Non-vanishing of the twisted cohomology on the complement of hypersurfaces

Generically, the cohomology with coefficients in a local system of rank one on the complement in of the union of a finite number of hypersurfaces vanishes except in the highest dimension. We study the non-generic case, in which the cohomology in other dimensions does not vanish. When the hypersurfaces are hyperplanes, many examples of this kind are known. In this paper, we consider the case in which the hypersurfaces need not be hyperplanes. We prove that the hypersurfaces given by some particular linear systems have non-vanishing local system cohomologies.

     

极小圈模对与二元域拟阵的特征

研究极小圈模对与二元域拟阵的特征.首先给出拟阵M的极小圈模对,模对的并的秩与相应的超平面的交的秩三者的等价关系.在两个极小圈不等的条件下,证明了满足极小圈消去公理的极小圈是唯一的并且极小圈模对的对称差包含在其中,结合极小圈的对称差的表示,证明了极小圈与基的差的绝对值大于等于2.后面两个证明都把原来的必要条件推广为充要条件.最后,用M上不相同的极小圈,极小圈模对,极小圈的对称差表示,M上不相等的超平面,超平面的并不等于E及满足的秩等式极简单地刻划了二元域拟阵M的特征.     

Small faces in stationary Poisson hyperplane tessellations

We consider the tessellation induced by a stationary Poisson hyperplane process in d‐dimensional Euclidean space. Under a suitable assumption on the directional distribution, and measuring the k‐faces of the tessellation by a suitable size functional, we determine a limit distribution for the shape of the typical k‐face, under the condition of given size and this tending to zero. The limit distribution is concentrated on simplices. This extends a result of Gilles Bonnet.     

Diameters of sections and coverings of convex bodies

We study the diameters of sections of convex bodies in R^N determined by a random N×n matrix Γ, either as kernels of Γ^* or as images of Γ. Entries of Γ are independent random variables satisfying some boundedness conditions, and typical examples are matrices with Gaussian or Bernoulli random variables. We show that if a symmetric convex body K in R^N has one well bounded k-codimensional section, then for any m>ck random sections of K of codimension m are also well bounded, where c?1 is an absolute constant. It is noteworthy that in the Gaussian case, when Γ determines randomness in sense of the Haar measure on the Grassmann manifold, we can take c=1.     

Improved estimation of duality gap in binary quadratic programming using a weighted distance measure

We present in this paper an improved estimation of duality gap between binary quadratic program and its Lagrangian dual. More specifically, we obtain this improved estimation using a weighted distance measure between the binary set and certain affine subspace. We show that the optimal weights can be computed by solving a semidefinite programming problem. We further establish a necessary and sufficient condition under which the weighted distance measure gives a strictly tighter estimation of the duality gap than the existing estimations.     

分担处于一般位置超平面的亚纯映射唯一性定理

本文研究从Cn到复射影空间PN(C)上亚纯映射唯一性问题.根据杨乐处理重值的方法和Dethloff、Quang、Tan等人的技巧,我们分别得到了两个广泛的唯一性定理,改进和推广了一些分担处于一般位置超平面的亚纯映射唯一性结果.     

The Study of Minimax Inequalities, Abstract Economics and Applications to Variational Inequalities and Nash Equilibria

In this survey, a new minimax inequality and one equivalent geometricform are proved. Next, a theorem concerning the existence of maximalelements for an LC-majorized correspondence is obtained.By the maximal element theorem, existence theorems of equilibrium point fora noncompact one-person game and for a noncompact qualitative game withLC-majorized correspondences are given. Using the lastresult and employing 'approximation approach', we prove theexistence of equilibria for abstract economies in which the constraintcorrespondence is lower (upper) semicontinuous instead of having lower(upper) open sections or open graphs in infinite-dimensional topologicalspaces. Then, as the applications, the existence theorems of solutions forthe quasi-variational inequalities and generalized quasi-variationalinequalities for noncompact cases are also proven. Finally, with theapplications of quasi-variational inequalities, the existence theorems ofNash equilibrium of constrained games with noncompact are given. Our resultsinclude many results in the literature as special cases.     

Optimum Gas Journal Bearing with the Flexible Surface

The optimum shape of the cylindrical internal deformable (flexible) surface of a gas journal bearing of infinite length is designed. The variational problem of determining the clearance shape giving the maximum bearing load capacity is formulated and solved.     

Generalized Exponents and Forms

We consider generalized exponents of a finite reflection group acting on a real or complex vector space V. These integers are the degrees in which an irreducible representation of the group occurs in the coinvariant algebra. A basis for each isotypic component arises in a natural way from a basis of invariant generalized forms. We investigate twisted reflection representations (V tensor a linear character) using the theory of semi-invariant differential forms. Springer’s theory of regular numbers gives a formula when the group is generated by dim V reflections. Although our arguments are case-free, we also include explicit data and give a method (using differential operators) for computing semi-invariants and basic derivations. The data give bases for certain isotypic components of the coinvariant algebra.     

Central quotients of biautomatic groups

The quotient of a biautomatic group by a subgroup of the center is shown to be biautomatic. The main tool used is the Neumann-Shapiro triangulation of S ^n-1, associated to a biautomatic structure on . Among other applications, a question of Gersten and Short is settled by showing that direct factors of biautomatic groups are biautomatic. Received: October 4, 1994