A type of new loop algebra GM is constructed by making use of the concept of cycled numbers. As its application, an isospectral problem is designed and a new multi-component integrable hierarchy with multi-potential f...A type of new loop algebra GM is constructed by making use of the concept of cycled numbers. As its application, an isospectral problem is designed and a new multi-component integrable hierarchy with multi-potential functions is worked out, which can be reduced to the famous KN hierarchy.展开更多
This paper suggests a systematic method based on supersymmetric quantum mechanics for generating conditionally exactly soluble potentials, and uses the variational supersymmetric WKB method to obtain the approximate v...This paper suggests a systematic method based on supersymmetric quantum mechanics for generating conditionally exactly soluble potentials, and uses the variational supersymmetric WKB method to obtain the approximate values of the energy spectrum of the whole class.展开更多
The space-fractional telegraph equation is analyzed and the Fourier transform of its funda-mental solution is obtained and discussed.A symmetric process with discontinuous trajectories, whose transition function satis...The space-fractional telegraph equation is analyzed and the Fourier transform of its funda-mental solution is obtained and discussed.A symmetric process with discontinuous trajectories, whose transition function satisfies thespace-fractional telegraph equation, is presented. Its limiting behaviour and the connectionwith symmetric stable processes is also examined.展开更多
As an important foundation for promoting social progress and economic development, natural resources play an important role in the sustainable development of cities. However, the increasing demand of human beings for ...As an important foundation for promoting social progress and economic development, natural resources play an important role in the sustainable development of cities. However, the increasing demand of human beings for natural resources has led to various ecological environmental problems, such as excessive population density, serious environmental pollution, the continuous decline of total natural resources and per capita resources, all of which have hindered sustainable development. Therefore, the study of natural resources and sustainable development has become the focus of many current scholars. In this paper, CiteSpace is used as an analysis tool to analyze the literature on natural resources and sustainable development over the past 20 years. First of all, this paper deeply analyzes the research status of this field in terms of academic research trends, authors and research institutions, co-occurrence of keywords, etc., and on this basis, it then deeply analyzes its evolutionary path and research hot spots in the past 20 years through keyword emergence. Finally, according to the visualization of the analysis results, the future development trends of this research field are speculated:(1) Grasp the current research focus;(2) Improve the research accuracy;(3) Enrich the theoretical system of research;and(4) Establish an interdisciplinary research system.展开更多
基金The project supported by National Natural Science Foundation of China under.Grant No. 10371070
文摘A type of new loop algebra GM is constructed by making use of the concept of cycled numbers. As its application, an isospectral problem is designed and a new multi-component integrable hierarchy with multi-potential functions is worked out, which can be reduced to the famous KN hierarchy.
文摘This paper suggests a systematic method based on supersymmetric quantum mechanics for generating conditionally exactly soluble potentials, and uses the variational supersymmetric WKB method to obtain the approximate values of the energy spectrum of the whole class.
基金Project supported by the National Natural Science Foundation of China (No. 10071014).
文摘The space-fractional telegraph equation is analyzed and the Fourier transform of its funda-mental solution is obtained and discussed.A symmetric process with discontinuous trajectories, whose transition function satisfies thespace-fractional telegraph equation, is presented. Its limiting behaviour and the connectionwith symmetric stable processes is also examined.
基金The National Natural Science Foundation of China (41601581)The Science Technology Plan Project for Construction Industry of Anhui Province (2011YF-32)。
文摘As an important foundation for promoting social progress and economic development, natural resources play an important role in the sustainable development of cities. However, the increasing demand of human beings for natural resources has led to various ecological environmental problems, such as excessive population density, serious environmental pollution, the continuous decline of total natural resources and per capita resources, all of which have hindered sustainable development. Therefore, the study of natural resources and sustainable development has become the focus of many current scholars. In this paper, CiteSpace is used as an analysis tool to analyze the literature on natural resources and sustainable development over the past 20 years. First of all, this paper deeply analyzes the research status of this field in terms of academic research trends, authors and research institutions, co-occurrence of keywords, etc., and on this basis, it then deeply analyzes its evolutionary path and research hot spots in the past 20 years through keyword emergence. Finally, according to the visualization of the analysis results, the future development trends of this research field are speculated:(1) Grasp the current research focus;(2) Improve the research accuracy;(3) Enrich the theoretical system of research;and(4) Establish an interdisciplinary research system.
