Using module class C R=Mx∈M,xRT=0,T∈I , we introduced the concepts of C R finitely generated module, C R finitely presented module and C R regular ring. We also discussed the criterion for C ...Using module class C R=Mx∈M,xRT=0,T∈I , we introduced the concepts of C R finitely generated module, C R finitely presented module and C R regular ring. We also discussed the criterion for C R regular ring,and the relations between C R regular ring and C R FP injective module.展开更多
Based on the relationship between water environment system and human society, water environment carrying capacity （WECC） probes into supporting ability of complex water environment system to the human society. Recen...Based on the relationship between water environment system and human society, water environment carrying capacity （WECC） probes into supporting ability of complex water environment system to the human society. Recent years, due to the shortage of water resources and serious water pollution in several watersheds in China, the research of watershed water environment carrying capacity （WWECC） becomes very important. The conception, connotation and method of representation of WWECC are discussed deeply in this paper. It shows that WWECC is a kind of index that instructs whether the water environment system in watershed can continue to support the development of social economy and ecology, it is dimensionless number.展开更多
In this paper,we give the explicit expressions of level k (r 1,r 2,…,r k) circulant matrices of order n 1n 2…n k,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind...In this paper,we give the explicit expressions of level k (r 1,r 2,…,r k) circulant matrices of order n 1n 2…n k,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind level k (r 1,r 2,…,r k) circulant matrices are derived,and it is also proved that the sort of matrices are diagonalizable.展开更多
In this paper, we give the explicit expressions of level-k circulant matrices of type (n1,n2,…nk) and of order n1n2…nk,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of th...In this paper, we give the explicit expressions of level-k circulant matrices of type (n1,n2,…nk) and of order n1n2…nk,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind level-k circulant matrices are derived,and it is also proved that the sort matrices are unitarily diagonalizable.展开更多
Map data display is the basic information representation mode under embedded real-time navigation. After a navigation display data set （NDIS_SET） with several dimensions and corresponding mathematical description fo...Map data display is the basic information representation mode under embedded real-time navigation. After a navigation display data set （NDIS_SET） with several dimensions and corresponding mathematical description formula are designed, a series of rules and algorithms are advanced to optimize embedded navigation data and promote data index and input efficiency. A new parallel display algorithm with navigation data named N PDIS is then presented to adapt to limited embedded resources of computation and memory after a normal navigation data display algorithm named NDIS and related problems are analyzed, N_PDIS can synchronously create two preparative bitmapa by two parallel threads and switch one of them to screen automatically. Compared with NDIS, the results show that N_PDIS is more effective in improving display efficiency.展开更多
Based on a new discrete three-by-three matrix spectral problem, a hierarchy of integrable lattice equations with three potentials is proposed through discrete zero-curvature representation, and the resulting integrabl...Based on a new discrete three-by-three matrix spectral problem, a hierarchy of integrable lattice equations with three potentials is proposed through discrete zero-curvature representation, and the resulting integrable lattice equation reduces to the classical Toda lattice equation. It is shown that the hierarchy possesses a HamiItonian structure and a hereditary recursion operator. Finally, infinitely many conservation laws of corresponding lattice systems are obtained by a direct way.展开更多
The authors prove the stability of the rings of highest weight vectors of the action of Om x GLn on the complex polynomial rings on Cm,n. As an application, the structure of the rings for m = 3 is determined.
We construct a fermion analogue of the Fock representation of quantum toroidal algebra and construct the fermion representation of quantum toroidal algebra on the K-theory of Hilbert scheme.
