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1.
$L$ is a line in a plane through the origin, with an angle $$\alpha$$ to the $x$-axis,$$0 < \alpha < \pi$$.$M$ is a point process on positive $x$-axis, Through the nth point of $M$ draw a line with a random angle $${\theta _n}$$ to $x$-axis, $${\varphi ^ + }$$ is the set of intersections of those lines with $${L^ + }$$. Let $$m = EM$$. If, for every $$c > 0$$, then $${\varphi ^ + }$$ is locally finite on $L$, and let $$\tilde M$$ be the point process constructed by $${\varphi ^ + }$$ , then $$E\tilde M$$ exists. If, for all interval $$L \subset {L^ + }$$, $$\int_0^\infty {r(I,x)M(dx)} = \infty$$ then $${\varphi ^ + }$$ is dense on $${L^ + }$$. If $L$ is drawn parallel to $x$-axis,. the same results can be got，and this time $$\tilde M$$ is a cluster point process with cluster center $M$.  相似文献

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Let M and N be nonzero subspaces of a Hilbert space H, and PM and PN denote the orthogonal projections on M and N, respectively. In this note, an exact representation of the angle and the minimum gap of M and N is obtained. In addition, we study relations between the angle, the minimum gap of two subspaces M and N, and the reduced minimum modulus of （I - PN）PM,  相似文献

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Values of new series sum（（（2n-1）!ζ（2n））/（2n ＋ 2k）!）α2n from n=1 to ∞,sum（（（2n-1）!ζ（2n））/（2n＋2k ＋1）!）β2n from n=1 to ∞ are given concerning ζ（2k ＋ 1）,where k is a positive integer,α can be taken as 1,1/2,1/3,2/3,1/4,3/4,1/6,5/6 and β can be taken as 1,1/2.Some previous results are included as special cases in the present paper and new series converges more rapidly than those exsiting results for α = 1/3,or α = 1/4,or α = 1/6.  相似文献

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In this paper, the author proves the following resu: It Let K be a skew field and A be an automorphism of SL(2, K). Then there exists A∈GL(2, K), an automorphism σ or an anti-automorphism τ of K, such that A is of theform AX=AX~σA~(-1) for all X∈SL(2, K)or AX=A(X~τ~2)~(-1)A~(-1) for all X∈SL(2, K),where X~σ, X~τ are the matrices obtained by applying σ, τ on X respee tively and X' is thetranspose of X.  相似文献

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Let F be a field of characteristic 0, Mn（F） the full matrix algebra over F, t the subalgebra of Mn（F） consisting of all upper triangular matrices. Any subalgebra of Mn（F） containing t is called a parabolic subalgebra of Mn（F）. Let P be a parabolic subalgebra of Mn（F）. A map φ on P is said to satisfy derivability if φ（x·y） = φ（x）·y＋x·φ（y） for all x,y ∈ P, where φ is not necessarily linear. Note that a map satisfying derivability on P is not necessarily a derivation on P. In this paper, we prove that a map φ on P satisfies derivability if and only if φ is a sum of an inner derivation and an additive quasi-derivation on P. In particular, any derivation of parabolic subalgebras of Mn（F） is an inner derivation.  相似文献