Let $mathcal {A} $ and $mathcal {B} $ be C$^*$-algebras. Assume that $mathcal {A}$ is of real rank zero and unital with unit $I$ and $k>0$ is a real number. It is shown that if $Phi:mathcal{A} tomathcal{B}$ is an additive map preserving $|cdot|^k$ for all normal elements; that is, $Phi(|A|^k)=|Phi(A)|^k $ for all normal elements $Ainmathcal A$, $Phi(I)$ is a projection, and there exists a posit...

The set of periodic points of self-maps of intervals has been studied for different reasons. The functions with smaller sets of periodic points are more likely not to share a periodic point. Of course, one has to decide what “big” or “small” means and how to describe this notion. In this direction one would be interested in studying the size of the sets of periodic points of self-maps of an int...

We study unfrustrated spin Hamiltonians that consist of commuting tensor products of Pauli matrices. Assuming translation-invariance, we observe that the Hamiltonian is described by a map between modules over the translation group algebra, so homological methods are applicable. We show universal properties of topologically ordered phases in low spatial dimensions. Particularly, we prove that in...

Let S be a subset of a normed space X = (X ,‖ · ‖) and T and I self-mappings of X . Then T is called (1) nonexpansive on S if ‖Tx− Ty‖ ≤ ‖x− y‖ for all x, y ∈ S; (2) Inonexpansive on S if ‖Tx − Ty‖ ≤ ‖Ix − I y‖ for all x, y ∈ S; (3) I-contraction on S if there exists k ∈ [0,1) such that ‖Tx − Ty‖ ≤ k‖Ix − I y‖ for all x, y ∈ S. The set of fixed points of T (resp., I) is denoted by F(T) (resp., ...

Active commuting between home and place of work or study is often cited as an interesting source of physical activity in a public health perspective. However, knowledge about these behaviors is meager. This was therefore studied in adult active commuters (n = 1872) in Greater Stockholm, Sweden, a Nordic metropolitan setting. They received questionnaires and individually adjusted maps to draw th...

This studyutilized the mobile signaling data to conductthe impact analysis of jobs-housing spatial mismatch on commuting behavior, with eight typical employment centers of three categories selected as the research subjects. Based on the analysis of the characteristics and indictors including commuting distance, accessibilities from cumulative opportunity model etc., this study demonstrates that...

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 sufficient condition for the groupoid G(n) to be commuting regular.