ON UNIQUENESS OF SOLUTION TO POINTWISE LANDAU PROBLEM ON THE FINITE INTERVAL

1. Introduction Let W_∞~((r)) (β) = {f| f∈W_∞~((r)) [-1,1], ||f||_(C[-1,1]) β, ||f~((r))||_∞ 1}.In this paper, we will consider the following Landau problem:λf~((k))(ξ) + μf~((k-1)) (ξ) →inf, f∈W_∞~((r)) (β), (1.1)where ξ∈[-1,1], 1(?)k(?)r-1, and λ, μ real and not all zero, (if k=1,suppose λ≠0 in addition ). A. Pinkus studied it first. To begin with, we introduce some fundamental definitions anddenotions. The perfect spline f, which satisfies || f~((r))||_∞ = 1 andhas n knots and n+r+1 points of equioscillation in [-1,1], isdenoted by x_(nr), which is refered as Tchebyshev perfect spline. And     

广义B—D逆及其应用

本文首先给出了著名的Bott-Duffrin逆(简称B-D逆)A_(L)~((-1))的许多进一步的性质与新的应用,指出了A_(L)~((-1))的存在性与方程组的解的两种唯一性之间的紧密联系;然后定义了广义B-D逆A_(L)~(+)=P_L(AP_L+P_L~⊥)~+,讨论了A_(L)~(+)的一些性质,给出了当A为一般方阵与当A为L=N(B)—非负定阵时关于方程组(1)的可解性的方便的判别条件以及有解时其解的显式,统一处理了在最优化、线性统计推断、二维插值中出现的方程组(1)与约束二次极值问题的求解问题。     

ON OPTIMAL INTERPOUTION FOR A DIFFERENTIABLE FUNCTION CLASS (Ⅰ)

§1. Introduction Given an integer. Let W_∞~((n))(IR) be a class of differentiablefunctions defined on IR, where for each f∈ W_∞~((n)) (IR) f~((n-1)) is absolu-tely continuous on any finite interval and || f~((n))||_∞     

约束线性方程组通解的显式表示及Cramer法则

本文研究了一般的约束线性方程组Ax=b,x∈T, (1.1)其中A∈C~(m×n),b∈R(A),T为C~n中任意取定的子空间。给出了(1.1)有唯一解的充要条件;在有唯一解时,利用B-D逆(A~*A)_((T))~((-1))给出了唯一解的显式及cramer法则;在有解但解不唯一时,利用B-D逆(A~*A)_((?))~((-1))(这里(?)=R(R_TA~*))给出了(1.1)的通解的显式及Cramer法则。其结果改进并推广了文[2,3,4,5,6]中的有关结果。 另外,本文研究了A的T-约束M-P逆(AP_T)~+与A~*A的B-D逆(A~*A)_((?))~((-1))的关系,证明了下列事实:(AP_T)~+=(A~*A)_((?))~((-1))A~*,特别,当T∩N(A)={0}时,(AP_T)~+=(A~*A)_((?))~((-1))A~*。     

加法与乘法逆特征值问题的可解性

1.引言 本文讨论如下代数特征值反问题可解的充分条件: 问题A(加法逆特征值问题)。给定一Hermite矩阵A=(a_(ij))_(n×n)及n个实数λ_1,…,λ_n,求一实对角阵D=diag(c_1…,c_n),使得A+D的特征值为λ_1,…,λ_n。 问题M(乘法逆特征值问题)。给定一正定Hermite矩阵A=(a_(ij))_(n×n)和n个正实数     

单位上三角矩阵群的注记

记Tr_1(n,Z)是整数环Z上对角线元素全是1的全体上三角矩阵组成的群,k_(ij)(1≤i相似文献   

超图的r-截口

设H=(X;E_1,E_2,…,E_m)是一个超图,H的r-截口,记作H_((r)),定义为(X;ε_((r)),其中ε_((r))={F;FX,|≤| F |≤r,且存在E_i使FE_i}.对任一超图H,H_((r))唯一存在,但并非任一秩不超过r的超图是某个超图的r-截口。本文给出了以给定超图为     

关于Fuzzy矩阵的广义逆

本文分别给出了Fuzzy矩阵存在广义{1,3}-逆、广义{1,4}-逆以及Moore-Penrose广义逆Fuzzy矩阵的一些充要条件。又得到求上述广义逆Fuzzy矩阵的一些公式。主要的结果有: 1.Fuzzy矩阵A的广义{1,3}-逆A~((1.3))(广义{1,4}-逆A~((1.4))存在的充要条件是Fuzzy关系方程有解。2.Fuzzy矩阵A的Moore-Penrose广义逆A~T存在的充要条件是Fuzzy关系方程均有解。3.如果B、C分别为Fuzzy关系方程的一个解,那么。     

