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Modelling and Data Analysis
2021. Vol. 11, no. 1, 40–60
https://doi.org/10.17759/mda.2021110104
ISSN: 2219-3758 / 2311-9454 (online)

On Different Approaches to Solving Extreme Problems

 
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Abstract

The article discusses the geometric and analytical methods for solving known extreme problems and identifies the logical relationships between these problems, the preference for using one or another method for solving extreme problems is shown by specific examples.

General Information

Keywords: Extreme problems, Lemoine point, Lhuillier point, isogonality, centroid, Lagrange multiplier method, triangle, tetrahedron

Journal rubric: Optimization Methods

OpenAlex citations: 10

OpenAlex trends: Industrial Engineering and Technologies, Engineering Diagnostics and Reliability, Heat Transfer and Mathematical Modeling

Information about the work in OpenAlex

Number of citations: 10

Topics

Industrial Engineering and Technologies

This cluster of papers focuses on the intersection of digital economy, sustainable development, and technological innovation within the mineral resource sector. It covers topics such as energy efficiency, carbon sequestration, hydrogen initiatives, lithium-ion batteries, and renewable energy, with a specific emphasis on resource efficiency and circular economy principles.

Number of works: 42099  |  Total number of citations: 59991

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Engineering Diagnostics and Reliability

This cluster of papers focuses on materials engineering in industrial applications, particularly in the fields of corrosion, steel strength, pipeline durability, deformation processes, and industrial safety. It addresses issues such as fatigue, electrochemical parameters, friction welding, and heat resistance in various mechanical components and equipment used in oil and gas, power generation, and other industrial sectors.

Number of works: 66124  |  Total number of citations: 120610

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Heat Transfer and Mathematical Modeling

This cluster of papers covers a wide range of topics in mechanical engineering and materials science, including ultrasonic treatment, polymer adsorption, finite element method, thermal protection, nanoparticle synthesis, elasticity theory, heat transfer, composite materials, numerical modeling, and aerospace industry.

Number of works: 6954  |  Total number of citations: 17702

Topic detailsв OpenAlex

Work details in OpenAlex

DOI: https://doi.org/10.17759/mda.2021110104

Published

For citation: Kulanin, Y.D., Nurkaeva, I.M., Stepanov, M.E. (2021). On Different Approaches to Solving Extreme Problems. Modelling and Data Analysis, 11(1), 40–60. (In Russ.). https://doi.org/10.17759/mda.2021110104

© Kulanin Y.D., Nurkaeva I.M., Stepanov M.E., 2021

License: CC BY-NC 4.0

References

  1. Kulanin E.D., Nurkaeva I.M. On two geometric problems on the extremum // Mathematics in School. M., 2019. No. 4. – pp. 35–40.
  2. Kulanin E.D., Stepanov M.E., Nurkaeva I.M. Propaedeutics of solving extreme problems in the school course of mathematics. // Data modeling and analysis. 2019. No. 4. – pp. 127–144.
  3. Kulanin E.D., Stepanov M.E., Nurkaeva I.M. The role of figurative thinking in scientific thinking. // Data modeling and analysis. 2020. – vol. 10. – No. 2, pp. 110–128.
  4. Ponarin Y.P. Elementary geometry: in 2 t. – T. 2: solid geometry, transform space. – M.: MCNMO, 2006.
  5. Prasolov V.V. Problems of plane geometry: a tutorial. – 6th ed. stereotype. – M.: MCNMO, 2007. – pp. 282–283.
  6. Stepanov M.E. The image of the force field as a heuristic model in mathematics”. Data modeling and analysis. Proceedings of the Faculty of Information Technologies of MSPPU. – 2007, Issue 3.
  7. Prasolov V.V., Tikhomirov V.M. Geometry. MCNMO, 1997.

Information About the Authors

Yevgeny D. Kulanin, Candidate of Science (Physics and Matematics), Professor, Moscow State University of Psychology and Education, Moscow, Russian Federation, ORCID: https://orcid.org/0000-0001-6093-7012, e-mail: lucas03@mail.ru

Irina M. Nurkaeva, Candidate of Science (Education), Associate Professor of the Department of Applied Informatics and Multimedia Technologies, Moscow State University of Psychology and Education, Moscow, Russian Federation, ORCID: https://orcid.org/0000-0002-1949-6734, e-mail: nurkaevaim@yandex.ru

Mikhail E. Stepanov, Candidate of Science (Education), Associate Professor, Department of Applied Mathematics, Faculty of Information Technologies, Moscow State University of Psychology and Education, Moscow, Russian Federation, ORCID: https://orcid.org/0000-0003-4803-8211, e-mail: mestepanov@yandex.ru

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