While there is a hereditary component to tori, this does not explain all cases. Tori tend to appear more frequently during middle age of life; the torus palatinus is more commonly observed in females, but this is not the case with the torus mandibularis. Certain ethnic groups are more prone to one torus or the other. The torus is mainly removed due to prostodontic reasons, as it may also be use...

In 1965 Willmore conjectured that the integral of the square of the mean curvature of a torus immersed in R3 is at least 2π2 and attains this minimal value if and only if the torus is a Möbius transform of the Clifford torus. This was recently proved by Marques and Neves in [13]. In this paper, we show for tori there is a gap to the next critical point of the Willmore energy and we discuss an a...

Torus/mesh-based machines have received increasing attention. It is natural to identify the maximum healthy submeshes in a faulty torus/mesh so as to lower potential performance degradation, because the time for executing a parallel algorithm tends to depend on the size of the assigned submesh. This paper proposes an efficient approach for identifying all the maximum healthy submeshes present i...

We consider the local bifurcations that can happen to a quasiperiodic orbit in a 3-dimensional map: (a) a torus doubling resulting in two disjoint loops, (b) a torus doubling resulting in a single closed curve with two loops, (c) the appearance of a third frequency, and (d) the birth of a stable torus and an unstable torus. We analyze these bifurcations in terms of the stability of the point at...

Fractalization of torus and its transition to chaos in a quasi-periodically forced logistic map is re-investigated in relation with a strange nonchaotic attractor, with the aid of functional equation for the invariant curve. Existence of fractal torus in an interval in parameter space is confirmed by the length and the number of extrema of the torus attractor, as well as the Fourier mode analys...

Given an abstract triangulation of a torus, there is a unique point in moduli space which supports a circle packing for this triangulation. We will describe combinatorial deformations analogous to the process of conformal welding. These combinatorial deformations allow us to travel in moduli space from any packable torus to a point arbitrarily close to any other torus we choose. We also provide...

In this paper we investigate the problem of how to schedule n independent jobs on an m m torus based network. We develop a model to to quantify the effect of contention for communication links on the dilation of job execution time when multiple jobs share communication links; we then design an efficient algorithm to schedule a set of n independent jobs with different torus size requirements on ...

1. If the geodesic flow of a metric G on the torus T 2 is quadratically integrable then the torus T 2 isometrically covers a torus with a Liouville metric on it. 2. The set of quadratically integrable geodesic flows on the Klein bottle is described. §

We give explicit deformations of embeddings of abstractly planar graphs that lie on the standard torus T 2 ⊂ R3 and that contain neither a nontrivial knot nor a nonsplit link into the plane. It follows that ravels do not embed on the torus. Our results provide general insight into properties of molecules that are synthesized on a torus.

D0-brane theory on a torus with a nonvanishing B field is embedded into a string theory in the weak coupling limit. It is shown that the usual supersymmetric Yang-Mills theory on a noncommutative torus can not be the whole story. The Born-Infeld action survives the noncommutative torus limit.