无圈超图的1—因子定理

本文证明了一个无圈超图 H=(X,E)有1-因子当且仅当(?)S(?)X,sum from i=1 to r-1(r-i)q_i≤|S|,其中 q_i 表示 H 的子超图 H-S 的顶点数模 r 等于 i 的连通分支数,r 是超图 H 的秩.     

矩阵的WZ分解及其误差分析

在[1]中,对矩阵A进行WZ分解,其中矩阵W=(w_(i,j))和Z=(z_(i,j))形状如下: 1, i=j, w_(i,j)=任意,min(i,n-i+1)相似文献   

Boundedness of Solutions for Duffing Equation with Low Regularity in Time

It is shown that all solutions are bounded for Duffing equation x+ x~(2n+1)+2∑i=nPj(t)x~j= 0, provided that for each n + 1 ≤ j ≤ 2 n, P_j ∈ C~y(T~1) with γ 1-1/n and for each j with 0 ≤ j ≤ n, Pj ∈ L(T~1) where T~1= R/Z.     

Q过程的不变分布(Ⅱ)

设E为一个可数集,Q＝(qi,j;j,j∈E)为E×E上的矩阵,满足qi,j≥0(i≠j),∑qi,k=-qii≤∞, i∈E.k≠im为E上的概率分布满足∑miqi=-mjqj,j≤∞, j∈E.i≠j何时存在Q过程,使得m是它的不变分布?这个问题由Williams(1979)作为一个开问题提出.文[15]对全稳定情形,解决了这个问题;本文对单瞬时情形,完整地解决了该问题.     

Highest weight representations of a Lie algebra of Block type

For a field F of characteristic zero and an additive subgroup G of F, a Lie algebra B(G) of the Block type is defined with the basis {Lα,i, c|α∈G, -1≤i∈Z} and the relations [Lα,i,Lβ,j] = ((i 1)β- (j 1)α)Lα β,i j αδα,-βδi j,-2c,[c, Lα,i] = 0. Given a total order (?) on G compatible with its group structure, and anyα∈B(G)0*, a Verma B(G)-module M(A, (?)) is defined, and the irreducibility of M(A,(?)) is completely determined. Furthermore, it is proved that an irreducible highest weight B(Z )-module is quasifinite if and only if it is a proper quotient of a Verma module.     

关于算子的J-正常扩张

1.在文献[1,2]中,Halmos和Bram证明了Hilbert空间H中有界线性算子T在Hilbert空间K(?)H中有正常扩张的充要条件是对一切x_0,x_1,…,x_r∈H,均有sum from i,j=0 to r (T~jx_i,T~ix_j)≥0. Bram还得到T有上述扩张的另一个充要条件是e~(-(?)T)e~(ζT)为复平     

2004年亚太地区数学奥林匹克

有关本栏目的稿件,请直接寄给熊斌(2 0 0 0 6 2 ,华东师范大学数学系　E -mail:xiongbin @sh16 3.com) ,或冯志刚(2 0 0 2 31,上海市上海中学　E -mail:zhgfeng @online .sh .cn) .提供试题及解答请尽量注明出处.　　本期给出第16届亚太地区数学奥林匹克(2 0 0 4年3月)的试题与解答.由上海中学冯志刚先生提供.　　2 0 0 4年亚太地区数学奥林匹克1　求所有的非空有限的正整数集S ,使得对任意i,j∈S ,数i+j(i,j) ∈S ,这里(i,j)表示i与j的最大公约数.2　设O ,H分别为锐角△ABC的外心和垂心.证明:△AOH ,△BOH ,△COH中有一个的面积等…     

常系数非齐线性递推式的解的显式表示

本文给出常系数非齐线性递推式(?)的解的显式表达式 H(m)=sum from i=0 to k-1(sum from j=i to k-1 b_ja_(k-j+i))D_(m-k-i)+sum from i=0 to m-k D_if(m-i)(m≥k)其中D_m=sum x_1+2x_2+…+kx_k=m x_j≥0(i=1,2,…,k)(?)a_1~x1a_2~x2…a_k~xk.     

