On a Liu--Yau type inequality for surfaces

Let $\Omega$ be a compact and mean-convex domain with smooth boundary $\Sigma:=\partial\Omega$, in an initial data set $(M^3,g,K)$, which has no apparent horizon in its interior. If $\Sigma$ is spacelike in a spacetime (\E^4,g\_\E) with spacelike mean curvature vector $\mathcal{H}$ such that $\Sigma$ admits an isometric and isospin immersion into $\mathbb{R}^3$ with mean curvature $H\_0$, then: \begin{eqnarray*} \int\_{\Sigma}|\mathcal{H}|d\Sigma\leq\int\_{\Sigma}\frac{H\_0^2}{|\mathcal{H}|}d\Sigma. \end{eqnarray*} If equality occurs, we prove that there exists a local isometric immersion of $\Omega$ in $\mathbb{R}^{3,1}$ (the Minkowski spacetime) with second fundamental form given by $K$. In Theorem liu-yau-minkowski, we also examine, under weaker conditions, the case where the spacetime is the $(n+2)$-dimensional Minkowski space $\mathbb{R}^{n+1,1}$ and establish a stronger rigidity result

Lydia H. Liu. Translingual practice : literature, national culture, and translated modernity : China, 1900-1937

This article reviews the book Translingual Practice: Literature, National Culture, and Translated Modernity—China, 1900-1937 , written by Lydia H. Liu

Liu, Mengxiong

University of Michigan, Ann Arbor, MI, School of Informational & Library Studies, Ph.D., 1990 University of Denver, Denver, CO, Graduate School of Librarianship & Information Management, M.L.S., 1983 International Studies University, Shanghai, China, English Department, B.A., 1968https://scholarworks.sjsu.edu/erfa_bios/1273/thumbnail.jp

The professional and personal characteristics of basic school teachers in the Irbid / Jordan Kasbah from the teachers ’point of view Abstract

The study aimed to identify the professional and personal features of primary school teachers in the Irbid / Jordan Kasbah from the teachers ’point of view, and the study adopted the descriptive survey approach, and to achieve the objectives of the study, a questionnaire was developed to measure the professional and personal characteristics of school teachers and its validity and reliability were ascertained. 3670) male and female teachers, distributed among (1897) teachers, and (2773) female teachers, and the study sample consisted of (354) male and female teachers who were selected in the available way, and the results of the study showed that basic school teachers\u27 practice of professional and personal characteristics in the Irbid The teachers ’eyesight came with a (high) degree. The results revealed that there were no statistically significant differences in the occupational and personal characteristics of basic school teachers due to the variable (scientific qualification), and the presence of statistically significant differences in the variable (gender), and came in favor of (females), and the results also showed the presence of statistically significant differences in the practice of Basic school teachers have professional and personal characteristics attributed to the variable (years of experience) and the differences came in favor of (from 5 to less than 10 years). The researchers recommend the necessity of continuing professional and personal characteristics of basic school teachers in the Irbid city in general, by studying the causes and factors that enhance the level of Stick to it

Legislative Alert: Nomination of Goodwin Liu

[Excerpt] I am writing on behalf of the AFL-CIO in support of the nomination of Professor Goodwin Liu to the U.S. Court of Appeals for the Ninth Circuit. Professor Liu is extraordinarily well-qualified and I urge you to vote for cloture, and to vote for his confirmation

A Corpus-Based Study of English Synonyms: Small, Little, Tiny and Petite

Synonymy is one of the complex linguistic features that learners of English face as a second language. This study investigates the similarities and differences among the four English synonyms, i.e., small, little, tiny, and petite, concerning their genres, comparison, grammatical patterns, and collocations. The data is driven from (COCA) as a native corpus and (CLC) as the non-native. The results of both corpora show that small and little are frequently used, while petite is rarely used in COCA but not used at all in CLC. Besides, little is mainly used in TV and fiction genres, whereas small, tiny, and petite are used in news and magazine genres. The grammatical patterns are similar except for one pattern with little in COCA. Further, outcomes unveiled that there is no comparison form for petite in both corpora, whereas; little has two comparison forms with differences in meaning. A few recommendations were suggested by the researchers

Expansion of a compressible gas in vacuum

Tai-Ping Liu \cite{Liu\_JJ} introduced the notion of "physical solution' of the isentropic Euler system when the gas is surrounded by vacuum. This notion can be interpreted by saying that the front is driven by a force resulting from a H\"older singularity of the sound speed. We address the question of when this acceleration appears or when the front just move at constant velocity. We know from \cite{Gra,SerAIF} that smooth isentropic flows with a non-accelerated front exist globally in time, for suitable initial data. In even space dimension, these solutions may persist for all $t\in\R$ ; we say that they are {\em eternal}. We derive a sufficient condition in terms of the initial data, under which the boundary singularity must appear. As a consequence, we show that, in contrast to the even-dimensional case, eternal flows with a non-accelerated front don't exist in odd space dimension. In one space dimension, we give a refined definition of physical solutions. We show that for a shock-free flow, their asymptotics as both ends $t\rightarrow\pm\infty$ are intimately related to each other