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1.
本文考察不等式:tr(AB)≤tr(A),m=1,2,3,…,其中A,B为K阶方阵.证明了当A正定B对称幂等条件下上述不等式成立.还考察了A,B为非负矩阵时的情形  相似文献   

2.
R2,1中类时Weingarten曲面的B?cklund变换   总被引:3,自引:0,他引:3       下载免费PDF全文
本文利用平行变换,得到3维Minkowski空间R2,1中的K-2mH+m2-l2=0(H2> K,0≤m<l)类时Weingarten曲面的B?cklund定理.  相似文献   

3.
Hardy空间中的Bloch函数   总被引:1,自引:0,他引:1  
本文利用单位圆盘内解析函数的Shimizu-Ahlfors特征函数分给出了Hardy空间中Bloch函数和BMOA的新特征。由此我们发现了B∩H(0<p<∞)与BMOA之间的本质差别。  相似文献   

4.
《数学研究及应用》1995,15(2):227-232
在En考虑椭圆方程(?)其中A,B满足如下的结构条件:(?)本文证明如果广义整解u∈Wp,loc1(En)∩ Lα(En),其中(?)那么u≡0.  相似文献   

5.
设Euclid空间n+1元点集A,B及其度量和C所构成的单形的体积、外接球半径分别为V,V2,V和R,R2,R.本文给出不等式V2/n≥V12/n+V22/n,R2≤R12+R22一种简单的证法.该  相似文献   

6.
本文讨论了算子A∈B(H)为算子T∈B(H)的算子点谱的判定条件,特别得到:当T为亚正常算子时,A为T的算子点谱的判定条件,另外还得到kerτT,A=kerτT,A成立的充分条件  相似文献   

7.
投影下的Gronwall不等式   总被引:7,自引:1,他引:6  
本文对J.K.Hale曾提出的一类广泛的投影下的Gronwal不等式问题作了讨论,对满足u(t)≤a(t)+∫tb(t-s)u(s)ds+∫c(s)u(t+s)ds,(?)t≥0的函数u(t)∈Cb0(R+,R+)作了估计.其结果对讨论微分方程的有界解、不变流形及其Foliation和进一步讨论奇性Gronwal不等式都有意义  相似文献   

8.
本文在对两个模型定义了α,β,n-扩充的基础上,利用广义Ehrenfeucht Game理论证明了T(Q)的模型可归约性,从而得到:对无限基数α,β,(α≥β>N),对于模型(?)则存在模型(?)使得AαβB;以及任意自然数m>0,存在模型(?),使得(?).  相似文献   

9.
一类拟线性椭圆型偏微分方程的先验界的估计   总被引:1,自引:0,他引:1  
近几年对边值问题-div(|Du|p-2Du)=λf(u)}在Ω上u|(?)Ω=0正解方面已经得到了许多结果.这里λ>0,Ω是有界区域和对s≥0,f(s)≥0.在本文中在条件N≥p>1,Ω=B={x∈RN,|x|<1}和f∈C1(0,∞)∩C0([0,∞)),f(0)=0,研究了这类问题的正对称解的先验界估计.  相似文献   

10.
α型β级Bazilevic函数的Fekete-Szeg?问题   总被引:14,自引:0,他引:14  
设B(α,β)(α>0,0≤β<1)表示在单位圆盘内定义的规范化的α型β级Bazilevic函数类.本文对B(α,β)中函数f(z)=z+∑from∞to(n=2)a得到|a3-λa22|(0≤λ≤1)的准确估计.  相似文献   

11.
Let μ denote a symmetric probability measure on [−1,1] and let (pn) be the corresponding orthogonal polynomials normalized such that pn(1)=1. We prove that the normalized Turán determinant Δn(x)/(1−x2), where , is a Turán determinant of order n−1 for orthogonal polynomials with respect to . We use this to prove lower and upper bounds for the normalized Turán determinant in the interval −1<x<1.  相似文献   

12.
In this paper, we prove a combinatorial rule describing the restriction of any irreducible representation of U(n+m) to the subgroup U(nU(m). We also derive similar rules for the reductions from SU(n+m) to S(U(nU(m)), and from SU(n+m) to SU(nSU(m). As applications of these representation-theoretic results, we compute the spectra of the Bochner–Laplacian on powers of the determinant bundle over the complex Grassmannian . The spectrum of the Dirac operator acting on the spin Grassmannian is also partially computed. A further application is given by the determination of the spectrum of the Hodge–Laplacian acting on the space of smooth functions on the unit determinant bundle over .  相似文献   