γ-可图序列与γ-完全子图

一个r-图是一个无环的无向图,其中任何两个顶点之间至多被r条边连接.一个m+1个顶点的r-完全图,记为K_(m+1)^((r)),是一个m+1个顶点的r-图,其中任何两个顶点之间恰好被r条边连接.一个非增的非负整数序列π=(d_1,d_2,…,d_n)称为是r-可图的如果它是某个n个顶点的r-图的度序列.一个r-可图序列π称为是蕴含(强迫)K_(m+1)((r)),是一个m+1个顶点的r-图,其中任何两个顶点之间恰好被r条边连接.一个非增的非负整数序列π=(d_1,d_2,…,d_n)称为是r-可图的如果它是某个n个顶点的r-图的度序列.一个r-可图序列π称为是蕴含(强迫)K_(m+1)^((r))可图的如果π有一个实现包含K_(m+1)((r))可图的如果π有一个实现包含K_(m+1)^((r))作为子图(π的每一个实现包含K_(m+1)((r))作为子图(π的每一个实现包含K_(m+1)^((r))作为子图).设σ(K_(m+1)((r))作为子图).设σ(K_(m+1)^((r)),n)(τ(K_(m+1)((r)),n)(τ(K_(m+1)^((r)),n))表示最小的偶整数t,使得每一个r-可图序列π=(d_1,d_2,…,d_n)具有∑_(i=1)((r)),n))表示最小的偶整数t,使得每一个r-可图序列π=(d_1,d_2,…,d_n)具有∑_(i=1)ⁿ d_i≥t是蕴含(强迫)K_(m+1)n d_i≥t是蕴含(强迫)K_(m+1)^((r))-可图的.易见,σ(K_(m+1)((r))-可图的.易见,σ(K_(m+1)^((r)),n)是Erds等人的一个猜想从1-图到r-图的扩充且τ(K_(m+1)((r)),n)是Erds等人的一个猜想从1-图到r-图的扩充且τ(K_(m+1)^((r)),n)是经典Turan定理从1-图到r-图的扩充.本文给出了蕴含K_(m+1)((r)),n)是经典Turan定理从1-图到r-图的扩充.本文给出了蕴含K_(m+1)^((r))的r-可图序列的两个简单充分条件.此两个条件包含了Yin和Li在[Discrete Math.,2005,301:218-227]中的两个主要结果和当n≥max{m((r))的r-可图序列的两个简单充分条件.此两个条件包含了Yin和Li在[Discrete Math.,2005,301:218-227]中的两个主要结果和当n≥max{m²+3m+1-[(m2+3m+1-[(m²+m)/r],2m+1+[m/r]]}时,σ(K_(m+1)2+m)/r],2m+1+[m/r]]}时,σ(K_(m+1)^((r)),n)之值.此外,我们还确定了当n≥m+1时,τ(K_(m+1)((r)),n)之值.此外,我们还确定了当n≥m+1时,τ(K_(m+1)^((r)),n)之值.     

H（n,≥）中矩阵广义逆的单调性问题

在文献[4—7]基础上,本文给出了Lowner偏序下半正定自共轭四元数矩阵的单调性解集A{1;≥,Υ_1;≤B~((1))},B{1;≥,Υ_2;≥A~((1))}的显式及单调性“A≥BB~((1,2))≥A~((1,2))”成立的充要条件。     

On a conjecture on maximal planar sequences

Let d1 d2 dp denote the nonincreasing sequence d₁, …, d₁, d₂, …, d₂, …, d_p, …, d_p, where the term d_i appears k_i times (i = 1, 2, …, p). In this work the author proves that the maximal 2-sequences: 7³6¹5¹⁵, 7⁵6¹5¹⁷, 7⁷6¹5¹⁹ are planar graphical, in contrast to a conjecture by Schmeichel and Hakimi.     

Size bipartite Ramsey numbers

Let B, B₁ and B₂ be bipartite graphs, and let B→(B₁,B₂) signify that any red-blue edge-coloring of B contains either a red B₁ or a blue B₂. The size bipartite Ramsey number is defined as the minimum number of edges of a bipartite graph B such that B→(B₁,B₂). It is shown that is linear on n with m fixed, and is between c₁n²2ⁿ and c₂n³2ⁿ for some positive constants c₁ and c₂.     

Nilpotent Lie Algebras of Maximal Rank and of Kac–Moody Type: E6

Let be the Kac–Moody algebra associated to the affine Cartan matrix E₆⁽¹⁾. Each nilpotent Lie algebra of type E₆⁽¹⁾ is isomorphic to a quotient of the positive part of . We determine the isomorphism classes of nilpotent Lie algebras of type E₆⁽¹⁾.     

LOCAL TIME ANALYSIS OF ADDITIVE LEVY PROCESSES WITH DIFFERENT L(E)VY EXPONENTS

Let X1 XN be independent, classical Levy processes on R^d with Levy exponents ψ1,…, ψN, respectively. The corresponding additive Levy process is defined as the following N-parameter random field on R^d, X（t） △= X1（t1） ＋ ... ＋ XN（tN）, At∈N. Under mild regularity conditions on the ψi＇s, we derive estimate for the local and uniform moduli of continuity of local times of X = {X（t）; t ∈R^N}.     

Finite orbit modules for parabolic subgroups of exceptional groups

Let G be a reductive linear algebraic group, P a parabolic subgroup of G and P_u its unipotent radical. We consider the adjoint action of P on the Lie algebra _u of P_u. Each higher term _u^(l) of the descending central series of _u is stable under this action. For classical G all instances when P acts on _u^(l) with a finite number of orbits were determined in [9], [10], [3] and [4]. In this note we extend these results to groups of type F₄ and E₆. Moreover, when P acts on _u^(l) with an infinite number of orbits, we determine whether P still acts with a dense orbit. For G of type E₇ and E₈ we investigate only the case of a Borel subgroup.We present a complete classification of all instances when _u^(l) is a prehomogeneous space for a Borel subgroup B of a reductive algebraic group for any l ≥ 0.