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

Knowledge-Driven Distractor Generation for Cloze-style Multiple Choice Questions

In this paper, we propose a novel configurable framework to automatically generate distractive choices for open-domain cloze-style multiple-choice questions, which incorporates a general-purpose knowledge base to effectively create a small distractor candidate set, and a feature-rich learning-to-rank model to select distractors that are both plausible and reliable. Experimental results on datasets across four domains show that our framework yields distractors that are more plausible and reliable than previous methods. This dataset can also be used as a benchmark for distractor generation in the future.Comment: To appear at AAAI 202

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