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...

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...

A refined form of the ‘Folk Theorem’ that a smooth action by a compact Lie group can be (canonically) resolved, by iterated blow up, to have unique isotropy type is proved in the context of manifolds with corners. This procedure is shown to capture the simultaneous resolution of all isotropy types in a ‘resolution structure’ consisting of equivariant iterated fibrations of the boundary faces. T...

In the two-dimensional rotor-router walk (defined by Jim Propp and presented beautifully in [4]), the first time a particle leaves a site x it departs east; the next time this or another particle leaves x it departs south; the next departure is west, then north, then east again, etc. More generally, in any dimension d ≥ 1, for each site x ∈ Z fix a cyclic ordering of its 2d neighbors, and requi...

Binary-coded genetic algorithms (BGAs) traditionally use a uniform mapping to decode strings to corresponding real-parameter variable values. In this paper, we suggest a non-uniform mapping scheme for creating solutions towards better regions in the search space, dictated by BGA’s population statistics. Both variable-wise and vector-wise non-uniform mapping schemes are suggested. Results on fiv...

In recent decades, there have been strong calls for reforms in mathematics education, and in particular for changes in classroom practices. Teachers have been encouraged to organize instruction so that students participate in more collaborative, discussion-based activities with an eye to supporting a community of learners, rather than a set of individuals working on mathematics (NCTM, 1991). Or...