In this note I review the current determination of the unitarity triangle parameters by using the theoretical and experimental informations available until summer 2000.

Superquadrics are able to represent a large variety of objects with only a few parameters and a single equation. We present a superquadric representation strategy for automotive parts composed of 3-D triangle meshes. Our strategy consists of two major steps of part decomposition and superquadric fitting. The originalities of this approach include the following two features. First, our approach ...

The r-Hofstadter triangle and the (1 − r)-Hofstadter triangle are proved perspective, and homogeneous trilinear coordinates are found for the perspector. More generally, given a triangle DEF inscribed in a reference triangle ABC, triangles A′B′C′ and A′′B′′C′′ derived in a certain manner from DEF are perspective to each other and to ABC. Trilinears for the three perspectors, denoted by P ∗, P1,...

Metric spaces provide a framework for analysis and have several very useful properties. Many of these properties follow in part from the triangle inequality. However, there are several applications in which the triangle inequality does not hold but in which we may still like to perform analysis. This paper investigates what happens if the triangle inequality is removed all together, leaving wha...

The (negative) Torricelli triangle T1(ABC) of a nondegenerate (positively oriented) triangle ABC is defined to be the triangle A1B1C1, where ABC1, BCA1, and CAB1 are the equilateral triangles drawn outwardly on the sides of ABC. It is known that not every triangle is the Torricelli triangle of some initial triangle, and triangles that are not Torricelli triangles are characterized in [28]. In t...

This paper is concerned with the following elliptic system:$$ left{ begin{array}{ll} -triangle u + b(x)nabla u + V(x)u=g(x, v), -triangle v - b(x)nabla v + V(x)v=f(x, u), end{array} right. $$ for $x in {R}^{N}$, where $V $, $b$ and $W$ are 1-periodic in $x$, and $f(x,t)$, $g(x,t)$ are super-quadratic. In this paper, we give a new technique to show the boundedness of Cerami sequences and estab...

In the field of view-dependant continuous level of detail of triangle-meshes it is often necessary to extract the current LOD triangle by triangle. Thus, triangle strips are only of very limited use, or only usable with a high effort. In this work a method is proposed that allows a stepwise reduction of a great, fine stepped LOD hierarchy by merging nodes. The result of this process is a reduce...

We present a novel framework for the efficient simulation and animation of discrete thin shells. Our method takes a point sampled surface as input and performs all necessary computations without intermediate triangulation. We discretize the thin shell functional using so-called fibers. Such fibers are locally embedded parametric curves crisscrossing individual point samples. In combination, the...

We determine the possible eigenvalues of elliptic matrices A,B, C in PU(2, 1) satisfying ABC = 1. This is done by describing geometrically the image of a certain momentum map for the (non-compact) group action of PU(2, 1) by conjugation on C1 × C2 where C1 and C2 are fixed elliptic conjugacy classes in PU(2, 1). Surprisingly, this image is not always convex, rather it is the union of one, two o...

We report on the initial measurements of the angle γ and the sum of angles 2β + γ of the Unitarity Triangle. When compared with indirect information on the value of γ from other measurements of CKM parameters, the measurement of these angles will provide a precise test of Standard Model predictions, as statistics increase. There are several methods for directly measuring γ and 2β + γ. We report...