We propose the decay modes B → a0(→ ηπ)π to determine the CKM phase α. One can analyze these modes through (i) the B → a0π isospin pentagon, (ii) the time dependent Dalitz plot of B0(t) → a±0 π → ηπ+π−, and (iii) the time dependence of B0(t) → a0(→ ηπ0)π0. We show that the a0π modes have certain advantages as compared to the ρπ modes, and strongly recommend the time dependent Dalitz plot analys...

We present methods for evaluating the Feynman parameter integrals associated with the pentagon diagram in 4 − 2 dimensions, along with explicit results for the integrals with all masses vanishing or with one non-vanishing external mass. The scalar pentagon integral can be expressed as a linear combination of box integrals, up to O( ) corrections, a result which is the dimensionallyregulated ver...

In this paper we consider deflations (inverse pocket flips) of n-gons for small n. We show that every pentagon can be deflated after finitely many deflations, and that any infinite deflation sequence of a pentagon results from deflating an induced quadrilateral on four of the vertices. We describe a family of hexagons that deflate infinitely for a specific deflation sequence, yet induce no infi...

Representations of planar triangulations as contact graphs of a set of internally disjoint homothetic triangles or respectively of a set of internally disjoint homothetic squares have received quite some attention in recent years. In this paper we investigate representations of planar triangulations as contact graphs of a set of internally disjoint homothetic pentagons. Surprisingly such a repr...

An acute triangulation is a triangulation whose triangles have all their angles less than π 2 . In this paper we prove that i) every planar pentagon can be triangulated into at most 54 acute triangles, and ii) every double pentagon can be triangulated into at most 76 acute triangles.

We prove the following generalised empty pentagon theorem: for every integer ` ≥ 2, every sufficiently large set of points in the plane contains ` collinear points or an empty pentagon. As an application, we settle the next open case of the “big line or big clique” conjecture of Kára, Pór, and Wood [Discrete Comput. Geom. 34(3):497–506, 2005].

[1] Since the terrorist attacks on the World Trade Center and the Pentagon, nearly every angle of these events has been explored in print, pertaining to everything from the individuals and nations involved to the political and historical precursors and ongoing social ramifications of the attacks. Yet few writers have seriously analyzed the actual arguments that Osama bin Laden and al-Qaeda have...

where (35) follows from the independence of X? and X,", and (36) and (37) follow because the channel is memoryless. Similarly, we have (38) 1 1 " In order to show that C, 1 C Cllm, it suffices to show that for any Pdyl and PA^, the corners of the pentagon,