Mathematical Modeling
Vol. 5 (2021), Issue 3

Table of Contents

  • THEORETICAL FOUNDATIONS AND SPECIFICITY OF MATHEMATICAL MODELLING

    • 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.

    • 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

  • MATHEMATICAL MODELLING OF TECHNOLOGICAL PROCESSES AND SYSTEMS

    • Temperature field in a layered plate with local heating

      pg(s) 90-94

      In this paper, analytical expressions are obtained for determining the temperature distribution in a two-layer medium with local heating concentrated on the interface surface of the layers for a stable and linearly variable relative to the temperature of the thermal conductivity coefficient of the materials of the layers. Numerical calculations are given, and on this basis, the curves of temperature distribution as a function of spatial coordinates were constructed, which make it possible to
      analyze the temperature regimes in a two-layer plate.

    • Modeling transient signals in power lines

      pg(s) 95-98

      Modeling in PSCAD / EMTDS of traveling waves in a single-wire power transmission line is considered. Traveling waves of the terrestrial mode are generated at the beginning and in the middle of the line in different ways. The effects of dispersion, w hich lead to the dependence of the recording time of a traveling wave on the value of the registration threshold and on the distance traveled, are considered. The term of instantaneous and average speed is introduced. The values of the instantaneous speed with multiple runs of the line length drop to 250 m / μs. The average speed of a traveling wave with a single run of the line decreases by 4-6% relative to the speed of light for real thresholds of signal registration.

    • Investigation of bending strength and modulus of elasticity of a new type of black locust plywood for construction

      pg(s) 101-103

      The mechanical properties bending strength and modulus of elasticity in bending of a new type plywood for construction, based on black locust wood, have been investigated in relationship with the bonding technological factors. The experimental investigation is based on an optimal composite design with four control factors – temperature, pressure, bonding duration and specific glue consumption. Regression models describing the dependence of bending strength and modulus of elasticity in bending on the investigated technological bonding parameters are estimated. The obtained experimental and model-based results are analysed and discussed

    • Modelling uncertainty in multisensory systems at conflict measurements with dempstershafer combinatorial rule

      pg(s) 104-105

      Decision making in conflict data is a problem that plague the information fusion. It is usually resolved by the use of probabilistic methods such as Bayes. Still Bayes becomes impractical in strong presence of conflicts or lack of data. In that case Dempster–Shafer (DS) evidence theory is applied, because of its ability to handle conflicting sensor inputs. Because of that, DS-based information fusion is very popular in decision-making applications, although the classic combinatorial rule may produce counter intuitive results, especially when combining evidences with high level of conflict. The paper present a method which can be applied to the decision making process, thus resolving this problem.

  • MATHEMATICAL MODELLING OF SOCIO-ECONOMIC PROCESSES AND SYSTEMS

    • Adiabatical thermodynamic manner of the description of the carbon dioxide pollutant excess of Earth’s atmosphere

      pg(s) 106-111

      The problem of study of the atmospheric state with the accumulation of polluting gases in the atmosphere as a result of anthropogenic activity is very actually. One of the major polluting gases at large ratios is carbon dioxide. The recent study aims to obtain a quantitative expression of the variation of the atmospheric temperature as the result of the variations of carbon dioxide con centrations. It is known that the state of the atmospheric gas is described approximately by the model of the ideal gas. As the altitude increases, the gas pressure and the temperature in the troposphere decrease. The adiabatic constant of atmospheric air can be found from the adiabatic equation which is based on the ideal gas model. The natural logarithm of the pressure depending on the natural logarithm of the temperature allows the determination of this adiabatic constant. The obtained result coincides within the limits of the real ones, fact that denotes the correctness of the application of the ideal gas model. The known data of the pressure as a function of height allow to determine the fictive molar mass of the atmospheric gas from the dependence of the natural logarithm of pressure as a function of the a ltitudes and the result of the fictive molar mass coincides within the limits of the real ones. NASA observatories periodically record from the 1980s until now the permanent increase of the average temperature of the atmosphere with a speed of the order of (0,02 oC/year) and of the concomitant increasing of the concentration of carbon dioxide in the atmosphere. This fact currently concludes that the increase of global average temperature is influenced by the increase of the concentration of carbon dioxide. These concomitant increases allow to elaborate one empirical expression of the variation of the global average temperature depending on the variation of the carbon dioxide concentration. The obtaining of this empirical expression is based on the equation of state of the ideal gas and also on the adiaba tic equation. The graphical representation of the temperature variation as a function of the concentration variation allows the recalculation of the adia batic constant of the atmospheric air which value is within the limits of the real ones and denotes the validity and correctness of the suggested method. The recalculated values of the temperature variation according to the empirical formula must coincide with the real ones recorded. The coincidence is confirmed by the functional dependence ΔTe = f (ΔT). In order to ascertain the average speed of accumulation of carbon dioxide in the atmosphere, the graph of the dependence ΔC = f (time) is represented which proportionality coefficient is the accumulation speed of order (3,833 mg / m3/ year).

  • MATHEMATICAL MODELLING OF MEDICAL-BIOLOGICAL PROCESSES AND SYSTEMS

    • Smoluchowski’s coagulation equation with injections: applications to clustering of nano-particles

      pg(s) 112-115

      The coagulation equation, proposed by Smoluchowski, has been widely used to describe aggregation phenomena in many fields of science since its inception. It considers a physical system of many particles, and each particle is characterized by a change of some nonnegative scalar quantity (e.g. volume). Assuming such a system to be spatially homogeneous and unbounded, considering only pairwise interactions and a balance relation of interacting particles, the Smoluchowski equation can be used to describe the evolution of a system of many particles. In this study, we construct an exact solution to this integro-differential equation containing an exponentially-decaying source term. This solution, in particular, describes the steady-state structural density of endosomes per cell carrying the nanoparticles (particles smaller than 100 nm). In addition, we derived an exact analytical solution to the unsteady-state coagulation equation in the Laplace transform image space. This solution can be inverted using numerical methods for Laplace transform inversion. For practical use, we derive an analytical solution to the non-stationary coagulation equation stitching the steady-state and initial distributions of structural density. Choosing the particular form of stitching functions, we demonstrate that the nonstationary solution evolves between the initial and steady-state distribution functions. Thus, analytical solutions obtained represent a general theoretical basis to describe the dynamics of cargo distributions in the endosomal network.