Mathematical Modeling
Vol. 1 (2017), Issue 2

Table of Contents

  • THEORETICAL FOUNDATIONS AND SPECIFICITY OF MATHEMATICAL MODELLING

    • EVOLUTIONARY MATHEMATICAL MODELS WITH DISTRIBUTED PARAMETERS ON THE NET AND NETLIKE DOMAIN

      pg(s) 72-74

      Mathematical models of evolutionary processes on the network and setepodobnoj area. The method, which applies to many tasks of optimal control of differential systems, the status of which is defined by the weak solutions of evolutionary equations of mathematical physics on networks and setepodobnyh areas. This method is very common and is applicable to a wide class of linear tasks that have an interesting analogy with also multi-phase tasks of mechanics (in particular, the theory of plasticity). The results obtained in this manner for a specific equation with distributed parameters in the setepodobnoj area, serve not only to demonstrate the method, but also of interest to applications.

    • CONCEPTUAL CYBERNETIC MODEL OF TEACHING AND LEARNING

      pg(s) 80-83

      The article describes conceptual models of learning and teaching as a managed cybernetic system to achieve the knowledge and skills required by the standards. In the article, the learning process is examined as a system for building a knowledge system of a learner actively which is managed and directed by the tutor or teacher to achieve specified learning goal. The information received by the learner has a multimedia nature. The recipient receives the information through various channels (sensors), sight, hearing, smell, taste and touch. The received information arrives in the short-term memory where it is processed – confronted with the previous knowledge in long-term memory of the individual. New information and knowledge can reinforce and extend the recipient’s long-term knowledge system if they are consistent logically. If there is a conflict between new information and old knowledge and information – the conflict needs to be solved. The solution can be the clarification of the knowledge system, correction of misconceptions so they are in line with objective reality and relevant knowledge about the subject of learning. It means, learning is not a constant storage of isolated information and information units in memory, but their transformation into active knowledge which is connected to logical structures and forms the knowledge system of the learner. The actual knowledge system enables an individual to solve non-standard problems not only in everyday life but also in science and technology and in various research areas from which the necessary, suitable and useable knowledge (expert) system is built.

  • MATHEMATICAL MODELLING OF TECHNOLOGICAL PROCESSES AND SYSTEMS

    • ROTATING OF A BALL IN CHAMBER FILLED WITH A FLUID

      pg(s) 88-91

      Influece of form errors of a chamber filled with a liquid on the movement and stability of a ball, rotating in the chamber, is studied. Two cases of the influence of a chamber form errors on the forces, acting on the ball, are defined. The first case describes the situation when limitations on the rotor shift are not imposed and disturbances of the chamber form are set by spherical harmonics not above the first order. Then the chamber of a disturbed form, form the point of view of the reaction forces of the liquid and their moments, does not differ from a similar spherical chamber. In the second case disturbance of a chamber form are arbitrary and the rotor shift is supposed small. Then the force, acting on the rotor, depends on its displacement only, and the momentum does not depend on shift. A chamber of any form is equivalent to an ellipsoid. A rising here diflective moment tends to direct the angular speed vector along the small semiaxis of the ellipsoid, i.e., a stable position of the rotor appears.

    • SOFTWARE ASSURANCE OF THE SYNTHESIS AND DESIGN OF HYPERBOLOID GEAR DRIVES

      pg(s) 92-95

      The study presents a brief description of the type’s software, applicable to the synthesis and design of gear transmissions. The main accent is put on the approach to the computer synthesis, for which the optimization process is carried out by the method of directed search of the optimal variant of a synthesized mechanism. The specific features of the programs, applied by the authors, oriented to the synthesis of spatial gear mechanisms with linear contacting teeth with face meshing (Spiroid and Helicon) are studied in detail.

    • THE EFFECT OF OPTICAL AND RECOMBINATION LOSSES IN CU2ZNSN(S,SE)4-BASED THIN-FILM SOLAR CELLS WITH CDS, ZNSE, ZNS WINDOW AND ITO, ZNO CHARGE-COLLECTING LAYERS

      pg(s) 96-99

      We reported the investigation the effect of the optical and recombination losses in solar cells (SCs) based on nCdS(ZnSe, ZnS)/p-Cu2ZnSn(S,Se)4 heterojunctions with n-ITO(ZnO) frontal charge-collecting contacts on the internal (Qint), external (Qext) quantum yields, short-circuit current density (Jsc) and maximum efficiency (η) of solar cells.

