Ligularia,an important genus of the Compositae family,has captured the interest of natural product chemists for years.Phytochemical investigations on the title genus have led to isolation of hundreds of secondary meta...Ligularia,an important genus of the Compositae family,has captured the interest of natural product chemists for years.Phytochemical investigations on the title genus have led to isolation of hundreds of secondary metabolites with various skeletons.Herein,we summarized the chemical constituents of this genus and their biological activities over the past few decades.展开更多
Differential equations of free/forc ed vibrations of stepped rectangular thin plates on Winkler's foundation are estab lished by using singular functions, and their general solutions are also solved for expressi...Differential equations of free/forc ed vibrations of stepped rectangular thin plates on Winkler's foundation are estab lished by using singular functions, and their general solutions are also solved for expression of vibration mode function and frequency equations on usual suppo rts derived with W operator, as well as forced responses of such plates unde r different_type loads disc ussed with Fourier expansion of generalized functions.展开更多
Let A. （R） be a real Clifford algebra and Gan open connected set in R<sup>n</sup> . By [1], the function with val-ues in A<sub>n</sub> （R） may be written aswhere B ={r<sub>1</sub&g...Let A. （R） be a real Clifford algebra and Gan open connected set in R<sup>n</sup> . By [1], the function with val-ues in A<sub>n</sub> （R） may be written aswhere B ={r<sub>1</sub>,r<sub>2</sub>,…,r<sub>h</sub>} {1,2,…,n}represent that from the sum for’lst and 2nd indi-sates respectively, and we have the following result.Theorem A Function f （x） with values in A. （R） is regular in G if and only ifLet G be the unit hyperball and L the unit hypersphere. Cutting G by the plane: x<sub>3</sub>= a<sub>3</sub>, …,x<sub>n</sub> = a<sub>n</sub>（n3） , we obtain a section domain G<sub>a</sub> in the x<sub>1</sub>x<sub>2</sub> plane. Let L<sub>a</sub> be the boundary of G<sub>a</sub>, and its center is writ-ten as 0<sub> </sub> = （0,0,α<sub>3</sub>,...,α<sub>n</sub>） .展开更多
I. In recent years, I have done some researches on H<sub>R. K</sub>（W） space, and solved one type of non-linear sin-gular integration equations with displacement:where the conditions for the existence an...I. In recent years, I have done some researches on H<sub>R. K</sub>（W） space, and solved one type of non-linear sin-gular integration equations with displacement:where the conditions for the existence and uniqueness of the solution can be found there is also a method in-volving successive approximation by which the solution can be estimated. The research on this type of equa-tion provides a theoritical foundation for the solution of the non-linear Riemann boundary value problem.Ha, R<sub>R. K</sub>（W） defined as follows;展开更多
Isopaxametric quadrilateral elements are widely used in the finite element method. However, they have a disadvantage of accuracy loss when elements are distorted. Spline functions have properties of simpleness and con...Isopaxametric quadrilateral elements are widely used in the finite element method. However, they have a disadvantage of accuracy loss when elements are distorted. Spline functions have properties of simpleness and conformality. A 17onode quadrilateral element has been developed using the bivaxiate quaxtic spline interpolation basis and the triangular area coordinates, which can exactly model the quartic displacement fields. Some appropriate examples are employed to illustrate that the element possesses high precision and is insensitive to mesh distortions.展开更多
基金This work was supported by the Important Directional Project of the Chinese Academy of Sciences(No.KSCX2-EW-R-15)the National Natural Science Foundation of China(No.21075127).
文摘Ligularia,an important genus of the Compositae family,has captured the interest of natural product chemists for years.Phytochemical investigations on the title genus have led to isolation of hundreds of secondary metabolites with various skeletons.Herein,we summarized the chemical constituents of this genus and their biological activities over the past few decades.
文摘Differential equations of free/forc ed vibrations of stepped rectangular thin plates on Winkler's foundation are estab lished by using singular functions, and their general solutions are also solved for expression of vibration mode function and frequency equations on usual suppo rts derived with W operator, as well as forced responses of such plates unde r different_type loads disc ussed with Fourier expansion of generalized functions.
文摘Let A. （R） be a real Clifford algebra and Gan open connected set in R<sup>n</sup> . By [1], the function with val-ues in A<sub>n</sub> （R） may be written aswhere B ={r<sub>1</sub>,r<sub>2</sub>,…,r<sub>h</sub>} {1,2,…,n}represent that from the sum for’lst and 2nd indi-sates respectively, and we have the following result.Theorem A Function f （x） with values in A. （R） is regular in G if and only ifLet G be the unit hyperball and L the unit hypersphere. Cutting G by the plane: x<sub>3</sub>= a<sub>3</sub>, …,x<sub>n</sub> = a<sub>n</sub>（n3） , we obtain a section domain G<sub>a</sub> in the x<sub>1</sub>x<sub>2</sub> plane. Let L<sub>a</sub> be the boundary of G<sub>a</sub>, and its center is writ-ten as 0<sub> </sub> = （0,0,α<sub>3</sub>,...,α<sub>n</sub>） .
文摘I. In recent years, I have done some researches on H<sub>R. K</sub>（W） space, and solved one type of non-linear sin-gular integration equations with displacement:where the conditions for the existence and uniqueness of the solution can be found there is also a method in-volving successive approximation by which the solution can be estimated. The research on this type of equa-tion provides a theoritical foundation for the solution of the non-linear Riemann boundary value problem.Ha, R<sub>R. K</sub>（W） defined as follows;
基金supported by the Natural Science Foundation of China China (Nos. 60533060, 10672032, and 10726067)the Science Foundation of Dalian University of Technology (No. SFDUT07001)
文摘Isopaxametric quadrilateral elements are widely used in the finite element method. However, they have a disadvantage of accuracy loss when elements are distorted. Spline functions have properties of simpleness and conformality. A 17onode quadrilateral element has been developed using the bivaxiate quaxtic spline interpolation basis and the triangular area coordinates, which can exactly model the quartic displacement fields. Some appropriate examples are employed to illustrate that the element possesses high precision and is insensitive to mesh distortions.
