二阶曲线间的射影映射

平面上的射影变换,将二阶曲线变为另一二阶曲线,这个射影变换也可以称为这两个二阶曲线间的射影映射.若两个二阶曲线相切,则存在以切点为射影中心的两个二阶曲线间的射影映射;若两个二阶曲线相离,则存在以两个二阶曲线公切线交点为射影中心的射影映射;若两个二阶曲线相交,则存在以其中一交点为射影中心的两个二阶曲线间的射影映射.     

利用射影平面中的二次曲线构作结合方案

设C是射影平面H=PG(2,Fq)中的一条二次曲线.把H看作射影空间PG(3,Fq)的无穷远超平面,那么H在PG(3,Fq)中的补空间是仿射空间X=AG(3,Fq).我们把H上的点集划分为2个或3个子集的并.设a≠b∈X.若线ab与H的交点属于第i个集合,定义a和b属于第i个结合类.我们证明上述构作是结合方案.最后,把H的某一点集作为处理集,构作出结合方案.     

非奇异射影子簇的算术亏格及其外在几何

证明当复射影空间CPⁿ中维数不大于3的非奇异子簇的各维线性子空间截面的算术亏格满足一定条件时,它一定包含在一个高一维的极小次子簇上或是射影正规的.     

Hilbert空间H上正交射影对的一个注记

本文研究了Hilbert空间H上正则射影对的性质和结构，证明了酉算子V与正交射影对（P，Q）交织（i．e．，VP=QV，PV=VQ）的充分必要条件是dim（R（P）∩N（Q））=dim（N（P）∩R（Q）），给出了满足上述条件均酉算子V均一般形式．     

利用射影空间中的埃尔米特簇构作结合方案

本文把N+1维射影空间看作一个N+1维仿射空间X和一个N维无穷远超平面H的并,利用埃尔米特簇把H上的点集划分为3个子集,对X中任两点a和b,如果线ab与H的交点属于第i个子集,定义a和b属于第i个结合类,我们证明上述构作是一个结合方案,并计算出其参数。     

射影空间的故事(二)

3.射影空间在寻常的直线上加上一个无穷远点,就扩充成了射影直线;在寻常的平面上加上所有无穷远点,就扩充成了射影平面,其中所有无穷远点组成无穷远直线.在数学上怎样刻画射影平面呢?     

度量射影和余度量射影的线性选择

本文讨论了度量射影和余度量射影的关系,并在L_p(T)和C(T)空间中讨论了它们的线性选择的性质.     

一类射影平坦的球对称的芬斯勒度量

本文研究了射影平坦芬斯勒度量的构造问题.通过分析射影平坦的球对称的芬斯勒度量的方程的解,构造了一类新的射影平坦的芬斯勒度量,并得到了射影平坦的球对称的芬斯勒度量的射影因子和旗曲率.     

射影空间的故事（二）

3.射影空间在寻常的直线上加上一个无穷远点,就扩充成了＂射影直线＂;在寻常的平面上加上所有无穷远点,就扩充成了＂射影平面＂,其中所有无穷远点组成无穷远直线.在数学上怎样刻画射影平面呢？     

射影平面的模型和莫比乌斯带

射影几何研究图形在射影变换下的不变性,射影变换可以直观地看成是由连续施行若干次中心投影所得到的变换,为了使中心投影成为两平面的点之间的一一对应,我们必须把通常的欧氏平面加以拓广,添加无穷远点和无穷远直线,即对平面上的一族平行线添加一个无穷远点,且规定平面上所有无穷远点的集合为一条无穷远直线,这和经过拓广以后的平面,若对     

正交投影的积与差的Moore-Penrose逆

运用分块算子矩阵的方法,给出了HIlbert空间上两个正交投影的和与差的Moore-Penrose逆的一个新的表达式.     

An explicit algorithm for monotone variational inequalities

We introduce a fully explicit method for solving monotone variational inequalities in Hilbert spaces, where orthogonal projections onto the feasible set are replaced by projections onto suitable hyperplanes. We prove weak convergence of the whole generated sequence to a solution of the problem, under only the assumptions of continuity and monotonicity of the operator and existence of solutions.     

