(I,K)-(m,n)-内射环

引入了(I,K)-(m,n)-内射环的概念,给出了(I,K)-(m,n)-内射环的等价刻划.讨论了(I,K)-(m,n)-内射环与(I,K)-(m,1)-内射环之间的关系及左(I,K)-(m,n)-内射环和右(I,K)-(m,n)-内射环的关系.证明了R是右(I,K)-(m,n)-内射环当且仅当如果z=(m1,m2,…,mn)∈Kn且A∈Im×n,rR(A)∈rRn(z),则存在y∈Km,使得z=yA推广了已知的相关结论.     

体上特征矩阵的法式与弱法式存在定理

<正> 设 K 为任意体(非交换域),A 为 K 上一个 n 阶矩阵.在[1]文中,我们证明了:特征矩阵λI—A 在非交换多项式环 K[λ]上的初等变换下,可以化为(其中φ_1|φ_2表可左、右整除):     

B(H)上的酉可导映射

设H是维数大于2的复Hilbert空间,B(H)表示H上所有有界线性算子构成的代数.若φ∶B(H)→B(H)上的有界线性映射,如果对所有的A∈B(H)且A~*A=AA~*=I,有φ(A)~*A+A~*φ(A)=φ(A)A~*+Aφ(A)~*=φ(I),则存在数λ∈R和算子S∈B(H),且S+S~*=λI,使得对所有的A∈B(H),有φ(A)=AS-SA.     

CHARACTERIZATIONS OF JORDAN (?)-SKEW MULTIPLICATIVE MAPS ON OPERATOR ALGEBRAS OF INDEFINITE INNER PRODUCT SPACES

Let H and K be indefinite inner product spaces. This paper shows that a bijective map φ:B(H)→B(K) satisfies φ(AB B A) =φ(A)φ(5) φ(B) φ(A) for every pair A,B ∈B(H) if and only if either φ(A) = cU AU for all A or φ(A) = cUA U for all A; φsatisfies φ(AB A) = φ(A)φ(B) φ(A) for every pair A,B ∈B(H) if and only if either φ(A) = UAV for all A or φ(A) = UA V for all A, where A denotes the indefinite conjugate of A, U and V are bounded invertible linear or conjugate linear operators with U U = c-1I and V V = cI for some nonzero real number c.     

上期课外练习解答

高一年级1.(1)B≠φ时,-2√2相似文献   

非交换Lipschitz-φ算子代数

本文引入由紧距离空间(K,d)到给定Banach代数A中的Lipschitz-φ算子构成的非交换Banach代数L~φ(K,A)与l~φ(K,A),证明了它们都是由K到A的全体连续算子构成的非交换Banach代数C(K,A)的子代数,并且关于范数||f||φ=L_φ(f)+||f||∞是Banach代数,研究了不同 Lipschitz尺度函数φ对应的大(小)Lipschitz代数之间的关系。特别当φ(t)=t~α时,引入了极限代数lim_(α→0+)l~α(K,A),lim_(α→+∞)l~α(K,A),lim_(α→0+)L~α(K,A)与lim_(α→+∞)L~α(K,A)以及距离空间的Lipschitz连通性,得到了lim_(α→+∞)l~α(K,A)=A的充要条件,也给出了lim_(α→0+)L~α(K,A)=C(K,A)的条件。     

J-子空间格代数上中心化子和广义导子的刻画

设L是Banach空间X上的J-子空间格,AlgL是相应的(J-子空间格代数.设φ:AlgL→AlgL是可加映射,对每个K∈(J)(L),dimK≥2.该文证明了下列表述等价:(1)φ是中心化子;(2)φ满足AB=0■φ(A)B=Aφ(B)=0;(3)φ满足AB+BA=0■φ(A)B+φ(B)A=Aφ(B)+Bφ(A)=0;(4)φ满足ABC+CBA=0■φ(A)BC+φ(C)BA=ABφ(C)+CBφ(A)=0.作为应用,得到AlgL上在零点广义可导的可加映射的完全刻画.     

套代数上的广义Jordan中心化子

设H是实数域或复数域F上的Hilbert空间,N为H上的非平凡套,τ(N)为相应的套代数,并且φ:τ(N)→τ(N)是一个可加映射.本文证明了如果存在正整数m,n,p,使得(m+n)φ(A~(p+1))=mφ(A)A~p+nA~pφ(A)或φ(A~(m+n+1))=A~mφ(A)A~n对所有的A∈τ(N)成立,则存在λ∈F,使得对所有的A∈τ(N),有φ(A)=λA.     

