scholarly journals The development of scientific outlook of students when teaching inverse problems for differential equations

2019 ◽  
Vol 16 (1) ◽  
pp. 46-55
Author(s):  
Viktor Semenovich Kornilov
Keyword(s):  
Inverse Problems ◽  
Differential Equations ◽  
Mathematical Models ◽  
Research Work ◽  
Teaching Experience ◽  
Physical Processes ◽  
Mathematical Methods ◽  
Important Place ◽  
The World ◽  
Scientific Worldview

Problem and goal. Modern achievements of the world Science of nature and the world, physical laws and laws should be disclosed at an accessible level to University students. Among the scientific methods of research of physical processes and phenomena, an important place is the method of mathematical modeling, because mathematical models have scientific and cognitive potential and versatility (see, for example, [2-4]). The use of mathematical models of inverse problems for differential equations (IPDE) allows to effectively investigate many processes and phenomena occurring in the air, earth and water environment. It is not surprising that in some Russian universities in the physical and mathematical areas of training are taught IPDE in the form of a choice of courses. The goals and objectives of such teaching are set, as a result of which students would develop creative mathematical abilities, formed fundamental knowledge in the field of physical education, developed a scientific worldview. Methodology. The development of scientific outlook of students of physical and mathematical directions of preparation, as a result of teaching IPDE, ensured the successful will be implemented in practice, such conditions as: 1. the involvement of experts in the field IPDE with teaching experience at the university; 2. development of the content of lectures and practical classes on the basis of modern achievements of the theory of inverse and incorrect problems, taking into account the professional orientation of training students; 3. the implementation of the principles, methods and means of education IPDE; 4. involvement of students in research work in scientific seminars and participation in scientific conferences devoted to IPDE; 5. implementation of methodological approaches that allow students to develop the skills and abilities of independent analysis of applied and humanitarian nature of the results of research of IPDE. Results. In practical classes on the IPDE students acquire the ability and skills to apply effective approaches and mathematical methods of finding solutions to inverse problems, followed by a logical analysis of their solutions. As a result, students gain useful experience in the analysis of new information about the studied physical processes and phenomena, form new scientific knowledge about the world on the basis of which develop a scientific worldview. Conclusion. Developed, in the process of teaching IPDE, the scientific outlook helps students to understand that mathematical models IPDE are relevant to theory, experiment and philosophy - the basic methods of knowledge researchers; to understand the humanitarian value of mathematical models IPDE.

scholarly journals Ecology through the eyes of a non-ecologist

2020 ◽  
Vol 18 (5) ◽  
pp. 259-270
Author(s):  
Janusz Uchmański
Keyword(s):  
Differential Equations ◽  
Mathematical Models ◽  
Density Dependence ◽  
Evolutionary Biology ◽  
Ecological Systems ◽  
Living Environment ◽  
Mathematical Methods ◽  
Nature Protection ◽  
Practical Applications ◽  
The Stability

Ecology is a branch of biology that deals with the life of plants and animals in their environment. Nature protection are practical actions where ecology is applied. Ecology is the most biological branch of biology because it deals with individuals in their living environment, and individuals "exist" only in biology. The most important issue being considered in ecology is biodiversity: its changes and its persistence. In their research, ecologists focus on the functioning of ecological systems. In classical terms, they assume that the most important mechanism is density dependence. Mathematical models traditionally applied in ecology include ordinary difference and differential equations, which fits well with the assumption of density dependence, but this results in ecology being dominated by considerations of the stability of ecological systems. Evolutionary biology and ecology have separate areas of interest. Evolutionary biology explains the formation of optimal characteristics of individuals. Ecology also takes into account those individuals who have lost in the process of natural selection. The mathematical methods used in classical ecology were developed for the use of physics. The question arises whether they give a precise picture of the dynamics of ecological systems. Recently, a view has emerged stating that in order to see the importance of full-scale biodiversity, we should refer to individuals (rather than population density) as basic "atoms" that make up ecological systems. In ecology, we call this an individual-based approach. However, it gives a very complex picture of how ecological systems work. In ecology, however, there is an alternative way to describe the dynamics of ecological systems, i.e. through the circulation of matter in them and the flow of energy through them. It allows the use of traditional difference and differential equations in the formulation of mathematical models, which has proven itself in practical applications many times.

scholarly journals Development of ICT competence among students when teaching inverse problems for differential equations with the use of computer technology

2019 ◽  
Vol 16 (4) ◽  
pp. 328-337
Author(s):  
Viktor S. Kornilov
Keyword(s):  
Inverse Problems ◽  
Differential Equations ◽  
Mathematical Models ◽  
Computer Technology ◽  
Three Dimensional ◽  
Theory And Practice ◽  
Computational Mathematics ◽  
Modern Computer ◽  
Computer Technologies ◽  
Ict Competence

