- Turkish Journal of Mathematics
- Vol: 42 Issue: 1
- Various centroids and some characterizations of catenary rotation hypersurfaces
Various centroids and some characterizations of catenary rotation hypersurfaces
Authors : Dong-soo Kim, Young Ho Kim, Dae Won Yoon
Pages : 360-372
View : 7 | Download : 4
Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :We study positive $C^1$ functions $z=f(x), x=(x_1,\cdots, x_n)$ defined on the $n$-dimensional Euclidean space $ \mathbb R^{n}$. For $x=(x_1,\cdots, x_n)$ with nonzero numbers $x_1, \cdots, x_n$, we consider the rectangular domain $I(x)=I(x_1)\times \cdots \times I(x_n)\subset \mathbb R^{n}$, where $I(x_i)= [0, x_i]$ if $x_i>0$ and $I(x_i)= [x_i,0]$ if $x_iKeywords : Centroid, surface centroid, volume, surface area, catenary rotation hypersurface