A classification of Hermitian representations for the recently introduced fuzzy torus algebra is presented. This is carried out by regarding the fuzzy torus algebra as a q-deformation of parafermion. In addition to the known representations, new representations of both finite and infinite dimension are found. Using the infinite dimensional representation, coherent state for the fuzzy torus is c...

By means of an example it is shown that a supercritical bifurcation of an invariant 2-torus into an invariant 3-torus prevailing in the case of nonresonance may be replaced by a transcritical bifurcation into a pinched invariant 3-torus in the case of resonance. The connections of these bifurcation phenomena with the properties of the spectrum of the underlying invariant 2-torus are discussed. ...

In this paper we show that the torus knots Tp,q for 3 ≤ p ≤ q are homologically thick. Even more, we show that we can reduce the number of twists q without changing certain part of homology, and consequently we show that there exists stable homology for torus knots conjectured in [4]. Also, we calculate Khovanov homology groups of low homological degree for torus knots, and we conjecture that t...

One kind of hierarchical wave functions of Fractional Quantum Hall Effect (FQHE) on the torus are constructed. The multi-component nature of anyon wave functions and the degeneracy of FQHE on the torus are very clear reflected in this kind of wave functions. We also calculate the braid statistics of the quasiparticles in FQHE on the torus and show they fit to the picture of anyons interacting w...

We discuss consequences of the concept of a clumpy and dusty torus around AGN. Cloud-cloud collisions lead to an effective viscosity and a geometrically thick accretion disk, which has the required properties of a torus. A quantitative comparison of radiative transfer calculations for dust re-emission from the torus with NIR images, longbaseline visibilities and spectral energy distributions fo...

Using a unified framework, we show that a pruned 3D torus can be. explicitly specified by its pruning direction along which the links are uniformly removed from a complete 3D torus. The resulting networks, that offer the advantages of lower node degree and simpler layout, are inherently node-symmetric and maintain the same diameter as the original torus. It nuns out that the simplest pruning sc...

in this paper we describe, in the case of short messages, an efficient gossiping algorithm for 3-dimensional torus networks (wrap-around or toroidal meshes) that uses synchronous circuitswitched routing. The algorithm is based on a recursive decomposition of a torus. The algorithm requires an optimal number of rounds and a quasi-optimal number of intermediate switch settings to gossip in an 7i ...

recent experiments on the spherical tokamak have discovered the conditions to create a powerful plasma and ensure easy shaping and amplification of stability, high bootstrap current and confinement energy. the spherical tours (st) fusion energy development path is complementary to the tokamak burning plasma experiment such as nstx and higher toroidal beta regimes and improves the design of a po...