Застосування універсальних багатоточкових інваріантів у евклідовому та псевдоевклідовому просторах
Examples of application in a metric space and a space with indefinite metric of the universal multipoint invariant (UMP invariant) known as the Cayley – Menger determinant for four points are considered. Such an invariant, as the results show, determines the metric structure of the Euclidean and pse...
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| Date: | 2018 |
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| Main Author: | |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of NAS of Ukraine
2018
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| Subjects: | |
| Online Access: | http://journals.iapmm.lviv.ua/ojs/index.php/APMM/article/view/apmm2018.16.50-57 |
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| Journal Title: | Prykladni Problemy Mekhaniky i Matematyky |
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Prykladni Problemy Mekhaniky i Matematyky| Summary: | Examples of application in a metric space and a space with indefinite metric of the universal multipoint invariant (UMP invariant) known as the Cayley – Menger determinant for four points are considered. Such an invariant, as the results show, determines the metric structure of the Euclidean and pseudo-Euclidean spaces of dimension n=2. For these spaces, expressions for UMP invariants associated with the use of appropriate pseudo distances are also obtained and analyzed. The considered approach can be applied also in spaces with dimension n>2. Cite as: D. O. Dziakovych, “Application of universal multipoint invariants in Euclidean and pseudo-Euclidean spaces,” Prykl. Probl. Mekh. Mat., Issue 16, 50–57 (2018) (in Ukrainian), https://doi.org/10.15407/apmm2018.16.50-57 |
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