We prove that three spaces of importance in topological combinatorics are homeomorphic to closed balls: the totally nonnegative Grassmannian, compactification space electrical networks, and cyclically symmetric amplituhedron.

This paper examines the complexity of several geometric problems due to un bounded dimension The problems considered are i minimum cover of points by unit cubes ii minimum cover of points by unit balls and iii minimum number of lines to hit a set of balls Each of these problems is proven not to have a poly nomial approximation scheme unless P NP Speci c lower bounds on the error ratios attainab...

Abstract: Ball mills are used in the last stage of ore processing for grinding raw materials. Forged 70Cr2 alloy steel and Austempered Ductile Iron (ADI) balls are materials from which grinding balls are made for Sarcheshmeh Copper Plant (SCP) ball mills. In the present study wear and impact properties of these two kinds of balls have been investigated. Some balls randomly were selected as ...

In this paper, we show that the worst-case combinatorial complexity of the set of maximal non-occluded line segments among n unit balls is Θ(n). This improves on the trivial Ω(n) and O(n) bounds and also on the Ω(n) lower bound for the restricted setting of arbitrary-size balls [Devillers and Ramos, 2001]. We also prove an Ω(n) lower bound on the complexity of the set of non-occluded lines amon...