On Invariant Line Arrangements

We classify all arrangements of ten lines in the real projective plane that are invariant under a polynomial differential equation of degree 4.     

Long Monotone Paths in Line Arrangements

We show how to construct an arrangement of n lines having a monotone path of length (n^{2 – (d/\sqrt{log n})}), where d > 0 is some constant, and thus nearly settle the long standing question on monotone path length in line arrangements.     

输油管道的布置

本文建立了非线性规划模型,解决了输油管线布置问题,并给出了输油管线铺设的最佳方案.     

Cohomology of Real Diagonal Subspace Arrangements via Resolutions

We express the cohomology of the complement of a real subspace arrangement of diagonal linear subspaces in terms of the Betti numbers of a minimal free resolution. This leads to formulas for the cohomology in some cases, and also to a cohomology vanishing theorem valid for all arrangements.     

实无限维线性空间中的较多序

本文引入实无限维线性空间中的较多锥和严格较多锥,利用它们定义较多序,讨论较多序的性质,由此得出,实无限维线性空间中的任何两个元素都可以按较多序进行比较．     

The Homogeneous Geometries of Real Hyperbolic Space

We describe the holonomy algebras of all canonical connections of homogeneous structures on real hyperbolic spaces in all dimensions. The structural results obtained then lead to a determination of the types, in the sense of Tricerri and Vanhecke, of the corresponding homogeneous tensors. We use our analysis to show that the moduli space of homogeneous structures on real hyperbolic space has two connected components.     

On a Jacobian Identity Associated with Real Hyperplane Arrangements

For the mapping is onto R. It was shown by G. Boole in the 1850's that We give an n-dimensional analogue of this result. The proof makes use of the Griffiths–Harris residue theorem from algebraic geometry.     

Summation of Unordered Arrays

An approach to the summation of unordered number and matrix arrays based on ordering them by absolute value (greedy summation) is proposed. Theorems on products of greedy sums are proved. A relationship between the theory of greedy summation and the theory of generalized Dirichlet series is revealed. The notion of asymptotic Dirichlet series is considered.     

The Structure of Multiplicative Tilings of the Real Line

Journal of Fourier Analysis and Applications - Suppose $$\Omega , A \subseteq \mathbb {R}\backslash {\left\{ {0}\right\} }$$ are two sets, both of mixed sign, that $$\Omega $$ is Lebesgue...     

无序和的一个注记

对于任意集合上广义实数取值的非负函数,文献[1]给出了无序和的两种定义,文献[2]给出了无序和的第三种定义,文章证明了这三种定义相互等价.对于任意集合上绝对可和的复值函数,文献[1]和文献[2]分别给出了无序和的两种不同定义,文章证明了这两种定义等价.     

半直线伸缩调制框架集

本文研究右半直线平方可积函数空间L^2(R+)中的一类伸缩调制系.实际问题中时间变量不可取负值,L^2(R+)可模拟因果信号空间.但因R+按加法不能作成一个群,它不容许小波与Gabor系.我们研究L^2(R+)中由特征函数生成的伸缩调制系(MD-系)框架,引入了R+中MD-框架集的概念,利用"伸缩等价"与"基数函数"方法刻画了L^2(R+)中MD-Bessel集与完备集;得到了关于MD-Riesz基集的两个充分条件,并证明了通过对MD-Riesz基集进行有限可测分解可得到MD-框架集.     

Monotone Paths in Line Arrangements with a Small Number of Directions

We give subquadratic bounds on the maximum length of an x-monotone path in an arrangement of n lines with at most C log log n directions, where C is a suitable constant. For instance, the maximum length of an x-monotone path in an arrangement of n lines having at most ten slopes is O(n^67/34). In particular, we get tight estimates for the case of lines having at most five directions, by showing that previous constructions—(n^3/2) for arrangements with four slopes and (n^5/3) for arrangements with five slopes—due to Sharir and Matousek, respectively, are (asymptotically) best possible.     

实轴上Hermite插值算子的收敛性

The present paper investigates the convergence of Hermite interpolation operators on the real line. The main result is： Given 0 〈 δo 〈 1/2, 0 〈 εo 〈 1. Let f ∈ C（-∞,∞） satisfy ｜y｜= O（e^（1/2-δo）xk^2,） and ｜f（x）｜t= O（e^（1-εo ）x2^）. Then for any given point x ∈ R, we have limn→Hn,（f, x） = f（x）.     

实轴上Hermite插值算子的收敛性

The present paper investigates the convergence of Hermite interpolation operators on the real line.The main result is: Given 0 <δ0 < 1/2,0 < ε0 < 1.Let f ∈ C(-∞,∞) satisfy |yk| = O(e(1/2-δ0)x2k) and |f(x)| = O(e(1-ε0)x2).Then for any given point x ∈R,we have limn→∞ Hn(f,x) = f(x).     

The Moduli Space of Real Abelian Varieties with Level Structure

The moduli space of principally polarized Abelian varieties with real structure and with level N = 4m structure (with m1) is shown to coincide with the set of real points of a quasi-projective algebraic variety defined over , and to consist of finitely many copies of the quotient of the space GL(n, )/O(N) (of positive definite symmetric matrices) by the principal congruence subgroup of level N in GL(n, ).     

An Improved Bound for Joints in Arrangements of Lines in Space

Let L be a set of n lines in space. A joint of L is a point in R³ where at least three non-coplanar lines meet. We show that the number of joints of L is O(n^112/69 log^6/23n)=O(n^1.6232), improving the previous bound O(n^1.643) of Sharir.     

The Size of Exponential Sums on Intervals of the Real Line

We prove that there is a constant c>0 depending only on M≥1 and μ≥0 such that

Zero-energy Fields on Real Projective Space

A smooth 1-form on real projective space with vanishing integral along all geodesics is said to have zero energy. Such a 1-form is necessarily the exterior derivative of a smooth function. We formulate a general version of this theorem for tensor fields on real projective space and prove it using methods of complex analysis. A key ingredient is the cohomology of involutive structures.