The Lappo-Danilevskii method and trivial intersections of radicals in lower central series terms for certain fundamental groups

In this paper, it is proved that the intersection of the radicals of nilpotent residues for the generalized pure braid group corresponding to an irreducible finite Coxeter group or an irreducible imprimitive finite complex reflection group is always trivial. The proof uses the solvability of the Riemann—Hilbert problem for analytic families of faithful linear representations by the Lappo-Danilevskii method. Generalized Burau representations are defined for the generalized braid groups corresponding to finite complex reflection groups whose Dynkin—Cohen graphs are trees. The Fuchsian connections for which the monodromy representations are equivalent to the restrictions of generalized Burau representations to pure braid groups are described. The question about the faithfulness of generalized Burau representations and their restrictions to pure braid groups is posed.     

Curves on threefolds with trivial canonical bundle

C H Clemens has shown that homologically trivial codimension two cycles on a general hypersurface of degree five and dimension three form a subgroup of infinite rank inside the intermediate jacobian. We generalize this to other complete intersection threefolds with trivial canonical bundle.     

Two-row nilpotent orbits of cyclic quivers

We prove that the local intersection cohomology of nilpotent orbit closures of cyclic quivers is trivial when the two orbits involved correspond to partitions with at most two rows. This gives a geometric proof of a result of Graham and Lehrer, which states that standard modules of the affine Hecke algebra of GL_d corresponding to nilpotents with at most two Jordan blocks are multiplicity-free. Received: 7 February 2002 / Published online: 8 November 2002     

On a Generalized Finite Intersection Property

We continue the study of the right finite intersection property under a weaker condition on annihilators, introducing the concept of generalized right finite intersection property (simply, generalized right FIP). We observe the structure of rings with the generalized right FIP and examine the generalized right FIP for various kinds of basic extensions of rings with the property. We show that the generalized right FIP does not go up to polynomial rings, and that the 2-by-2 full matrix ring over a domain has the generalized right FIP. In the process, we also obtain an equivalent condition for which a nonzero polynomial, over the ring of integers modulo n ≥ 2, is a non-zero-divisor.     

Vector fields and framings on isolated complete intersection singularities

A theorem is proved for deciding as to when the complex orthogonal complement of a vector field on an isolated, complete intersection germ, is a trivial vector bundle.     

广义稠密随机交集图的度分布(英文)

广义随机交集图是一类重要的随机图模型,它是E-R随机图的变种,被广泛用于复杂社会网络的研究中.本文研究了在顶点度的期望趋于无穷的情况下,广义随机交集图的度分布.我们对二项模型给出了中心极限定理,并且对一致模型给出了极限定理.     

Towers of Hanoi problems: Deriving iterative solutions by program transformations

We present the iterative solutions of the Towers of Hanoi problems (standard, cyclic, and generalized) using the program transformation methodology of Burstall-Darlington. We derive algorithms with minimal time × space requirements. Their correctness proofs are trivial, as usual when applying the program transformation technique.     

Microbundles, manifolds and metrisability

The notion of a microbundle was introduced in the 1960s but the theory came to an abrupt halt when it was shown that for a metrisable manifold, microbundles are equivalent to fibre bundles. In this paper we consider microbundles over non-metrisable manifolds. In some cases microbundles are equivalent to fibre bundles but in others they are not. In particular, we show that a manifold is metrisable if and only if its tangent microbundle is equivalent to a fibre bundle. We also illustrate that for some non-metrisable manifolds every trivial microbundle contains a trivial fibre bundle whereas other manifolds may support a trivial microbundle not containing a trivial fibre bundle.

     

A class of Lie algebras arising from intersection matrices

We find a class of Lie algebras, which are defined from the symmetrizable generalized intersection matrices. However, such algebras are different from generalized intersection matrix algebras and intersection matrix algebras. Moreover, such Lie algebras generated by semi-positive definite matrices can be classified by the modified Dynkin diagrams.     

On the intersection of conjugate nilpotent subgroups in permutation groups

We prove that, with exception of finitely many explicitly indicated cases, for a nilpotent subgroup in a symmetric or an alternating group there always exists a subgroup conjugate to it such that the intersection of the subgroups is trivial.     

