In this paper, we firstly re-present the results of Bondar et al. (2013). Then, following the approach taken in it, we use the method of Operational Dynamic Modeling (ODM) to deal with the situation where thebackground mechanics is varying between quantum and classical mechanics.

The aim of this study is to figure out the optimization of survival probability of the generals in the card game "Legends of the Three Kingdoms". First, based on combinatorics and probability theory, the PASCAL program was performed to analyze the probabilities of success when several popular generals perform their special skills in the game. The results are as follows: Second, seven typical generals, including Zhou Tai, Zhang Jiao, Zhen Ji, Lu Xun, Ma Chao, Xiahou Dun, and Guo Jia, were chosen, and their abilities including attacking and defense were arbitrarily quantified according to a model constructed in the present study. The scores are as follows: Card-drawing Changing Attacking Defense Blood-selling Zhen Ji 5.62 Zhou Tai 1.04 Ma Chao 1.68 Xiahou Dun 1.19 Guo Jia 3.36 Lu Xun 3.55 Zhang Jiao 2.55 The abilities of different generals were sorted, and by comparison with the statistical record online, the reliability of the model was proved. Thus, the irrationality of the game is identified in this study, and we recommend the game designer to modify the abilities of some generals and to obtain an optimized value according to the output of the model, by which the game would be more popular.

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.

This paper proposes an Integrated Obesity Index (IOI) based on height, weight, waist, and hip, physical indexes that can be accessed through regular physical examinations, on top of common obesity standards, including Body Mass Index (BMI), Waist‐Hip Ratio (WHR), and Body Fat Percentage (BFP). Integrated Obesity Index is aimed to be feasible and convenient under application, as well as comprehensive, compensating for the limitations of existing classifications of obesity. Thus, this paper proposes and examines the application formula of the IOI by establishing geometric models. Adopting the data from epidemiological survey, this papers brings physical indicators, gender, BFP and other variables into the model for data analysis, applies linear regression on the resulting images, and obtains the IOI cut‐off point. By conducting comprehensive data analyses to various obesity classifications, the paper demonstrates that the IOI has significant advantages over BMI, WHP, or BFP and will compensate for the deficiencies of the existing obesity classifications to a certain extent in application.

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.