ar X iv : m at h - ph / 0 51 10 23 v 1 6 N ov 2 00 5 Open Subsystems of Conservative Systems

ar X iv : h ep - l at / 0 11 00 06 v 3 6 N ov 2 00 1 1 Matrix elements of ∆ S = 2 operators with Wilson fermions

ar X iv : m at h - ph / 0 51 10 74 v 1 2 5 N ov 2 00 5 1 / f Noise in Fractal Quaternionic Structures

We consider the logistic map over quaternions H ∼ R 4 and different 2D projections of Mandelbrot set in 4D quaternionic space. The approximations (for finite number of iterations) of these 2D projections are fractal circles. We show that a point process defined by radiuses Rj of those fractal circles exhibits pure 1/f noise.

ar X iv : m at h - ph / 0 51 10 25 v 1 7 N ov 2 00 5 L 2 - index of the Dirac operator of generalized Euclidean Taub - NUT metrics

We compute the axial anomaly for the Taub-NUT metric on R. We show that the axial anomaly for the generalized Taub-NUT metrics introduced by Iwai and Katayama is finite, although the Dirac operator is not Fredholm. We show that the essential spectrum of the Dirac operator is the whole real line. Pacs: 04.62.+v

ar X iv : 0 71 1 . 23 72 v 1 [ m at h . G R ] 1 5 N ov 2 00 7 Braid groups and Artin groups

ar X iv : m at h - ph / 0 51 10 23 v 2 1 2 Ja n 20 06 Open Subsystems of Conservative Systems

The subject under study is an open subsystem of a larger linear and conservative system and the way in which it is coupled to the rest of system. Examples are a model of crystalline solid as a lattice of coupled oscillators with a finite piece constituting the subsystem, and an open system such as the Helmholtz resonator as a subsystem of a larger conservative oscillatory system. Taking the vie...