We describe ERIT, a collection of C routines for eeciently and reliably handling intersection queries between pairs of primitive objects in 3D. ERIT supports intersection queries between the following pairs of primitives: triangle/line-segment, triangle/triangle, sphere/line-segment, sphere/triangle, cylinder/line-segment, cylinder/triangle, cylinder/sphere, cone/line-segment, cone/triangle, to...

We present the numbers of spanning forests on the Sierpinski gasket SGd(n) at stage n with dimension d equal to two, three and four, and determine the asymptotic behaviors. The corresponding results on the generalized Sierpinski gasket SGd,b(n) with d = 2 and b = 3, 4 are obtained. We also derive the upper bounds of the asymptotic growth constants for both SGd and SG2,b.

Gender differences in human social and communication behavior have long been observed in various contexts. This study investigates such differences in the case of online social networking. We find a general tendency towards gender homophily, more marked for women, however users having a large circle of friends tend to have more connections with users of the opposite gender. We also inspect the ...

We present a method for compact encoding of attributes such as normal vectors defined on a triangle mesh of arbitrary topology suitable in the context of view-dependent simplification. It is based on the recently introduced CAME data structure (Compressed Adaptive Multiresolution Encoding). In accordance with the vertex hierarchy defined by mesh simplification, we define an attribute hierarchy ...

Bowditch showed that a one-ended hyperbolic group which is not a triangle group splits over a two-ended group if and only if its boundary has a local cut point. As a corollary one obtains that splittings of hyperbolic groups over twoended groups are preserved under quasi-isometries. In this note we give a more direct proof of this corollary.

Let E be a closed set in R, and suppose that there is a k ≥ 1 such that every x, y ∈ E can be connected by a rectifiable path in E with length ≤ k |x−y|. This condition is satisfied by chord-arc curves, Lipschitz manifolds of any dimension, and fractals like Sierpinski gaskets and carpets. Note that length-minimizing paths in E are chord-arc curves with constant k. A basic feature of this condi...

Heron triangles have the property that all three of their sides as well as their area are positive integers. In this paper, we give some estimates for the number of Heron triangles with two of their sides fixed. We provide a general bound on this count H(a, b), where the sides a, b are fixed positive integers, and the estimate here is better than the one of Ionascu, Luca and Stănică for the gen...