On vanishing sums of m \,m\,th roots of unity in finite fields

In an earlier work, the authors have determined all possible weights $n$ for which there exists a vanishing sum $\zeta_1+\cdots +\zeta_n=0$ of $m$th roots of unity $\zeta_i$ in characteristic 0. In this paper, the same problem is studied in finite fields of characteristic $p$. For given $m$ and $p$, results are obtained on integers $n_0$ such that all integers $n\geq n_0$ are in the ``weight set'' $W_p(m)$. The main result $(1.3)$ in this paper guarantees, under suitable conditions, the existence of solutions of $x_1^d+\cdots+x_n^d=0$ with all coordinates not equal to zero over a finite field

The Radon Monitoring System in Daya Bay Reactor Neutrino Experiment

We developed a highly sensitive, reliable and portable automatic system (H$^{3}$) to monitor the radon concentration of the underground experimental halls of the Daya Bay Reactor Neutrino Experiment. H$^{3}$ is able to measure radon concentration with a statistical error less than 10\% in a 1-hour measurement of dehumidified air (R.H. 5\% at 25$^{\circ}$C) with radon concentration as low as 50 Bq/m$^{3}$. This is achieved by using a large radon progeny collection chamber, semiconductor $\alpha$-particle detector with high energy resolution, improved electronics and software. The integrated radon monitoring system is highly customizable to operate in different run modes at scheduled times and can be controlled remotely to sample radon in ambient air or in water from the water pools where the antineutrino detectors are being housed. The radon monitoring system has been running in the three experimental halls of the Daya Bay Reactor Neutrino Experiment since November 2013

Comparing two financial crises: the case of Hong Kong real estate markets

Hong Kong is no stranger to bubbles or crisis. During the Asian Financial Crisis(AFC), the Hong Kong housing price index drops more than 50% in less than a year. The same market then experiences the Internet Bubble, the SARS attack, and recently the Global Financial Crisis (GFC). This paper attempts to provide some “stylized facts” of the real estate markets and the macroeconomy, and follow the event-study methodology to examine whether the markets behave differently in the AFC and GFC, and discuss the possible linkage to the change in government policies (“learning effect”) and the flow of Chinese consumers and investors to Hong Kong (“China factor”).regime switching, structural change, small open economy, bounded rationality, banking policy

Ordering dynamics of the driven lattice gas model

The evolution of a two-dimensional driven lattice-gas model is studied on an L_x X L_y lattice. Scaling arguments and extensive numerical simulations are used to show that starting from random initial configuration the model evolves via two stages: (a) an early stage in which alternating stripes of particles and vacancies are formed along the direction y of the driving field, and (b) a stripe coarsening stage, in which the number of stripes is reduced and their average width increases. The number of stripes formed at the end of the first stage is shown to be a function of L_x/L_y^\phi, with \phi ~ 0.2. Thus, depending on this parameter, the resulting state could be either single or multi striped. In the second, stripe coarsening stage, the coarsening time is found to be proportional to L_y, becoming infinitely long in the thermodynamic limit. This implies that the multi striped state is thermodynamically stable. The results put previous studies of the model in a more general framework

Testing Alternative Theories of the Property Price-Trading Volume Correlation

This article examines the correlation between the real housing price and trading volume. Contrary to the predictions of standard rational expectation models, a robust positive correlation between the two variables is identified. While no clear lead-lag relationship is found in the raw data, which is more consistent with the downpayment effect model, the medium-run component of the trading volume tends to lead (and Granger cause) the corresponding component of the property price, which is more consistent with the search theoretic model. An explanation for this difference in behavior is suggested and several future research directions are provided.

Quasinormal Modes of Dirty Black Holes

Quasinormal mode (QNM) gravitational radiation from black holes is expected to be observed in a few years. A perturbative formula is derived for the shifts in both the real and the imaginary part of the QNM frequencies away from those of an idealized isolated black hole. The formulation provides a tool for understanding how the astrophysical environment surrounding a black hole, e.g., a massive accretion disk, affects the QNM spectrum of gravitational waves. We show, in a simple model, that the perturbed QNM spectrum can have interesting features.Comment: 4 pages. Published in PR