• Four-point bending of thin or thick beams

    pg(s) 43-46

    A paper recently published explains the differential equations for deflection of beams under bending, including the deflection due to transversal force [1]. The present article contains derivation of the main equations, according to the mentioned approach, for deformations of a simply supported beam that is symmetrically loaded with two forces, also known as four-point bending. These deformations are rotation and deflection of the neutral line due to bending moment and transversal force. For thick beams, deflection due to the transverse force is more than 1% from deflection caused by the bending moment. Special attention was paid to the third-point loading test. The presented model is applicable for calculating deflection due to bending moment and transverse force for both thin and thick beams.

  • A General 2-D CFD Code Development and Verification in Python

    pg(s) 36-42

    The technological progress in computer technologies gave rise to new possibilities and progresses for numerical and iterative methods. As being one of the computational studies, computational fluid dynamics is highly related to today’s advances. There are various types of methods and algorithms developed to model complex phenomena of fluid flow. In this study, we will introduce a new, still in development stage, CFD code with a pre-processor and a solver. Our research is focused on developing and studying a CFD code for mainly internal flows. Laminar and turbulent 2-dimensional flows can be analyzed using the software. The code is equipped with a graphical user interface (GUI) to make it simple to use. The GUI has the all-necessary components to define and analyze a fluid flow problem. We used an open-source post processor in order to visualize flow data and linked it to GUI, so the resulting software is a complete CFD package. The entire software is written using Python which has an easy code structure and rich code libraries. In order to decrease the time for convergence, code is modified with Numba and Cython libraries. To confirm accuracy of the solver, various basic test cases from the literature such as backward facing step flow, impinging jet flow, flow across a square cylinder, lid driven cavity flow are tested for both laminar and turbulent flows and the results was described in detail.

  • Special cases in determining the critical buckling load of Euler elastic columns

    pg(s) 33-35

    The Energy method is widely applied to determine the critical loads in elastic systems. A widely used variant of the method applies the Rayleigh-Ritz approach where the approximation of the buckling mode of the column is a function that satisfies the boundary conditions. A numerical example of a two-storey column is considered. An important aspect in the problem is the solution the complex integrals that emerge during the solution process. That problem could be overcome by the use of math software. The investigated column is hinged at its both ends and has an additional lateral support in the middle. It is loaded with a compressive distributed load alongside its length.

  • Some aspects of remote exams

    pg(s) 29-32

    The paper is devoted to distance exams, as in that the focus is on mathematical disciplines. Some advantages are standing out, as well as significant disadvantages have been discussed. Current modern tools are considered, which are applied both in the preparation of students and in distance exams.

  • Modeling of functional dependences by hermitian splines with exponential-power expression in links

    pg(s) 3-5

    The definitions of Hermitian splines with nonlinear expressions in the links are given. Formulas for the parameters of Hermitian splines with exponential-power links with four parameters are derived. The definition of the balance approximation of functions by splines is given. The formula for the balance approximation error for Hermitian splines with four parameters are obtained. The error of approximation of functions by polynomial Hermitian splines is compared with the error of approximation of functions by Hermitian splines with exponential-power expressions in the links

  • Consistent Presentation of the Beam Deflection Theory Including Shear Correction

    pg(s) 120-123

    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.

  • Formulation of axisymmetric boundary value problems of the linear theory of elasticity for canonical bodies in harmonic potentials

    pg(s) 116-119

    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.

  • Influence of data points density on geometrical accuracy of interpolation surface

    pg(s) 86-89

    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

  • Study of the model for estimating the degree of influence of distortion on image quality with the application of an entropic measure

    pg(s) 83-85

    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.

  • An approach of Feature Techniques using Warped frequencies

    pg(s) 52-54

    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).

  • Mathematical software tools applicable to remote learning and scientific research in case of isolation

    pg(s) 8-12

    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.

  • Analysis of the correlation properties of direct and inverse composite Walsh functions

    pg(s) 3-7

    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.