The model of the torus as a parallelogram in the plane with opposite sides identiied enables us to deene two families of parallel lines and to tessellate the torus, then to associate to each tessellation a toroidal map with an upward drawing. It is proved that a toroidal map has a tessellation representation if and only if its universal cover is 2-connected. Those graphs that admit such an embe...

A graph G containing a perfect matching is said to be m-extendable if m ≤ (|V (G)| − 2)/2 and for every matching M with |M | = m, there is a perfect matching F in G such that M ⊆ F . In a previous paper, four of the present five authors characterized those quadrangulations of the torus which are 2-extendable. In the present work a characterization of those which are 3-extendable is obtained. Si...

The observational limits on the present energy density of the Universe allow for a component that redshifts like 1/a and can contribute significantly to the total. We show that a possible origin for such a contribution is that the universe has a toroidal topology with ”wound” scalar fields around its cycles.

We present a novel differential-difference system in (2+1)-dimensional space-time (one discrete, two continuum), arisen from the Bogoyavlensky’s (2+1)-dimensional KdV hierarchy. Our method is based on the bilinear identity of the hierarchy, which is related to the vertex operator representation of the toroidal Lie algebra sl 2 .

We present a model of the establishment and maintenance of communication between mobile agents. We assume that the agents move through a fixed environment modeled by a motion graph and are able to communicate if they are within distance at most d of each other. As the agents move randomly, we analyze the evolution in time of the connectivity between a set of w agents, asymptotically for a large...

We study the two-point correlators of the currents of the E8 global symmetry in the N = (1, 0) superconformal six-dimensional theory as well as in the 4D superconformal theories upon toroidal compactification. From the high-energy behavior of the correlator we deduce that in 4D 10 copies of the superconformal theory with E8 global symmetry can be coupled to an N = 2 E8 gauge theory. We present ...

We show that type I string theory compactified in four dimensions in the presence of constant internal magnetic fields possesses N = 1 supersymmetric vacua, in which all Kähler class and complex structure closed string moduli are fixed. Furthermore, their values can be made arbitrarily large by a suitable tuning of the quantized magnetic fluxes. We present an explicit example for the toroidal c...

We propose the system of charge and current densities realizing static and non-static electric solenoids. There is a non-trivial electric vector potential outside the electrical cylindrical or toroidal solenoids. It cannot be eliminated by the gauge transformation. The non-static solenoids emit waves of electromagnetic potentials propagating with the velocity of light. Conditions under which th...

From a 4-hypercube colour space, spaces of the type hue-saturation-luminance are derived. The hue component may have the topology of a 2-sphere, a 2-torus or a 3-sphere, in several possibilities we consider.