Possible Spectrums of 3×3 Upper Triangular Operator Matrices

Let H1, H2 and H3 be infinite dimensional separable complex Hilbert spaces. We denote by M(D,E,F) a 3×3 upper triangular operator matrix acting on H1⊕H2⊕H3 of the form M(D,E,F)=(A D E 0 B F 0 0 C). For given A ∈ B(H1), B ∈ B(H2) and C ∈ B(H3), the sets UD,E,F σp(M(D,E,F)), ∪D,E,F σr(M(D,E,F)), ∪D,E,F σc(M(D,E,F)) and ∪D,E,F σ(M(D,E,F)) are characterized, where D ∈ B(H2,H1), E ∈ B(H3, H1), F ∈ B(H3, H2) and σ(·), σp(·), σr(·),σc(·) denote the spectrum, the point spectrum, the residual spectrum and the continuous spectrum, respectively.     

BRILL－NOETHER MATRIX FOR RANK TWO VECTOR BUNDLES

Lei X be an arbitrary smooth irreducible complex projective curve, E (?) X a rank two vector bundle generated by its sections. The author first represents E as a triple {D1,D2,f}, where D1 , D2 are two effective divisors with d = deg(D1) + deg(D2), and f ∈ H0(X, [D1] |D2) is a collection of polynomials. E is the extension of [D2] by [D1] which is determined by f. By using f and the Brill-Noether matrix of D1 + D2, the author constructs a 2g X d matrix WE whose zero space gives Im{H0(X,[D1]) (?) H0(X, [D1] |D1)}(?)Im{H0(X, E) (?) H0(X,[D2]) (?) H0(X,[D2] |D2)}. From this and H0(X,E) = H0(X, [D1]) (?) Im{H0(X, E) (?) H0(X, [D2])}, it is got in particular that dimH0(X, E) = deg(E) - rank(WE) + 2.     

3$\times$3阶上三角型算子矩阵的可能谱

Let H1, H2 and H3 be infinite dimensional separable complex Hilbert spaces. We denote by M（D,V,F） a 3×3 upper triangular operator matrix acting on Hi ＋H2＋ H3 of theform M（D,E,F）=（A D F 0 B F 0 0 C）.For given A ∈ B（H1）, B ∈ B（H2） and C ∈ B（H3）, the sets ∪D,E,F^σp（M（D,E,F））,∪D,E,F ^σr（M（D,E,F））,∪D,E,F ^σc（M（D,E,F）） and ∪D,E,F σ（M（D,E,F）） are characterized, where D ∈ B（H2,H1）, E ∈B（H3, H1）, F ∈ B（H3,H2） and σ（·）, σp（·）, σr（·）, σc（·） denote the spectrum, the point spectrum, the residual spectrum and the continuous spectrum, respectively.     

Quantification de la dualité de Grassmann

Let V be a complex vector space of dimension n, %plane1D;53E; (resp. %plane1D;53E;^*) the Grassmann manifold of p-dimensional (resp. (n — p)-dimensional) subspaces of V, and of Ω the relation of transversality in %plane1D;53E;*%plane1D;53E;^*. We announced in [6] equivalences between derived categories of sheaves and of D-modules on %plane1D;53E; and %plane1D;53E; defined by the integral transforms associated to Ω. We show here that these transforms exchange the D-modules associated to the holomorphic line bundles on %plane1D;53E; and %plane1D;53E;^*. This is equivalent to “quantizing” the underlying contact transformation between certain open dense subsets of the cotangent bundles. In the case p = 1, we recover already known results for the projective duality (see [1] and [5]).     

关于Pareto极值问题

[1]中研究了Pareto极值问题.[3]中部分地改进了[2]中的结果.本文给出Pareto极值存在的一个一般结论,这一结论包含了[2][3]中的有关结论作为特殊情况.利用弱拓扑还讨论了强-Pareto极值的存在性,从而在比[2][3]有关定理更弱的条件下,获得了更强的结论.     

