The objective of the study was to establish spatial land evaluation for oil palm cultivation using GIS （geographic information system）. The study area is situated in the KESEDAR region in the state of Kelantan, Mala...The objective of the study was to establish spatial land evaluation for oil palm cultivation using GIS （geographic information system）. The study area is situated in the KESEDAR region in the state of Kelantan, Malaysia. The evaluation of the land in terms of the suitability classes were based on the method of FAO （Food and Agriculture Oganization of the United Nations）. Five land qualities are important for determining the physical land suitability for oil palm; these are nutrient availability, oxygen availability, water availability, workability and availability of foothold for roots. Each of the above mentioned land qualities with associated attribute data were digitally encoded in a GIS database to create thermatic layers. Overlay operation on the layer produced resultant polygonal layer each of which is a land unit with characteristics of the land. The results from GIS overlay analyses showed that Bungor, Chat, Chempaka, Alluvium, Musang and Tok Yong series are highly suitable while Kawang series is moderately suitable for oil palm cultivation. The same results were obtained by using parametric-limitation method.展开更多
This paper gives and proofs a theorem, for any matrix A, do elementary column operations, change it to a matrix which is partitioned to two blocks which left one is column full rank and right one is zero matrix. That ...This paper gives and proofs a theorem, for any matrix A, do elementary column operations, change it to a matrix which is partitioned to two blocks which left one is column full rank and right one is zero matrix. That is, use a invertible matrix P to let AP = （B,O）, O is zero matrix with n-r columns, r and n is rank and column number of A, so the P＇s right n-r columns is just the basis of the null space of the matrix A. On the basis of the theorem, lots of problems of linear algebra can be resolved and lots of theorems can be proofed by elementary column operations. Perhaps the textbooks used in universities will have a lot of change with the result of the paper. This result is first found by author in 2010.12.8 in http：//www.paper.edu.cn/index.php/default/releasepaper/content/201012-232, but is not formal published.展开更多
Based on the PT-symmetric quantum theory, the concepts of PT-frame, PT-symmetric operator and CPT-frame on a Hilbert space K and for an operator on K are proposed. It is proved that the spectrum and point spectrum of ...Based on the PT-symmetric quantum theory, the concepts of PT-frame, PT-symmetric operator and CPT-frame on a Hilbert space K and for an operator on K are proposed. It is proved that the spectrum and point spectrum of a PT-symmetric linear operator are both symmetric with respect to the real axis and the eigenvalues of an unbroken PT-symmetric operator are real. For a linear operator H on Cd, it is proved that H has unbroken PT- symmetry if and only if it has d different eigenvalues and the corresponding eigenstates are eigenstates of PT. Given a CPT-frame on K, a new positive inner product on K is induced and called CPT-inner product. Te relationship between the CPT-adjoint and the Dirac adjoint of a densely defined linear operator is derived, and it is proved that an operator which has a bounded CPT-frame is CPT-Hermitian if and only if it is T-symmetric, in that case, it is similar to a Hermitian operator. The existence of an operator C consisting of a CPT-frame is discussed, These concepts and results will serve a mathematical discussion about PT-symmetric quantum mechanics.展开更多
文摘The objective of the study was to establish spatial land evaluation for oil palm cultivation using GIS （geographic information system）. The study area is situated in the KESEDAR region in the state of Kelantan, Malaysia. The evaluation of the land in terms of the suitability classes were based on the method of FAO （Food and Agriculture Oganization of the United Nations）. Five land qualities are important for determining the physical land suitability for oil palm; these are nutrient availability, oxygen availability, water availability, workability and availability of foothold for roots. Each of the above mentioned land qualities with associated attribute data were digitally encoded in a GIS database to create thermatic layers. Overlay operation on the layer produced resultant polygonal layer each of which is a land unit with characteristics of the land. The results from GIS overlay analyses showed that Bungor, Chat, Chempaka, Alluvium, Musang and Tok Yong series are highly suitable while Kawang series is moderately suitable for oil palm cultivation. The same results were obtained by using parametric-limitation method.
文摘This paper gives and proofs a theorem, for any matrix A, do elementary column operations, change it to a matrix which is partitioned to two blocks which left one is column full rank and right one is zero matrix. That is, use a invertible matrix P to let AP = （B,O）, O is zero matrix with n-r columns, r and n is rank and column number of A, so the P＇s right n-r columns is just the basis of the null space of the matrix A. On the basis of the theorem, lots of problems of linear algebra can be resolved and lots of theorems can be proofed by elementary column operations. Perhaps the textbooks used in universities will have a lot of change with the result of the paper. This result is first found by author in 2010.12.8 in http：//www.paper.edu.cn/index.php/default/releasepaper/content/201012-232, but is not formal published.
基金Supported by the National Natural Science Foundation of China under Grant No.11171197
文摘Based on the PT-symmetric quantum theory, the concepts of PT-frame, PT-symmetric operator and CPT-frame on a Hilbert space K and for an operator on K are proposed. It is proved that the spectrum and point spectrum of a PT-symmetric linear operator are both symmetric with respect to the real axis and the eigenvalues of an unbroken PT-symmetric operator are real. For a linear operator H on Cd, it is proved that H has unbroken PT- symmetry if and only if it has d different eigenvalues and the corresponding eigenstates are eigenstates of PT. Given a CPT-frame on K, a new positive inner product on K is induced and called CPT-inner product. Te relationship between the CPT-adjoint and the Dirac adjoint of a densely defined linear operator is derived, and it is proved that an operator which has a bounded CPT-frame is CPT-Hermitian if and only if it is T-symmetric, in that case, it is similar to a Hermitian operator. The existence of an operator C consisting of a CPT-frame is discussed, These concepts and results will serve a mathematical discussion about PT-symmetric quantum mechanics.
