Recombinant cxadr protein (>90%) [His]

A compact space X is said to be minimal if there exists a map f : X -> X such that the forward orbit of any point is dense in X. We consider rigid minimal spaces, motivated by recent results of Downarowicz, Snoha and Tywoniuk (J Dyn Differ Equ, 29:243-257, 2017) on spaces with cyclic group of homeomorphisms generated by a minimal homeomorphism, and results of the first author, Clark and Oprocha (Adv Math, 335:261-275, 2018) on spaces in which the square of every homeomorphism is a power of the same minimal homeomorphism. We show that the two classes do not coincide, which gives rise to a new class of spaces that admit minimal homeomorphisms, but no minimal maps. We modify the latter class of examples to show for the first time existence of minimal spaces with degenerate homeomorphism groups. Finally, we give a method of constructing decomposable compact and connected spaces with cyclic group of homeomorphisms, generated by a minimal homeomorphism, answering a question in Downarowicz et al.

Let Gamma be an N x n random matrix with independent entries and such that in each row entries are i.i.d. Assume also that the entries are symmetric, have unit variances, and satisfy a small ball probabilistic estimate uniformly. We investigate properties of the corresponding random polytope Gamma* B-1(N) in R-n (the absolute convex hull of rows of Gamma). In particular, we show that Gamma* B-1(N) superset of b(-1) (B-infinity(n) boolean AND root ln(N/n) B-2(n)), where b depends only on parameters in small ball inequality. This extends results of [A. E. Litvak, A. Pajor, M. Rudelson and N. Tomczak-Jaegermann, Smallest singular value of random matrices and geometry of random polytopes, Adv. Math. 195 (2005) 491-523] and recent results of [F. Krahmer, C. Kummerle and H. Rauhut, A quotient property for matrices with heavy-tailed entries and its application to noise-blind compressed sensing, preprint (2018); arXiv:1806.04261]. This inclusion is equivalent to socalled l(1)-quotient property and plays an important role in compressed sensing (see [F. Krahmer, C. Kummerle and H. Rauhut, A quotient property for matrices with heavy-tailed entries and its application to noise-blind compressed sensing, preprint (2018); arXiv:1806.04261] and references therein).