Generalizing a property of the pseudovariety of all aperiodic semigroups observed by Tilson, we c... more Generalizing a property of the pseudovariety of all aperiodic semigroups observed by Tilson, we call E-local a pseudovariety V which satisfies the following property: for a finite semigroup, the subsemigroup generated by its idempotents belongs to V if and only if so do the subsemigroups generated by the idempotents in each of its regular D-classes. In this paper, we present several sufficient or necessary conditions for a pseudovariety to be E-local or for a pseudoidentity to define an E-local pseudovariety. We also determine several examples of the smallest E-local pseudovariety containing a given pseudovariety.
We study Heisenberg model of classical spins lying on the toroidal support, whose internal and ex... more We study Heisenberg model of classical spins lying on the toroidal support, whose internal and external radii are r and R, respectively. The isotropic regime is characterized by a fractional soliton solution. Whenever the torus size is very large, R → ∞, its charge equals unity and the soliton effectively lies on an infinite cylinder. However, for R = 0 the spherical geometry is recovered and we obtain that configuration and energy of a soliton lying on a sphere. Vortex-like configurations are also supported: in a ring torus (R > r) such excitations present no core where energy could blow up. At the limit R → ∞ we are effectively describing it on an infinite cylinder, where the spins appear to be practically parallel to each other, yielding no net energy. On the other hand, in a horn torus (R = r) a singular core takes place, while for R < r (spindle torus) two such singularities appear. If R is further diminished until vanish we recover vortex configuration on a sphere. *
Generalizing a property of the pseudovariety of all aperiodic semigroups observed by Tilson, we c... more Generalizing a property of the pseudovariety of all aperiodic semigroups observed by Tilson, we call E-local a pseudovariety V which satisfies the following property: for a finite semigroup, the subsemigroup generated by its idempotents belongs to V if and only if so do the subsemigroups generated by the idempotents in each of its regular D-classes. In this paper, we present several sufficient or necessary conditions for a pseudovariety to be E-local or for a pseudoidentity to define an E-local pseudovariety. We also determine several examples of the smallest E-local pseudovariety containing a given pseudovariety.
We study Heisenberg model of classical spins lying on the toroidal support, whose internal and ex... more We study Heisenberg model of classical spins lying on the toroidal support, whose internal and external radii are r and R, respectively. The isotropic regime is characterized by a fractional soliton solution. Whenever the torus size is very large, R → ∞, its charge equals unity and the soliton effectively lies on an infinite cylinder. However, for R = 0 the spherical geometry is recovered and we obtain that configuration and energy of a soliton lying on a sphere. Vortex-like configurations are also supported: in a ring torus (R > r) such excitations present no core where energy could blow up. At the limit R → ∞ we are effectively describing it on an infinite cylinder, where the spins appear to be practically parallel to each other, yielding no net energy. On the other hand, in a horn torus (R = r) a singular core takes place, while for R < r (spindle torus) two such singularities appear. If R is further diminished until vanish we recover vortex configuration on a sphere. *
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Papers by Adrielly Moura