We study the existence of generalized transition fronts for a bistable reaction diffusion equation, ut − ∆u = f(u), in a heterogeneous medium, Ω = RN\K where K is a compact set of RN , with Neumann boundary condition and t ∈ R. In the paper, Bistable traveling waves around an obstacle (2009), H. Berestycki, F. Hamel and H. Matano prove the existence of a generalized transition front when K is s...

We show how any BSP tree TP for the endpoints of a set of n disjoint segments in the plane can be used to obtain a BSP tree of size O(n · depth(TP )) for the segments themselves, such that the range-searching efficiency remains almost the same. We apply this technique to obtain a BSP tree of size O(n log n) such that ε-approximate range searching queries with any constant-complexity convex quer...

In this paper, we are concerned with random sampling of an n dimensional integral point on an (n−1) dimensional simplex according to a multivariate discrete distribution. We employ sampling via Markov chain and propose two “hit-and-run” chains, one is for approximate sampling and the other is for perfect sampling. We introduce an idea of alternating inequalities and show that a logarithmic sepa...

Figure 1: Conceptual Model of Knowledge-Assisted Visual Analytics. The model is divided into two spaces (machine and human) and describes knowledge generation, conversion, and exploitation within the Visual Analytics (VA) process, in terms of artifacts: explicit knowledge Kε , data D , specification S , image I and tacit knowledge Kτ ; and processes: analysis A , visualization V , externalizati...

Let A be a m ×m complex matrix with zero trace and let ε > 0. Then there are m ×m matrices B and C such that A = [B, C] and ‖B‖‖C‖ ≤ Kεm‖A‖ where Kε depends only on ε. Moreover, the matrix B can be taken to be normal.

P.A. Martin / Wave Motion 51 (2014) 296–307 297 transmission coefficient is calculated exactly, as is the average transmission coefficient. These results do not assume that ε is small (compared to the spacing or wavelength) but they are complicated. We then approximate these results for small kε, and we show that they can be obtained more easily by assuming that kε is small from the outset. Thi...

We consider growing random networks {Gn}n≥1 where, at each time, a new vertex attaches itself to collection of existing vertices via fixed number m≥1 edges, with probability proportional function f (called attachment function) their degree. It was shown in [BB21] that such network models exhibit two distinct regimes: (i) the persistent regime, corresponding ∑i=1∞f(i)−2<∞, where top K maximal de...