This paper proposes a novel four-dimensional approach to the structural study of protein complexes. In the approach, the surface of a protein molecule is to be described using the intersection of a pair of four-dimens...This paper proposes a novel four-dimensional approach to the structural study of protein complexes. In the approach, the surface of a protein molecule is to be described using the intersection of a pair of four-dimensional triangular cones (with multiple top vertexes). As a mathematical toy model of protein complexes, we consider complexes of closed trajectories of n-simplices (n=2,3,4...), where the design problem of protein complexes corresponds to an extended version of the Hamiltonian cycle problem. The problem is to find “a set of” closed trajectories of n-simplices which fills the n-dimensional region defined by a given pair of n+1 -dimensional triangular cones. Here we give a solution to the extended Hamiltonian cycle problem in the case of n=2 using the discrete differential geometry of triangles (i.e., 2-simplices).展开更多
We give a complete classification of tilting bundles over a weighted projective line of type （2, 3, 3）. This yields another realization of the tame concealed algebras of type E6.
ⅠConcerning the Clifford theorem with the stability of vector bundles, Arrondo-Sols proposed the following conjecture.Arrondo-Sols’Conjecture. Let E be a rank two vector bundle of degree d on a smooth complex algebr...ⅠConcerning the Clifford theorem with the stability of vector bundles, Arrondo-Sols proposed the following conjecture.Arrondo-Sols’Conjecture. Let E be a rank two vector bundle of degree d on a smooth complex algebraic curve of genus g, -e be the minimal self-intersection number of a unisecant curve in the ruled surface p(E), and r+ 1 =h^0(E). If -e≤d≤4g-4+e and E≠L⊕L,展开更多
Let E be a vector bundle over a compact Riemannian manifold M. We construct a natural metric on the bundle space E and discuss the relationship between the killing vector fields of E and M. Then we give a proof of the...Let E be a vector bundle over a compact Riemannian manifold M. We construct a natural metric on the bundle space E and discuss the relationship between the killing vector fields of E and M. Then we give a proof of the Bott-Baum-Cheeger Theorem for vector bundle E.展开更多
文摘This paper proposes a novel four-dimensional approach to the structural study of protein complexes. In the approach, the surface of a protein molecule is to be described using the intersection of a pair of four-dimensional triangular cones (with multiple top vertexes). As a mathematical toy model of protein complexes, we consider complexes of closed trajectories of n-simplices (n=2,3,4...), where the design problem of protein complexes corresponds to an extended version of the Hamiltonian cycle problem. The problem is to find “a set of” closed trajectories of n-simplices which fills the n-dimensional region defined by a given pair of n+1 -dimensional triangular cones. Here we give a solution to the extended Hamiltonian cycle problem in the case of n=2 using the discrete differential geometry of triangles (i.e., 2-simplices).
文摘We give a complete classification of tilting bundles over a weighted projective line of type （2, 3, 3）. This yields another realization of the tame concealed algebras of type E6.
基金Project partly supported by the National Natural Science Foundation of China and the Institute of Mathematics, Academia Sinica.
文摘ⅠConcerning the Clifford theorem with the stability of vector bundles, Arrondo-Sols proposed the following conjecture.Arrondo-Sols’Conjecture. Let E be a rank two vector bundle of degree d on a smooth complex algebraic curve of genus g, -e be the minimal self-intersection number of a unisecant curve in the ruled surface p(E), and r+ 1 =h^0(E). If -e≤d≤4g-4+e and E≠L⊕L,
文摘Let E be a vector bundle over a compact Riemannian manifold M. We construct a natural metric on the bundle space E and discuss the relationship between the killing vector fields of E and M. Then we give a proof of the Bott-Baum-Cheeger Theorem for vector bundle E.