A contravaried bilinear pairing X on every M(ρ) × M(ρθ) is determined and it is provedthat M(ρ)is irreducible if and only if K is left nondegellerate. It is also proved that every cyclicpointed module is a qu...A contravaried bilinear pairing X on every M(ρ) × M(ρθ) is determined and it is provedthat M(ρ)is irreducible if and only if K is left nondegellerate. It is also proved that every cyclicpointed module is a quotient of some Verma-like poillted module; moreover if it is irreduciblethen it is a quotieDt of the Vermarlike poiDted module by the left kernel of some bilinearpairing K. In case the mass fUnction is symmetric, there exists a bilinear form on M(ρ). It isproved that unitals pointed modules are integrable. In addition, a characterization of the massfunctions of Kac-Moody algebras is given, which is a generalization of the finite dimensionalLie algebras case.展开更多
文摘Using module class C R=Mx∈M,xRT=0,T∈I , we introduced the concepts of C R finitely generated module, C R finitely presented module and C R regular ring. We also discussed the criterion for C R regular ring,and the relations between C R regular ring and C R FP injective module.
文摘Based on the relationship between water environment system and human society, water environment carrying capacity （WECC） probes into supporting ability of complex water environment system to the human society. Recent years, due to the shortage of water resources and serious water pollution in several watersheds in China, the research of watershed water environment carrying capacity （WWECC） becomes very important. The conception, connotation and method of representation of WWECC are discussed deeply in this paper. It shows that WWECC is a kind of index that instructs whether the water environment system in watershed can continue to support the development of social economy and ecology, it is dimensionless number.
文摘In this paper,we give the explicit expressions of level k (r 1,r 2,…,r k) circulant matrices of order n 1n 2…n k,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind level k (r 1,r 2,…,r k) circulant matrices are derived,and it is also proved that the sort of matrices are diagonalizable.
文摘In this paper, we give the explicit expressions of level-k circulant matrices of type (n1,n2,…nk) and of order n1n2…nk,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind level-k circulant matrices are derived,and it is also proved that the sort matrices are unitarily diagonalizable.
文摘Map data display is the basic information representation mode under embedded real-time navigation. After a navigation display data set （NDIS_SET） with several dimensions and corresponding mathematical description formula are designed, a series of rules and algorithms are advanced to optimize embedded navigation data and promote data index and input efficiency. A new parallel display algorithm with navigation data named N PDIS is then presented to adapt to limited embedded resources of computation and memory after a normal navigation data display algorithm named NDIS and related problems are analyzed, N_PDIS can synchronously create two preparative bitmapa by two parallel threads and switch one of them to screen automatically. Compared with NDIS, the results show that N_PDIS is more effective in improving display efficiency.
基金Supported by the Science and Technology Plan Project of the Educational Department of Shandong Province of China under Grant No.J09LA54the Research Project of"SUST Spring Bud"of Shandong University of Science and Technology of China under Grant No.2009AZZ071
文摘Based on a new discrete three-by-three matrix spectral problem, a hierarchy of integrable lattice equations with three potentials is proposed through discrete zero-curvature representation, and the resulting integrable lattice equation reduces to the classical Toda lattice equation. It is shown that the hierarchy possesses a HamiItonian structure and a hereditary recursion operator. Finally, infinitely many conservation laws of corresponding lattice systems are obtained by a direct way.
基金Project supported by the National Natural Science Foundation of China (No.19901015 and No. 19731004).
文摘The authors prove the stability of the rings of highest weight vectors of the action of Om x GLn on the complex polynomial rings on Cm,n. As an application, the structure of the rings for m = 3 is determined.
基金Supported by National Natural Science Foundation of China under Grant No.11031005Beijing Municipal Education Commission Foundation under Grant Nos.KZ201210028032 and KM201210028006
文摘We construct a fermion analogue of the Fock representation of quantum toroidal algebra and construct the fermion representation of quantum toroidal algebra on the K-theory of Hilbert scheme.
文摘A contravaried bilinear pairing X on every M(ρ) × M(ρθ) is determined and it is provedthat M(ρ)is irreducible if and only if K is left nondegellerate. It is also proved that every cyclicpointed module is a quotient of some Verma-like poillted module; moreover if it is irreduciblethen it is a quotieDt of the Vermarlike poiDted module by the left kernel of some bilinearpairing K. In case the mass fUnction is symmetric, there exists a bilinear form on M(ρ). It isproved that unitals pointed modules are integrable. In addition, a characterization of the massfunctions of Kac-Moody algebras is given, which is a generalization of the finite dimensionalLie algebras case.
