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.

     

A new Brézis‐Gallouët‐Wainger inequality from the viewpoint of the real interpolation functors

The Brézis‐Gallouët‐Wainger inequality describes a subtle embedding property into . The relation between the Brézis‐Gallouët‐Wainger inequality and the real interpolation functor together with the sharpness of the results is discussed in the present paper. As our first main results shows, it turns out that there are two intermediate terms between and the logarithmic boundedness, which is supposed to be the right‐hand side of the Brézis‐Gallouët‐Wainger inequality. As the second result, the first result is extended to inequalities which reflect the meaning of the second index of Besov spaces and the interpolation theorem.     

Simple eigenvalues for the Steklov problem in a domain with a small hole. A functional analytic approach

Let be a bounded open domain of . Let denote the outward unit normal of . We assume that the Steklov problem Δu = 0 in and on has a simple eigenvalue of . Then we consider an annular domain obtained by removing from a small‐cavity size of ε > 0, and we show that under proper assumptions there exists a real valued and real analytic function defined in an open neighborhood of (0,0) in and such that is a simple eigenvalue for the Steklov problem Δu = 0 in and on for all ε > 0 small enough, and such that . Here denotes the outward unit normal of , and δ_2,2 ≡ 1 and δ_2,n ≡ 0 if n ≥ 3. Then related statements have been proved for corresponding eigenfunctions. Copyright © 2013 John Wiley & Sons, Ltd.     

一对四元数矩阵方程的共轭延拓解

定义广义四元数共轭延拓矩阵的概念,利用矩阵分块和四元数矩阵的实表示方法,分别给出四元数矩阵方程AX=C和XB=D存在列共轭延拓解和行共轭延拓解的必要充分条件及解的表达式.     

方阵的开方问题

运用Jordan标准形理论,完整解决了复数方阵、实数方阵能否开平方、开立方的问题.     

基于MIV-BP型网络实验的房地产项目风险识别研究

为了更准确更客观地识别房地产项目中的风险,为房地产项目投资决策提供科学依据和参考,有效地规避风险,本研究在BP神经网络 (Back-Propagation Neural Network)建模的基础上,采取MIV(Mean Impact Value)算法对BP神经网络模型进行变量筛选的网络优化和改良,从而形成新的优化后的MIV-BP(Mean Impact Value Back-Propagation Neural Network)神经网络,并以此用于评价房地产项目中的风险度以及各因素在风险度中的影响作用大小;同时选取目前相关的房地产项目数据进行仿真实证分析和验证。验证实验结果表明,MIV-BP型神经网络对于房地产项目风险度识别具有良好的适应性和准确性,实验结果客观,达到专家评价的要求,并在风险因素作用度分析上具有良好的应用价值。     

确界原理的一个修正证明

分析了华东师大版《数学分析》（第四版）教材中关于确界原理证明的不足之处,给出更为细致的修正证明.     

A kinematic formula for integral invariant of degree 4 in real space form

In this paper,kinematic formulae in a real space form are investigated.A kinematic formula for homogeneous polynomial of degree 4 on the second fundamental forms in a real space form is obtained.The formula obtained is a concrete form of the result of Howard and the analogue of the known formula of Chen and Zhou.     

Strongly Real Special 2-Groups

Strongly real groups and totally orthogonal groups form two important subclasses of real groups. In this article we give a characterization of strongly real special 2-groups. This characterization is in terms of quadratic maps over fields of characteristic 2. We then provide examples of groups which are in one subclass and not the other. It is a conjecture of Tiep that such examples are not possible for finite simple groups.     

Real Hypersurfaces Having Many Pseudo-hyperplanes

Abstract

Let nand dbe natural integers satisfying n ≥ 3 and d ≥ 10. Let Xbe an irreducible real hypersurface Xin ? ⁿ of degree dhaving many pseudo-hyperplanes. Suppose that Xis not a projective cone. We show that the arrangement ? of all d ? 2 pseudo-hyperplanes of Xis trivial, i.e., there is a real projective linear subspace Lof ? ⁿ (?) of dimension n ? 2 such that L ? Hfor all H ∈ ?. As a consequence, the normalization of Xis fibered over ?¹in quadrics. Both statements are in sharp contrast with the case n = 2; the first statement also shows that there is no Brusotti-type result for hypersurfaces in ? ⁿ , for n ≥ 3.