By studying modular invariance properties of some characteristic forms, we get some generalized anomaly cancellation formulas on(4 r-1)-dimensional manifolds with no assumption that the 3 rd de-Rham cohomology of mani...By studying modular invariance properties of some characteristic forms, we get some generalized anomaly cancellation formulas on(4 r-1)-dimensional manifolds with no assumption that the 3 rd de-Rham cohomology of manifolds vanishes. These anomaly cancellation formulas generalize our previous anomaly cancellation formulas on(4 r-1)-dimensional manifolds. We also generalize our previous anomaly cancellation formulas on(4 r-1)-dimensional manifolds and the Han–Yu rigidity theorem to the(a, b) case.展开更多
The authors discuss the existence and classification of stable vector bundles of rank 3, with 2 3 or 4 linearly independent holomorphic sections. The sets of all such bundles are denoted by ω3^2,d and w3 respectivel...The authors discuss the existence and classification of stable vector bundles of rank 3, with 2 3 or 4 linearly independent holomorphic sections. The sets of all such bundles are denoted by ω3^2,d and w3 respectively. Our argument leads to sufficient and necessary conditions for the existence of both kinds of bundles. The conclusion is very interesting because of its contradiction to the conjectured dimension formula of stable bundles. Finally, we give a preliminary classification of ω3^2,4 and a complete discussion on the structure of ω3^3,2/3g＋2.展开更多
A quasi-rectangular mesh (denoted by △QR) is basically a rectangular mesh (△R) that allows local modifications, including T-mesh (△T) and L-mesh (△L). In this paper, the dimensions of the bivariate spline spaces S...A quasi-rectangular mesh (denoted by △QR) is basically a rectangular mesh (△R) that allows local modifications, including T-mesh (△T) and L-mesh (△L). In this paper, the dimensions of the bivariate spline spaces Skμ(△QR) are discussed by using the Smoothing Cofactor-Conformality method. The dimension formulae are obtained with some constraints depending on the order of the smoothness, the degree of the spline functions and the structure of the mesh as well.展开更多
基金Supported by NSFC(Grant Nos.11271062,NCET–13–0721)
文摘By studying modular invariance properties of some characteristic forms, we get some generalized anomaly cancellation formulas on(4 r-1)-dimensional manifolds with no assumption that the 3 rd de-Rham cohomology of manifolds vanishes. These anomaly cancellation formulas generalize our previous anomaly cancellation formulas on(4 r-1)-dimensional manifolds. We also generalize our previous anomaly cancellation formulas on(4 r-1)-dimensional manifolds and the Han–Yu rigidity theorem to the(a, b) case.
文摘The authors discuss the existence and classification of stable vector bundles of rank 3, with 2 3 or 4 linearly independent holomorphic sections. The sets of all such bundles are denoted by ω3^2,d and w3 respectively. Our argument leads to sufficient and necessary conditions for the existence of both kinds of bundles. The conclusion is very interesting because of its contradiction to the conjectured dimension formula of stable bundles. Finally, we give a preliminary classification of ω3^2,4 and a complete discussion on the structure of ω3^3,2/3g＋2.
基金the National Natural Science Foundation of China (Nos.60533060 10726067)+1 种基金the Natural Science Foundation for Doctoral Career of Liaoning Province (No.20061060)the Science Foundation of Dalian University of Technology (No.SFDUT07001)
文摘A quasi-rectangular mesh (denoted by △QR) is basically a rectangular mesh (△R) that allows local modifications, including T-mesh (△T) and L-mesh (△L). In this paper, the dimensions of the bivariate spline spaces Skμ(△QR) are discussed by using the Smoothing Cofactor-Conformality method. The dimension formulae are obtained with some constraints depending on the order of the smoothness, the degree of the spline functions and the structure of the mesh as well.
