It is a well-known result due to Busemann that the intersection body of an origin-symmetric convex body is also convex. Koldobsky introduced the notion of k-intersection bodies. We show that the k-intersection body of an origin-symmetric convex body is not necessarily convex if k > 1.

the purpose of this study was to identify daily changes in body weight of broiler chickens using image processing and multi-regression analysis. therefore, thirty 1-day-old broiler chickens were reared under standard rearing condition and after acquiring images they were weighted, individually. from 2490 digital images, six features (perimeter, area convex, major axis, minor axis, eccentricity)...

This is a review of various problems and results on the illumination of convex bodies in the spirit of combinatorial geometry. The topics under review are: history of the Gohberg–Markus–Hadwiger problem on the minimum number of exterior sources illuminating a convex body, including the discussion of its equivalent forms like the minimum number of homothetic copies covering the body; generalizat...

In this note, we prove the following inequality for norm N(K) of a convex body K in $$\mathbb {R}^n$$ , $$n\ge 2$$ : $$\begin{aligned} \le \frac{\pi ^{\frac{n-1}{2}}}{2 \Gamma \left( \frac{n+1}{2}\right) }\cdot {{\,\mathrm{length}\,}}(\gamma ) + ^{\frac{n}{2}-1}}{\Gamma \frac{n}{2}\right) } \cdot {{\,\mathrm{diam}\,}}(K), \end{aligned}$$ where $${{\,\mathrm{diam}\,}}(K)$$ is diameter K, $$\gamm...