In the recent study of infinite root systems, fractal patterns of ball packings were observed while visualizing roots in affine space. In fact, the observed fractals are exactly the ball packings described by Boyd and Maxwell. This correspondence is a corollary of a more fundamental result: given a geometric representation of a Coxeter group in Lorentz space, the set of limit directions of weig...

The ancient Gamow liquid drop model of nuclear energies has had a renewed life as an interesting problem in the calculus of variations: Find a set Ω ⊂ R3 with given volume A that minimizes the sum of its surface area and its Coulomb self energy. A ball minimizes the former and maximizes the latter, but the conjecture is that a ball is always a minimizer—when there is a minimizer. Even the exist...

In this work, we study an approximate control problem for the heat equation, with a nonstandard but rather natural restriction on the solution. It is well known that approximate controllability holds. On the other hand, the total mass of the solutions of the uncontrolled system is constant in time. Therefore, it is natural to analyze whether approximate controllability holds supposing the total...

A force-velocity relationship in overarm throwing was determined using ball weights varying from 0.2 to 0.8 kg. Seven experienced handball players were filmed at 240 frames per second. Velocity of joints of the upper extremity and ball together with the force on the ball were derived from the data. A statistically significant negative relationship between force and maximal ball velocity, as wel...

objecttive(s): despite the poor mechanical properties of hydroxyapatite, its unique biological properties leads we think about study on improving its properties rather than completely replacing it with other biomaterials. accordingly, in this study we introduced hydroxyapatite reinforced with hardystonite as a novel bio-nanocompositeand evaluate its in-vitro bioactivity with the aim of developi...

This paper describes the method employed to track and identify each robot during a Robocup match. Also, the playing ball is tracked with almost no extra processing effort. To track the robots it is necessary the use of adequate markers so that not only the position is extracted but also the heading. We discuss the difficulties associated with this problem, various possible approaches and justif...

Let M either be a closed real analytic Riemannian manifold or a closed C∞-Riemannian surface. We estimate from below the volume of a nodal domain component in an arbitrary ball, provided that this component enters the ball deeply enough. The proof combines a generalized form of Hadamard’s Three Circles Theorem due to Nadirashvili, Rapid Growth of Eigenfunctions in Narrow Domains and the Donnell...