A Central Limit Theorem for the Poisson-Voronoi Approximation

For a compact convex set $K$ and a Poisson point process $\eta$, the union of all Voronoi cells with a nucleus in $K$ is the Poisson-Voronoi approximation of $K$. Lower and upper bounds for the variance and a central limit theorem for the volume of the Poisson-Voronoi approximation are shown. The proofs make use of so called Wiener-It\^o chaos expansions and the central limit theorem is based on a more abstract central limit theorem for Poisson functionals, which is also derived.Comment: 22 pages, modified reference

Regular Polygonal Complexes of Higher Ranks in E^3

The paper establishes that the rank of a regular polygonal complex in 3-space E^3 cannot exceed 4, and that the only regular polygonal complexes of rank 4 in 3-space are the eight regular 4-apeirotopes

A Critique of Advertisements for Female Hygiene Products: A Silent Crisis in America

Female hygiene advertisements can be ambiguous due to the intimate nature of menstruation. This can result in a lack of information and invoke the need to hide signals of menstruation. Further, understanding the target audience’s desires and needs is crucial. Just like any other advertisement campaign, the women buying female hygiene products desire to know the benefits of one type over another. Adding an emotive appeal or a creative method to the advertisement is not wrong. This thesis does not suggest for a dull advertisement; however, there is a balance—a campaign designed to care for and inform women while meeting their body’s needs

Chiral polyhedra in ordinary space, II

A chiral polyhedron has a geometric symmetry group with two orbits on the flags, such that adjacent flags are in distinct orbits. Part I of the paper described the discrete chiral polyhedra in ordinary Euclidean 3-space with finite skew faces and finite skew vertex-figures; they occur in infinite families and are of types {4,6}, {6,4} and {6,6}. Part II completes the enumeration of all discrete chiral polyhedra in 3-space. There exist several families of chiral polyhedra with infinite, helical faces. In particular, there are no discrete chiral polyhedra with finite faces in addition to those described in Part I.Comment: 48 page

Simulation of an Intra-Pulse Interaction Point Feedback for Future Linear Colliders

In future normal-conducting linear colliders, the beams will be delivered in short bursts with a length of the order of 100 ns. The pulses will be separated by several ms. In order to maintain high luminosity, feedback is necessary on a pulse-to-pulse basis. In addition, intra-pulse feedback that can correct beam positions and angles within one pulse seem technically feasible. The likely performances of different feedback options are simulated for the NLC (Next Linear Collider) and CLIC (Compact Linear Collider).Comment: LINAC2000 Conference, Paper ID MOA0

Combinatorial Space Tiling

The present article studies combinatorial tilings of Euclidean or spherical spaces by polytopes, serving two main purposes: first, to survey some of the main developments in combinatorial space tiling; and second, to highlight some new and some old open problems in this area.Comment: 16 pages; to appear in "Symmetry: Culture and Science

Beam Dynamics Simulation for the CTF3 Drive-Beam Accelerator

A new CLIC Test Facility (CTF3) at CERN will serve to study the drive beam generation for the Compact Linear Collider (CLIC). CTF3 has to accelerate a 3.5 A electron beam in almost fully-loaded structures. The pulse contains more than 2000 bunches, one in every second RF bucket, and has a length of more than one microsecond. Different options for the lattice of the drive-beam accelerator are presented, based on FODO-cells and triplets as well as solenoids. The transverse stability is simulated, including the effects of beam jitter, alignment and beam-based correction.Comment: LINAC2000 Conference, Paper No MOA0

Polyhedra, Complexes, Nets and Symmetry

Skeletal polyhedra and polygonal complexes in ordinary Euclidean 3-space are finite or infinite 3-periodic structures with interesting geometric, combinatorial, and algebraic properties. They can be viewed as finite or infinite 3-periodic graphs (nets) equipped with additional structure imposed by the faces, allowed to be skew, zig-zag, or helical. A polyhedron or complex is "regular" if its geometric symmetry group is transitive on the flags (incident vertex-edge-face triples). There are 48 regular polyhedra (18 finite polyhedra and 30 infinite apeirohedra), as well as 25 regular polygonal complexes, all infinite, which are not polyhedra. Their edge graphs are nets well-known to crystallographers, and we identify them explicitly. There also are 6 infinite families of "chiral" apeirohedra, which have two orbits on the flags such that adjacent flags lie in different orbits.Comment: Acta Crystallographica Section A (to appear