one of the main algorithms of TDA, on some real data sets from the bio-medical field. Topological data analysis (TDA) is a field which is a synergy between mathematics, data science and computer science. The main goal of TDA is studying the shape of data using topological techniques. TDA proposes new algorithms that deal with these problems based on tools or concepts from algebraic topology and pure mathematics. We analyze the results and give a topological characterization of the dataset and propose to use them in future work.
A multiparameter metamodel of the eddy current probe with the volumetric excitation structure is constructed. As variable parameters of the metamodel, the spatial coordinates of the testing zone, the radii of the excitation coils and the height of their location above the testing object were used. Due to the use of hybrid construction of multiple neural networks using decomposition of the search space, an acceptable metamodel’s error of the eddy current probe with volumetric excitation structure is obtained.
The codes for error control (error-detecting and error-correcting codes) are extremely important part of the communication systems and storage devices, ensuring reliable data transmission and storage. In this paper using simulations, we analyze an error-detecting code. More specifically, we will be focused on the error-detecting capability of the code. Namely, using simulations we will obtain the number of errors that the code detects for sure, as an important parameter of every error-detecting code.
A model for calculating the permeability of two-layer powder filter materials (PFMs) is proposed taking into account the overlap area. Examples of calculating the permeability of PFMs on real powder structures are given.
The main disadvantages of transplanting machine are presented in the article and the mathematical modeling of the operating system of the carousel type transplanting machine with a new method of calculation of the design parameters of the system is proposed. As a result of theoretical research of the operating system of carousel type transplanting machine the rule of motion of the point F and the mathematical model for determining initial velocity V0 of the falling seedling have been obtained.
In modern industry self-powered devices are an important component. For such devices, the most important component is the energy storage device used, most often based on lithium-ion technology. The article presents an equivalent circuits of lithium-ion batteries and a mathematical description of charge-discharge processes. Investigated in Matlab / SimPowerSystems built-in library component of lithium-ion battery. Mathematical models of equivalent circuits of different types of lithium-ionic batteries have been analyzed.