Groundstate with Zero Eigenvalue for Generalized Sombrero-shaped Potential in NN-dimensional Space

Based on an iterative method for solving the goundstate of Schroedinger equation, it is found that a kind of generalized Sombrero-shaped potentials in N-dimensional space has groundstates with zero eigenvalue. The restrictions on the parameters in the potential are discussed.Comment: 8 pages, 3 figure

Empirical Study of Deep Learning for Text Classification in Legal Document Review

Predictive coding has been widely used in legal matters to find relevant or privileged documents in large sets of electronically stored information. It saves the time and cost significantly. Logistic Regression (LR) and Support Vector Machines (SVM) are two popular machine learning algorithms used in predictive coding. Recently, deep learning received a lot of attentions in many industries. This paper reports our preliminary studies in using deep learning in legal document review. Specifically, we conducted experiments to compare deep learning results with results obtained using a SVM algorithm on the four datasets of real legal matters. Our results showed that CNN performed better with larger volume of training dataset and should be a fit method in the text classification in legal industry.Comment: 2018 IEEE International Conference on Big Data (Big Data

Elastic parton scattering and non-statistical event-by-event mean-pt fluctuations in Au + Au collisions at RHIC

Non-statistical event-by-event mean-pt fluctuations in Au + Au collisions at sqrt(s_NN) = 130 and 200 GeV are analyzed in AMPT with string-melting, and the results are compared with STAR data. The analysis suggests that in-medium elastic parton scattering may contribute greatly to the mean-p_t fluctuations in relativistic heavy-ion collisions. Furthermore, it is demonstrated that non-statistical event-by-event mean-pt fluctuations can be used to probe the initial partonic dynamics in these collisions. The comparison shows that with an in-medium elastic parton scattering cross section sigma_p=10 mb, AMPT with string-melting can well reproduce sqrt(s_NN) = 130 GeV data on the centrality dependence of non-statistical event-by-event mean-pt fluctuations. The comparison also shows that the fluctuation data for sqrt(s_NN) = 200 GeV Au + Au collisions can be well reproduced with sigma_p between 6 and 10 mb.Comment: 6 pages, 3 figure

Iterative Solutions for Low Lying Excited States of a Class of Schroedinger Equation

The convergent iterative procedure for solving the groundstate Schroedinger equation is extended to derive the excitation energy and the wave function of the low-lying excited states. The method is applied to the one-dimensional quartic potential problem. The results show that the iterative solution converges rapidly when the coupling $g$ is not too small.Comment: 14 pages, 4 figure

The Friedberg-Lee model at finite temperature and density

The Friedberg-Lee model is studied at finite temperature and density. By using the finite temperature field theory, the effective potential of the Friedberg-Lee model and the bag constant $B(T)$ and $B(T,\mu)$ have been calculated at different temperatures and densities. It is shown that there is a critical temperature $T_{C}\simeq 106.6 \mathrm{MeV}$ when $\mu=0 \mathrm{MeV}$ and a critical chemical potential $\mu \simeq 223.1 \mathrm{MeV}$ for fixing the temperature at $T=50 \mathrm{MeV}$. We also calculate the soliton solutions of the Friedberg-Lee model at finite temperature and density. It turns out that when $T\leq T_{C}$ (or $\mu \leq \mu_C$), there is a bag constant $B(T)$ (or $B(T,\mu)$) and the soliton solutions are stable. However, when $T>T_{C}$ (or $\mu>\mu_C$) the bag constant $B(T)=0 \mathrm{MeV}$ (or $B(T,\mu)=0 \mathrm{MeV}$) and there is no soliton solution anymore, therefore, the confinement of quarks disappears quickly.Comment: 12 pages, 11 figures; version accepted for publication in Phys. Rev.