Problem and goal. The great need to apply the theory of inverse problems for differential equations (IP) in the research of applied problems is explained by the fact that it is possible to effectively study hard-to-reach or inaccessible objects and processes, to identify, for example, the location of objects, determine their shape, etc. In addition, it is possible to identify causeand-effect relationships of processes and phenomena (see, for example, [5; 6; 8; 11; 14; 17; 19]). It became possible, in many respects, thanks to modern computer technologies which allow to investigate various mathematical models of inverse problems, realize modern computational algorithms of the numerical solution of inverse problems for differential equations, carry out three-dimensional visualization of their decisions and control of accuracy of calculations. This circumstance explains the widespread introduction of modern computer technologies in the process of teaching students of IP educational institutions of physics and mathematics (see, for example, [2; 5; 6; 8; 10-14; 17; 19; 20]). In the process of teaching, goals are set to ensure that students form a system of fundamental knowledge in the field of theory and practice of inverse problems, applied and computational mathematics, acquire the skills to choose and apply computer technology to find solutions to inverse problems, develop their ICT competence. Methodology. The development of ICT competence among students of universities of physical and mathematical areas of training, as a result of learning IP, is ensured by how successfully the conditions will be implemented in practice, including: 1) involvement of specialists in the field of inverse problems for differential equations with experience in the use of computer technology in the study of inverse problems; 2) conducting lectures and practical classes using multimedia and computer technologies; 3) implementation of didactic principles of teaching inverse problems for differential equations using computer technologies; 4) attraction of students to performance of semester tasks, course and final qualifying works on inverse problems for differential equations with use of computer technologies. Results. In practical classes, students acquire the skills to apply modern computer technology in the study of IP. Students gain experience in analyzing new information about the studied physical processes and phenomena using computer technology. Students form knowledge about the role of computer technology in mobile research of mathematical models of inverse problems for differential equations, demonstrating ICT competence. Conclusion. Developed in the process of teaching inverse problems for differential equations using computer technologies, ICT competence will obviously allow students in their future professional activities to effectively apply a variety of computer technologies in the study of mathematical models of inverse problems.

scholarly journals MODELAGEM DO COMPORTAMENTO DISPERSIVO DE MATERIAL IMPACTANTE EM UM LAGO POR MEIO DA EQUAÇÃO DE DIFUSÃO-ADVECÇÃO

2016 ◽  
Vol 38 (2) ◽  
pp. 756
Author(s):  
Arinos Alves da Silva Lopes ◽  
Jessica Lemos Gomes ◽  
Lays Carolline Souza ◽  
Jaqueline Maria da Silva
Keyword(s):  
Quality Of Life ◽  
Differential Equations ◽  
Water Supply ◽  
Mathematical Models ◽  
Water Bodies ◽  
Aquatic Environments ◽  
World Population ◽  
Environment And Health ◽  
The World

The exponential and uncontrolled growth of the world population can affect the population’s quality of life and lead to various environment and health problems, such as deforestation to make way for new housing and an increase in the water supply demand and in the amount of pollutants released in the water bodies. Several mathematical models have been developed to try to understand and solve problems of dispersion of pollutants in aquatic environments. This article aims to study, analyze and model the dispersion behavior of contaminants and pollutants in a lake using the Diffusion-Advection differential equations model.

scholarly journals Improving the level of technical training of women in wrestling on alysh belts at the stage of initial training

2021 ◽  
pp. 107-112
Author(s):  
Bogdan Semeniv ◽  
Taras Prystavskyi ◽  
Julia Sopila ◽  
Myhailo Stahiv ◽  
Igor Yakimishin
Keyword(s):  
Research Methods ◽  
Healthy Lifestyle ◽  
Control Group ◽  
Physical Culture ◽  
Initial Training ◽  
Training Process ◽  
Mathematical Methods ◽  
Important Place ◽  
The World ◽  
Pedagogical Research

Human motor activity is one of the body's physical needs, which takes an important place in the life process. The formation and development of all organs and systems of the human body are inextricably associated with activity and muscle effectiveness. The systematic use of physical culture and sports in accordance with gender, age, state of health is one of the factors of a healthy lifestyle. Democratic changes in the world today have given impetus to the revival of historical, national and cultural traditions, including those related to physical culture and sports. The recent popularity of wrestling in many countries around the world is forcing professionals to reconsider their views on the methodology of the training process on the types of wrestling and look for new ways to improve the quality of the training process to maintain competitiveness. The purpose of the study: the formation of motor skills and abilities of women in wrestling in the "Alysh" belts at the stage of initial training. Research methods: analysis and generalization of scientific and methodical literature sources, psychophysiological research methods, pedagogical research methods, mathematical methods of data processing of scientific research. Conclusions. The results of the study indicate a positive effect of complexes of physical exercises and training regimes on the development of flexibility and coordination on the formation of technical actions of women in wrestling on "Alysh" belts at the initial stage, technical readiness of women increased 22.5% relative to the control group 5.1% , flexibility increased by 33.2% of the experimental group relative to the control group of 7.6%.

