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...

In this paper, we propose a method for locating 3D position of a soccer ball from monocular image sequence of soccer games. Toward this goal, we adopted ground-model-to-image transformation together with physics-based approach that a ball follows the parabolic trajectory in the air. By using the transformation the heights of a ball can be easily calculated using simple triangular geometric rela...

Generation of a sequence of behaviors is necessary for the RoboCup Humanoid league to realize not simply a individual robot performance but also cooperative ones between robots. A typical example task is passing a ball between two humanoids, and the issues are: (1) basic skill decomposition, (2) skill learning, and (3) planning to connect the learned skills. This paper presents three methods fo...

In this paper we prove that if φ : C → C is a K-quasiconformal map, 0 < t < 2, and E ⊂ C is a compact set contained in a ball B, then H(E) diam(B) ≤ C(K) ( H ′ (φ(E)) diam(φ(B))t′ ) t tK

The goal of this paper is to show that Serrin’s result on overdetermined problems holds true for symmetric non-smooth domains. Specifically, we show that if a non-smooth domain D satisfies appropriate symmetry and convexity assumptions, and there exists a positive solution to a general overdetermined problem on D, then D must be a ball. As an application, we improve results on symmetry of non-n...

SmartGoals is an embodied multi-agent system designed for soccer training. A single SmartGoal is an interactive soccer goal. It can be in an active or passive state, detect the passage of a ball, and communicate with other SmartGoals. Challenging and dynamic training situations emerge from the interaction between human players and SmartGoals.

This note describes a method for generating an infinite-dimensional family of nonlinear control laws for underactuated systems. For a ball and beam system, the entire family is found explicitly. Copyright c © 2000 IFAC

It is impossible to comb all the hairs of a fuzzy ball so that: i) each hair lies tangent to the surface of the ball, and ii) the angles of the hairs vary continuously over the surface of the ball. (By this we mean that the angle between two hairs at positions p and q say can be made arbitrarily small by choosing q sufficiently close to p.) Any attempt to accomplish this feat must produce a cow...