图的倍图与补倍图

计算机科学数据库的关系中遇到了可归为倍图或补倍图的参数和哈密顿圈的问题．对简单图C,如果V（D（G））：V（G）∪V（G′）E（D（G））=E（C）∪E（C″）U{vivj′｜vi∈V（G）,Vj′∈V（G′）且vivj∈E（G））那么,称D（C）是C的倍图,如果V（D（G））=V（C）∪V（G′）,E（D（C））：E（C）∪E（G′）∪{vivj′}vi∈V（G）,vj′∈V（G’）and vivj∈（G））,称D（C）是G的补倍图,这里G′是G的拷贝．本文研究了D（G）和D的色数,边色数,欧拉性,哈密顿性和提出了D（G） 的边色数是D（G）的最大度等公开问题．     

Connections between projective geometry and superassociative algebra

This paper establishes a connection between projective geometry and the superassociative algebra of multiplace functions. In Part I a quaternary operation is defined for the points on a line j in a projective plane π relative to a fixed quadrangle and the result of operating on A,B,C,D is denoted by A(B,C,D). It is shown that π is a Pappus plane if and only if this operation is superassociative: (A(B,C,D))(E,F,G)=A(B(E,F,G),C(E,F,G),D(E,F,G)) for any points A,B,C,D,E,F,G on j. Desargues and certain special Desargues planes are also characterized by restrictions of the superassociative law. In Part II projective geometry is developed over superassociative systems.     

On some properties of P-matrix sets

A nonempty set %plane1D;49E; in ^n×n is said to have the row-P-property if every row representative of %plane1D;49E; is a P-matrix. We show that this property is equivalent to saying that for every nonzero x in ⁿ there is an index i with x₁(Mx)₁ > 0 for all M%plane1D;49E;. We relate this concept to the unique solvability of certain nonlinear complementarily problems. We also show that when %plane1D;49E; is compact and has the row-P-property, there exists a vector u > 0 such that Mu > 0 for all M%plane1D;49E;.     

有向图n·■_m的优美性

给定有向图D(V,E),如果存在一个单射f:V(D)→{0,1,…,|E|}使得对于每条有向边(u,v),诱导函数f′:E(D)→{1,2,…,|E|}是一个双射函数,其中,f′(u,v)=[f(v)-f(u)](mod(|E|+1)),则f称为有向图D(V,E)的优美标号,f′称为有向图D(V,E)的诱导的边的优美标号.本文讨论了有向图n.■m的优美性,并且证明了当m=23且n为偶数时,n.■m是优美有向图.     

关于二阶常微分方程周期解的定理

本文研究非自治非线性二阶常微分方程存在周期解的充分条件．在满足本文定理的条件下，作者证明所研究的二阶方程在相空间中的Ｐｏｉｎｃａｒｅ映射是平面上有奇点的动力系统，从而证明原方程有周期解．这一结果全面推广已有的若干结论．     

Convergence analysis and error estimates for a parallel algorithm for solving the Navier-Stokes equations

Summary. This paper is concerned with the analysis of the convergence and the derivation of error estimates for a parallel algorithm which is used to solve the incompressible Navier-Stokes equations. As usual, the main idea is to split the main differential operator; this allows to consider independently the two main difficulties, namely nonlinearity and incompressibility. The results justify the observed accuracy of related numerical results. Received April 20, 2001 / Revised version received May 21, 2001 / Published online March 8, 2002 RID="*" ID="*" Partially supported by D.G.E.S. (Spain), Proyecto PB98–1134 RID="**" ID="**" Partially supported by D.G.E.S. (Spain), Proyecto PB96–0986 RID="**" ID="**" Partially supported by D.G.E.S. (Spain), Proyecto PB96–0986 RID="*" ID="*" Partially supported by D.G.E.S. (Spain), Proyecto PB98–1134 RID="**" ID="**" Partially supported by D.G.E.S. (Spain), Proyecto PB96–0986 RID="**" ID="**" Partially supported by D.G.E.S. (Spain) Proyecto PB96–0986     

Optimum Extrapolated Alternating Direction Implicit Schemes in the Presence of Singular Matrices

This paper shows how Extrapolated Alternating Direction Implicit(E.A.D.I.) methods can be used for the numerical solution ofLaplace's equation under Neumann boundary conditions. E.A.D.I.methods are applied with the Douglas set of parameters and optimumE.A.D.I. schemes are given.     

