In this paper we consider the ip operation for combinatorial pointed pseudo-triangulations where faces have size 3 or 4, so-called combinatorial 4-PPTs. We show that every combinatorial 4-PPT is stretchable to a geometric pseudo-triangulation, which in general is not the case if faces may have size larger than 4. Moreover, we prove that the ip graph of combinatorial 4-PPTs with triangular outer...

Inspired by the recent interest in combining geometry with random graph models, we explore in this paper two generalizations of the random dot product graph model proposed by Kraetzl, Nickel and Scheinerman, and Tucker [1, 2]. In particular we consider the properties of clustering, diameter and degree distribution with respect to these models. Additionally we explore the conductance of these mo...

We consider two classes of higher order proximity graphs defined on a set of points in the plane, namely, the k-Delaunay graph and the k-Gabriel graph. We give bounds on the following combinatorial and geometric properties of these graphs: spanning ratio, diameter, connectivity, chromatic number, and minimum number of layers necessary to partition the edges of the graphs so that no two edges of...

Entry of sand dunes into the railway tracks can result in sand deposition on tracks, railway obstruction, derailment, damage to track flexibility, and impairment of electrical signs and rail fleet. It is aimed to investigate the strategies and solutions for reducing sand aggregation on railway tracks (including construction of sand passage canals through embankments and modification of the geom...

Fuel nozzle is a key part of aero-engines. Due to the particularity fuel nozzle’s working environment, high machining requirements for surface quality and geometric accuracy hole were put forward. The existing process difficult meet requirements, so new proposed, which called flexible single-pass honing. For novel honing tool with diameter less than 1 mm, laws are not very clear, studies carrie...

The curvature effect on the electronic states of a deformed cylindrical conducting surface of variable diameter is theoretically investigated. The quantum confinement of electrons normal to the curved surface results in an effective potential energy that affects the electronic structures of the system at low energies. This suggests the possibility that ballistic transport of electrons in low-di...

In this paper we give some geometric characterizations of locally convex hypersurfaces. In particular, we prove that for a given locally convex hypersurface M with boundary, there exists r > 0 depending only on the diameter of M and the principal curvatures of M on its boundary, such that the r-neighbourhood of any given point on M is convex. As an application we prove an existence theorem for ...

1. INTRODUCTION. In his Almagest, Ptolemy inscribes triangles in a unit circle, a circle with diameter d = 1 (see [5], pp. 90–92). This way the length of each side (now chord) represents the value of the trigonometric function sine of the opposite angle. A similar geometric interpretation of the cosine function is possible. In Figure 1 we present Ptolemy's famous sketch, juxtaposed with a " dua...

€ σ z= 20 μm) at the SLAC FFTB has opened the way for very high gradient plasma wakefield acceleration experiments. We study here the use of these beams in a proposed Cerenkov wakefield experiment, where one may excite electromagnetic wakes in a simple dielectric tube with inner diameter of few100 microns that exceed the GV/m level. We discuss the scaling of the fields with design geometric des...

Structural and Algorithmic Properties of Static and Mobile Random Geometric Graphs by Alexandre de Oliveira Stauffer Doctor of Philosophy in Computer Science and the Designated Emphasis in Communication, Computation and Statistics University of California, Berkeley Professor Alistair Sinclair, Chair We study fundamental problems for static and mobile networks. First, we consider the random geom...