In this note we consider a simple shape operator discretization for general meshes, based on computing an interpolating quadratic function passing through vertices of a triangle and its edge-adjacent neighbors. This approximation is computationally simple and consistent for a broad class of meshes. However, its convergence properties in the context of mesh optimization problems are not as good ...

This note describes the geometrical pattern of zeroes and ones obtained by reducing modulo two each element of Pascal's triangle formed from binomial coefficients. When an infinite number of rows of Pascal's triangle are included, the limiting pattern is found to be "self-similar," and is characterized by a "fractal dimension" log2 3. Analysis of the pattern provides a simple derivation of the ...

A complex hyperbolic triangle group is a group generated by three complex reflections fixing complex slices (complex geodesics) in complex hyperbolic space. Our purpose in this paper is to improve the result in [3] and to discuss discreteness of complex hyperbolic triangle groups of type (n, n,∞; k).

In this paper we get a power estimate from above of the probability that Buffon’s needle will land within distance 3 of Sierpinski’s gasket of Hausdorff dimension 1. In comparison with the case of 1/4 corner Cantor set considered in Nazarov, Peres, and the second author [14]: we still need the technique of [14] for splitting the directions to good and bad ones, but the case of Sierpinski gasket...

A rational triangle is a triangle with rational sides and rational area. A Heron triangle is a triangle with integral sides and integral area. In this article we will show that there exist infinitely many rational parametrizations, in terms of s, of rational triangles with perimeter 2s(s + 1) and area s(s − 1). As a corollary, there exist arbitrarily many Heron triangles with all the same area ...

background: complete atrioventricular block (av block) is a serious complication of slow pathway ablation therapy in the treatment of atrioventricular nodal re-entrant tachycardia (avnrt).   the present study was aimed at determining whether the electroanatomical pace mapping of koch’s triangle could significantly improve the safety, efficiency, and efficacy of selective slow pathway ablation i...

The distribution of partition function zeros of the two-dimensional Ising model in the complex temperature plane is studied within the context of triangular decorated lattices and their triangle-star transformations. Exact recursion relations for the zeros are deduced for the description of the evolution of the distribution of the zeros subject to the change of decoration level. In the limit of...

We present an algorithm to generate point distributions with high-quality blue noise characteristics on discrete surfaces. It is based on the concept of Capacity-Constrained Surface Triangulation (CCST), which approximates the underlying continuous surface as a well-formed triangle mesh with uniform triangle areas. The algorithm takes a triangle mesh and the number of sample points as input, an...

We show that an improvement to the best known quantum lower bound for Graph-Collision problem implies an improvement to the best known lower bound for Triangle problem in the quantum query complexity model. In Graph-Collision we are given free access to a graph (V,E) and access to a function f : V → {0, 1} as a black box. We are asked to determine if there exist (u, v) ∈ E, such that f(u) = f(v...

Vertex coloring is a central concept in graph theory and an important symmetry-breaking primitive in distributed computing. Whereas degree-∆ graphs may require palettes of∆+1 colors in the worst case, it is well known that the chromatic number of many natural graph classes can be much smaller. In this paper we give new distributed algorithms to find (∆/k)-coloring in graphs of girth 4 (triangle...