Arc exchange systems and renormalization

We exhibit the construction of stable arc exchange systems from the stable laminations of hyperbolic diffeomorphisms. We prove a one-to-one correspondence between (i) Lipshitz conjugacy classes of C(1+H) stable arc exchange systems that are C(1+H) fixed points of renormalization and (ii) Lipshitz conjugacy classes of C(1+H) diffeomorphisms f with hyperbolic basic sets Lambda that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Lambda. Let HD(s)(Lambda) and HD(u)(Lambda) be, respectively, the Hausdorff dimension of the stable and unstable leaves intersected with the hyperbolic basic set L. If HD(u)(Lambda) = 1, then the Lipschitz conjugacy is, in fact, a C(1+H) conjugacy in (i) and (ii). We prove that if the stable arc exchange system is a C(1+HDs+alpha) fixed point of renormalization with bounded geometry, then the stable arc exchange system is smooth conjugate to an affine stable arc exchange system.

Study of led lamps technologies impact on the utility

With the growing interest in the issue of reducing powerconsumption in electricity applications, energy-saving devises and the problem of their operation gains more attention. The increase in the utilization of energy-saving lamps, especially LED lamps, leads to the wide interest in their influence on the power system. The impact of discussed devices on the voltage and current in the grid must be thoroughly studied before launching devices into the market. The studies undertaken on the LED lamps present in a wide range the issue of harmonic emission from lamps and their influence on power quality. Due to many anufacturing technologies, different LED devices can have various effects on the utility. It is significant to carry out researches concerning the adverse effects of energy-saving lamps in order to utilize devices that meet certain requirements which are set by the international commissions.