The problem of sex in the religions of the Abrahamic tradition

2001 ◽  
pp. 29-36
Author(s):  
N. Nedzelska
Keyword(s):  
Homo Sapiens ◽  
Gender Issues ◽  
First Person ◽  
Important Place ◽  
The World ◽  
Religious Systems

The paradox of the existence of the species Homo sapiens is that we do not even know: Who are we? Why are we? Where did you go from? Why? At all times - from antiquity to our time - the philosophers touched on this topic. It takes an important place in all religions of the world. These eternal questions include gender issues. In the religious systems of the religions of the Abrahamic tradition there is no single answer to the question of which sex was the first person. Recently, British scientists have even tried to prove that Eve is 84 thousand years older Adam

The inverse problem of recovering the coefficients of a differential equations on a graph

2020 ◽  
Vol 28 (5) ◽  
pp. 727-738
Author(s):  
Victor Sadovnichii ◽  
Yaudat Talgatovich Sultanaev ◽  
Azamat Akhtyamov
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Finite Number ◽  
Characteristic Equation ◽  
Arbitrary Number ◽  
New Class ◽  
Finite Set

AbstractWe consider a new class of inverse problems on the recovery of the coefficients of differential equations from a finite set of eigenvalues of a boundary value problem with unseparated boundary conditions. A finite number of eigenvalues is possible only for problems in which the roots of the characteristic equation are multiple. The article describes solutions to such a problem for equations of the second, third, and fourth orders on a graph with three, four, and five edges. The inverse problem with an arbitrary number of edges is solved similarly.

scholarly journals Approximate Analytical Analysis of Unsteady MHD Mixed Flow of Non-Newtonian Hybrid Nanofluid over a Stretching Surface

Fluids ◽  
2021 ◽  
Vol 6 (4) ◽  
pp. 138
Author(s):  
Ali Rehman ◽  
Zabidin Salleh
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Base Fluid ◽  
Research Work ◽  
Hybrid Nanofluid ◽  
Stretching Surface ◽  
Optimal Homotopy Analysis Method ◽  
Analytical Analysis ◽  
Transfer Ratio ◽  
The Impact

This paper analyses the two-dimensional unsteady and incompressible flow of a non-Newtonian hybrid nanofluid over a stretching surface. The nanofluid formulated in the present study is TiO2 + Ag + blood, and TiO2 + blood, where in this combination TiO2 + blood is the base fluid and TiO2 + Ag + blood represents the hybrid nanofluid. The aim of the present research work is to improve the heat transfer ratio because the heat transfer ratio of the hybrid nanofluid is higher than that of the base fluid. The novelty of the recent work is the approximate analytical analysis of the magnetohydrodynamics mixed non-Newtonian hybrid nanofluid over a stretching surface. This type of combination, where TiO2+blood is the base fluid and TiO2 + Ag + blood is the hybrid nanofluid, is studied for the first time in the literature. The fundamental partial differential equations are transformed to a set of nonlinear ordinary differential equations with the guide of some appropriate similarity transformations. The analytical approximate method, namely the optimal homotopy analysis method (OHAM), is used for the approximate analytical solution. The convergence of the OHAM for particular problems is also discussed. The impact of the magnetic parameter, dynamic viscosity parameter, stretching surface parameter and Prandtl number is interpreted through graphs. The skin friction coefficient and Nusselt number are explained in table form. The present work is found to be in very good agreement with those published earlier.

Regenerative flow pumps, blowers and compressors – A review

2021 ◽  
pp. 095765092110181
Author(s):  
M Sreekanth ◽  
R Sivakumar ◽  
M Sai Santosh Pavan Kumar ◽  
K Karunamurthy ◽  
MB Shyam Kumar ◽  
...  
Keyword(s):  
Quantitative Data ◽  
Research Work ◽  
Future Research ◽  
Performance Parameters ◽  
The World ◽  
Working Principle ◽  
Computational Fluid Dynamics Cfd ◽  
Specific Speed ◽  
Regenerative Flow ◽  
Product Description

This paper presents a detailed and objective review of regenerative flow turbomachines, namely pumps, blowers and compressors. Several aspects of turbomachines like design and operating parameters, working principle, flow behaviour, performance parameters and analytical and Computational Fluid Dynamics (CFD) related details have been reviewed and summarized. Experimental work has been put in perspective and the most useful results for optimized performance have been presented. Consolidated plots of specific speed-specific diameter have been plotted which can be helpful in the early stages of design. Industrial outlook involving details of suppliers from various parts of the world, their product description and applications too are included. Finally, future research work to be carried out to make these machines widespread is suggested. This review is targeted at designer engineers who would need quantitative data to work with.

Sign in / Sign up

Export Citation Format

Share Document