The optimal mass transportation problem, proposed by Monge, is dominated by the Monge-Ampere equation. In general, as the Monge-Ampere equation is highly non-linear, this type of partial dierential equations is beyond the solving ability of a conventional nite element method. This diculty led Gu et al. alternatively to the discrete optimal mass transportation problem. They developed variational principles for this problem and reported the calculation for the optimal mapping, based on theorem that among all possible cell decompositions, with constrained measures, the trans- portation cost of the discrete mapping from cells to the corresponding discrete points is minimized by the decomposition induced by a power Voronoi diagram. Their research inspired us to consider a similar discrete optimal mass transportation problem. Here we replace the L2 Euclidean distance by the length of the shortest path connecting two points on a line network. To solve the optimal trans- portation problem on a line network, we study a type of Voronoi diagram on undirected and connected networks and propose an elegant construction algorithm. We further consider weighted distances in a network and develop a method to compute the centroidal Voronoi tessellation (CVT) for a network. By using real geographic data, the method proposed is proved ecient and eective in several practical applications, including charging station distribution in a trac network, and trash can distribution in a park.

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A physical method is developed to analyze the Riemann zeta function and the L-function. First, a physical model of an elastic bar fixed at both ends and subjected to symmetric axial loads with respect to the mid-span is constructed. The axial force of the bar at the left end is calculated with two methods: the equilibrium of forces and the principle of minimum potential energy. With the help of the orthogonality of {sinix} (i 1, 2, 3, ) , the Parseval identity and the Bessel inequality of the physical model are obtained. Further, it is proven that, in all the possible displacements which satisfy the boundary conditions, the real one minimizes the total potential energy of the bar. With the equivalence of the two methods, an identity of a type of infinite series is derived. Based on the identity, L(1) , L(3) , a recurrence formula of L(2k 1) (k  3) ,  (2) ,  (4) , and a relationship between  (2k) (k  2) and L(2i 1) (i  1, 2, ..., k) are then deduced with power axial load functions. The upper and lower bounds for the Riemann zeta function  (2k -1) and the L-function L(2k) are given. The numerical results show that the upper and lower bounds are in excellent agreement with the accurate value. Finally, two improvement methods are proposed for estimating the circumference ratio. The numerical results show that the two methods can estimate the circumference ratio with high accuracy and that the L -function is more efficient than the Riemann zeta function in estimating the circumference ratio.

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Sign language bridges the communication between the deaf-mute and the rest of the world. With the development of computer technology, the research on sign language recognition is prospering. Currently, there are two kinds of research methods. One is based on machine vision, the other is based on wearable input devices. Comparing with machine vision, wearable devices have the advantage of being able to get real-time information of the bend of the fingers and the movement of the hand. The essay applies recent technology in the field of voice recognition, and aims at finding out the best algorithm for medium vocabulary continuous sign language recognition. By building a hybrid Deep Neural Network-Hidden Markov Model, and designing and making a low-cost digital glove, the essay successfully compares the features between Dynamic Time Warping (DTW), Gaussian Mixture Model-Hidden Markov Model (GMM-HMM) and Deep Neural Network-Hidden Markov Model (DNN-HMM) as of solving the problem of sign language recognition. Tests show that in terms of calculating the observation probability, DNN has a much better performance than HMM, especially when syntax is not provided, meaning that DNN better suits the developing trend of sign language recognition. Real-time recognition is achieved on the intelligent terminal with an accuracy of over 97%, using the trained model and a decoding program.