A circle graph is the intersection graph of chords drawn in a circle. The best known general upper bound on the chromatic number of circle graphs with clique number k is 50 · 2. We prove a stronger bound of 2k − 1 for graphs in a simpler subclass of circle graphs, so called clean graphs. Based on this result we prove that the chromatic number of every circle graph with clique number at most 3 i...

The main purpose of this paper is to consider an explicit form of the Padé-type operators. To do so, we consider the representation of Padétype approximants to the Fourier series of the harmonic functions in the open disk and of the L-functions on the circle by means of integral formulas, and, then we define the corresponding Padé-type operators. We are also concerned with the properties of the...

We consider Gromov–Thurston examples of negatively curved nmanifolds which do not admit metrics of constant sectional curvature. We show that for each n ≥ 4 some of the Gromov–Thurston manifolds admit strictly convex real–projective structures.

A curve, also shown in introductory maths textbooks, seems like a circle. But it is actually a different curve. This paper discusses some easy approaches to classify the result, including a GeoGebra applet construction.

A notion of random walks for circle packings is introduced. The geometry behind this notion is discussed, together with some applications. In particular, we obtain a short proof of a result regarding the type problem for circle packings, which shows that the type of a circle packing is closely related to the type of its tangency graph.

Using notions of Minkowski geometry (i.e., of the geometry of finite dimensional Banach spaces) we find new characterizations of centrally symmetric convex bodies, equiframed curves, bodies of constant width and certain convex bodies with modified constant width property. In particular, we show that straightforward extensions of some properties of bodies of constant Euclidean width are also val...

This self-contained paper is part of a series [FF1, FF2] seeking to understand groups of homeomorphisms of manifolds in analogy with the theory of Lie groups and their discrete subgroups. Plante-Thurston proved that every nilpotent subgroup of Diff(S) is abelian. One of our main results is a sharp converse: Diff(S) contains every finitely-generated, torsion-free nilpotent group.

Permeability, the ability of rocks to flow hydrocarbons, is directly determined from core. Due to high cost associated with coring, many techniques have been suggested to predict permeability from the easy-to-obtain and frequent properties of reservoirs such as log derived porosity. This study was carried out to put clustering methods (dynamic clustering (DC), ascending hierarchical clustering ...