The farming-pastoral zone of northern China plays a dual role in ecological conditions and production and occupies an important position in the national economy. In this paper, the methodology of system engineering is...The farming-pastoral zone of northern China plays a dual role in ecological conditions and production and occupies an important position in the national economy. In this paper, the methodology of system engineering is introduced to construct and optimize an eco-productive paradigm system for the typical areas of the farming-pastoral zone. The system was constructed in the following steps: (1) design the framework of the paradigm system based on the data of physical site characteristics, biocommunities, production and economy, social culture and historical changes; (2) analyze the vegetation patterns, the interactions between vegetation and environmental factors (natural, social, economic, etc.) and the contributions of vegetation to the area, including the synthesis of the existing researches; and (3) provide the spatial arrangements of ecosystems and planning of each area, raise a comprehensive indicators of evaluation, evaluate the feasibility and soundness, and determine the optimum eco-productive paradigms for policy-makers which were land-use patterns within the threshold of ecological conservation. Three primitive paradigms of Maowusu (Mu Us) Ssandy Land, Loess Plateau and Huailai Basin in the farming-pastoral zone of northern China were proposed according to this paradigm system.展开更多
We present a general approach to the construction of conservation laws for the nonholonomic singular Lagrange system. Firstly, the differential equations of motion of the system are written, the definition of integrat...We present a general approach to the construction of conservation laws for the nonholonomic singular Lagrange system. Firstly, the differential equations of motion of the system are written, the definition of integrating factors is given for the system. Next, the necessary conditions for the existence of the conserved quantity are studied in detail. Finally, the conservation theorem and its inverse are established for the system, an example is given to illustrate the application of the result.展开更多
In this paper, the investigation is focused on a （3＋1）-dimensional variable-coefficient Kadomtsev- Petviashvili （vcKP） equation, which can describe the realistic nonlinear phenomena in the fluid dynamics and plas...In this paper, the investigation is focused on a （3＋1）-dimensional variable-coefficient Kadomtsev- Petviashvili （vcKP） equation, which can describe the realistic nonlinear phenomena in the fluid dynamics and plasma in three spatial dimensions. In order to study the integrability property of such an equation, the Painlevé analysis is performed on it. And then, based on the truncated Painlevé expansion, the bilinear form of the （3＋1）-dimensionaJ vcKP equation is obtained under certain coefficients constraint, and its solution in the Wronskian determinant form is constructed and verified by virtue of the Wronskian technique. Besides the Wronskian determinant solution, it is shown that the （3＋1）-dimensional vcKP equation also possesses a solution in the form of the Grammian determinant.展开更多
文摘The farming-pastoral zone of northern China plays a dual role in ecological conditions and production and occupies an important position in the national economy. In this paper, the methodology of system engineering is introduced to construct and optimize an eco-productive paradigm system for the typical areas of the farming-pastoral zone. The system was constructed in the following steps: (1) design the framework of the paradigm system based on the data of physical site characteristics, biocommunities, production and economy, social culture and historical changes; (2) analyze the vegetation patterns, the interactions between vegetation and environmental factors (natural, social, economic, etc.) and the contributions of vegetation to the area, including the synthesis of the existing researches; and (3) provide the spatial arrangements of ecosystems and planning of each area, raise a comprehensive indicators of evaluation, evaluate the feasibility and soundness, and determine the optimum eco-productive paradigms for policy-makers which were land-use patterns within the threshold of ecological conservation. Three primitive paradigms of Maowusu (Mu Us) Ssandy Land, Loess Plateau and Huailai Basin in the farming-pastoral zone of northern China were proposed according to this paradigm system.
基金The project supported by National Natural Science Foundation of China under Grant No. 10272034 and the Doctoral Program Foundation of China under Grnt No. 20030558025
文摘We present a general approach to the construction of conservation laws for the nonholonomic singular Lagrange system. Firstly, the differential equations of motion of the system are written, the definition of integrating factors is given for the system. Next, the necessary conditions for the existence of the conserved quantity are studied in detail. Finally, the conservation theorem and its inverse are established for the system, an example is given to illustrate the application of the result.
基金Supported by the Specialized Research Fund for the Doctoral Program of Higher Education under Grant Nos. 20060006024 and 20080013006Chinese Ministry of Education, by the National Natural Science Foundation of China under Grant No. 60772023+2 种基金by the Open Fund of the State Key Laboratory of Software Development Environment under Grant No. SKLSDE-07-001Beijing University of Aeronautics and Astronauticsby the National Basic Research Program of China (973 Program) under Grant No. 2005CB321901
文摘In this paper, the investigation is focused on a （3＋1）-dimensional variable-coefficient Kadomtsev- Petviashvili （vcKP） equation, which can describe the realistic nonlinear phenomena in the fluid dynamics and plasma in three spatial dimensions. In order to study the integrability property of such an equation, the Painlevé analysis is performed on it. And then, based on the truncated Painlevé expansion, the bilinear form of the （3＋1）-dimensionaJ vcKP equation is obtained under certain coefficients constraint, and its solution in the Wronskian determinant form is constructed and verified by virtue of the Wronskian technique. Besides the Wronskian determinant solution, it is shown that the （3＋1）-dimensional vcKP equation also possesses a solution in the form of the Grammian determinant.
