For several important classes of manifolds acted on by the torus, the information about the action can be encoded combinatorially by a regular n-valent graph with vector labels on its edges, which we refer to as the torus graph. By analogy with the GKM-graphs, we introduce the notion of equivariant cohomology of a torus graph, and show that it is isomorphic to the face ring of the associated si...

Intersection algorithms are very important in computation of geometrical problems. Algorithms for a line intersection with linear or quadratic surfaces are quite efficient. However, algorithms for a line intersection with other surfaces are 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 in...

The detection of outgassing water vapor from Enceladus is one of the great breakthroughs of the Cassini mission. The fate of this water once ionized has been widely studied; here we investigate the effects of purely neutral-neutral interactions within the Enceladus torus. We find that, thanks in part to the polar nature of the water molecule, a cold (∼ 180 K) neutral torus would undergo rapid v...

A peculiarity of the geometry of the euclidean 3-sphere S is that it allows for the existence of compact without boundary minimally immersed surfaces. Despite a wealthy of examples of such surfaces, the only known tori minimally embedded in S are the ones congruent to the Clifford torus. In 1970 Lawson conjectured that the Clifford torus is, up to congruences, the only torus minimally embedded ...

The torus is a popular interconnection topology and several commercial multicomputers use a torus as the basis of their communication network. Moreover, there are many parallel algorithms with torus-structured and mesh-structured task graphs have been developed. If one network can embed a mesh or torus network, the algorithms with mesh-structured or torus-structured can also be used in this net...

The time and angle dependent line and continuum emission from a dense torus around a cosmological gamma-ray burst source is simulated, taking into account photoionization, collisional ionization, recombination, and electron heating and cooling due to various processes. The importance of the hydrodynamical interaction between the torus and the expanding blast wave is stressed. Due to the rapid d...

let $g=(v,e)$ be a connected simple graph. a labeling $f:v to z_2$ induces two edge labelings $f^+, f^*: e to z_2$ defined by $f^+(xy) = f(x)+f(y)$ and $f^*(xy) = f(x)f(y)$ for each $xy in e$. for $i in z_2$, let $v_f(i) = |f^{-1}(i)|$, $e_{f^+}(i) = |(f^{+})^{-1}(i)|$ and $e_{f^*}(i) = |(f^*)^{-1}(i)|$. a labeling $f$ is called friendly if $|v_f(1)-v_f(0)| le 1$. for a friendly labeling $f$ of...

We consider the situation of a compact irreducible subvariety of a smooth compact complex variety equipped with a Kähler form preserved by a torus action. We study the image of that subvariety under the moment map of the Kähler form. 1. Main result The moment map of a Hamiltonian T -symplectic/Kähler manifold has been one of the main interests of study for mathematical as well as physical reaso...

AIM To determine the prevalence of tori in Jordanian edentulous patients, the sex variation in their distribution, and their clinical characteristics. METHODS Three hundred and thirty eight patients were examined in the Prosthodontic Clinic in the Department of Restorative Dentistry at Jordan University of Science and Technology. The location, extent, and clinical presentation of tori were re...

In this letter we study D particle quantum mechanics on a torus in the limit that one or more cycles of the torus have a zero length.