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1.
设m阶方阵A,B满足AB=αBA,其中α=e~(2kπi/n),k,n为互素整数且n≥2.证明了σ(AB)■{α~(j-((n-1)/2))λ_AλB|λA∈σ(A),λB∈σ(B),j=0,1,…,n-1}及其它相关的结果,其中σ(A)表示方阵A的所有特征值的集合.  相似文献   

2.
设A=(a_(ij))_(n×n)为n阶复矩阵,记 σ_i=sum from j=1,j≠i to n(|a_(ij)|,i=l,2,…,n)。若|a_(ij)|>σ_i(i=1,2,…n),则称A为(按行)严格对角占优阵,记为A∈D,若|a_(ii)|·|a_(jj)|>σ_iσ_j(i≠j,i,j=1,2,…,n)则称A为严格对角乘积占优阵,记为A∈D_p(在〔1〕中此类矩阵称为广义对角占优阵,并记为GD)。若存在非奇对角阵Q=diag(q_l,…,q_n)使Q~(-1)AQ∈D,则称A为准严格对角占优阵,记为A∈D′(见〔2〕)。若存在非奇对角阵Q=diag(q_1,…,q_n)使Q~(-1)AQ∈D_p,则称A为准严格对角乘积占优阵。记为A∈D′_p。  相似文献   

3.
Let σ = {σ_i | i ∈ I} be some partition of the set of all primes P. A set H of subgroups of G is said to be a complete Hall σ-set of G if every member ≠ 1 of H is a Hall σ_i-subgroup of G, for some i ∈ I, and H contains exactly one Hall σ_i-subgroup of G for every σ_i ∈σ(G). A subgroup H of G is said to be: σ-permutable or σ-quasinormal in G if G possesses a complete Hall σ-set H such that HA~x= A~xH for all A ∈ H and x ∈ G:σ-subnormal in G if there is a subgroup chain A = A_0≤A_1≤···≤ A_t = G such that either A_(i-1)■A_i or A_i/(A_(i-1))A_i is a finite σ_i-group for some σ_i ∈σ for all i = 1,..., t.If M_n M_(n-1) ··· M_1 M_0 = G, where Mi is a maximal subgroup of M_(i-1), i = 1, 2,..., n, then M_n is said to be an n-maximal subgroup of G. If each n-maximal subgroup of G is σ-subnormal(σ-quasinormal,respectively) in G but, in the case n 1, some(n-1)-maximal subgroup is not σ-subnormal(not σ-quasinormal,respectively) in G, we write m_σ(G) = n(m_(σq)(G) = n, respectively).In this paper, we show that the parameters m_σ(G) and m_(σq)(G) make possible to bound the σ-nilpotent length l_σ(G)(see below the definitions of the terms employed), the rank r(G) and the number |π(G)| of all distinct primes dividing the order |G| of a finite soluble group G. We also give the conditions under which a finite group is σ-soluble or σ-nilpotent, and describe the structure of a finite soluble group G in the case when m_σ(G) = |π(G)|. Some known results are generalized.  相似文献   

4.
设A_2(n)={(ij)|1≤ij≤n,(ij,n)=1},A_3(n)={(ijl),(ilj))|1≤ijl≤n,(ijl,n)=1},其中(x_1 x_2…x_k)表示循环置换,当ik时,把x_i映射到x_(i+1),x_k映射到x_1,其他元素映射到自身.我们得到了∑σ∈A~2(n)∑nk+1 σ(k)/k~m和∑∑nk+1 σ(k)/k~m的同余式,其中σ表示置换.同时,令素数p≥5,H(k)=∑_(i=1)~k1/i,我们证明了∑σ∈A_2(p)∑p=1k=1σ~m(k)H(k)≡2B_m(mod p) ∑σ∈A_3(p)∑p=1k=1σ~m(k)H(k)≡-5B_m(mod p).  相似文献   

5.
在文[1]中定义了强p除环Ω,即满足如下条件(1)—(4)的除环Ω: (1)存在Ω的对合反自同构σ(即σ为反自同构,且σ(σ(α))=α Aα∈Ω) (2)Aα_i∈Ω,i=1,…,n(n∈N) sum from i=1 to n(α_iσ(α_i)=0 α_i=0,i=1,2,…,n)。 (3)命R={α∈Ω|σ(α)=α},则R含在Ω的中心中。 (4)Aα_i∈Ω,i=1,2,…,n(n∈N)方程x~2-sum from i-1 to n(α_iσ(α_i))=0在Ω中有且只有两解。 事实上,除了平凡的情况外,强p除环Ω就是R上的四元数除环。确切地说,我们有 定理1 设Ω为强p除环,则Ω为(1)R,(2)R+R_i或(3)R上的四元数除环。这里  相似文献   