向量极值问题的回归点解释

设 X 为欧氏空间 R~n,Y 为欧氏空间 R~m,g 为映 X 到 Y 的映射,A(?)X 是任意非空子集.在下述向量极值问题(VMP)(VMP) max g(x),s.t.x∈A中,K 是 Y 中非平凡闭凸锥,K≠{0},如果{x∈A|g(x)-g(x_0)∈K\{0}}=φ,则称 x_0∈A 为(VMP)的有效解;如果 intK≠φ,并且{x∈A|g(x)-g(x_0)∈intK)=φ,则称 x_0∈A 为(VMP)的弱有效解.     

Fixed Pansystems Theorems and Pansystems Catastrophe Analysis of Panweighted Network

Let I={(x,x)|∈G}, δ∈P(G~2),I≤δ,δ=δ~(-1),G_i=max{E|EG, E~2≤δ} do notbe reduced to single point; gG~2×W, DW, ψ=gD. Ifψ∨ψ~(-1)∨I≤δ,then G_i∩(G_iψ∪ψG_i)≠φIf (ψ∧ψ~(-1))1ψ∨I≤δ, then G_i∩G_iψ∩ψG_i≠φ.If (ψ~t∧ψ(-t)∧ψ(-t))∨I≤δ,then there exist positive integers m, n, such that G_i∩G_iψ~(m)∩ψ~(n)G_i≠φ, whereψ~t is the transitive closure of ψ, and ψ~(m) is the composition of m times of ψ it-     

LIE ALGEBRA K$(n,\mu _j,m)$ OF CARTAN TYPE OF CHARACTERISTIC p=2

Let $K(n,\mu _j,m),n=2r+1$,denote the Lie algebra of characteristic p=2,which is defined in [4].In the paper the restrictability of $K(n,\mu _j,m)$ is discussed and it is proved that,when $r\equiv 1(mod 2)$ and $r>1,I(ad f)=n+1$ if and only if $0\neq f \in $. Then the invariance of some filtrations of K(n,\mu,m) and the condition of isomorphism of K(n,\mu _i,m) and K(n',\mu _j ^',m') are obtained.Besides,the generators and the derivation algebra of K(n,\mu _i,m) are discussed.The results also hold,when $r\equiv 0 (mod 2)$ and r>0.     

复合形在欧氏空间中的实现问题Ⅲ

<正> 设 K 是一个有限单形复合形,我们恒可视 K 为一充分高维数 N 的欧氏空间中的欧氏复合形,此时其所定空间将记为(?).在研究 K 是否可实现于某一确定维数 m 的欧氏盘间R~m 中的时候,我们曾引进下面的一些定义(见[1],记号略有不同):     

关于纤维锥的Hilbert系数

Let （R, m） be a Cohen-Macaulay local ring of dimension d, I an mprimary ideal and K an ideal containing I. Assuming that I has minimal （almost minimal） mixed multiplicity with respect to K, we get some results on the Hilbert coefficients of fiber cones.     

套链分解

Let X1,X2,...,Xk be k disjoint subsets of S with the same cardinality m.Define H(m,k) = {X (C) S: X (C) Xi for 1 ≤I ≤k} and P(m,k) = {X (C) S : X ∩ Xi ≠φ for at least two Xi's}.Suppose S = Uki=1 Xi,and let Q(m,k,2) be the collection of all subsets K of S satisfying|K ∩ Xi|≥ 2 for some 1 ≤ I ≤ k.For any two disjoint subsets Y1 and Y2 of S,we define F1,j = {X (C) S : either |X ∩ Y1|≥ 1 or |X ∩ Y2|≥ j}.It is obvious that the four posers are graded posets ordered by inclusion.In this paper we will prove that the four posets are nested chain orders.     

