Formalization of the fundamental group in untyped set theory using auto2

We present a new framework for formalizing mathematics in untyped set theory using auto2. Using this framework, we formalize in Isabelle/FOL the entire chain of development from the axioms of set theory to the definition of the fundamental group for an arbitrary topological space. The auto2 prover is used as the sole automation tool, and enables succinct proof scripts throughout the project.Comment: 17 pages, accepted for ITP 201

Many-body dynamics of a Bose system with attractive interactions on a ring

We investigate the many-body dynamics of an effectively attractive one-dimensional Bose system confined in a toroidal trap. The mean-field theory predicts that a bright-soliton state will be formed when increasing the interparticle interaction over a critical point. The study of quantum many-body dynamics in this paper reveals that there is a modulation instability in a finite Bose system correspondingly. We show that Shannon entropy becomes irregular near and above the critical point due to quantum correlations. We also study the dynamical behavior of the instability by exploring the momentum distribution and the fringe visibility, which can be verified experimentally by releasing the trapComment: 6 pages,5 figure

Potential of Geo-neutrino Measurements at JUNO

The flux of geoneutrinos at any point on the Earth is a function of the abundance and distribution of radioactive elements within our planet. This flux has been successfully detected by the 1-kt KamLAND and 0.3-kt Borexino detectors with these measurements being limited by their low statistics. The planned 20-kt JUNO detector will provide an exciting opportunity to obtain a high statistics measurement, which will provide data to address several questions of geological importance. This paper presents the JUNO detector design concept, the expected geo-neutrino signal and corresponding backgrounds. The precision level of geo-neutrino measurements at JUNO is obtained with the standard least-squares method. The potential of the Th/U ratio and mantle measurements is also discussed.Comment: 8 pages, 6 figures, an additional author added, final version to appear in Chin. Phys.

On Beltrami Model of de Sitter Spacetime

Based on some important properties of $dS$ space, we present a Beltrami model ${\cal B}_\Lambda$ that may shed light on the observable puzzle of $dS$ space and the paradox between the special relativity principle and cosmological principle. In ${\cal B}_\Lambda$, there are inertial-type coordinates and inertial-type observers. Thus, the classical observables can be defined for test particles and light signals. In addition, by choosing the definition of simultaneity the Beltrami metric is transformed to the Robertson-Walker-like metric. It is of positive spatial curvature of order $\Lambda$. This is more or less indicated already by the CMB power spectrum from WMAP and should be further confirmed by its data in large scale.Comment: 4 page

Medium-Term Earthquake Forecast Using Gravity Monitoring Data: Evidence from the Yutian and Wenchuan Earthquakes in China

Gravity changes derived from regional gravity monitoring data in China from 1998 to 2005 exhibited noticeable variations before the occurrence of two large earthquakes in 2008 in China—the 2008 Yutian (Xinjiang) Ms=7.3 earthquake and the 2008 Wenchuan (Sichuan) Ms=8.0 earthquake. Based on these gravity variations, a group of researchers at the Second Crust Monitoring and Application Center of China Earthquake Administration made a suggestion in December of 2006 that the possibility for the Yutian (Xinjiang) and Wenchuan (Sichuan) areas to experience a large earthquake in either 2007 or 2008 was high. We review the gravity monitoring data and methods upon which the researchers reached these medium-term earthquake forecasts. Experience related to the medium-term forecasts of the Yutian and Wenchuan earthquakes suggests that gravity changes derived from regional gravity monitoring data could potentially be a useful medium-term precursor of large earthquakes, but significant additional research is needed to validate and evaluate this hypothesis

Cylindrical vector beams for rapid polarization-dependent measurements in atomic systems

We demonstrate the use of cylindrical vector beams - beams with spatially varying polarization - for detecting and preparing the spin of a warm rubidium vapor in a spatially dependent manner. We show that a modified probe vector beam can serve as an atomic spin analyzer for an optically pumped medium, which spatially modulates absorption of the beam. We also demonstrate space-variant atomic spin by optical pumping with the vector beams. The beams are thus beneficial for making singleshot polarization-dependent measurements, as well as for providing a means of preparing samples with position-dependent spin.Comment: 8 pages, 5 figures. Accepted in Optics Expres

The Multiphase Intracluster Medium in Galaxy Groups Probed by the Lyman Alpha Forest

The case is made that the intracluster medium (ICM) in spiral-rich galaxy groups today probably has undergone much slower evolution than that in elliptical-rich groups and clusters. The environments of proto-clusters and proto-groups at z > 2 are likely similar to spiral-rich group environments at lower redshift. Therefore, like the ICM in spiral-rich groups today, the ICM in proto-groups and proto-clusters at z > 2 is predicted to be significantly multiphased. The QSO Lyman alpha forest in the vicinity of galaxies is an effective probe of the ICM at a wide range of redshift. Two recent observations of Lyman alpha absorption around galaxies by Adelberger et al. and by Pascarelle et al are reconciled, and it is shown that observations support the multiphase ICM scenario. Galaxy redshifts must be very accurate for such studies to succeed. This scenario can also explain the lower metallicity and lower hot gas fraction in groups.Comment: 4 pages, 1 figure, replaced with the version after proo

Equity Incentives and corporate fraud in China

This is the author accepted manuscript. The final version is available from Springer Verlag via the DOI in this recordThis paper explores how managers’ and supervisors’ equity incentives impact the likelihood of committing corporate fraud in Chinese-listed firms. Previous research has shown that corporate fraud in China is a widespread phenomenon and has severe consequences for affected firms and executives. However, our understanding of the reasons that fraud is committed in a Chinese setting has been very limited thus far. This is an increasingly important topic, because corporate governance is rapidly changing in China, and it is unclear whether adopting the executive compensation practices of the West is appropriate for Chinese firms. We show that managers’ equity incentives increase their propensity to commit corporate fraud. We also find that this effect is more pronounced for state-owned firms. However, we find a negative but not significant relationship between the equity incentives of the supervisory board and the incidence of fraud

Mass Hierarchy Determination Using Neutrinos from Multiple Reactors

We report the results of Monte Carlo simulations of a medium baseline reactor neutrino experiment. The difference in baselines resulting from the 1 km separations of Daya Bay and Ling Ao reactors reduces the amplitudes of 1-3 oscillations at low energies, decreasing the sensitivity to the neutrino mass hierarchy. A perpendicular detector location eliminates this effect. We simulate experiments under several mountains perpendicular to the Daya Bay/Ling Ao reactors, considering in particular the background from the TaiShan and YangJiang reactor complexes. In general the hierarchy can be determined most reliably underneath the 1000 meter mountain BaiYunZhang, which is 44.5 km from Daya Bay. If some planned reactors are not built then nearby 700 meter mountains at 47-51 km baselines gain a small advantage. Neglecting their low overhead burdens, hills near DongKeng would be the optimal locations. We use a weighted Fourier transform to avoid a spurious dependence on the high energy neutrino spectrum and find that a neural network can extract quantities which determine the hierarchy marginally better than the traditional RL + PV.Comment: 22 pages, added details on the neural network (journal version