约化环和半交换环

讨论了在约化条件下,比平凡扩张更广泛的一类扩张环的半交换性.通过给出半交换模的定义,得到平凡扩张是半交换环的一个充要条件.     

The two-well problem in three dimensions

We study properties of generalized convex hulls of the set with . If K contains no rank-1 connection we show that the quasiconvex hull of K is trivial if H belongs to a certain (large) neighbourhood of the identity. We also show that the polyconvex hull of K can be nontrivial if H is sufficiently far from the identity, while the (functional) rank-1 convex hull is always trivial. If the second well is replaced by a point then the polyconvex hull is trivial provided that there are no rank-1 connections. Received: March 25, 1999 / Accepted: April 23, 1999     

Matrix Rings with Summand Intersection Property

A ring R has right SIP (SSP) if the intersection (sum) of two direct summands of R is also a direct summand. We show that the right SIP (SSP) is the Morita invariant property. We also prove that the trivial extension of R by M has SIP if and only if R has SIP and (1 – e)Me = 0 for every idempotent e in R. Moreover, we give necessary and sufficient conditions for the generalized upper triangular matrix rings to have SIP.     

Further Results on Generalized Intersection Searching Problems: Counting,Reporting, and Dynamization

In a generalized intersection searching problem, a set, S, of colored geometric objects is to be preprocessed so that given some query object, q, the distinct colors of the objects intersected by q can be reported efficiently or the number of such colors can be counted efficiently. In the dynamic setting, colored objects can be inserted into or deleted from S. These problems generalize the well-studied standard intersection searching problems and are rich in applications. Unfortunately, the techniques known for the standard problems do not yield efficient solutions for the generalized problems. Moreover, previous work (R. Janardan and M. Lopez, Generalized intersection searching problems, Internat. J. Comput. Geom. Appl.3 (1993), 39-69) on generalized problems applies only to the static reporting problems. In this paper, a uniform framework is presented to solve efficiently the counting/reporting versions of a variety of generalized intersection searching problems in static/dynamic settings. These problems include 1-, 2-, and 3-dimensional range searching, quadrant searching, interval intersection searching, 1- and 2-dimensional point enclosure searching, and orthogonal segment intersection searching.     

Mazur交性质

主要考虑关于Mazur交性质的问题．我们通过赋范半群的对偶,给出了一个赋范空间只有平凡Mazur集白々等价刻画．另外,我们还讨论乘积空间对Mazur交性质的继承性,对Sersouri和Roy的结论作了一定的改进,将范数推广至更一般的情形．     

On the summands of near-rings with ATM

We say that a near-ring (N,+,·) has an almost trivial multiplication (ATM) if the product of two elements belongs to the intersection of the additive cyclic groups generated by these two elements. We show that every finite near-ring with ATM can be decomposed to a direct sum where the summands are either near-rings defined on cyclic groups or near-rings whose minimal ideals are zero near-rings. Finally, we show how to construct these summands on cyclic groups.     

关于某些多边形积的剩余有限性

讨论嵌入子群是循环群的有限p-群的多边形积,得到了多边形积为剩余有限的一个充分条件.     

Tetragonal curves, scrolls and surfaces

In this paper we establish a theorem which determines the invariants of a general hyperplane section of a rational normal scroll of arbitrary dimension. We then construct a complete intersection surface on a four-dimensional scroll and prove it is regular with a trivial dualizing sheaf. We determine the invariants for which the surface is nonsingular, and hence a surface. A general hyperplane section of this surface is a tetragonal curve; we use the first theorem to determine for which tetragonal invariants such a construction is possible. In particular we show that for every genus there is a tetragonal curve of genus that is a hyperplane section of a surface. Conversely, if the tetragonal invariants are not sufficiently balanced, then the complete intersection must be singular. Finally we determine for which additional sets of invariants this construction gives a tetragonal curve as a hyperplane section of a singular canonically trivial surface, and discuss the connection with other recent results on canonically trivial surfaces.

     

Hamiltonian type Lie bialgebras

We first prove that,for any generalized Hamiltonian type Lie algebra H,the first co- homology group H~1(H,H(?)H) is trivial.We then show that all Lie bialgebra structures on H are triangular.