Let G be a subgroup of PSL(2, C). The discreteness problem for G is the problem of determining whether or not G is discrete. In this paper we assume that all groups considered are non-elementary. If G is generated by two elements, A and B of PSL(2, C), we have what is called the two-generator discreteness problem. Two-generator groups are important because, by a result of Jorgensen, an arbitrar...

Bloch-like oscillations induced by charge discreteness in quantum mesoscopic rings. We study the effect of charge discreteness in a quantum mesoscopic ring wih inductance L. The ring is pierced by a time depending external magnetic field. When the external magnetic flux varies uniformly, the current induced in the ring oscillates with a frequency proportional to the charge discreteness and the ...

We study a simple chemical reaction system and effects of the internal noise. Although stochastic differential equations are often used in order to study the fluctuations, they can not treat the discreteness in the number of components (molecules, individuals, and so on) because they are based on the continuum approximation which is justified by the large system size. The discreteness of compon...