A charged particle in a uniform magnetic field in a two-dimensional torus has a discrete noncommutative translation symmetry instead of a continuous commutative translation symmetry. We study topology and symmetry of a particle in a magnetic field in a torus of arbitrary dimensions. The magnetic translation group (MTG) is defined as a group of translations that leave the gauge field invariant. ...

The response of an oscillator to a small amplitude periodic excitation is discussed. In particular, sufficient conditions are formulated for the perturbed oscillator to have an invariant torus in the phase cylinder. When such an invariant torus exists, some perturbed solutions are in the basin of attraction of this torus and are thus entrained to the dynamical behavior of the perturbed system o...

INTRODUCTION Osteonecrosis of the palate is a rare condition which is even rarer when occurring on a torus palatinus and associated with bisphosphonate (BP). CASE PRESENTATION We report an uncommon case of osteonecrosis of a torus palatinus. Our patient was a 67-year-old white female who presented with a painful intraoral ulcer associated with necrotic bone tissue of her torus palatinus, due ...

The torus is one of the popular topologies for the interconnecting processors to build high-performance multicomputers. This paper presents methods to generate edge-disjoint Hamil-tonian cycles in 2D tori. 1. Introduction. A multicomputer system consists of multiple nodes that communicate by exchanging messages through an interconnection network. At a minimum, each node normally has one or more...

Twisted torus knots and links are given by twisting adjacent strands of a torus link. They are geometrically simple and contain many examples of the smallest volume hyperbolic knots. Many are also Lorenz links. We study the geometry of twisted torus links and related generalizations. We determine upper bounds on their hyperbolic volumes that depend only on the number of strands being twisted. W...

Unified schemes of active galactic nuclei (AGN) require an obscuring dusty torus around the central engine. Torus sizes of hundreds of parsecs were deduced from early theoretical modeling efforts, but high-resolution IR observations now show that the torus size is no more than a few parsecs. This conflict is resolved when the clumpy nature of the torus is taken into account. The compact torus m...

Tropical algebraic geometry offers new tools for elimination theory and implicitization. We determine the tropicalization of the image of a subvariety of an algebraic torus under any homomorphism from that torus to another torus.

We present preliminary results from high resolution (∼ 0.05”) adaptive optics observations of Cygnus A. The images show a bi-conic structure strongly suggestive of an obscuring torus around a quasar nucleus. A bright (K′ = 18.5) point source is found near the expected position of the nucleus. We interpret this source as the hot inner rim of the torus seen through the opening of the torus. Using...

Generalized honeycomb torus is a candidate for interconnection network architectures, which includes honeycomb torus, honeycomb rectangular torus, and honeycomb parallelogramic torus as special cases. Existence of Hamiltonian cycle is a basic requirement for interconnection networks since it helps map a “token ring” parallel algorithm onto the associated network in an efficient way. Cho and Hsu...

We give a presentation for the (integral) torus-equivariant Chow ring of the quot scheme, a smooth compactification of the space of rational curves of degree d in the Grassmannian. For this presentation, we refine Evain’s extension of the method of Goresky, Kottwitz, and MacPherson to express the torus-equivariant Chow ring in terms of the torus-fixed points and explicit relations coming from t...