  • MATHEMATICAL MODELLING OF SOCIO-ECONOMIC PROCESSES AND SYSTEMS

    • INTEGRAL ASSESSMENT OF ENVIRONMENTAL QUALITY AND THE QUALITY OF LIFE OF THE POPULATION OF THE ARCTIC REGIONS OF RUSSIA IN THE PERIOD FROM 2003 TO 2015

      pg(s) 100-104

      The integral assessment of environmental quality and quality of life of the population of 9 regions of the Arctic zone of the Russian Federation in the period from 2003 to 2015 is considered. To build integrated indicators, we used: summary indicators, randomized summary indicators, and "ASPID methodology" (analysis and synthesis of indicators in the information deficit). When calculating weights, incomplete, inaccurate, non-numeric information was taken into account) about the criteria and priorities of the evaluation. To assess the quality of the environment, 8 parameters were used. To assess the quality of life of the population, the state of three subsystems was taken into account: ecological (8 parameters), economic (5 parameters), social (5 parameters). The choice of criteria was made taking into account the information available on the website of the Federal Service of State Statistics of the Russian Federation, in the collections "Regions of Russia" and in state reports "On the state of the environment …" To assess the quality of the environment in the regions and the quality of life of the population of the regions, five quality classes were introduced (I – high, II – above average, III – average, IV – below average, V – low). In constructing integral indicators, the sum of the normalized values of the indicators within subsystems (blocks) and between them was used as a synthesizing function, taking into account the equilibrium or nonequilibrium setting of priorities. When assessing the quality of the environment, all regions fall into the third class (middle – the right border of the class) with a slight temporal change. In evaluating the quality of life, three groups of regions were identified. In the first group, the quality of life for the period under review improved by 10 percent or more. The second group includes regions with an improvement in the quality of life by 5-10%, the third group includes regions with an improvement in the quality of life up to 5%. For the same time interval, the quality of life of the APR regions was compared with the regions of Central Russia (Tver Region). The forecast scenarios of a possible change in the quality of the environment and the quality of life of the population in the regions are considered. The studies were carried out with the support of the RFBR grant No. 16-05-00715-a.

    • TRENDS IN DATA ANALISYS: STATE, DEVELOPMENT PROSPECTS

      pg(s) 105-109

      The article suggests the consideration of data analysis ideology in the context of knowledge creation process and the technological patterns of social development. The problems of singularity (human misunderstanding of data processing results) associated with increase in data variety, volume and further intellectualization of the corresponding technologies for their processing are proposed to be solved by creating new formalization techniques that allow retransmission.

    • EXACT RECONSTRUCTION VERSION OF RADON TRANSFORMATION IN TOMOSYNTHESIS

      pg(s) 110-112

      The purpose of this study is a method of exact reconstruction in the Radon problem, which consists in refusal of the approximate transformation kernel usage. A comparison of the methods that are currently used in tomosynthesis was conducted. Model experiments were performed; the results of the application of the proposed method in real tomography studies in tomography are given.

    • APPLICATION OF FUZZY MODELING TO PREDICT THE DISEASE OF STAFF FROM EXPOSURE TO WORKING CONDITIONS

      pg(s) 113-116

      A fuzzy model for determining the morbidity rate of employees of a refinery with diseases of the respiratory organs is analyzed on the basis of an analysis of the concentrations of pollutants in all occupational environments using a mathematical apparatus of fuzzy sets. The results of visualization of the developed fuzzy model in the MATLAB Fuzzy Logic Toolbox medium are presented.

    • SIMULATION MODELING OF AUDITORY FUNCTION

      pg(s) 117-120

      The hypothese concerning encoding of information in the peripheral part of the human’s auricular analyzer are presented. A brief critical analysis of contemporary trends in theoretical concepts concerning principles of work of the cochlea of the inner ear are conducted. Prerequisites for the construction of an alternative theory of coding of information in it are formulated in order to optimize the design and software of cochlear implants. The principle of constructing an imitation model of the generation of electric signals formed in the cochlea of the inner ear are proposed.