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双语推荐：L′evy过程

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本文研究了L′evy过程驱动的随机二维Navier-Stokes方程弱解的指数性态.给出了不同条件下解的长时间形态,获得了一些特殊情形下解的样本轨道的指数稳定性.
In this paper, some results on the pathwise exponential stability are established for the weak solutions of stochastic 2D Navier-Stokes equation driven by L′evy noise. Also, some results and comments concerning the stabilizability and stabilization of these equations are stated.

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本文研究了由一维L′evy过程驱动的倒向随机微分方程（BSDE）的反比较定理。利用一般g -期望下BSDE的反比较定理的证明方法，推导出了一般f -期望下BSDE的反比较定理，并给出了一般f -期望下Jensen不等式成立的充分必要条件。
In this paper, we are devoted to the converse comparison theorem for backward stochastic differential equations (BSDEs, for short) driven by 1-dimensional L′evy processes. With the similar method of the converse comparison theorem under g-expectation, we prove the converse comparison theorem under f-expectation. Moreover, we provide a necessary and su?cient condition for the Jensen’s inequality to hold under the f-expectation, the nonlinear expectation defined by BSDEs driven by L′evy processes.

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随机供应中断和退货环境下库存变化，失去传统上的单调性，呈现复杂的随机波动状态，从而，极大地增加了控制难度。为解决系统库存的短缺和超储问题，本文提出一个应急控制(包括应急采购和应急处理)策略。在库存水平的动态变化表示为L′evy过程条件下，利用连续时间Markov链、更新过程和鞅理论，构建了系统期望折扣总利润模型，并设计了交叉熵法确定最优控制策略。仿真结果表明，中断强度和类型及退货批次和批量，对最优应急处理水平和应急采购量均有较大影响。而退货类型仅影响最优应急处理水平，对最优应急采购量影响较小。
The evolution of the inventory level under stochastic supply disruptions and returns no longer varies mono-tonically but fluctuates stochastically, which makes it very difficult to control the inventory level. In order to solve the inventory shortage and overstock problems, a contingent control (including contingent sourcing and contingent disposal) policy is proposed in this paper. Under the condition that the inventory level process is expressed as a L′evy process, the expected total discounted profit model is derived by utilizing continuous-time Markov chain, renewal process and martingale theorems. Subsequently, the cross-entropy method is designed to obtain the optimal control policy. Numerical results show that the intensity and the types of disruptions, as well as the arrival rates and the batch sizes of returns are critical determinants of the optimal contingent disposal level and contingent sourcing size. However, the types of returns have big impacts on the optimal

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针对大区域森林植被生长变化规律的应用需求，采用统计分析的方法，利用选取的EVI和NDVI两种植被指对中国6种典型森林2000-2011年的生长期变化进行监测，并对监测结果进行了比较。结果表明，从提取的生长期拐点的出现时间及生长期的变化趋势可知，2种植被指数提取的6种典型森林的生长变化时间范围基本相同，都能较好地反映森林生长期的变化过程，说明利用植被指数进行森林生长期监测的方法是可行的；但对高森林植被覆盖区域的森林植被变化及对云等干扰因素的敏感性来看，EVI比NDVI更适合用于大区域空间范围、多种类型的森林植被变化的监测。
To study the growth variation of the large regional forest vegetation,this paper selected two vegetation indices data-EVI and NDVI to monitor the changes of growth period from 2000 to 201 1 in six typical forests in China,then compared the results by using the statistical analysis.The results show that from the growing trend and the time when growing season appeared,the time range of growth changes extracted from two kinds of vegetation indi-ces are basically the same in the six typical forest types and could perfectly reflect the process of change of forest growing season.This indicates that the method of using vegetation index to monitor forest growing season is feasible. EVI is more effective to the changes of forest vegetation for high forest coverage area and less sensitive to disturbances such as cloud.In conclusion,EVI is more suitable for monitoring the changes in the forest which has various types′forest vegetation in large area space than NDVI.

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