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Dergiler / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 72 Issue: 1

Invariants of a mapping of a set to the two-dimensional Euclidean space

Djavvat Khadjiev(National University of Uzbekistan named after Mirzo Ulugbek)0000-0001-7056-5662
Gayrat Beshimov(National University of Uzbekistan named after Mirzo Ulugbek)0000-0002-5394-2179
İdris Ören(KARADENIZ TECHNICAL UNIVERSITY)0000-0003-2716-3945
Sayfa
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Yayın Tarihi
2023-03-30
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Complete systems of relations between elements of the obtained complete systems of $G$-invariants are given for these groups.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Let $E_{2}$ be the $2$-dimensional Euclidean space and $T$ be a set such that it has at least two elements.
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Temel Bulgular & Veri:A mapping $\alpha : T\rightarrow E_{2}$ will be called a $T$-figure in $E_{2}$.
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Sonuç & Katkı:Complete systems of relations between elements of the obtained complete systems of $G$-invariants are given for these groups.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Euclidean geometry · invariant · figure

Abstract

Let $E_{2}$ be the $2$-dimensional Euclidean space and $T$ be a set such that it has at least two elements. A mapping $\alpha : T\rightarrow E_{2}$ will be called a $T$-figure in $E_{2}$. Let $O(2, R)$ be the group of all orthogonal transformations of $E_{2}$. Put $SO(2, R)=\left\{ g\in O(2, R)|detg=1\right\}$, $MO(2, R)=\left\{F:E_{2}\rightarrow E_{2}\mid Fx=gx+b, g\in O(2,R), b\in E_{2}\right\}$, $MSO(2, R)= \left\{F\in MO(2, R)|detg=1\right\}$. The present paper is devoted to solutions of problems of $G$-equivalence of $T$-figures in $E_{2}$ for groups $G=O(2, R), SO(2, R)$, $MO(2, R)$, $MSO(2, R)$. Complete systems of $G$-invariants of $T$-figures in $E_{2}$ for these groups are obtained. Complete systems of relations between elements of the obtained complete systems of $G$-invariants are given for these groups.

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Bu Makaleye Atıf Yap

Khadjiev, D., Beshimov, G., Ören, İ. (2023). Invariants of a mapping of a set to the two-dimensional Euclidean space. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 72 Issue: 1. https://doi.org/10.31801/cfsuasmas.1003511

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