We present binary labelings for the angles of quadrangulations and plane Laman graphs, which are in analogy with Schnyder labelings for triangulations [W. Schnyder, Proc. 1st ACM-SIAM Symposium on Discrete Algorithms, 1990] and imply a special tree decomposition for quadrangulations. In particular, we show how to embed quadrangulations on a 2-book, so that each page contains a non-crossing alte...

We study weighted path lengths (depths) and distances for increasing tree families. For those subclasses of increasing tree families, which can be constructed via an insertion process, e.g., recursive trees, plane-oriented recursive trees and binary increasing trees, we can determine the limiting distribution which can be characterized as a generalized Dickman’s infinitely divisible distribution.

We associate with a plane meromorphic curve f a tree model T (f) based on its contact structure. Then we give a description of the y-derivative of f (resp. the Jacobian J(f, g)) in terms of T (f) (resp. T (fg)). We also characterize the regularity of f in terms of its tree.

A hyperbolic plane can be modeled by a structure called the enhanced binary tree. We study the ferromagnetic Ising model on top of the enhanced binary tree using the renormalization-group analysis in combination with transfer-matrix calculations. We find a reasonable agreement with Monte Carlo calculations on the transition point, and the resulting critical exponents suggest the mean-field surf...

Let P be a set of n points on the euclidean plane. Let Ls(P) and Lm(P) denote the lengths of the Steiner minimum tree and the minimum spanning tree on P, respectively. In 1968, Gilbert and Pollak conjectured that for any P, Ls(P) >/= (radical3/2)Lm(P). We provide an abridged proof for their conjecture in this paper.

background: in general, measurements of solar ultraviolet (uv) radiation are related to horizontal surfaces. while the hu­mans walking and standing outdoors expose to the natural solar uv radiation, their eyes, cheeks, extremities, trunks, or many other anatomical sites are close to vertical plane and random orient to different directions. in this study, we character­ized the diurnal variations...

M. C. Hernando1, F. Hurtado1, A. M arquez2, M. Mora1, M. Noy1

Part of the authors introduced in [C. Huemer, S. Kappes, A binary labelling for plane Laman graphs and quadrangulations, in Proceedings of the 22nd European Workshop on Computational Geometry 83–86, 2006] a binary labeling for the angles of plane quadrangulations, similar to Schnyder labelings of the angles of plane triangulations since in both cases the labelings are equivalent to tree decompo...

culture and folk beliefs are noticeably reflected in persian literature in general and in its poetry in particular. paying attention to such beliefs is sometimes useful while correcting a text and identifying a preferred record. on this basis, the present article examines two verses of sanai’s hadiqa al-haqiqa and offers the proposed correction. verses from other poets have been presented to fu...