International Scientific Journals
of Scientific Technical Union of Mechanical Engineering "Industry 4.0"

This article explains a mathematically consistent approach for solving the equations of Timoshenko’s beam theory for statically loaded beams. Theoretic sections 3.4 – 3.5 give a good description of the shear deformation and the primary approach for calculating deflections of beams under bending, taking into account both causes for deflection: bending moment and shear force. Values for the shear correction factor are discussed in section 4. This work was started to check the validity of an equation for deflection of a symmetrically loaded short rectangular beam with span/height ratio = 3 under four-point bending with upper-span/span ratio = 1/3. The exact solution is not presented here, but we can confirm that the presented theory, when applied for the mentioned loading scheme, leads to thi s equation using a shear correction factor k = 5/6.

The paper is based on the representation of the fundamental solution of the linear elasticity theory of the mechanics of a deformable solid in the J. Dougall’s form through spatial harmonic functions. The axisymmetric problem of the elasticity theory in a cylindrical coordinate system for bodies bounded by a canonical surface is formulated. As a case, the boundary value problem of pure torsion is formulated and the elastic characteristics and structure of the corresponding external loads on the side surface of a given isotropic elastic body in the above-mentioned harmonic potentials are presented. This approach makes it possible to obtain and extend the set of exact analytical solutions of boundary value problems of the spatial elasticity theory and is the theoretical basis for calculating the strength parameters of mechanical systems.

Interpolation is one of widely used methods reconstructing the shape of a freeform surface from data points obtained by measurement. The geometrical accuracy of the resulting reconstructed surface is expressed as a range of normal deviations of the surface from the original shape and depends mainly on the density of the input data points. In the paper, a method to determine the g eometrical accuracy of the interpolation surface fitted through a set of definition points arranged in a structured quadrilateral mesh with a given density is described. Practical application of this method is demonstrated on the processing of experimental data mathematically generated from a known CAD model of suitably chosen freeform surface

The article deals with the problem of comparative analysis of the experimental results of using standard-free quality assessment measures depending on the type of distortion applied to the image. The previously developed measure based on the Weibullian model of the gradient magnitude and the entropy measures applied both to the original image and to the gradient characteristics of the ima ge are considered as No-Reference quality measures. Weibull distribution parameters are estimating using a set of image gradient magnitudes using the Sobel operator. A series of experiments was carried out on texture images from the well-known Brodatz texture database and the TID2013 database, which contains images distorted by various types. It was observed that texture images are in good agreement with the Weibullian model, which makes it possible to effectively apply the above-mentioned No-Reference measures and carry out a comparative analysis. The use of the TID2013 database with 3000 images, distorted by 24 types, each at five levels, makes it possible to evaluate additionally the effectiveness of the entropy approach to assessing image quality, comparing them with visual assessments also given in the database. Then it was illustrated that applying the entropy approach directly to the original image gives a worse result than applying image gradients to the magnitude. At the same time, a higher sensitivity to structural changes from the level and type of applied distortions is observed. The problem of the expediency of calculating the entropy using estimates of the parameters of the Weibull distribut ion instead of the histogram of the array of gradient magnitudes is investigated separately. The paper contains numerical and graphical materials illustrating the obtained results.

In this paper we will use different feature extraction approach in order to compare the stability of the Automatic Speech Recognition (ASR) on different SNR noise, in different situations. By using the classic feature extraction like: Mel filter Bank, Fast Fourier Transformation (FFT), Discrete Fourier Transformation (DFT). After we implement this methods for the different situations then we will warp the frequency of this methods directly on the spectrum in order to see if we get better results. The results will be compared with one another using the Word Error Rate algorithm (WER).

This paper is devoted to some up-to-date computational tools, which are on-line available and appropriate to remote learning as well as to scientific research implementation relevant to mathematics and their applications.
The following aspects are concerned and discussed: some of the opportunities and benefits afforded by the software tools which are taken into consideration; necessary requirements which have to be met in order to use these tools; some disadvantages and drawbacks which may arise.
Comparison of fees and prices for different mathematical software tools is done.
For purpose of illustration realistic examples are also given.

The article discusses the correlation properties of pseudo-random sequences (PRS) used in the formation of noise-like signals in code division coupled communication systems. The direct and inverse composite Walsh functions are considered. Comparative analysis of the correlation properties of the PRS is carried out in the Matlab medium. It is shown that the correlation properties of certain ensembles of composite Walsh functions are independent of the time shift. The possibility of using these signals in the development of systems with channels code separation in order to reduce the level of interference of multiple access is justified. Directions for further research have been determined.

Cyber-physical systems (CPS) integrate computing, networking and physical dynamics and are characterized by a high degree of heterogeneity and parallelism, with high dimensionality and complexity, including a variety of decision-making capabilities and control logic. Modeling and simulation of cyber-physical systems are considered important stages in the design, development and operation of CPS and their components. The main aim of the paper is to describe and analyze the evolution of agent based approach in the field of CPS and to define the basic requirements to the agent based systems regarding CPS. Based on O-MaSE methodology a software process model for agent based development of CPS is proposed. The approach includes the creation of 10 models reflecting various aspects and functionality of the CPS. The suggested approach is analyzed in terms of meeting the basic requirements for agent-based systems, imposed by the peculiarities of cyber-physical systems and fundamental requirements for their introducing, such as flexibility/changeability, reliability, reconfigurability, adaptability/agility and dependability.

In this study, the convergence behavior of the ξ approximants transform given as determined by () functions for the exponential operators is investigated on the entire complex plain. An algorithm is developed to observe how to transform a initial region on the complex plane defined by ξ approximants.

The electron beam technological processes like electron beam welding, electron beam additive technologies, etc. depend strongly on the characteristics of the electron beam, generated by the electron gun. In this work the estimation of the 3D radial current density distribution using training, testing and validation of different artificial neural networks is considered. The model estimation is based on experimental measurements of the electron beam current distribution in three cross-sections of the beam at different distances from the magnetic lens of the electron gun. The estimated neural models with different structures are compared. Graphical user interface for the evaluation of the radial electron beam distribution in any cross-sections of the beam is developed.

The problem of convective stability in a medium containing settling heavy solid particles are discussed. A study is made of the stability of steady convective flow of a medium containing an additive between vertical plates heated to different temperatures. It is shown that the presence of settling solid particles has a significant stabilizing effect on convective stability.

This article discusses the problems of teaching non-standard tasks at school. Currently, one of the main tasks of secondary schools is to identify creative thinking abilities of students and solve problems of their development. The report was identified as the main tool for developing students ‘ mental and thinking abilities. Problem solving is the most productive form of learning mathematics, and this process should be a necessary component of all extracurricular activities conducted in mathematics. Problems at the mathematical Olympiad are non-standard problems. Olympic tasks will usually help you learn a lot, find independent non-standard methods of solving problems. The high school curriculum provides for the use of the definition of inequality, proving using known inequalities, using the relationship between the arithmetic mean and geometric mean of positive numbers, and proving them using methods other than reverse-trip methods