An automated reasoning method, based on Wu’s method and calculus of differential forms, is proposed for mechanical theorem proving in local theory of space surfaces in differential geometry. The method has been used ...An automated reasoning method, based on Wu’s method and calculus of differential forms, is proposed for mechanical theorem proving in local theory of space surfaces in differential geometry. The method has been used to simplify one of Chern’s theorems: "The non-trivial families of isometric surfaces having the same principal curvatures are W-surfaces." Some other theorems are also tested by this method. The proofs are generally simpler than those in differential geometry textbooks.展开更多
There are various sand tipples in the natural world. The viewpoint of Yalin is that local disturbances result in laminar instability and in sand-tipple formation, namely, local disturbance^the instability of the lamin...There are various sand tipples in the natural world. The viewpoint of Yalin is that local disturbances result in laminar instability and in sand-tipple formation, namely, local disturbance^the instability of the laminar flow→the formation of sand ripples. Based on this viewpoint, a theoretical model of the resonant triad interaction and its nonlinear interaction with the sediment is established. The purpose of this model is to explain the formation and evolution of the sand-tipple and allow for analysis of the instability of open-channel flow caused by it and sand-tipple hydro-dynamic process. This model will not only pave a road to explore the mechanism of interaction between bed-form and turbulence, but also provide a good base for the study of aeolian sand-tipple formation.展开更多
For the normalized Fourier coefficients of Maass cusp forms λ（n） and the normalized Fourier coefficients of holomorphic cusp forms a（n）, we give the bound of
Interviewing is one of the most common and most powerful research methods in sociology. To provide an overview of interviewing in social research, the preliminaries and some tactics applied in interviewing are illustr...Interviewing is one of the most common and most powerful research methods in sociology. To provide an overview of interviewing in social research, the preliminaries and some tactics applied in interviewing are illustrated firstly. Secondly, various forms of interviewing employed in social research are analyzed specifically. Finally, the issues of interviewing are critically examined.展开更多
基金Project supported partially by the National Natural Science Foundation of China.
文摘An automated reasoning method, based on Wu’s method and calculus of differential forms, is proposed for mechanical theorem proving in local theory of space surfaces in differential geometry. The method has been used to simplify one of Chern’s theorems: "The non-trivial families of isometric surfaces having the same principal curvatures are W-surfaces." Some other theorems are also tested by this method. The proofs are generally simpler than those in differential geometry textbooks.
基金supported by the National Natural Science Foundation of China (Grant No. 50979066)the Science Fund for Creative Research Groups of the National Natural Science Foundation of China (Grant No. 51021004)
文摘There are various sand tipples in the natural world. The viewpoint of Yalin is that local disturbances result in laminar instability and in sand-tipple formation, namely, local disturbance^the instability of the laminar flow→the formation of sand ripples. Based on this viewpoint, a theoretical model of the resonant triad interaction and its nonlinear interaction with the sediment is established. The purpose of this model is to explain the formation and evolution of the sand-tipple and allow for analysis of the instability of open-channel flow caused by it and sand-tipple hydro-dynamic process. This model will not only pave a road to explore the mechanism of interaction between bed-form and turbulence, but also provide a good base for the study of aeolian sand-tipple formation.
基金Acknowledgements This work was supported in part by the Natural Science Foundation of Jiangxi Province （Nos. 2012ZBAB211001, 20132BAB2010031）.
文摘For the normalized Fourier coefficients of Maass cusp forms λ（n） and the normalized Fourier coefficients of holomorphic cusp forms a（n）, we give the bound of
文摘Interviewing is one of the most common and most powerful research methods in sociology. To provide an overview of interviewing in social research, the preliminaries and some tactics applied in interviewing are illustrated firstly. Secondly, various forms of interviewing employed in social research are analyzed specifically. Finally, the issues of interviewing are critically examined.
