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...

Full description

Saved in:
Bibliographic Details
Main Author: V. Yu. Yurkov
Format: Article
Language:English
Published: Omsk State Technical University, Federal State Autonoumos Educational Institution of Higher Education 2024-11-01
Series:Омский научный вестник
Subjects:
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
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1850245373434527744
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