单峰扩张映射的捏制序列

设Ｐ及ＡＣ均是准素序列并满足ｍｉｎ｛Ｐ，ＡＣ｝ＲＬＲ∞，ρ（Ｐ）及ρ（ＡＣ）分别是Ｐ及ＡＣ的特征值．设ｆ∈Ｃ０（Ｉ，Ｉ）是个单峰扩张映射并具有扩张常数λ，ｍ是个非负整数．本文证明了若λ（ρ（Ｐ））１／２ｍ，则ｆ的捏制序列Ｋ（ｆ）（ＲＣ）ｍＰ；若λ＞（ρ（ＡＣ））１／２ｍ，则对任极大序列Ｅ，Ｋ（ｆ）＞（ＲＣ）ｍＡＣＥ．（ρ（Ｐ））１／２ｍ及（ρ（ＡＣ））１／２ｍ均是下述意义下的最佳值，即若其中任一个被较小的值代替，则相应的结论便不成立．     

Metric theorems related to the Kronecker-Weyl theorem modm

Let (Ω, ?,P) be the infinite product of identical copies of the unit interval probability space. For a Lebesgue measurable subsetI of the unit interval, let \(A(N,I,\omega ) = \# \left\{ {n \leqslant N|\omega _n \varepsilon I} \right\}\) , where ω=(ω₁,ω₂,...). For integersm>1, and 0≤r<m, define $$\varepsilon (k,r,m,I,\omega ) = \left\{ {\begin{array}{*{20}c} {1\,if\,A(k,I,\omega ) \equiv r(\bmod m)} \\ {0\,otherwise} \\ \end{array} } \right.$$ and $$\eta (k,m,I,\omega ) = \left\{ {\begin{array}{*{20}c} {1\,if\,(A(k,I,\omega ),m) \equiv 1} \\ {0\,otherwise.} \\ \end{array} } \right.$$ A theorem ofK. L. Chung yields an iterated logarithm law and a central limit theorem for sums of the variables ε(k) and η(k).     

Some pseudovariety joins involvinglocally trivial semigroups

This paper is concerned with the computation of pseudovariety joins involving the pseudovariety L I of locally trivial semigroups. We compute, in particular, the join of L I with any subpseudovariety of CR(m in circle)N, the Mal’cev product of the pseudovariety of completely regular semigroups and the pseudovariety of nilpotent semigroups. Similar studies are conducted for the pseudovarieties K, D and N, where K (resp. D) is the pseudovariety of all semigroups S such that eS=e (resp. Se=e ) for each idempotent e of S .     

Some Pseudovariety Joins InvolvingLocally Trivial Semigroups

This paper is concerned with the computation of pseudovariety joins involving the pseudovariety L I of locally trivial semigroups. We compute, in particular, the join of L I with any subpseudovariety of CR(m in circle)N, the Mal'cev product of the pseudovariety of completely regular semigroups and the pseudovariety of nilpotent semigroups. Similar studies are conducted for the pseudovarieties K, D and N, where K (resp. D) is the pseudovariety of all semigroups S such that eS=e (resp. Se=e ) for each idempotent e of S . May 5, 1999     

复合形在欧氏空间中的实现问题(Ⅱ)

<正> 并于复合形或更一般的空间在欧氏空间中的实现问题,曾经有过下面几个重要的结果:1°Van Kampen 在1932时证明有不能在2n维欧氏空间中实现的 n 维复合形 K 存在。Van Kampen 的证明倚赖于由及的约化二重对称积 K 作出的一个不变量.作者在[2]中指出 Van Kampen 不变量只是一组不变量(?),(I_m=整数加法群 I 或法2整数群 I_2,视 m 为偶或奇而定)其中极端的一个,即Φ~(2n),而Φ~m=0为     

The Fractional Calculus for Some Stochastic Processes

Abstract

The integration and differentiation of fractional orders are well known concepts for deterministic functions (see Miller, K.S.; Ross, B. An Introduction to Fractional Calculus and Fractional Differential Equations; John Wiley: New York, 1993; I. Podlubny and Ahmed M.A. El-Sayed, On two definitions of fractional calculus Slovak Academy of Sciences Institute of experimental Phys. UEF-03-96 ISBN 80-7099-252-2, 1996; Podlubny, I. Fractional Differential Equations; Acad. Press: San Diego – New York, London etc. 1999; Samko, S.G.; Kilbas, A.A.; Marichev, O. Integral and derivatives of the fractional orders and some of their applications. Nauka i Teknika Minisk 1983). In earlier work, we have studied the fractional calculus for mean square continuous stochastic processes. In this work, we shall study the mean square (m.s.) fractional calculus for stochastic processes which are m.s. Riemann-integrable and prove some its properties.