In this paper we investigate algebraic and topological properties of McAlister semigroups. We show that for a non-zero cardinal ? the group automorphisms semigroup M? is isomorphic to direct product Sym(?)×Z2, where Sym(?) permutations ?. semigroups admit unique compact Hausdorff topology. Each element semitopological isolated. It follows free inverse over singleton admits only discrete shift-c...

The purity, Tr(q), measures how pure or mixed a quantum state q is. It is well known that quantum dynamical semigroups that preserve the identity operator (which we refer to as unital) are strictly purity-decreasing transformations. Here, we provide an almost complete characterization of the class of strictly purity-decreasing quantum dynamical semigroups. We show that in the case of finite-dim...

Abstract Twisted étale groupoid algebras have recently been studied in the algebraic setting by several authors connection with an abstract theory of Cartan pairs rings. In this paper we show that extensions ample groupoids correspond a precise manner to Boolean inverse semigroups. particular, discrete twists over certain abelian semigroups, and they are classified Lausch’s second cohomology gr...

in this paper we study the existence of commuting regular elements, verifying the notion left (right) commuting regular elements and its properties in the groupoid g(n) . also we show that g(n) contains commuting regular subsemigroup and give a necessary and sucient condition for the groupoid g(n) to be commuting regular.

Quantum walks are considered to be quantum counterparts of classical random walks. With the advancements in quantum information theory, different version of quantum walks and quantum random walks have been developed for application in quantum algorithms and mimicking/simulating dynamics of various physical systems. In this talk I will introduce both, the discrete-time and continuous-time versio...

We consider flows (X,T), given by actions (t,x)→tx, on a compact metric space X with discrete T as an acting group. study new class of - the Strongly Rigid (SR) flows, that are properly contained in distal (D) and contain all equicontinuous (EQ) flows. Thus, EQflows⫋SRflows⫋Dflows. The concepts equicontinuity, strong rigidity distality coincide for induced flow (2X,T). observe strongly rigid (X...

Decoherence in quantum computers is formulated within the semigroup approach. The error generators are identified with the generators of a Lie algebra. This allows for a comprehensive description which includes as a special case the frequently assumed spin-boson model. A generic condition is presented for errorless quantum computation: decoherence-free subspaces are spanned by those states whic...

We present quantum query complexity bounds for testing algebraic properties. For a set S and a binary operation on S, we consider the decision problem whether S is a semigroup or has an identity element. If S is a monoid, we want to decide whether S is a group. We present quantum algorithms for these problems that improve the best known classical complexity bounds. In particular, we give the fi...

S (in alphabetic order by speaker surname) Speaker: William Beckner (University of Texas at Austin) Title: Hypercontractivity and the Logarithmic Sobolev Inequality – from Quantum Field Theory to Geometric Inequalities Abstract: This talk will feature a quick historical survey of connections between the log Sobolev inequality and now classical problems in analysis, physics and probability. Spea...