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The article discusses methods for accelerating the operation of convolutional neural networks for autonomous robotics learning. The analysis of the theoretical possibility of modifying the neural network learning mechanism is carried out. Classic semiotic analysis and the theory of neural networks is proposed to union. An assumption is made about the possibility of using the symmetry mechanism to accelerate the training of convolutional neural networks. A multilayer neural network to represent how space is an attempt has been made. The conclusion was based on the laws on the plane obtained earlier. The derivation of formulas turned out to be impossible due to the problems of modern mathematics. A new approach is proposed, which involves combining the gradient descent algorithm and the stochastic completion of convolutional filters by the principles of symmetries. The identified algorithms allow increasing the learning rate from 5% to 15%, depending on the problem that the neural network solves.

The geometric model accuracy is crucial for product design. More complex surfaces are represented by the approximation methods. On the contrary, the approximation methods reduce the design quality. A new alternative calculation method is proposed. The new method can calculate both conical sections and more complex curves. The researcher is able to get an analytical solution and not a sequence of points with the destruction of the object semantics. The new method is based on permutation and other symmetries and should have an origin in the internal properties of the space. The classical method consists of finding transformation parameters for symmetrical conic profiles, however a new procedure for parameters of linear transformations determination was acquired by another method. The main steps of the new method are theoretically presented in the paper. Since a double result is obtained in most stages, the new calculation method is easy to verify. Geometric modeling in the AutoCAD environment is shown briefly. The new calculation method can be used for most complex curves and linear transformations. Theoretical and practical researches are required additionally.

This paper presents the technology of production of synthetic fibrous materials from PET-row by vertical blowing method. The formation of fibers from the melt of thermoplastics by vertical blowing method is accompanied by complex and specific phenomena, so creation of new progressive technologies, high-performance machines and units for producing such materials is impossible without process modeling, which can significantly reduce the number of natural tests, cost and development time and choose optimal operating modes. The motion of the molten material in the melting unit of the hydrostatic type is determined from the Poiseuille formula. Also in the article proved that the greatest impact on process productivity is made by the melting unit, exactly by outlet radius and the pressure change of compressed air, acting on the molten material surface. The increase in the height of the molten material column in the main cylindrical chamber of melting unit also leads to increase of process productivity.