We present an algorithm to compute the geodesic $$L_1$$ farthest-point Voronoi diagram of m point sites in presence n rectangular obstacles plane. It takes $$O(nm+n \log + m\log m)$$ construction time using O(nm) space. This is first optimal for constructing obstacles. can construct a data structure same and space that answers farthest-neighbor query $$O(\log (n+m))$$ time.

Heyde proved that the Gaussian distribution on real line is characterized by symmetry of conditional one linear form given another. The present article devoted to a group analogue theorem. We describe distributions independent random variables $$\xi _1$$ and _2$$ with values in $$X=\mathbf {R}^n\times D$$ , where D discrete Abelian group, which are $$L_2 = \xi _1 + \delta $$L_1 $$\delta $$ topo...