Mixing properties of generalized T,T−1 transformations

Mixing properties of induced random transformations

Let S(N) be a random walk on a countable abelian group G which acts on a probability space E by measure–preserving transformations (Tv)v∈G. For any Λ ⊂ E we consider the random return time τ at which TS(τ) ∈ Λ. We show that the corresponding induced skew product transformation is K–mixing whenever a natural subgroup of G acts ergodically on E.

Generalized Jordan-Wigner transformations.

We introduce a new spin-fermion mapping, for arbitrary spin S generating the SU(2) group algebra, that constitutes a natural generalization of the Jordan-Wigner transformation for S = 1/2. The mapping, valid for regular lattices in any spatial dimension d, serves to unravel hidden symmetries. We illustrate the power of the transformation by finding exact solutions to lattice models previously u...

Properties of Generalized Berwald Connections

Generalized Catalan Numbers and Generalized Hankel Transformations

so that an is the sum of the n th and n + 1 Catalan numbers. Then the Hankel transform of {a0, a1, a2, . . .} begins 2, 5, 13, 34, . . .. Layman first conjectured in the On-Line Encyclopedia of Integer Sequences ([4], see sequence A001906) that this sequence consists of every other Fibonacci number, and subsequently Cvetković, Rajković and Ivković [2] proved this conjecture. The current paper a...

New Spectral Multiplicities for Mixing Transformations

It is shown that if E is any subset of N such that either 1 ∈ E or 2 ∈ E then there is a mixing transformation whose set of spectral multiplicities is E.