Domains of Injectivity for the Gross-Hopkins Period Map

We determine the domain of injectivity of the Gross-Hopkins Period map around each points in the deformation space for a fixed formal module $\bar{F}$ of height 2 that defined over a finite field. And then we will use this to conclude some local analyticity result of the group action for the automorphism group of $\bar{F}$ on the deformation space.Comment: This second version provides a totally different approach to the question. This theoretic approach uses arguments as in Lubin-Tate theory and relates the structure of the fiber of the Period map with quasi-isogenies. In the first version, the Newton's Polygon of the local Taylor series expansion is determined. And we add some local analyticity results to second versio

Information and Communication Technologies and Informal Scholarly Communication: A Review of the Social Oriented Research

This article reviews and analyzes findings from research on computer mediated informal scholarly communication. Ten empirical research papers, which show the effects and influences of information & communication technologies (ICTs), or the effects of social contexts on ICTs use in informal scholarly communication, were analyzed and compared. Types of ICTs covered in those studies include e-mails, collaboratories, and electronic forums. The review shows that most of the empirical studies examined the ICTs use effects or consequences. Only a few studies examined the social shaping of ICTs and ICT uses in informal scholarly communication. Based on comparisons of the empirical findings this article summarizes the ICT use effects/consequences as identified in the studies into seven categories and discusses their implications

Spectral function and fidelity susceptibility in quantum critical phenomena

In this paper, we derive a simple equality that relates the spectral function $I(k,\omega)$ and the fidelity susceptibility $\chi_F$, i.e. $\chi_F=\lim_{\eta\rightarrow 0}\frac{\pi}{\eta} I(0, i\eta)$ with $\eta$ being the half-width of the resonance peak in the spectral function. Since the spectral function can be measured in experiments by the neutron scattering or the angle-resolved photoemission spectroscopy(ARPES) technique, our equality makes the fidelity susceptibility directly measurable in experiments. Physically, our equality reveals also that the resonance peak in the spectral function actually denotes a quantum criticality-like point at which the solid state seemly undergoes a significant change.Comment: 5 pages, 2 figure