Interval sets in applied geometry
Geometric modeling of interval sets of multidimensional space is considered. The interval set is determined as a set of k-planes of uncertain interval parameters. Interval parameters may be given by means of interval basis which are k-simplexes having vertex coordinates which are not fully presen...
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| Format: | Article |
| Language: | English |
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Omsk State Technical University, Federal State Autonoumos Educational Institution of Higher Education
2024-11-01
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| Series: | Омский научный вестник |
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| Online Access: | https://www.omgtu.ru/general_information/media_omgtu/journal_of_omsk_research_journal/files/arhiv/2024/%E2%84%964%20(192)%20(%D0%9E%D0%9D%D0%92)/29-34%20%D0%AE%D1%80%D0%BA%D0%BE%D0%B2%20%D0%92.%20%D0%AE..pdf |
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| author | V. Yu. Yurkov |
| author_facet | V. Yu. Yurkov |
| author_sort | V. Yu. Yurkov |
| collection | DOAJ |
| description | Geometric modeling of interval sets of multidimensional space is considered. The
interval set is determined as a set of k-planes of uncertain interval parameters.
Interval parameters may be given by means of interval basis which are k-simplexes
having vertex coordinates which are not fully presented (only up to range of
values). Geometric images of the sets have combinatorial structure formed by some
part of the space and bordered by a set of peace linear hyper-surfaces. Analytic
model is a system of interval equations which may be transformed to equations with
uncertain parameters. The set of interval parameters generate an interval function
and geometric image of it is some domain in parametric space. Analyses of mutual
position of all domains allows us to determine the behavior of interval sets. Some
properties of interval line sets are considered in detail as examples of the proposed
approach. |
| format | Article |
| id | doaj-art-056894b838aa495ca6c4262d6df73295 |
| institution | OA Journals |
| issn | 1813-8225 2541-7541 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Omsk State Technical University, Federal State Autonoumos Educational Institution of Higher Education |
| record_format | Article |
| series | Омский научный вестник |
| spelling | doaj-art-056894b838aa495ca6c4262d6df732952025-08-20T01:59:30ZengOmsk State Technical University, Federal State Autonoumos Educational Institution of Higher EducationОмский научный вестник1813-82252541-75412024-11-014 (192)293410.25206/1813-8225-2024-192-29-34Interval sets in applied geometryV. Yu. Yurkov0https://orcid.org/0000-0003-2667-8103Omsk State Technical UniversityGeometric modeling of interval sets of multidimensional space is considered. The interval set is determined as a set of k-planes of uncertain interval parameters. Interval parameters may be given by means of interval basis which are k-simplexes having vertex coordinates which are not fully presented (only up to range of values). Geometric images of the sets have combinatorial structure formed by some part of the space and bordered by a set of peace linear hyper-surfaces. Analytic model is a system of interval equations which may be transformed to equations with uncertain parameters. The set of interval parameters generate an interval function and geometric image of it is some domain in parametric space. Analyses of mutual position of all domains allows us to determine the behavior of interval sets. Some properties of interval line sets are considered in detail as examples of the proposed approach.https://www.omgtu.ru/general_information/media_omgtu/journal_of_omsk_research_journal/files/arhiv/2024/%E2%84%964%20(192)%20(%D0%9E%D0%9D%D0%92)/29-34%20%D0%AE%D1%80%D0%BA%D0%BE%D0%B2%20%D0%92.%20%D0%AE..pdfgeometric modelinterval setparametric determinationk-planepiecewise linear structureinterval parameterhyper-plane |
| spellingShingle | V. Yu. Yurkov Interval sets in applied geometry Омский научный вестник geometric model interval set parametric determination k-plane piecewise linear structure interval parameter hyper-plane |
| title | Interval sets in applied geometry |
| title_full | Interval sets in applied geometry |
| title_fullStr | Interval sets in applied geometry |
| title_full_unstemmed | Interval sets in applied geometry |
| title_short | Interval sets in applied geometry |
| title_sort | interval sets in applied geometry |
| topic | geometric model interval set parametric determination k-plane piecewise linear structure interval parameter hyper-plane |
| url | https://www.omgtu.ru/general_information/media_omgtu/journal_of_omsk_research_journal/files/arhiv/2024/%E2%84%964%20(192)%20(%D0%9E%D0%9D%D0%92)/29-34%20%D0%AE%D1%80%D0%BA%D0%BE%D0%B2%20%D0%92.%20%D0%AE..pdf |
| work_keys_str_mv | AT vyuyurkov intervalsetsinappliedgeometry |