In this paper, we introduce the notion of generalized multiresolution structure (GMS) in the set-ting of reducing subspaces of L2(Rd). For a general expansive matrix, we obtain a necessary and sufficient condition for...In this paper, we introduce the notion of generalized multiresolution structure (GMS) in the set-ting of reducing subspaces of L2(Rd). For a general expansive matrix, we obtain a necessary and sufficient condition for GMS, and prove the existence of GMS in a reducing subspace. Using GMS, we obtain a pyramid decomposition and a frame-like expansion for signals in reducing subspaces.展开更多
Two kinds of mudstones from the Tarim Basin and the Tuna Basin were treated with C8 and C18 alkylammonium cations. Both of them were dated by the K-Ar method. One kind of rock contains mainly diagenetic illite, and th...Two kinds of mudstones from the Tarim Basin and the Tuna Basin were treated with C8 and C18 alkylammonium cations. Both of them were dated by the K-Ar method. One kind of rock contains mainly diagenetic illite, and the other contains mixed layer illite/smectite (I/S). Sample separation and alkylamnionium cations treatment were performed first, and K-Ar dating followed. The result shows that fine-grained minerals have younger K-Ar ages and coarse-grained components have older ages. Plots of K-Ar age versus K2O (%) are linear, the range of diagenetic age can be estimated by extrapolation. The reaction results of the above samples are different after alkylamnionium cations treatments. The samples containing mainly illite show a decrease in K2O and an increase in age by 1-25 Ma, suggesting that preferential exchange of young diagenetic clay rather than detrital clay by alkylamnionium cations, therefore the age of diagenetic illite can be calculated directly by the % K2O and radiogenic 40Ar removed. For the展开更多
基金Supported by the National Natural Science Foundation of China(11601076)the Science and Technology Project of Jiangxi Provincial Education Department(GJJ170473)
基金supported by Beijing Natural Science Foundation (Grant No. 1122008)the Scientific Research Common Program of Beijing Municipal Commission of Education (Grant No.KM201110005030)
文摘In this paper, we introduce the notion of generalized multiresolution structure (GMS) in the set-ting of reducing subspaces of L2(Rd). For a general expansive matrix, we obtain a necessary and sufficient condition for GMS, and prove the existence of GMS in a reducing subspace. Using GMS, we obtain a pyramid decomposition and a frame-like expansion for signals in reducing subspaces.
基金This workwas supported by the National Natural Science Foundation of China (Grant No. 4997249).
文摘Two kinds of mudstones from the Tarim Basin and the Tuna Basin were treated with C8 and C18 alkylammonium cations. Both of them were dated by the K-Ar method. One kind of rock contains mainly diagenetic illite, and the other contains mixed layer illite/smectite (I/S). Sample separation and alkylamnionium cations treatment were performed first, and K-Ar dating followed. The result shows that fine-grained minerals have younger K-Ar ages and coarse-grained components have older ages. Plots of K-Ar age versus K2O (%) are linear, the range of diagenetic age can be estimated by extrapolation. The reaction results of the above samples are different after alkylamnionium cations treatments. The samples containing mainly illite show a decrease in K2O and an increase in age by 1-25 Ma, suggesting that preferential exchange of young diagenetic clay rather than detrital clay by alkylamnionium cations, therefore the age of diagenetic illite can be calculated directly by the % K2O and radiogenic 40Ar removed. For the
