Almost mixing transformations

Some Remarks on Almost Periodic Transformations

1. Recurrent and almost periodic transformations. Notations. Let ƒ be a continuous mapping (not necessarily a homeomorphism) of a topological space X in itself (that is, f(X)QX). We say that ƒ is recurrent a t a point # £ X , or that x is recurrent under ƒ, if, given any neighbourhood U(x) of x, there exist infinitely many positive integers n for which f(x)ÇE.U(x). (This definition is equivalen...

Almost Optimal Explicit Johnson-Lindenstrauss Transformations

The Johnson-Lindenstrauss lemma is a fundamental result in probability with several applications in the design and analysis of algorithms in high dimensional geometry. Most known constructions of linear embeddings that satisfy the Johnson-Lindenstrauss property involve randomness. We address the question of explicitly constructing such embedding families and provide a construction with an almos...

Almost Degenerate Neutrinos with Maximal Mixing

We point out that if the observed deficit of solar and atmospheric neutrinos are to be understood as consequences of oscillations between different neutrino flavors, the simplest way to reconcile it with mixed dark matter picture of the universe and a possible sub-electron volt upper limit on the νe Majorana mass is to have a scenario of three light almost degenerate Majorana neutrinos (νe, νμ ...

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.

Infinite Measure Preserving Transformations with "mixing"