We introduce some basic concepts such as random (sub-)transition function,q-function in random environment, q-process in random environment and some basic lemmas. For any continuous q-function in random environment, w...We introduce some basic concepts such as random (sub-)transition function,q-function in random environment, q-process in random environment and some basic lemmas. For any continuous q-function in random environment, we prove that the q-process in random environment always exists, and that any q-process in random environment satisfies the random Kolmogorov backward equation and the minimal q-process in random environment always exists. When q is a continuous and conservative q-function in random environment, the necessary and sufficient conditions for the uniqueness of q-process in random environment are given. Finally the special cases, homogeneous random transition functions and homogeneous q-processes in random environments are considered.展开更多
In China, rural settlements are usually multifunctional complex of natural societies and they also play important productive function. This study explored the spatiotemporal evolution of the productive function of thr...In China, rural settlements are usually multifunctional complex of natural societies and they also play important productive function. This study explored the spatiotemporal evolution of the productive function of three rural settlements, i.e.,Hetaoyuan, Dawengshan, and Gaoqiao, in the Yimeng Mountain in Shandong province of eastern China.Residents lived in this three types of rural settlements were all involved in agricultural production(i.e., grain threshing, drying and storage), which had remained dominant in Hetaoyuan. Dawengshan became an industrial-oriented settlement, while Gaoqiao became a commercial-oriented settlement. This evolution was reflected in the livelihood strategy changes of rural households and the transition of rural settlements changes. The choice of livelihood strategy was affected by the livelihood assets and policies, which resulted in the spatiotemporal evolution of the productive function of rural settlements. This study can provide references for the implementation and adjustment of rural residential land consolidation policies and the improvement of production and the quality of rural life in future.展开更多
基金This work was supported by the National Natural Science Foundation of China(Grant No:10371092)the Foundation of Wuhan University.
文摘We introduce some basic concepts such as random (sub-)transition function,q-function in random environment, q-process in random environment and some basic lemmas. For any continuous q-function in random environment, we prove that the q-process in random environment always exists, and that any q-process in random environment satisfies the random Kolmogorov backward equation and the minimal q-process in random environment always exists. When q is a continuous and conservative q-function in random environment, the necessary and sufficient conditions for the uniqueness of q-process in random environment are given. Finally the special cases, homogeneous random transition functions and homogeneous q-processes in random environments are considered.
基金supported by the National Natural Science Foundation of China(Grant Nos.41671519 and 41771560)
文摘In China, rural settlements are usually multifunctional complex of natural societies and they also play important productive function. This study explored the spatiotemporal evolution of the productive function of three rural settlements, i.e.,Hetaoyuan, Dawengshan, and Gaoqiao, in the Yimeng Mountain in Shandong province of eastern China.Residents lived in this three types of rural settlements were all involved in agricultural production(i.e., grain threshing, drying and storage), which had remained dominant in Hetaoyuan. Dawengshan became an industrial-oriented settlement, while Gaoqiao became a commercial-oriented settlement. This evolution was reflected in the livelihood strategy changes of rural households and the transition of rural settlements changes. The choice of livelihood strategy was affected by the livelihood assets and policies, which resulted in the spatiotemporal evolution of the productive function of rural settlements. This study can provide references for the implementation and adjustment of rural residential land consolidation policies and the improvement of production and the quality of rural life in future.
