Erdős et al. (Canad. J. Math. 18 (1966) 106–112) conjecture that there exists a constant dce such that every simple graph on n vertices can be decomposed into at most dcen circuits and edges. We consider toroidal graphs, where the graphs can be embedded on the torus, and give a polynomial time algorithm to decompose the edge set of an even toroidal graph on n vertices into at most (n + 3)/2 cir...

Single Helical Axis (SHAx) states obtained in high current reversed field pinch (RFP) plasmas display, aside from a dominant mode in the m=1 spectrum, also a dominant m=0 mode, with the same toroidal mode number as the m=1 one. The two modes have a fixed phase relationship. The island chain created by the m=0 mode across the reversal surface gives rise, at shallow reversal of the toroidal field...

We propose a proof of the recent observation due to Varagnolo and Vasserot that the q-deformed Fock spaces are modules of the quantum toroidal algebra U ′ q(sln,tor) (n ≥ 3) with the level (0, 1). The quantum toroidal action on the Fock space depends on a certain parameter κ. We find that with a specific choice of this parameter the action on the Fock spaces gives rise to the toroidal action on...

Globally coherent modes which are observed during formation in the S-1 Spheromak plasma occur during flux conversion and plasma relaxation toward a minimum-energy state, suggesting that these modes provide a means for relaxation. A significant finding is the temporal progression of these modes through a sequence n = 5, 4, 3, 2, m = 1, as q rises through rational fractions m/n, where n and m are...

Lower hybrid (LH) waves (Ωci ω Ωce, where Ωi,e ≡ Zi,eeB/mi,ec) have the attractive property of damping strongly via electron Landau resonance on relatively fast tail electrons and consequently are well-suited to driving current. Established modeling techniques use WKB expansions with self-consistent non-Maxwellian distributions. Higher order WKB expansions have shown some effects on the paralle...

In the context of loop quantum gravity, we construct the phase-space of the isolated horizon with toroidal topology. Within the loop quantum gravity framework, this horizon is described by a torus with N punctures and the dimension of the corresponding phase-space is calculated including the toroidal cycles as degrees of freedom. From this, the black hole entropy can be calculated by counting t...