In this parer, applications of the fractional calculus to the form (Az 2+Bz+C)ψ 2+(Dz+G)ψ 1+Eψ=f and the partial differential equation 2μz 2(Az 2+Bz+C)+(Dz+G)μz+δμ(z,t)=M 2μT 2+NμT, where ψ 1...In this parer, applications of the fractional calculus to the form (Az 2+Bz+C)ψ 2+(Dz+G)ψ 1+Eψ=f and the partial differential equation 2μz 2(Az 2+Bz+C)+(Dz+G)μz+δμ(z,t)=M 2μT 2+NμT, where ψ 1= d ψ d z and ψ 2= d 2ψ d z 2 are presented.展开更多
A Riemannian manifold (M, g) is called Einstein manifold if its Ricci tensor satisfies r=c.g for some constant c. General existence results are hard to obtain, e.g., it is as yet unknown whether every compact manifo...A Riemannian manifold (M, g) is called Einstein manifold if its Ricci tensor satisfies r=c.g for some constant c. General existence results are hard to obtain, e.g., it is as yet unknown whether every compact manifold admits an Einstein metric. A natural approach is to impose additional homogeneous assumptions. M. Y. Wang and W. Ziller have got some results on compact homogeneous space G/H. They investigate standard homogeneous metrics, the metric induced by Killing form on G/H, and get some classification results. In this paper some more general homogeneous metrics on some homogeneous space G/H are studies, and a necessary and sufficient condition for this metric to be Einstein is given. The authors also give some examples of Einstein manifolds with non-standard homogeneous metrics.展开更多
In this paper,a semi-analytical method for the analysis of pile-supported embankments is proposed.The mathematic model describes the cooperative behavior of pile,pile cap,foundation soil,and embankment fills.Based on ...In this paper,a semi-analytical method for the analysis of pile-supported embankments is proposed.The mathematic model describes the cooperative behavior of pile,pile cap,foundation soil,and embankment fills.Based on Terzaghi's 1D consolidation theory of saturated soil,the consolidation of foundation soil is calculated.The embankments with two different types of piles:floating piles and end-bearing piles are investigated and discussed.The results of axial force and skin friction distributions along the pile and the settlements of pile-supported embankments are presented.It is found that it takes a longer time for soil consolidation in the embankment with floating piles,compared with the case using end-bearing piles.The differential settlement between the pile and surrounding soil at the pile top is larger for the embankment with end-bearing piles,compared with the case of floating piles.展开更多
文摘In this parer, applications of the fractional calculus to the form (Az 2+Bz+C)ψ 2+(Dz+G)ψ 1+Eψ=f and the partial differential equation 2μz 2(Az 2+Bz+C)+(Dz+G)μz+δμ(z,t)=M 2μT 2+NμT, where ψ 1= d ψ d z and ψ 2= d 2ψ d z 2 are presented.
基金Project supported by the National Natural Science Foundation of China (No. 10431040, No.10501025) and the Liu Hui Center for Applied Mathematics.
文摘A Riemannian manifold (M, g) is called Einstein manifold if its Ricci tensor satisfies r=c.g for some constant c. General existence results are hard to obtain, e.g., it is as yet unknown whether every compact manifold admits an Einstein metric. A natural approach is to impose additional homogeneous assumptions. M. Y. Wang and W. Ziller have got some results on compact homogeneous space G/H. They investigate standard homogeneous metrics, the metric induced by Killing form on G/H, and get some classification results. In this paper some more general homogeneous metrics on some homogeneous space G/H are studies, and a necessary and sufficient condition for this metric to be Einstein is given. The authors also give some examples of Einstein manifolds with non-standard homogeneous metrics.
基金Project supported by the Research Committee of the University of Macao (Nos. MYRG189(Y2-L3)-FST11-ZWH and MYRG067(Y1-L2)-FST12-ZWH),Macao SAR,China
文摘In this paper,a semi-analytical method for the analysis of pile-supported embankments is proposed.The mathematic model describes the cooperative behavior of pile,pile cap,foundation soil,and embankment fills.Based on Terzaghi's 1D consolidation theory of saturated soil,the consolidation of foundation soil is calculated.The embankments with two different types of piles:floating piles and end-bearing piles are investigated and discussed.The results of axial force and skin friction distributions along the pile and the settlements of pile-supported embankments are presented.It is found that it takes a longer time for soil consolidation in the embankment with floating piles,compared with the case using end-bearing piles.The differential settlement between the pile and surrounding soil at the pile top is larger for the embankment with end-bearing piles,compared with the case of floating piles.