Suppose that Φ(x)∈L 2(R) with compact support and V= span{Φ(x-k)|k∈Z}. In this note, we prove that if {Φ(x-k)k|k∈Z} is tight frame with bound 1 in V, then {Φ(x-k)|k∈Z} must be an orthonormal basis of V.
Soil classification is the foundation for exchange and extension of research findings in soil science and for modern management of soil resources. This study explained database and research methodology to create a cro...Soil classification is the foundation for exchange and extension of research findings in soil science and for modern management of soil resources. This study explained database and research methodology to create a cross-reference system for translating the Genetic Soil Classification of China (GSCC) into the Chinese Soil Taxonomy (CST). With the help of the CST keys, each of the 2 540 soil species in GSCC has been interpreted to its corresponding soil order, suborder, great group, and sub-group in CST. According to the methodology adopted, the assigned soil species have been linked one another to their corresponding polygons in the 1:1000000 digital soil map of China. Referencibility of each soil species between the GSCC and CST systems was determined statistically on the basis of distribution area of each soil species at a high taxon level of the two systems. The soils were then sorted according to their maximum referencibility and classified into three categories for discussion. There were 19 soil great groups in GSCC with maximum referencibility > 90% and 22 great groups between 60%-90%. These soil great groups could serve as cross-reference benchmarks. There were 19 great groups in GSCC with maximum referencibility < 60%, which could be used as cross-reference benchmarks until new and better results were available. For these soils, if the translation was made at a lower soil taxon level or on a regional basis, it would improve their referencibility enabling them to serve as new cross-reference benchmarks.展开更多
文摘Suppose that Φ(x)∈L 2(R) with compact support and V= span{Φ(x-k)|k∈Z}. In this note, we prove that if {Φ(x-k)k|k∈Z} is tight frame with bound 1 in V, then {Φ(x-k)|k∈Z} must be an orthonormal basis of V.
基金Project supported by the National Natural Science Foundation of China (No. 40471081)the Frontal Field Project of the Chinese Academy of Sciences (No. ISSASIP0201) the Key Innovation Project of Chinese Academy of Sciences (No.KZCX3-SW-427).
文摘Soil classification is the foundation for exchange and extension of research findings in soil science and for modern management of soil resources. This study explained database and research methodology to create a cross-reference system for translating the Genetic Soil Classification of China (GSCC) into the Chinese Soil Taxonomy (CST). With the help of the CST keys, each of the 2 540 soil species in GSCC has been interpreted to its corresponding soil order, suborder, great group, and sub-group in CST. According to the methodology adopted, the assigned soil species have been linked one another to their corresponding polygons in the 1:1000000 digital soil map of China. Referencibility of each soil species between the GSCC and CST systems was determined statistically on the basis of distribution area of each soil species at a high taxon level of the two systems. The soils were then sorted according to their maximum referencibility and classified into three categories for discussion. There were 19 soil great groups in GSCC with maximum referencibility > 90% and 22 great groups between 60%-90%. These soil great groups could serve as cross-reference benchmarks. There were 19 great groups in GSCC with maximum referencibility < 60%, which could be used as cross-reference benchmarks until new and better results were available. For these soils, if the translation was made at a lower soil taxon level or on a regional basis, it would improve their referencibility enabling them to serve as new cross-reference benchmarks.
