A note on Tutte polynomials and Orlik–Solomon algebras

Let be a (central) arrangement of hyperplanes in and the dependence matroid of the linear forms . The Orlik–Solomon algebra of a matroid is the exterior algebra on the points modulo the ideal generated by circuit boundaries. The graded algebra is isomorphic to the cohomology algebra of the manifold . The Tutte polynomial is a powerful invariant of the matroid . When is a rank 3 matroid and the θ_Hi are complexifications of real linear forms, we will prove that determines . This result partially solves a conjecture of Falk.     

全纯曲线的例外超平面∗

文章讨论了到复射影空间P^N (C)的全纯曲线交超平面的问题,借助Vandermonde行列式, 构造了一些具有N+1个例外超平面的非线性退化的全纯曲线和具有2N个例外超平面的线性退化的非常映射全纯曲线,说明了 Nochka 的全纯曲线的第二基本定理是最优的.最后还构造了具有2N个例外值的N值非常数代数体函数.     

Some exact iterative procedures for finding the puncture point of a convex set

LetK be a convex set in the Hilbert spaceH, and let the ray {c: R} punctureK at *c. Some algorithms are given for finding *. Each algorithm results in a nonincreasing sequence { _i } which converges to *. The points _j c lie in successive supporting hyperplanes toK. The normal to thenth hyperplane is obtained by a minimization over a set no larger than the unitn cube. It is assumed that the subset ofK which maximizes (,x) forx inK is found relatively easily.This research was sponsored by NSF Grant No. MCS-76-11040.     

A Proof of Hadwiger's Covering Conjecture for Dual Cyclic Polytopes

In 1957, H. Hadwiger conjectured that a convex body K in a Euclidean d-space, d 1, can always be convered by 2 ^d smaller homotheti copies of K. We verify this conjecture when K is the polar of a cyclic d-polytope.