关于短区间的并集中Woods问题的一个推广

本文利用不完全Kloosterman和的估计来研究短区间的并集中Woods问题的一个推广,并且给出了渐近公式.具体来讲,设p是奇素数,1≤H≤p,实数δ满足0δ≤1,并设I~((j))(1≤j≤J)是(0,p)的互不相交的子区间,满足H/2≤|I(j)|≤H.定义I=U_(j=1)~JI~((j)),以及A(δ,p)={a∈Z:1≤a,a瓦≤p-1,|a-a|δp},其中瓦是a关于模p的乘法逆,满足aa≡1(mod p).设x是模p的Dirichlet非主特征.本文证明了Σx∈Ix∈A(δ,p)1=1/p∫_0~(|δ,p|)((Σx∈Ix≤p-1-t)1+(Σx∈Ix≥t+1)1)dt+O(J~(1/2)P~(1/2)logHlog~2p),以及Σx∈Ix∈A(δ,p)X(x)《J~(1/2)P~(1/2)logHlog~2p.     

紧支撑正交插值的多小波和多尺度函数

本文给出一类伸缩因子为α的紧支撑正交插值多尺度函数和多小波的构造方法.设{Vj}是尺度函数Φ(x)=[φ1(x),φ2(x),…,φa(x)]T生成的多分辨分析,Vj(?)L2(R)是{a-j/2φ(?)(ajx-k),k∈Z,(?)=1,2,…,a)线性扩张构成的子空间,其插值性是指φ1(x),φ2(x),…,φa(x)满足φj(k+(?)/a)=δk,0δj,e,j,(?)∈{1,2,…,a).当Φ(x)是正交插值的,则多分辨分析的分解或重构系数能用采样点表示而不需要用计算内积的方法产生.基于此,我们建立多小波采样定理,即如果一个连续信号f(x)∈VN,则f(x)=∑i=0a-1∑k∈Zf(k/aN+i/aN+1)φi+1(aNx-k),并给出对应多小波的显式构造公式.更进一步,证明了本文构造的多小波也有插值性.最后,还给出一个构造算例.     

GENERALIZED HILBERT OPERATOR AND FEJR-RIESZ TYPE INEQUALITIES ON THE POLYDISC

Let f be a holomorphic function on the unit polydisc Dn,with Taylor expansion f(z) = ∞ |k|=0 akzk ≡∞ (k1+···+kn=0) (ak1,···,kn zk1 1znkn)where k = (k1, , kn) ∈ Z+n. The authors define generalized Hilbert operator on Dn by Hγ,n(f)(z) = ∞ |k|=0 i1,···,in≥0 ai1,···,in n j=1 Γ(γj + kj + 1)Γ(kj + ij + 1) Γ(kj + 1)Γ(kj + ij + γj + 2) zk,where γ∈ Cn, such that R γj > -1, j = 1, 2, , n. An upper bound for the norm of the operator on Hardy spaces Hp(Dn) is found. The authors also present a Fejér-Riesz type inequalit...     

REGULARITY OF H~1 ∩L~(n((γ-1)/(2-γ))) WEAK SOLUTIONS FOR NONLINEAR ELLIPTIC SYSTEMS

Let us consider the following elliptic systems of second order-D_α(A_i~α(x, u, Du))=B_4(x, u, Du), i=1, …, N, x∈Q(?)R~n, n≥3 (1) and supposeⅰ) |A_i~α(x, u, Du)|≤L(1+|Du|);ⅱ) (1+|p|)~(-1)A_i~α(x, u, p)are H(?)lder-continuous functions with some exponent δ on (?)×R~N uniformly with respect to p, i.e.ⅲ) A_i~α(x, u, p) are differentiable function in p with bounded and continuous derivativesⅳ)ⅴ) for all u∈H_(loc)~1(Ω, R~N)∩L~(n(γ-1)/(2-γ))(Ω, R~N), B(x, u, Du)is ineasurable and |B(x, u, p)|≤a(|p|~γ+|u|~τ)+b(x), where 1+2/n<γ<2, τ≤max((n+2)/(n-2), (γ-1)/(2-γ)-ε), (?)ε>0, b(x)∈L2n/(n+2), n~2/(n+2)+e(Ω), (?)ε>0.Remarks. Only bounded open set Q will be considered in this paper; for all p≥1, λ≥0, which is clled a Morrey Space.Let assumptions ⅰ)-ⅳ) hold, Giaquinta and Modica have proved the regularity of both the H~1 weak solutions of (1) under controllable growth condition |B|≤α(|p|~γ+|u|~((n+2)/(n-2))+b, 0<γ≤1+2/n and the H~1∩L~∞ weak solutions of (1) under natural     