Convergence of non-cyclic infinite products of operators

Using a geometric approach (in particular, angles between subspaces), we establish useful estimates regarding convergence of infinite products involving orthogonal projections and other (possibly nonlinear) nonexpansive operators in Hilbert space.     

On the Projections of the Mutual Multifractal Rényi Dimensions

In this paper, we compare the mutual multifractal Rényi dimensions to the mutual multifractal Hausdorff and pre-packing dimensions. We also provide a relationship between the mutual multifractal Rényi dimensions of orthogonal projections of a couple of measures $(\mu,\nu)$ in $\mathbb{R}^n$. As an application, we study the mutual multifractal analysis of the projections of measures.     

正压缩算子Jordan积的最大最小谱点

主要讨论了正压缩算子Jordan积的谱,刻画了正压缩算子Jordan积的最大最小谱点以及正交投影Jordan积的谱.     

Composite orthogonal projection methods for large matrix eigenproblems

For classical orthogonal projection methods for large matrix eigenproblems, it may be much more difficult for a Ritz vector to converge than for its corresponding Ritz value when the matrix in question is non-Hermitian. To this end, a class of new refined orthogonal projection methods has been proposed. It is proved that in some sense each refined method is a composite of two classical orthogonal projections, in which each refined approximate eigenvector is obtained by realizing a new one of some Hermitian semipositive definite matrix onto the same subspace. Apriori error bounds on the refined approximate eigenvector are established in terms of the sine of acute angle of the normalized eigenvector and the subspace involved. It is shown that the sufficient conditions for convergence of the refined vector and that of the Ritz value are the same, so that the refined methods may be much more efficient than the classical ones. Project supported by the China State Major Key Projects for Basic Researches, the National Natural Science Foundation of China (Grant No. 19571014), the Doctoral Program (97014113), the Foundation of Excellent Young Scholors of Ministry of Education, the Foundation of Returned Scholars of China and the Liaoning Province Natural Science Foundation.     

Projections,Birkhoff Orthogonality and Angles in Normed Spaces

Let $X$ be a Minkowski plane, i.e., a real two dimensional normed linear space. We use projections to give a definition of the angle $A_q(x, y)$ between two vectors $x$ and $y$ in $X$, such that $x$ is Birkhoff orthogonal to $y$ if and only if $A_q(x, y) =\frac{π}{2}$. Some other properties of this angle are also discussed.     

An infeasible-interior-point algorithm using projections onto a convex set

We present a new class of primal-dual infeasible-interior-point methods for solving linear programs. Unlike other infeasible-interior-point algorithms, the iterates generated by our methods lie in general position in the positive orthant of ² and are not restricted to some linear manifold. Our methods comprise the following features: At each step, a projection is used to recenter the variables to the domainx _i s _i . The projections are separable into two-dimensional orthogonal projections on a convex set, and thus they are seasy to implement. The use of orthogonal projections allows that a full Newton step can be taken at each iteration, even if the result violates the nonnegativity condition. We prove that a short step version of our method converges in polynomial time.Research performed while visiting the Institut für Angewandte Mathematik, University of Würzburg, D-87074 Würzburg, Germany, as a Research Fellow of the Alexander von Humboldt Foundation.     

Orthogonal projection regularization operators

Tikhonov regularization often is applied with a finite difference regularization operator that approximates a low-order derivative. This paper proposes the use of orthogonal projections as regularization operators, e.g., with the same null space as commonly used finite difference operators. Applications to iterative and SVD-based methods for Tikhonov regularization are described. Truncated iterative and SVD methods are also considered. Research of L. Reichel was supported in part by an OBR Research Challenge Grant. Research of F. Sgallari was supported in part by PRIN 2004 grant 2004014411-005.     

Subspaces,angles and pairs of orthogonal projections

We give a new proof for the Wedin theorem on the simultaneous unitary similarity transformation of two orthogonal projections and show that it is equivalent to Halmos' theorem on the unitary equivalence of projection pairs. As a consequence of these theorems, we derive several results on pairs of orthogonal projections, relative subspace positions and oblique projections as well.