On certain recurrent and automatic sequences in finite fields

In this work we extend our study on a link between automaticity and certain algebraic power series over finite fields. Our starting point is a family of sequences in a finite field of characteristic $2$, recently introduced by the first author in connection with algebraic continued fractions. By including it in a large family of recurrent sequences in an arbitrary finite field, we prove its automaticity. Then we give a criterion on automatic sequences, generalizing a previous result and this allows us to present new families of automatic sequences in an arbitrary finite field.Comment: 10 page

Hyperquadratic continued fractions over a finite field of odd characteristic with partial quotients of degree 1

In 1986, some examples of algebraic, and nonquadratic, power series over a finite prime field, having a continued fraction expansion with partial quotients all of degree one, were discovered by W. Mills and D. Robbins. In this note we show how these few examples are included in a very large family of continued fractions for certain algebraic power series over an arbitrary finite field of odd characteristic

Enhanced quantum teleportation in the background of Schwarzschild spacetime by weak measurements

It is commonly believed that the fidelity of quantum teleportation in the gravitational field would be degraded due to the heat up by the Hawking radiation. In this paper, we point out that the Hawking effect could be eliminated by the combined action of pre- and post-weak measurements, and thus the teleportation fidelity is almost completely protected. It is intriguing to notice that the enhancement of fidelity could not be attributed to the improvement of entanglement, but rather to the probabilistic nature of weak measurements. Our work extends the ability of weak measurements as a quantum technique to battle against gravitational decoherence in relativistic quantum information.Comment: 9 pages, 5 figures, comments are welcom

Measuring economic downside risk and severity - Growth at Risk

Output collapses, and crises are a fact of life. Severe economic downturns occur periodically, and have grave consequences on the poor. The authors propose a new measurement for economic downside risk, and severity: Growth at risk. Similar to the concept of Value at Risk in finance, Growth at Risk summarizes the expected maximum economic downturn over a target horizon at a given confidence level. After providing a taxonomy of growth risks, the authors construct a panel data, set on Growth at Risk for 84 countries, over the period 1980-98. On average, different regional groups experience very distinct Growth at Risk patterns over time. 1) Non-OECD countries experience a higher downturn risk, while OECD countries'downturn risks for both big, and small recessions are the lowest among all groups. 2) East Asia countries, which had been growing faster, had a high Growth at Risk for big downturns, at around six percent, and it rose dramatically at the end of the 1990s. 3) Latin America, and Sub-Saharan Africa also maintained high Growth at Risk for both big, and small recessions through 1980-98. But for Latin America, Growth at Risk for big recessions declined in the 1990s. The authors then investigate the relationship between downside risks, and long-term average growth in a cross-country analysis. They find that higher perceived levels of downside growth risk, seem to be negatively associated with long-term growth. When a country's perceived level of downside growth risk is relatively high, both domestic, and foreign investors might be deterred from making long-term investments in the country, and instead invest elsewhere. The results suggest that prudent, and consistent pursuit of socioeconomic, and political stability, contributes to long-term growth, and that risk management in a broader sense, should be a vital part of the pro-growth, and poverty reduction strategy.Public Health Promotion,Economic Theory&Research,Economic Conditions and Volatility,Health Monitoring&Evaluation,Labor Policies,Achieving Shared Growth,Economic Growth,Economic Theory&Research,Governance Indicators,Health Monitoring&Evaluation

A power-law coupled three-form dark energy model

We consider a field theory model of coupled dark energy which treats dark energy as a three-form field and dark matter as a spinor field. By assuming the effective mass of dark matter as a power-law function of the three-form field and neglecting the potential term of dark energy, we obtain three solutions of the autonomous system of evolution equations, including a de Sitter attractor, a tracking solution and an approximate solution. To understand the strength of the coupling, we confront the model with the latest Type Ia Supernova (SN Ia), Baryon Acoustic Oscillations (BAO) and Cosmic Microwave Backround (CMB) radiation observations, with the conclusion that the combination of these three databases marginalized over the present dark matter density parameter $\Omega_{m0}$ and the present three-form field $\kappa X_{0}$ gives stringent constraints on the coupling constant, $-0.017< \lambda <0.047$ ($2\sigma$ confidence level), by which we give out the model applicable parameter range.Comment: 16 pages, 5 figures, refernces added, Eur. Phys. J. C (2018

Sources of China's economic growth, 1952-99 : incorporating human capital accumulation

China's performance in economic growth, and poverty reduction has been remarkable. There is an ongoing debate about whether this growth is mainly driven by productivity, or factor accumulation. But few past studies have incorporated information on China's human capital stock, and thus contained an omission bias. The authors construct a measure of China's human capital stock from 1952 to 1999, and, using a simple growth accounting exercise, incorporate it in their analysis of the sources of growth, during the pre-reform (1952-77), and the reform period (1978-99). They find that the accumulation of human capital in China (as measured by the average years of schooling for the population aged 15 to 64) was quite rapid, and contributed significantly to growth, and welfare. After incorporating human capital, they also find that the growth of total factor productivity, still plays a positive, and significant role during the reform period. In contrast, productivity growth was negative in the pre-reform period. The results are robust to changes in labor shares in GDP. The recent declining rate of human capital accumulation is a cause for concern, if China is to sustain its improvements in growth, and welfare in the coming decade. Funding for basic education is unevenly distributed, and insufficient in some poor regions.Labor Policies,Environmental Economics&Policies,Capital Markets and Capital Flows,Economic Theory&Research,Public Health Promotion,Achieving Shared Growth,Health Monitoring&Evaluation,Economic Theory&Research,Economic Growth,Environmental Economics&Policies