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H■rmander向量场上变指数空间的嵌入定理
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作者 李炳耀 李霞 李有文 《重庆理工大学学报(自然科学)》 CAS 北大核心 2019年第10期203-211,共9页
给出了Hormander向量场上变指数空间的嵌入定理,当Ω是R^N上具有锥性质的区域,如果p(x)是定义在Ω^-上且满足1<p-≤p+<Q/k的Lipschitz连续函数,则对任意Ω^-上的可测函数q(x)满足p(x)≤q(x)≤p^*(x)Qp(x)/Q-kp(x),a.e.x∈Ω^-,有W... 给出了Hormander向量场上变指数空间的嵌入定理,当Ω是R^N上具有锥性质的区域,如果p(x)是定义在Ω^-上且满足1<p-≤p+<Q/k的Lipschitz连续函数,则对任意Ω^-上的可测函数q(x)满足p(x)≤q(x)≤p^*(x)Qp(x)/Q-kp(x),a.e.x∈Ω^-,有W^k,p(x)(Ω)→L ^q(x)(Ω)。 展开更多
关键词 H rmander向量场 变指数空间 性质 嵌入性质
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Elastic solutions for partially embedded single piles subjected to simultaneous axial and lateral loading 被引量:4
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作者 张磊 龚晓南 俞建霖 《Journal of Central South University》 SCIE EI CAS 2014年第11期4330-4337,共8页
In order to improve the design level of partially embedded single piles under simultaneous axial and lateral loads, the differential solutions were deduced, in which the soil was treated as an ideal, elastic, homogene... In order to improve the design level of partially embedded single piles under simultaneous axial and lateral loads, the differential solutions were deduced, in which the soil was treated as an ideal, elastic, homogeneous, semi-infinite isotropic medium. A comparison was made between model test results and the obtained solutions to show their validity. The calculation results indicate that the horizontal displacement and bending moment of the pile increase with increases of the axial and lateral loads. The maximum horizontal displacement and bending moment decrease by 37.9% and 13.9%, respectively, when the elastic modulus of soil increases from 4 MPa to 20 MPa. The Poisson ratio of soil plays a marginal role in pile responses. There is a critical pile length under the ground, beyond which the pile behaves as though it was infinitely long. The presented solutions can make allowance for the continuous nature of soil, and if condition permits, they can approach exact ones. 展开更多
关键词 pile-soil interaction simultaneous axial and lateral loads difference method elastic modulus displacement
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