Solving Dirac Equation with New Ring-Shaped Non-Spherical Harmonic Oscillator Potential

A new ring-shaped non-harmonic oscillator potential is proposed. The precise bound solution of Dirac equation with the potential is gained when the scalar potential is equal to the vector potential. The angular equation and radial equation are obtained through the variable separation method. The results indicate that the normalized angle wave function can be expressed with the generalized associated-Legendre polynomial, and the normalized radial wave function can be expressed with confluent hypergeometric function. And then the precise energy spectrum equations are obtained. The ground state and several low excited states of the system are solved. And those results are compared with the non-relativistic effect energy level in Phys. Lett. A 340 （2005） 94. The positive energy states of system are discussed and the conclusions are made properly.

Vision-based behavior prediction of ball carrier in basketball matches

A new vision-based approach was presented for predicting the behavior of the ball carrier—shooting, passing and dribbling in basketball matches. It was proposed to recognize the ball carrier’s head pose by classifying its yaw angle to determine his vision range and the court situation of the sportsman within his vision range can be further learned. In basketball match videos characterized by cluttered background, fast motion of the sportsmen and low resolution of their head images, and the covariance descriptor, were adopted to fuse multiple visual features of the head region, which can be seen as a point on the Riemannian manifold and then mapped to the tangent space. Then, the classification of head yaw angle was directly completed in this space through the trained multiclass LogitBoost. In order to describe the court situation of all sportsmen within the ball carrier’s vision range, artificial potential field (APF)-based information was introduced. Finally, the behavior of the ball carrier—shooting, passing and dribbling, was predicted using radial basis function (RBF) neural network as the classifier. Experimental results show that the average prediction accuracy of the proposed method can reach 80% on the video recorded in basketball matches, which validates its effectiveness.

A function associated with spherically convex sets

This paper introduced a kind of functions associated with spherically convex sets and discussed their basic properties.Finally,it proved the spherical convexity/concavity of these functions in lower dimensional cases,which provides useful information for the essential characteristics of these functions determining spherically convex sets.The results obtained here are helpful in setting up a systematic spherical convexity theory.