6.
A_1,…,A_n的(n-1)-换位子记为p_n(A_1,…,A_n).令M是von Neumann代数,n≥2是任意正整数,L:M→M是一个映射.本文证明了,若M不含I_1型中心直和项,且L满足L(p_n(A_1,…,A_n))=∑_(k=1)~np_n(A_1,…,A_(k-1),L(A_k),A_(k+1),…,A_n)对所有满足条件A_1A_2=0的A_1,A_2,…,A_n∈M成立,则L(A)=φ(A)+f(A)对所有A∈M成立,其中φ:M→M和f:M→E(M)(M的中心)是两个映射,且满足φ在P_iMP_j上是可加导子,f(p_n(A_1,A_2,…,A_n))=0对所有满足A_2A_2=0的A_1,A_2,…,A_n,∈P_iMP_j成立(1≤i,j≤2),P_1∈M是core-free投影,P_2=I-P_1;若M还是因子且n≥3,则L满足条件L(p_n(A_1,A_2,…,A_n))=∑_(k=1)~n=p_n(A_1,…,A_(k-1),L(A_k),A_(k+1),…,A_n)对所有满足A_1A_2A_1=0的A_1,A_2,…,A_n∈M成立当且仅当L(A)=Φ(A)+h(A)I对所有A∈M成立,其中Φ是M上的可加导子,h是M上的泛函且满足h(p_n(A_1,A_2,…,A_n))=0对所有满足条件A_1A_2A_1=0的A_1,A_2,…,A_n∈M成立.  相似文献   

7.
非奇H矩阵的简捷判据   总被引:96,自引:1,他引:96  
黄廷祝 《计算数学》1993,15(3):318-328
非奇H矩阵在计算数学和矩阵理论的研究中很重要,但简便实用的判定条件较少见。本文给出几个简捷判据。[1,2,3]的主要结果是本文定理1的特例。 记M_n(C)为n阶复阵集合,M_n(R)为n阶实阵集合。设A=(a_(ij))∈M_n(C),记Λ_i(A)=sum from j≠i to |a_(ij)|,i,j∈N≡{1,2,…,n}。若|a_(ii)|>Λ_i(A),i∈N,则称A  相似文献   

8.
一个四元数矩阵方程的可解性   总被引:3,自引:0,他引:3  
§ 1  IntroductionL et R be the real number field,C=R Ri be the complex numberfield,and H=C Cj=R Ri Rj Rk be the quaternion division ring over R,where k:=ij=- ji,i2 =j2 =k2 =- 1 .Ifα=a1 +a2 i+a3 j+a4 k∈ H ,where ai∈ R,then letα=a1 - a2 i- a3 j- a4 k bethe conjugate ofα.L et Hm× nbe the setof all m× n matrices over H.If A=(aij)∈ Hn× n ,L etATbe the transpose matrix of A,A be the conjugate matrix of A,and A* =(aij) T be thetranspose conjugate matrix of A.A∈Hn× nis said…  相似文献   

9.
非奇异H-矩阵的新判据   总被引:1,自引:0,他引:1  
1引言与记号设A=(a_(ij))∈C~(n×n),记N={1,2,…,n},∧_i(?)∧_i(A)=sum from j≠i|a_(ij)|,S_i(?)S_i(A)=sum from j≠i|a_(ij)|,(?)i,j∈N。若|a_(ij)>∧_i(A),(?)i∈N,则称A为严格对角占优矩阵。  相似文献   

10.
对于Mn(C)(所有n×n矩阵的全体)中的不可约矩阵得到以下结果:对于任意A∈Mn(C),设λ1,λ2,…,λm为A的所有特征值,这里m≤n而且当i≠j时,λi≠λj.则A是不可约的当且仅当任意P∈A'(A),P*=P=P2,有σ(P|ker(A-λ1))=σ(P|ker(A-λ2))=…=σ(P|ker(A-λm))为单点集.  相似文献   

11.
Yushkov  E. V. 《Mathematical Notes》2011,90(3-4):597-610
Mathematical Notes - We study the initial boundary-value problem for three-dimensional systems of equations of pseudoparabolic type. The system is similar to the Oskolkov system, but differs from...  相似文献   

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14.
The asymptotic distribution of tensors of degree N in symmetry types is studied in this paper.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 155, pp. 181–186, 1986.  相似文献   

15.
We give a characterization of the types of asymptotic discernibility of families of hypotheses in the case of hypothetical measures that are not, in general, mutually absolutely continuous. The case when the logarithm of the likelihood ratio admits an asymptotic expansion of the type of an expansion with local asymptotic normality is examined in detail. Examples are studied.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 64–71, 1987.  相似文献   

16.
An estimate of stability of characterization of distribution types is obtained for the case of additive types. Under some conditions, the estimate has the order ε1/3L(ε), where L(ε) is a slowly varying function. Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, Russia, 1996, Part I.  相似文献   

17.
杨海宣 《数学学报》1998,41(4):727-730
本文研究了完全正则半群簇的子簇格[V+∩PV,V+∩PV]的某些格运算性质,我们证明了簇V+∩PV可分解为V与V+∩PV的并;对任意完全正则半群簇W,有W∩(V∨V+∩PV)=(W∩V)∨(W∩V+∩PV).特别地,我们得到了等式V+∩PV=V成立的若干条件.  相似文献   

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19.
In this paper, we prove that any subreduct of the class of representable relation algebras whose similarity type includes intersection, relation composition and converse is a non-finitely axiomatizable quasivariety and that its equational theory is not finitely based. We show the same result for subreducts of the class of representable cylindric algebras of dimension at least three whose similarity types include intersection and cylindrifications. A similar result is proved for subreducts of the class of representable sequential algebras. Received October 7, 1998; accepted in final form September 10, 1999.  相似文献   

20.
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