On the K-power free number sequence

The main purpose of this paper is to study the distribution properties of the k-power free numbers, and give an interesting asymptotic formula for it

On the uniqueness of the foliation of spheres of constant mean curvature in asymptotically flat 3-manifolds

In this note we study constant mean curvature surfaces in asymptotically flat 3-manifolds. We prove that, in an asymptotically flat 3-manifold with positive mass, stable spheres of given constant mean curvature outside a fixed compact subset are unique. Therefore we are able to conclude that there is a unique foliation of stable spheres of constant mean curvature in an asymptotically flat 3-manifold with positive mass.Comment: 22 page

Local Entanglement and quantum phase transition in spin models

Due to the phase interference of electromagnetic wave, one can recover the total image of one object from a small piece of holograph, which records the interference pattern of two laser light reflected from it. Similarly, the quantum superposition principle allows us to derive the global phase diagram of quantum spin models by investigating a proper local measurement. In the present paper, we study the two-site entanglement in the antifferomagnetic spin models with both spin-1/2 and 1. We show that its behaviors reveal some important information on the global properties and the quantum phase transition of these systems.Comment: 6 pages, 7 figure

How information graphics promote interactions between the media and audiences

The purpose of this study is to understand how employing information graphics in the traditional newsrooms takes place and how the uses of the information graphics facilitate the interactions between the reporters and the readers and among readers. In order to answer the research questions, first, interviews with reporters from the six news outlets (i.e., the Washington Post, the New York Times, the Chicago Tribune, the USA Today, the Wall Street Journal and the Guardian of London) were conducted to gain insights into the visual journalists' perceptions on the impacts of information graphics on facilitating conversations between the news organizations and the readers. Overall, the interviews showed that journalists in general consider information graphics as efficient and vital tools for data delivery and complex storytelling, and in each of the newsrooms, an increase in readers' discussion participation is observed when articles are accompanied with graphics. Secondly, a quantitative content analysis was conducted using 248 articles from the six news outlets. The articles selected are half with information graphics and half without. The comparisons between those articles (i.e., with information graphics vs. without information graphics) were made on the number of comments and the number of unique commenters along with the features of the graphics. The results showed that in general, articles with graphics received greater numbers of comments and higher numbers of unique commenters compared to articles without graphics. It was also evident that a good information graphics is a product for a number of reasons. Yet no simple feature stood out as the prominent reason for the differences of comment numbers across different news organizations