3×3上三角算子矩阵的Weyl型定理

设A∈B(H1),B∈B(H2),C∈B(H3)为给定的三个算子,用M(D,E,F)= 表示一个作用在H1(?)H2(?)H3上的3×3算子矩阵．本文首先给出存在算子D∈B(H2,H1),E∈B(H3,H1),F∈B(H3,H2),使得M(D,E,F)为上半Fredholm算子(下半Fredholm算子)的充要条件．同时研究了3×3算子矩阵 M(D,E,F)的Weyl定理,α-Weyl定理,Browder定理和α-Browder定理．     

极大单调映象的零点定理的推广

设Ｅ是自反Ｂａｎａｃｈ空间，极大单调满足其中Ω为Ｅ中有界开集且０∈Ω∩Ｄ（Ｔ），则Ｔ在中有零点．     

某些Lie单群的传递性

设D为有限线性空间，且T G Aut（T），其中T是非交换单群，并且同构于^2B2（g），Cn（g）（n≥3），^3D4（g），E7（q），E8（q），F4（q），^2F4（q），G2（q），^2G2（q）。假设D不是射影平面，G线传递作用在D上，则T点传递。     

Extremal Convex Planar Sets

Each convex planar set K has a perimeter C, a minimum width E, an area A, and a diameter D. The set of points (E,C, A^1/2, D) corresponding to all such sets is shown to occupy a cone in the non-negative orthant of R⁴with its vertex at the origin. Its three-dimensional cross section S in the plane D = 1 is investigated. S lies in a rectangular parallelepiped in R³. Results of Lebesgue, Kubota, Fukasawa, Sholander, and Hemmi are used to determine some of the boundary surfaces of S, and new results are given for the other boundary surfaces. From knowledge of S, all inequalities among E, C ,A, and D can be found.     

Banach空间中Reich-Takahashi迭代法的强收敛定理

设E是具有一致正规结构的实Banach空间,其范数是一致Gateaux可微的;设D是E的非空有界闭凸子集,T:D→D是渐近非扩张映象.本文证明了,在一些适当的条件下,由修正的Reich-Takahashi迭代法(1.2)式所定义的序列{xn}强收敛到渐近非扩张映象的不动点,其中x0是D中一任给点,{αn},{β}是区间[0,1]中满足某些限制的实数列.     

Cohomologies of spaces of Schwartz test functions

We calculate cohomologies of the Schwartz algebras D and S, which are basic spaces (test-function spaces) of the distribution theory. In the process, we find special cohomologies of the quotient algebras E/D and M/S (E andMare also test-function spaces), which are quite unusual from the standpoint of the standard functional analysis and are interesting for theoretical and mathematical physics.     

Banach空间中渐近非扩张映象具误差的强收敛定理

设E是一实的Banach空间,其范数是一致Gteaux可微的;D是E的一非空闭凸子集,设T:D→D是具有序列{k_n}[1,∞),lim_(n→∞) k_n=1的渐近非扩张映象.本文证明了,在一定条件下,由(1.3)和(1.5)式定义的具误差的迭代序列{x_n}强收敛于T的不动点.本文结果也推广和改进了最近一些人的最新结果.     

Numerical Solution of the Robin Problem by Extrapolated A. D. I. Methods

In this paper the Robin problem for elliptic equations is consideredand its numerical integration by several variants of the Extrapolatedform of the Alternating Direction Implicit (E.A.D.I.) methodsis discussed. A comparison among the E.A.D.I. variants includedhere as well as those studied in an earlier paper is carriedout.