负指标情形的非线性椭圆型复方程的非线性Hilbert边值问题

本文研究非线性椭圆型复方程的非线性Hilbert边值问题: W_=H(Z,W,W_),Z∈G:|Z|<1 Re[Z~(-u)W(Z)]=φ(Z,W(Z))+Re[λ_o+sum from k=1 to (|n|-1)(λ_k+iλ_(-k)Z~k)],Z∈Γ:|Z|=1,n<0. 通过建立先验估计及运用与Newton迭相结合的嵌入方法,证明了上述问题在空间C~(1+a)()(0<α<1)中的解存在且唯一。     

Some Properties of a Pure Jump Markov Chain after a Cut

Let X={X_t(ω),t≥0} be a pure jump Markov chain with minimal state space I={0,1,2,…} on a probability triple (Ω,F,P), The sample function X(·,ω) is right lower semi-continuous: We denote the transition matrix by p(t)=(p_(ij)(t)) and Q-matrix by Q=(q_(ij))=(p_(ij)~′(0)), i,j∈I, where 0≤sum from f≠i (q_ij)=-q_(ij)=q_i<∞. In this paper let q_i≠0 and. without loss of generality, p(X_n(ω)=i)=1. We define     

有理插值算子的连续性

1.引言 设m,n为给定的非负整数,X={z_i:z_i∈C,0≤i≤s},且z_i彼此互异。所谓有理插值问题,就是对于给定的,寻求有理函数R=P/Q∈R(m,n)(即?(P)≤m,?(Q)≤n)使得 R~(j)(z_i)=y_i~(j),j=0,1,…,k_i;i=0,1,…,s。 (1.1)而与此对应的“线性化”的问题是求P/Q∈R(m,n),使得     

The Normal Form on the Inverses of M-Matrices

Let μ denote the set of all n×n nonsingular M-matrices. If A∈μ, then there exists a permutation matrix p such that where B_ⅱ(1≤i≤m) is an irreducble nonsingular M-matrix, B_(ij)≤0 (ij). Let V=B~(-1). Then V is a block upper triangular matrix of the form     

Indecomposable modules of the intermediate series over W(a, b)

For any complex parameters a and b,W(a,b)is the Lie algebra with basis{Li,Wi|i∈Z}and relations[Li,Lj]=(j i)Li+j,[Li,Wj]=(a+j+bi)Wi+j,[Wi,Wj]=0.In this paper,indecomposable modules of the intermediate series over W(a,b)are classified.It is also proved that an irreducible Harish-Chandra W(a,b)-module is either a highest/lowest weight module or a uniformly bounded module.Furthermore,if a∈/Q,an irreducible weight W(a,b)-module is simply a Vir-module with trivial actions of Wk’s.     

两类对角占优矩阵的特征值分布

§1.引言 由于矩阵特征值分布的重要性,迄今已有许多人对其进行研究,国内这方面的主要工作参见[1]—[5]。本文将进一步研究以下两类矩阵的特征值分布。 定义1 设A=(a_ij)_n×n为n阶复矩阵,记,若对任意都成立,称A∈DD_0(R). 定义2 若2|Rea_(ij)|+|Rea_(ij)|>以Λ_i+Λ_j对任意i≠j,i,j∈N均成立,称A∈SD(R).若|Rea_(ij)|+|Rea_(ij)|≥Λ_i+Λ_j对任意i≠j,i,j∈N均成立,称A∈SD_0(R).     

数学竞赛之窗

本期给出 2 0 0 4年美国数学奥林匹克的试题与解答 ,由上海中学冯志刚老师与林运成同学提供 .第 33届美国数学奥林匹克(第一天　 2 0 0 4年 4月 2 7日 )1　设ABCD是一个有内切圆为凸四边形 ,它的每个内角和外角都不小于 6 0° .证明 :13|AB3 -AD3 |≤ |BC3 -CD3 |≤ 3|AB3 -AD3 | .等号何时成立 ?2　设a1,a2 ,… ,an 是整数 ,它们的最大公约数等于1.设S是具有下述性质的一个由整数组成的集合 :1)ai∈S ,i=1,2 ,… ,n ;2 )ai-aj∈S ,1≤i,j≤n (i,j可以相同 ) ;3)对任意整数x ,y∈S ,若x +y∈S ,则x -y∈S .证明 :S等于由所有整数…     

最小Q过程的鞅方法

设Q矩阵(q_(ij))_(i,j∈E)满足0相似文献