We investigate the x log x condition for a general (Crump–Mode– Jagers) multi-type branching process with arbitrary type space by constructing a size-biased population measure that relates to the ordinary population measure via the intrinsic martingale Wt. Sufficiency of the x log x condition for a non-degenerate limit of Wt is proved and conditions for necessity are investigated. GENERAL BRANC...

A five-level four-pulse phase-sensitive extended stimulated Raman adiabatic passage scheme is proposed to realize complete control of the population transfer branching ratio between two degenerate target states. The control is achieved via a three-node null eigenstate that can be correlated with an arbitrary superposition of the target states. Our results suggest that complete suppression of th...

The spectral branching behavior of the 2 × 2 operator matrix of the magneto-hydrodynamic α−dynamo is analyzed numerically. Some qualitative aspects of level crossings are briefly discussed with the help of a simple toy model which is based on a Z2−gradedpseudo-Hermitian 2× 2 matrix. The considered issues comprise: the underlying SU(1, 1) symmetry and the Krein space structure of the system, exc...

The spectral branching behavior of the 2 × 2 operator matrix of the magneto-hydrodynamic α−dynamo is analyzed numerically. Some qualitative aspects of level crossings are briefly discussed with the help of a simple toy model which is based on a Z2−gradedpseudo-Hermitian 2× 2 matrix. The considered issues comprise: the underlying SU(1, 1) symmetry and the Krein space structure of the system, exc...

Weak uniqueness is established for the martingale problem associated to a family of catalytic branching networks. This martingale problem corresponds to a stochastic differential equation with a degenerate Hölder continuous diffusion matrix. Our approach uses the semigroup perturbation method of Stroock and Varadhan and a modification of a Banach space of weighted Hölder continuous functions in...

Diiusion processes on the Sierpinski gasket and the abc-gaskets are constructed as limits of random walks. In terms of the associated renor-malization group, the present method uses the inverse trajectories which converge to unstable xed points corresponding to the random walks on one-dimensional chains. In particular, non-degenerate xed points are unnecessary for the construction. A limit theo...