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Sample size determination is commonly encountered in modern medical studies for two independent binomial experiments. A new approach for calculating sample size is developed by combining Bayesian and frequentist idea when a hypothesis test between two binomial proportions is conducted. Sample size is calculated according to Bayesian posterior decision function and power of the most powerful test under 0-1 loss function. Sample sizes are investigated for two cases that two proportions are equal to some fixed value or a random value. A simulation study and a real example are used to illustrate the proposed methodologies.

The rhizosphere microbe plays an important role in removing the pollutant generated from industrial and agricultural production. To investigate the dynamics of the microbial degradation, a nonlinear mathematical model of the rhizosphere microbial degradation is proposed based on impulsive state feedback control. The sufficient conditions for existence of the positive order-1 or order-2 periodic solution are obtained by using the geometrical theory of the semicontinuous dynamical system. We show the impulsive control system tends to an order-1 periodic solution or order-2 periodic solution if the control measures are achieved during the process of the microbial degradation. Furthermore, mathematical results are justified by some numerical simulations.

In this paper, we study the file management mechanism of large-scale cloud-based log data. With the rise of big data, there are more and more the Hadoop-based applications. Log analysis is an important part of network security management, but the existing network log analysis system can't deal with huge amounts of log data, or only use offline mode which with a longer response delay. Therefore, building the online Hadoop-based log processing system is necessary. However, how to effectively manage vast amounts of log data have become the key problems of such system. To this end, this paper puts forward a new hierarchical file archiving (HFA) mechanism which can realize the hierarchical and sorted storage of massive amounts of log data. In addition, some feasible methods for the mechanism are also proposed. Through the HFA mechanism, the traditional log analysis mode and Hadoopbased offline analysis mode can be combined to achieve the online Hadoop-based log analysis system, which have good scalability that can effectively store and handle the massive log data, and faster response speed for user request to meet the requirements of online processing. The feasibility and effectiveness of the HFA mechanism have been verified by the experiment of a small log process system.

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