In this paper, we consider general Markov chains with discrete time in an arbitrary measurable (phase) space. are given by a classical transition function that generates pair of conjugate linear operators Banach space bounded functions and finitely additive measures. We study sequences Cesaro means powers on the set probability It is proved all limit measures (points) such weak topology generat...

The technical lemma underlying the 5-dimensional topological s-cobordism conjecture and the 4-dimensional topological surgery conjecture is a purely smooth category statement about locating ~-null immersions of disks. These conjectures are theorems precisely for those fundamental groups ("good groups") where the ~l-null disk lemma (NDL) holds. We expand the class of known good groups to all gro...

A finite word u is said to be bordered if u has a proper prefix which is also a suffix of u, and unbordered otherwise. Ehrenfeucht and Silberger proved that an infinite word is purely periodic if and only if it contains only finitely many unbordered factors. We are interested in abelian and weak abelian analogues of this result; namely, we investigate the following question(s): Let w be an infi...

— We investigate the representation theory of the polynomial core T S of the quantum Teichmüller space of a punctured surface S. This is a purely algebraic object, closely related to the combinatorics of the simplicial complex of ideal cell decompositions of S. Our main result is that irreducible finite-dimensional representations of T S are classified, up to finitely many choices, by group hom...

— We investigate the representation theory of the polynomial core T S of the quantum Teichmüller space of a punctured surface S. This is a purely algebraic object, closely related to the combinatorics of the simplicial complex of ideal cell decompositions of S. Our main result is that irreducible finite-dimensional representations of T S are classified, up to finitely many choices, by group hom...

One of the main tools to classify C∗-algebras is the study of its projections and its unitaries. It was proved by Cuntz in [Cun81] that if A is a purely infinite simple C∗-algebra, then the kernel of the natural map for the unitary group U(A) to the Ktheory groupK1(A) is reduced to the connected component U(A), i.e. A isK1-injective (see §3). We study in this note a finitely generated C∗-algebr...

We prove that the quasi-periodic Schrödinger operator with a finitely differentiable potential has purely absolutely continuous spectrum for all phases if frequency is Diophantine and sufficiently small in corresponding $$C^k$$ topology. This extends work of Eliasson [19] Avila–Jitomirskaya [5] from analytic topology to one which much broader, revealing interesting phenomenon oscillation leads ...

It is known that there is a sound and faithful translation of the full intuitionistic propositional calculus into the atomic polymorphic system Fat, a predicative calculus with only two connectives: the conditional and the second-order universal quantifier. The faithfulness of the embedding was established quite recently via a model-theoretic argument based in Kripke structures. In this paper w...

We produce giant, purely long-range helium dimers by photoassociation of metastable helium atoms in a magnetically trapped, ultracold cloud. The photoassociation laser is detuned close to the atomic 2(3)S1-2(3)P0 line and produces strong heating of the sample when resonant with molecular bound states. The temperature of the cloud serves as an indicator of the molecular spectrum. We report good ...