Solving Dirac equations on a 3D lattice with inverse Hamiltonian and spectral methods

A new method to solve the Dirac equation on a 3D lattice is proposed, in which the variational collapse problem is avoided by the inverse Hamiltonian method and the fermion doubling problem is avoided by performing spatial derivatives in momentum space with the help of the discrete Fourier transform, i.e., the spectral method. This method is demonstrated in solving the Dirac equation for a given spherical potential in 3D lattice space. In comparison with the results obtained by the shooting method, the differences in single particle energy are smaller than $10^{-4}$~MeV, and the densities are almost identical, which demonstrates the high accuracy of the present method. The results obtained by applying this method without any modification to solve the Dirac equations for an axial deformed, non-axial deformed, and octupole deformed potential are provided and discussed.Comment: 18 pages, 6 figure

The qq-log-convexity of Domb's polynomials

In this paper, we prove the $q$-log-convexity of Domb's polynomials, which was conjectured by Sun in the study of Ramanujan-Sato type series for powers of $\pi$. As a result, we obtain the log-convexity of Domb's numbers. Our proof is based on the $q$-log-convexity of Narayana polynomials of type $B$ and a criterion for determining $q$-log-convexity of self-reciprocal polynomials.Comment: arXiv admin note: substantial text overlap with arXiv:1308.273

On the qq-log-convexity conjecture of Sun

In his study of Ramanujan-Sato type series for $1/\pi$, Sun introduced a sequence of polynomials $S_n(q)$ as given by $$S_n(q)=\sum\limits_{k=0}^n{n\choose k}{2k\choose k}{2(n-k)\choose n-k}q^k,$$ and he conjectured that the polynomials $S_n(q)$ are $q$-log-convex. By imitating a result of Liu and Wang on generating new $q$-log-convex sequences of polynomials from old ones, we obtain a sufficient condition for determining the $q$-log-convexity of self-reciprocal polynomials. Based on this criterion, we then give an affirmative answer to Sun's conjecture

Geochemistry and petrogenesis of volcanic rocks from Daimao Seamount (South China Sea) and their tectonic implications

The South China Sea (SCS) experienced three episodes of seafloor spreading and left three fossil spreading centers presently located at 18°N, 17°N and 15.5°N. Spreading ceased at these three locations during magnetic anomaly 10, 8, and 5c, respectively. Daimao Seamount (16.6. Ma) was formed 10. my after the cessation of the 17°N spreading center. Volcaniclastic rocks and shallow-water carbonate facies near the summit of Daimao Seamount provide key information on the seamount's geologic history. New major and trace element and Sr-Nd-Pb isotopic compositions of basaltic breccia clasts in the volcaniclastics suggest that Daimao and other SCS seamounts have typical ocean island basalt-like composition and possess a 'Dupal' isotopic signature. Our new analyses, combined with available data, indicate that the basaltic foundation of Daimao Seamount was formed through subaqueous explosive volcanic eruptions at 16.6. Ma. The seamount subsided rapidly (>. 0.12. mm/y) at first, allowing the deposition of shallow-water, coral-bearing carbonates around its summit and, then, at a slower rate (<. 0.12. mm/y). We propose that the parental magmas of SCS seamount lavas originated from the Hainan mantle plume. In contrast, lavas from contemporaneous seamounts in other marginal basins in the western Pacific are subduction-related

The long-term effects of alfalfa on soil water content in the Loess Plateau of northwest China

Soil desiccation is the most serious problem in forest vegetations and grassland, which lead to widespread land degradation in the Loess Plateau of China. The soil water variations at 0 to 1000 cm depth of different vegetations were studied to explore the hydrological effects of vegetations and determine the optimal length of alfalfa (Medicago sativa L.) phase at the Zhenyuan Agri-ecological Station of the Loess Plateau in China. Eight treatments were designed in this study: waste land, wheat land and six continuous growing alfalfa treatments, including 4-year-old (4 year), 6-year-old (6 year), 8- year-old (8 year), 12-year-old (12 year), 18-year-old (18 year) and 26-year-old (26 year) alfalfa grasslands.  Results showed that the wheat field had the best soil water content and no dry soil layer, while slightly dry soil layer occurred in wasteland and 4, 6 and 8 year alfalfa grasslands. After alfalfa grew for > 8 years, moderately dry soil layer appeared in the grassland and expanded beyond 500 cm soil depth. The result also showed that wheat field, wasteland and the alfalfa grasslands growing for 4, 6 and 8 years had no unfavorable impacts on the ecological environments of the soil moisture but the grasslands for 12, 18 and 26 years did exert relatively stronger unfavorable influences on the hydrological effects. Considering all the factors, this study recommends that the optimal length of alfalfa phase should be 8 years.Key words: Different vegetation, alfalfa grasslands, soil water content, ecological effect, soil desiccation, Loess Plateau of China

China's grave demographic challenges in coming decades

This paper systematically analyzes the uncertainties of major demographic indicators from China's 2000 census, such as fertility, gender ratio at birth, and age structure, and through a probability demographic forecast gives an assessment of the situation facing the country. Research outcomes suggest that great differences exist in the estimate of China's fertility, gender ratio at birth and low-age child population. These differences directly affect China's current and future demographic uncertainties, and have implications for policy and future research. The demographic uncertainties caused by current conditions are of great value to decision-makers and the public alike

A new 111 type iron pnictide superconductor LiFeP

A new iron pnictide LiFeP superconductor was found. The compound crystallizes into a Cu2Sb structure containing an FeP layer showing superconductivity with maximum Tc of 6K. This is the first 111 type iron pnictide superconductor containing no arsenic. The new superconductor is featured with itinerant behavior at normal state that could helpful to understand the novel superconducting mechanism of iron pnictide compounds.Comment: 3 figures + 1 tabl

Performance of Photosensors in the PandaX-I Experiment

We report the long term performance of the photosensors, 143 one-inch R8520-406 and 37 three-inch R11410-MOD photomultipliers from Hamamatsu, in the first phase of the PandaX dual-phase xenon dark matter experiment. This is the first time that a significant number of R11410 photomultiplier tubes were operated in liquid xenon for an extended period, providing important guidance to the future large xenon-based dark matter experiments.Comment: v3 as accepted by JINST with modifications based on reviewers' comment