We study two notions. One is that of lens-convexity. A set of circumradius not greater than one is lens-convex if, for any pair of its points, it contains every shorter unit circular arc connecting them. The other objects of study are bodies obtained as an intersection of finitely many balls of the same radius, called ball-polyhedra. We find analogues of several results on convex polyhedral set...

Hitters in fast ball-sports do not align their gaze with the ball throughout ball-flight; rather, they use predictive eye movement strategies that contribute towards their level of interceptive skill. Existing studies claim that (i) baseball and cricket batters cannot track the ball because it moves too quickly to be tracked by the eyes, and that consequently (ii) batters do not - and possibly ...

In this paper we propose an effective algorithm for detection of a soccer ball and players. In the currently available methods, the ball may not be detected when it is attached to the lines in the ground. To overcome this problem, we introduce a method to separate lines from the ball and segment the ball effectively. At first we detect the ground and the edges of the original image. Then an eff...

In formal concept analysis, it is well-known that the number of concepts can be exponential in worst case. To analyze average case, we introduce a probabilistic model for random contexts and prove has superpolynomial asymptotic lower bound.

The purpose of this study is to identify and explain hierarchical structure of knowledge in basketball game that can be applied to the entire formal tree model in sport games with the ball. Structural approach was used in the analysis of knowledge in basketball game. Here knowledge is shown as a hierarchical structured binary tree. The basic categories of the tree in this hypothetical model fro...

We investigate a new class of codes for the optimal covering of vertices in an undirected graphG such that any vertex in G can be uniquely identified by examining the vertices that cover it. We define a ball of radius t centered on a vertex v to be the set of vertices in G that are at distance at most t from v: The vertex v is then said to cover itself and every other vertex in the ball with ce...

A geodesic metric space is δ-hyperbolic in the sense of Gromov if and only if the intersection of any two metric balls is almost a ball. In particular, R-trees can be characterised by the property that the intersection of any two metric balls is again a metric ball.

Three different Swedish lightweight multistory buildings have been investigated with respect to the flanking transmission over an inner wall. Among the buildings analysed, one of them had been used by residents for three years and the two other were only just erected and being built respectively. A tapping machine and a Japanese ball were used as excitation sources so as to produce vibrations i...

The main purpose of this paper is to address two open questions raised by Reichel (2009) in [2] on characterizations of balls in terms of the Riesz potential and fractional Laplacian. For a bounded C1 domainΩ ⊂ RN , we consider the Riesz-potential u(x) = ∫ Ω 1 | x− y |N−α dy for 2 ≤ α = N . We show that u = constant on ∂Ω if and only if Ω is a ball. In the case of α = N , the similar characteri...