The hard palate is formed anteriorly by the palatine processes of maxillae and posteriorly by the horizontal plates of palatine bones. The region of the median palatal intermaxillary suture is occasionally raised in whole or part of its length into a prominent ridge known as torus palatinus. A similar longitudinal maxillary torus may also appear on the palate. Torus palatinus is the most common...

There is no 5,7-triangulation of the torus, that is, no triangulation with exactly two exceptional vertices, of degree 5 and 7. Similarly, there is no 3, 5-quadrangulation. The vertices of a 2, 4-hexangulation of the torus cannot be bicolored. Similar statements hold for 4, 8-triangulations and 2, 6-quadrangulations. We prove these results, of which the first two are known and the others seem t...

Intersection algorithms are very important in computation of geometrical problems. An intersection of a line with linear or quadratic surfaces is well done, however a line intersection with other surfaces is more complex and time consuming. In this case the object is usually closed into a simple bounding volume to speed up the cases when the given line cannot intersect the given object. In this...

We use a relativistic ray-tracing code to analyze the X-ray emission from a pressure-supported oscillating relativistic torus around a black hole. We show that a strong correlation exists between the intrinsic frequencies of the torus normal modes and the extrinsic frequencies seen in the observed light curve power spectrum. This correlation demonstrates the feasibility of the oscillating-torus...

Two embeddings Ψ1 and Ψ2 of a graph G in a surface Σ are equivalent if there is a homeomorphism of Σ to itself carrying Ψ1 to Ψ2. In this paper, we classify the flexibility of embeddings in the torus with representativity at least 4. We show that if a graph G has an embedding Ψ in the torus with representativity at least 4, then one of the following holds: (i) Ψ is the unique embedding of G in ...

There is no 5,7-triangulation of the torus, that is, no triangulation with exactly two exceptional vertices, of degree 5 and 7. Similarly, there is no 3,5-quadrangulation. The vertices of a 2,4-hexangulation of the torus cannot be bicolored. Similar statements hold for 4,8-triangulations and 2,6-quadrangulations. We prove these results, of which the first two are known and the others seem to be...

A design analysis and comparison of a product network generated from torus and hypercube networks known as torus embedded hypercube scalable interconnection network suitable for parallel computers is presented in this paper. It is shown here that with minor modifications in architecture of the existing mesh embedded hypercube interconnection network how good a torus embedded hypercube interconn...

The torus manifolds have been defined and studied by Masuda and Panov ([7]) who in particular also describe its cohomology ring structure. In this note we shall describe the topological K-ring of a class of torus manifolds (those for which the orbit space under the action of the compact torus is a homology poytope whose nerve is shellable) in terms of generators and relations. Since these torus...

In this paper we construct the spectral curve and the Baker–Akhiezer function for the Dirac operator which form the data of the Weierstrass representation of the Clifford torus. This torus appears in many conjectures from differential geometry (see Section 2). By constructing this Baker–Akhiezer function we demonstrate a general procedure for constructing Dirac operators and their Baker–Akhieze...

The zero modes of closed strings on a torus –the torus coordinates plus dual coordinates conjugate to winding number– parameterize a doubled torus. In closed string field theory, the string field depends on all zero-modes and so can be expanded to give an infinite set of fields on the doubled torus. We use string field theory to construct a theory of massless fields on the doubled torus. Key to...