Let A be a unital separable simple C∗-algebra with TR(A) ≤ 1 and α be an automorphism. We show that if α satisfies the tracially cyclic Rokhlin property then TR(A ⋊α Z) ≤ 1. We also show that whenever A has a unique tracial state and αm is uniformly outer for each m and αr is approximately inner for some r > 0, α satisfies the tracial cyclic Rokhlin property. By applying the classification theo...

BACKGROUND Previous studies have indicated that the cognitive deficits in patients with Alzheimer's disease (AD) may be due to topological deteriorations of the brain network. However, whether the selection of a specific frequency band could impact the topological properties is still not clear. Our hypothesis is that the topological properties of AD patients are also frequency-specific. METHO...

We study topological properties of conjugacy classes in Polish groups, with emphasis on automorphism groups of homogeneous countable structures. We first consider the existence of dense conjugacy classes (the topological Rokhlin property). We then characterize when an automorphism group admits a comeager conjugacy class (answering a question of Truss) and apply this to show that the homeomorphi...

We study various mixing properties for subshifts, which allow words in the language to be concatenated into a new word in the language given certain gaps between them. All are defined in terms of an auxiliary gap function f : N → N, which gives the minimum required gap length as a function of the lengths of the words on either side. In this work we focus mostly on topological transitivity, topo...

Topological insulator (TI), a promising quantum and semiconductor material, has gapless surface state and narrow bulk band gap. Firstly, the properties, classifications and compounds of TI are introduced. Secondly, the preparation and doping of TI are assessed. Some results are listed. (1) Although various preparation methods are used to improve the crystal quality of the TI, it cannot reach th...

The duality between “regular” and “topological” as convergence space properties extends in a natural way to the more general properties “p-regular” and “p-topological.” Since earlier papers have investigated regular,p-regular, and topological Cauchy completions, we hereby initiate a study of p-topological Cauchy completions. A p-topological Cauchy space has a p-topological completion if and onl...

A function from the group GL(2, R) to itself is called polynomial if it can be written as some product of constant functions, the identity function, and the function that maps every element to its inverse. We give a necessary topological condition for a function to be polynomial. As a consequence we prove that transposition is not polynomial. Mathematics Subject Classification 2000. 08A40 (20G20)