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In this study, the numerical calculation of optimal policy pairs in two-person zero-sum stochastic games with unbounded reward functions and state-dependent discount factors are studied. First, the expected discount criterion, ε −optimal values, and policy pairs are defined for zero-sum stochastic game model. Then, an iterative algorithm is given and the correctness of the algorithm is verified. At last, an example of inventory system is stated, the numerical simulation is obtained according to the iterative algorithm steps, and the difference between varying discount factors and a constant discount factor is obtained in further discussion.

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In this study, a method for identifying residual antibiotics in food was developed based on chromium black T and europium ion as colorimetric and fluorescent probes (EBT/Eu 3+ ) coupled with pattern recognition in machine learning. The changes in color and fluorescence of four antibiotics with the addition of EBT/Eu 3+ were obtained using smart phone and fluorescence measurements. Assisted by pattern recognition, the four antibiotics in honey were successfully identified. This experiment is highly comprehensive; it integrates multiple knowledge points, such as twochannel probe preparation, color recognition based on smart phone, fluorescence measurements, machine learning, and identification of various antibiotics.

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This article attempted to construct a multi-factor quantitative stock selection model, analyze the financial indicators and transaction data of listed companies in detail via the big data statistical test method, and to find out the alpha excess return relative to the market in the case of short stock index futures as a hedge in the Chinese market.

This paper analyses the mathematics teachers need and urgency of cultivating the ability of innovation, discusses the mathematics students innovation consciousness lack of factors, put forward the theoretical basis for using first class, through the second classroom for mathematics teachers to carry out flexible space, rich contents, various forms of activities, promote students using the brain and hand, give full play to students' subjective initiative, in time to find new problem solving new problems, so as to promote the innovation ability of students.

This paper is concerned with the asymptotic optimality of quantized stationary policies for continuous-time Markov decision processes (CTMDPs) in Polish spaces with state-dependent discount factors, where the transition rates and reward rates are allowed to be unbounded. Using the dynamic programming approach, we first establish the discounted optimal equation and the existence of its solutions. Then, we obtain the existence of optimal deterministic stationary policies under suitable conditions by more concise proofs. Furthermore, we discretize and incentivize the action space and construct a sequence of quantizer policies, which is the approximation of the optimal stationary policies of the CTMDPs, and get the approximation result and the rates of convergence on the expected discounted rewards of the quantized stationary policies. Also, we give an iteration algorithm on the approximate optimal policies. Finally, we give an example to illustrate the asymptotic optimality.