$G$-deviations of polygons and their applications in Electric Power Engineering
For any metric space $X$ endowed with the action of a group $G$, and two $n$-gons $\vec x=(x_1,\dots,x_n)\in X^n$ and $\vec y=(y_1,\dots,y_n)\in X^n$ in $X$, we introduce the $G$-deviation $d(G\vec x,\vec y\,)$ of $\vec x$ from $\vec y$ as the distance in $X^n$ from $\vec y$ to the $G$-orbit $G\vec...
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Ivan Franko National University of Lviv
2021-06-01
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| Series: | Математичні Студії |
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| Online Access: | http://matstud.org.ua/ojs/index.php/matstud/article/view/229 |
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| author | T. Banakh O. Hryniv V. Hudym |
| author_facet | T. Banakh O. Hryniv V. Hudym |
| author_sort | T. Banakh |
| collection | DOAJ |
| description | For any metric space $X$ endowed with the action of a group $G$, and two $n$-gons $\vec x=(x_1,\dots,x_n)\in X^n$ and $\vec y=(y_1,\dots,y_n)\in X^n$ in $X$, we introduce the $G$-deviation $d(G\vec x,\vec y\,)$ of $\vec x$ from $\vec y$ as the distance in $X^n$ from $\vec y$ to the $G$-orbit $G\vec x$ of $\vec x$ in the $n$-th power $X^n$ of $X$. For some groups $G$ of affine transformations of the complex plane, we deduce simple-to-apply formulas for calculating the $G$-deviation between $n$-gons on the complex plane. We apply these formulas for defining new measures of asymmetry of triangles. These new measures can be applied in Electric Power Engineering for evaluating the quality of 3-phase electric power. One of such measures, namely the affine deviation, is espressible via the unbalance degree, which is a standard characteristic of quality of three-phase electric power. |
| format | Article |
| id | doaj-art-b381e0f1eea8469ab609e2c7c7464fd7 |
| institution | Kabale University |
| issn | 1027-4634 2411-0620 |
| language | deu |
| publishDate | 2021-06-01 |
| publisher | Ivan Franko National University of Lviv |
| record_format | Article |
| series | Математичні Студії |
| spelling | doaj-art-b381e0f1eea8469ab609e2c7c7464fd72025-08-20T03:33:32ZdeuIvan Franko National University of LvivМатематичні Студії1027-46342411-06202021-06-0155218820010.30970/ms.55.2.188-200229$G$-deviations of polygons and their applications in Electric Power EngineeringT. Banakh0O. Hryniv1V. Hudym2Ivan Franko National University of LvivIvan Franko National University of LvivLviv National Agrarian UniversityFor any metric space $X$ endowed with the action of a group $G$, and two $n$-gons $\vec x=(x_1,\dots,x_n)\in X^n$ and $\vec y=(y_1,\dots,y_n)\in X^n$ in $X$, we introduce the $G$-deviation $d(G\vec x,\vec y\,)$ of $\vec x$ from $\vec y$ as the distance in $X^n$ from $\vec y$ to the $G$-orbit $G\vec x$ of $\vec x$ in the $n$-th power $X^n$ of $X$. For some groups $G$ of affine transformations of the complex plane, we deduce simple-to-apply formulas for calculating the $G$-deviation between $n$-gons on the complex plane. We apply these formulas for defining new measures of asymmetry of triangles. These new measures can be applied in Electric Power Engineering for evaluating the quality of 3-phase electric power. One of such measures, namely the affine deviation, is espressible via the unbalance degree, which is a standard characteristic of quality of three-phase electric power.http://matstud.org.ua/ojs/index.php/matstud/article/view/229polygondeviationgroup actionelectric power engineering |
| spellingShingle | T. Banakh O. Hryniv V. Hudym $G$-deviations of polygons and their applications in Electric Power Engineering Математичні Студії polygon deviation group action electric power engineering |
| title | $G$-deviations of polygons and their applications in Electric Power Engineering |
| title_full | $G$-deviations of polygons and their applications in Electric Power Engineering |
| title_fullStr | $G$-deviations of polygons and their applications in Electric Power Engineering |
| title_full_unstemmed | $G$-deviations of polygons and their applications in Electric Power Engineering |
| title_short | $G$-deviations of polygons and their applications in Electric Power Engineering |
| title_sort | g deviations of polygons and their applications in electric power engineering |
| topic | polygon deviation group action electric power engineering |
| url | http://matstud.org.ua/ojs/index.php/matstud/article/view/229 |
| work_keys_str_mv | AT tbanakh gdeviationsofpolygonsandtheirapplicationsinelectricpowerengineering AT ohryniv gdeviationsofpolygonsandtheirapplicationsinelectricpowerengineering AT vhudym gdeviationsofpolygonsandtheirapplicationsinelectricpowerengineering |