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- Fred Shultz
- 2004

With each piecewise monotonic map τ of the unit interval, a dimension triple is associated. The dimension triple, viewed as a Z[t, t −1 ] module , is finitely generated, and generators are identified. Dimension groups are computed for Markov maps, unimodal maps, multimodal maps, and interval exchange maps. It is shown that the dimension group defined here… (More)

- Jianxin Chen, Hillary Dawkins, +5 authors Bei Zeng
- 2015

Uniqueness of quantum states compatible with given measurement results," Phys. We discuss the uniqueness of quantum states compatible with given measurement results for a set of observables. For a given pure state, we consider two different types of uniqueness: (1) no other pure state is compatible with the same measurement results and (2) no other state,… (More)

- FRED SHULTZ
- 2004

Any continuous, transitive, piecewise monotonic map is determined up to a binary choice by its dimension module with the associated finite sequence of generators. The dimension module by itself determines the topological entropy of any transitive piecewise monotonic map, and determines any transitive unimodal map up to conjugacy. For a transitive piecewise… (More)

- Alan Shuchat, Fred Shultz
- 1994

- Erik Alfsen, Fred Shultz
- 2009

Let S k be the set of separable states on B(C m ⊗ C n) admitting a representation as a convex combination of k pure product states, or fewer. If m > 1, n > 1, and k ≤ max (m, n), we show that S k admits a subset V k such that V k is dense and open in S k , and such that each state in V k has a unique decomposition as a convex combination of pure product… (More)

Complete positivity of the map from a basis to its dual basis," J. Articles you may be interested in States that " look the same " with respect to every basis in a mutually unbiased set Positive mass theorems for higher dimensional Lorentzian manifolds The dual of a matrix ordered space has a natural matrix ordering that makes the dual space matrix ordered… (More)

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