Abstract. In [7], the second author classified configurations of the singularities on tame sextics of torus type. In this paper, we give a complete classification of the singularities on irreducible sextics of torus type, without assuming the tameness of the sextics. We show that there exists 121 configurations and there are 5 pairs and a triple of configurations for which the corresponding mod...

Abstract. Let Mn be the set of equivariant unoriented cobordism classes of all ndimensional 2-torus manifolds, where an n-dimensional 2-torus manifold M is a smooth closed manifold of dimension n with effective smooth action of a rank n 2-torus group (Z2) . Then Mn forms an abelian group with respect to disjoint union. This paper determines the group structure of Mn and shows that each class of...

The FPP, grid, cyclic, torus and e-torus quorum systems satisfy the rotation closure property and have the optimal or near optimal quorum sizes. They can be used to achieve asynchronous power-saving algorithms in mobile ad hoc networks with the lowest or near lowest active ratios. The algorithms guarantee that a node receives one or more beacons from every neighboring node within a round of bea...

We use the Bradlow parameter expansion to construct the metric tensor in the space of solutions of the Bogomolny equations for the Abelian Higgs model on a twodimensional torus. Using this metric we study the dynamics and scattering of vortices on the torus within the geodesic approximation. For small torus volumes the metric is determined in terms of a small number of parameters. For large vol...

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

We study drawings of graphs on the torus with crossings allowed. A question posed in [4], specialized to the case of the torus, asks, whether for every disconnected graph there is a drawing in the torus with the minimal number of crossings, such that one of the graphs is drawn in a planar disc. We reduce the problem to an interesting question from the geometry of numbers and solve a special case.

This paper describes a fault-tolerant routing mechanism to facilitate data routing in Torus embedded hypercube interconnection network subject to node failures in parallel computing. It is shown that by only using feasible paths routing can be substantially simplified. Though there are algorithms for fault tolerant communication in torus and hypercube networks, there exits no efficient algorith...

In this paper we give a necessary and sufficient condition in which a sequence of Kleinian punctured torus groups converges. This result tells us that every exotically convergent sequence of Kleinian punctured torus groups is obtained by the method due to Anderson and Canary (Invent. Math. 1996). Thus we obtain a complete description of the set of points at which the space of Kleinian punctured...

We present results from a new Monte Carlo radiative transfer computer code, STOKES, developed to model polarization induced by scattering off free electrons and dust grains. STOKES is freely available on the web and can be used to model scattering in a wide variety of astrophysical situations. For edge-on (type-2) viewing positions, the polarization produced by a dusty torus alone is largely wa...