13.
Let M n be the nonhomogeneous arithmetic minimum of the lattice Λ ? ?n of determinant Δ>0. It is proved that forn?1,1·n5, we have . One obtains other estimates of a similar type in the nonhomogeneous Minkowski conjecture, obtained for the first time by N. G. Chebotarev. These estimates strengthen the results of B. P. Skubenko.  相似文献   

14.
SupposeA is a bounded linear operator on a separable Hilbert space withA m of trace class for some positive integerm. A generalized determinant for the operatorIA is defined, its properties studied and this determinant is then used to exhibit an inversion formula forIA.  相似文献   

15.
Đocović and Szechtman [D.Ž. Đocović, F. Szechtman, Characterization of bilinear spaces with unimodular isometry group, Proc. Amer. Math. Soc. 133 (2005) 2853–2863] considered a vector space V endowed with a bilinear form. They proved that all isometries of V over a field of characteristic not 2 have determinant 1 if and only if V has no orthogonal summands of odd dimension (the case of characteristic 2 was also considered). Their proof is based on Riehm’s classification of bilinear forms. Coakley et al. [E.S. Coakley, F.M. Dopico, C.R. Johnson, Matrices with orthogonal groups admitting only determinant one, Linear Algebra Appl. 428 (2008) 796–813] gave another proof of this criterion over and using Thompson’s canonical pairs of symmetric and skew-symmetric matrices for congruence. Let M be the matrix of the bilinear form on V. We give another proof of this criterion over using our canonical matrices for congruence and obtain necessary and sufficient conditions involving canonical forms of M for congruence, of (MT,M) for equivalence, and of M-TM (if M is nonsingular) for similarity.  相似文献   

16.
行块矩阵M-P逆的充要条件   总被引:1,自引:1,他引:0  
通过使用矩阵秩方法,证明了如下结果:[A,B]+=[αA+βB+]βAA*αBB*.[A,B][A,B]+=αAA++βBB+R(A)=R(B).这里,α+β=1,α>0,β>0.这两个结果是2007年田永革在国际线性代数学会会刊中获得的相应结果的推广.  相似文献   

17.
Let S[i,j] denote the q-Stirling numbers of the second kind. We show that the determinant of the matrix (S[s+i+j,s+j])0i,jn is given by the product
. We give two proofs of this result, one bijective and one based upon factoring the matrix. We also prove an identity due to Cigler that expresses the Hankel determinant of q-exponential polynomials as a product. Lastly, a two variable version of a theorem of Sylvester and an application are presented.  相似文献   

18.
Let A and B be closed nonempty sets in the plane with A B=R2, A B=bdry A=bdry B=C. Assume that for every m 2 points in C, at least one of the corresponding segments is in A, at least one in B. Then each of A and B is locally expressible as a union of m–1 or fewer convex sets.  相似文献   

19.
The following inequalities for the torsion-free rank r0(G) of the group G=AB and for the p-rank rp(G) of the soluble-by-finite group G=AB are stated: $$\begin{gathered} r_0 (G) \leqslant r_0 (A) + r_0 (B) - r_0 (A \cap B), \hfill \\ r_p (G) \leqslant r_p (A) + r_p (B) - r_p (A \cap B). \hfill \\ \end{gathered} $$   相似文献   

20.
The following two problems are open.
  1. Do two sets of positiveintegers and exist, with at leasttwo elements each, suchthat + coincides with the set of primes for sufficiently largeelements?
  2. Let ={6, 12, 18}. Is there an infinite set of positiveintegerssuch that +1? A positive answer would imply that thereare infinitelymany Carmichael numbers with three prime factors.
In this paper we prove the multiplicative analogue of the firstproblem, namely that there are no two sets and , with at leasttwo elements each, such that the product coincides with anyadditively shifted copy +c of the set of primes for sufficientlylarge elements. We also prove that shifted copies of sets ofintegers that are generated by certain subsets of the primescannot be multiplicatively decomposed.  相似文献   

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