The asymptotic number (of isomorphism classes) of toroidal maps of type (3; 6) with at most n vertices is found, together with the fraction of those with multiplicity 1. Accurate lower and upper asymptotic estimates are provided for the number of toroidal maps of type (3; 6) with a Hamiltonian normal cycle and with at most n vertices. The case of type (6; 3) toroidal maps follows by duality. Si...

Geometrical and topological properties of the quasi-plane Szekeres model and of the plane symmetric dust model are discussed. Some related comments on the quasihyperbolical model are made. These properties include: (1) The pattern of expansion in the plane symmetric case, and the Newtonian model that imitates it; (2) The possibility of toroidal topology of the t = const sections in the plane sy...

A clique minor in a graph G can be thought of as a set of connected subgraphs in G that are pairwise disjoint and pairwise adjacent. The Hadwiger number η(G) is the maximum cardinality of a clique minor in G. It is one of the principle measures of the structural complexity of a graph. This paper studies clique minors in the Cartesian product G H. Our main result is a rough structural characteri...

The goal of magnetic confinement devices such as tokamaks is to produce energy from nuclear fusion reactions in plasmas at low densities and high temperatures. Experimentally, toroidal flows have been found to significantly improve the energy confinement, and therefore the performance of the machine. As extrinsic momentum sources will be limited in future fusion devices such as ITER, an underst...

Let X be any variety in characteristic zero. V?X an open subset that has toroidal singularities. We show the existence of a canonical desingularization except for V. It is morphism f:Y?X, which does not modify V and transforms into embedding Y, with singularities extending those on Moreover, exceptional divisor simple normal crossings Y. The theorem naturally generalizes Hironaka desingularizat...

bandwidth labelling is a well known research area in graph theory. we provide a new proof that the bandwidth of mobius ladder is 4, if it is not a $k_{4}$, and investigate the bandwidth of a wider class of mobius graphs of even strips.

Many effects influence toroidal flow evolution in tokamak plasmas. Momentum sources and radial transport due to collisional processes and microturbulence-induced anomalous transport are usually considered. In addition, toroidal flow can be affected by non-axisymmetric magnetic fields; resonant components cause localized electromagnetic toroidal torques near rational surfaces in flowing plasmas ...

A parametric study of electromagnetic effects on toroidal momentum transport has been performed. The work is based on a new version of the Weiland model where symmetry breaking toroidicity effects derived from the stress tensor have been taken into account. The model includes a self-consistent calculation of the toroidal momentum diffusivity, which contains both diagonal and off-diagonal contri...