A robust proof of the instability of naked singularities of a scalar field in spherical symmetry

Published in 1999, Christodoulou proved that the naked singularities of a self-gravitating scalar field are not stable in spherical symmetry and therefore the cosmic censorship conjecture is true in this context. The original proof is by contradiction and sharp estimates are obtained strictly depending on spherical symmetry. In this paper, appropriate a priori estimates for the solution are obtained. These estimates are more relaxed but sufficient for giving another robust argument in proving the instability, in particular not by contradiction. In another related paper, we are able to prove instability theorems of the spherical symmetric naked singularities under certain isotropic gravitational perturbations without symmetries. The argument given in this paper plays a central role.Comment: 14 page

Majorana Neutrino Masses from Neutrinoless Double-Beta Decays and Lepton-Number-Violating Meson Decays

The Schechter-Valle theorem states that a positive observation of neutrinoless double-beta ($0\nu \beta \beta$) decays implies a finite Majorana mass term for neutrinos when any unlikely fine-tuning or cancellation is absent. In this note, we reexamine the quantitative impact of the Schechter-Valle theorem, and find that current experimental lower limits on the half-lives of $0\nu \beta \beta$-decaying nuclei have placed a restrictive upper bound on the Majorana neutrino mass $|\delta m^{ee}_\nu| < 7.43 \times 10^{-29}~{\rm eV}$ radiatively generated at the four-loop level. Furthermore, we generalize this quantitative analysis of $0\nu \beta \beta$ decays to that of the lepton-number-violating (LNV) meson decays $M^- \to {M^\prime}^+ + \ell^-_\alpha + \ell^-_\beta$ (for $\alpha$, $\beta$ = $e$ or $\mu$). Given the present upper limits on these rare LNV decays, we have derived the loop-induced Majorana neutrino masses $|\delta m^{ee}_\nu| < 9.7 \times 10^{-18}~{\rm eV}$, $|\delta m^{e\mu}_\nu| < 1.6 \times 10^{-15}~{\rm eV}$ and $|\delta m^{\mu \mu}_\nu| < 1.0 \times 10^{-12}~{\rm eV}$ from $K^- \to \pi^+ + e^- + e^-$, $K^- \to \pi^+ + e^- + \mu^-$ and $K^- \to \pi^+ + \mu^- + \mu^-$, respectively. A partial list of radiative neutrino masses from the LNV decays of $D$, $D_s^{}$ and $B$ mesons is also given.Comment: 10 pages, 1 figure, clarification added and references updated, Phys. Lett. B in pres

Maternal pre-pregnancy infection with hepatitis B virus and the risk of preterm birth: a population-based cohort study

Background Preterm birth is the leading cause of child death in children younger than 5 years. Large cohort studies in developed countries have shown that maternal hepatitis B virus infection is associated with preterm birth, but there is little reliable evidence from China and other developing countries, where hepatitis B virus prevalence is intermediate or high. Hence, we designed this study to investigate the association between pre-pregnancy hepatitis B virus infection and risk of preterm and early preterm birth. Methods Between Jan 1, 2010, and Dec 31, 2012, we did a population-based cohort study using data from 489 965 rural women aged 21–49 years who had singleton livebirths from 220 counties of China who participated in the National Free Preconception Health Examination Project. Participants were divided into three groups according to their prepregnancy status of hepatitis B virus infection: women uninfected with hepatitis B virus (control group), women who were HBsAg positive and HBeAg negative (exposure group 1), and women who were both HBsAg and HBeAg positive (exposure group 2). The primary outcome was preterm birth (gestation at less than 37 weeks). We used log-binomial regression to estimate adjusted risk ratios (aRR) of preterm birth for women with pre-pregnancy hepatitis B virus infection, and risk of early preterm birth (gestation less than 34 weeks). Findings 489 965 women met inclusion criteria and were included in this study; of these, 20 827 (4·3%) were infected with hepatitis B virus. Compared with women who were not infected with hepatitis B virus, women who were HBsAg positive and HBeAg negative had a 26% higher risk of preterm birth (aRR 1·26, 95% CI 1·18–1·34) and women who were both HBsAg and HBeAg positive had a 20% higher risk of preterm birth (aRR 1·20, 1·08–1·32). Compared with women who were not infected with hepatitis B virus, women who were HBsAg positive and HBeAg negative manifested an 18% higher risk of early preterm birth (gestation less than 34 weeks; aRR 1·18, 1·04–1·34) and women who were both HBsAg and HBeAg positive had a 34% higher risk of early preterm birth (aRR 1·34, 1·10–1·61). Maternal pre-pregnancy hepatitis B virus infection was independently associated with higher risk of preterm birth and early preterm birth. These associations were similar in subgroups of participants as defined by baseline characteristics. Interpretation Besides mother-to-child transmission, the risk of preterm birth in women infected with hepatitis B virus should not be neglected. Comprehensive programmes that focus on early detection of hepatitis B virus infection before pregnancy and provide appropriate medical intervention for women infected with hepatitis B virus before and during pregnancy would be helpful in improving maternal and neonatal outcomes and reducing child mortality

Aerial small cells using coordinated multiple UAVs : an energy efficiency optimization perspective

Recently, unmanned aerial vehicle (UAV) communications have attracted great research interest. Due to the limited on-board energy, the optimization of energy efficiency (EE) is critical for UAV communications. In this paper, we propose an EE maximization scheme for UAV swarm-enabled small cell networks using large-scale channel state information at the transmitter (CSIT). The proposed scheme provides an agile coordination strategy for the UAVs in a swarm under energy constraints. We first formulate the EE maximization problem, where the objective function is defined as the ratio of the ergodic total data size to the total energy consumption. After that, an accurate approximation is derived to remove the intractable expectation operator in the objective function. As the newly formulated problem is non-convex, we decompose it into two subproblems to optimize the transmit power and the hovering time in an iterative way. Further by leveraging the max-min and linear optimization tools, both subproblems are efficiently solved. Simulation results demonstrate the superiority of our EE maximization scheme