按有理函数系展开函数成Fourier级数

In this paper we give some orthogonal system of rational functions on the unit circumference; We obtained the Riemann Lemma and some tests of convergence of Fourier series for this orthogonal system with the poles {α_k}₀^∞ satisfying some conditions, The conditions we obtained are weaker than those established in [2].     

一般Gauss—Markov模型下最小二乘估计是最佳估计的充要条件

In this paper, we discuss the decomposition of the space μ(X : V) and the invariance with respect to the choice of a generalized inverse of matrix X in the general Gauss-Markov model. In Theorem 1, we give necessary and sufficient conditions for the least squares estimator P_xy = BLUE(Xβ) under the general Gauss-Markov model M = {y,Xβ,σ²V}. In Theorem 2, we prove that P_xy= BLUE(Xβ) under model M and invariant with respect to the choice of a generalized inverse of matrix X are equivalent.     

四元数矩阵的特征值与奇异值估计

In this paper, we give accurate estimation of eigenvalues and singular values of A + B,C^*AC and AB, where A, B and C are quaternions matrices. These results improve and generalze the results in [4] and [5]. We also obtainsum (?),for k=1,…,n. Where A and B are self-conjugate quaternions matrices of order n, and λ₁≥…≥λ_n,μ₁≥μ_n,λ₁,(A + B)≥…≥λ_n(A+B) be the eigenvalues of A,B and A + B, respectively.     

C－余弦算子函数的谱

Let A be the generator of a C-cosine operator functions C(t) on a Banach space X .The spectrum characterization of (unbounded) cosine operator function C(t)C^-1 on R(C²) is derived. In particular， we characterize the spectrum of strongly continuous cosine operator on a Banach space.     

Cpa空间中的非线性逼近

In this paper, we establish the following Jackson and Bernstein inequalities for C_p^a space:(?)where σ=(α+ (1/p)^-1),α > 0,0 < p < ∞. Moreover, these inequalities are used to give characterizations of the approximation spaces resulted from two approximations verpectively by splines with free knots and approximation by rational functions.     

关于控制算子的若干注记

Let B(H) be the set of all bounded linear operators on a Hilbert space H. An operator T∈B(H) is called dominant if (T-λ)(T-λ)^*≤M_λ²(T-λ)^*(T-λ),?λ∈C.The numerical range of T is difined by W (T) = {(Tx, x): ‖x‖ = 1, x∈H}. In Section 1 some new characteristic of dominant operators are given. If C = AB - BA, we prove that O∈W(C)^- then A is a dominart or φ-quasihy ponor-mal. In Section 2 we prove that O∈σ_e(△_A^σ) if A is a dominant, where(?), we also prove that if A∈B(H) is a norm attaining Ф-quasihyponormal, then A has a non-trivial invariant subspace. In Section 3 we discuss the closeness of the range of bounded linear operator F_AB:X→AX-XB, and prove that R(δ_A)∩{A}′∩{Aⁿ}′=0, where δ_A:X→AX-XA.     

关于一类有理系数常微分方程的亚纯解

In this paper, we give an estimation of the number of meromorphic solu-tions and linearly independent meromorphic solutions of some class ordinary differential equations with rational coefficients (dw)/(dz)=a₀(z)+a₁(z)w+…+a_n(z)wⁿ (n≥3).     

Mt2上的强ω(α)轨道稳定性

In this paper we define the concept of strong ω-stability (α-stability) of trajectories on dynamical systems, and discuss some properties of them on M_t² Using those properties we discuss the existence of close orbits or singular close orbits on M_t².     

关于解析函数的一个不等式

Let P(Z) = 1 + P₁Z + P₂Z² +…be an analytic function in the unit disc D. In thispaper, we determine the value of φ(α,β) for which Re[P(Z) + αZP′(Z)] > β,Z ∈ D,α > 0,β < 1 implies that Re{P(Z)} >φ(α,β) for all Z ∈ D, and this result is sharp. Some of its interesting consequences are also given. In addition, we give a new univalence criterion.     

微分从属运算与保形映射

In this paper we give a sufficient condition on D^δg(z) such that with thecondition.it gnarantees that in the unit disk E implies Some interesting applions ofthis result are also given.     

非周期函数类WrHω的宽度估计

In this paper, we obtain the strong assymptotic values of n-width d_n(W^rH^ω, C)and d_n(W^rH^ω, L) for non-periodic function class W^rH^ω, wheve ω is a concave modulus of continuity.     

关于Banach空间凸性的几个定理

In this paper we show first a sufficient condition of URED space and URWC space. Secondly, we discuss some properties of W^*∪R, and point out the property W^*∪R is inherited by Ip-product spaces and quotient space.     

某些近于凸函数子类的极值点

In this paper the closed convex hulls and extreme points are determined for C(β) and C^*(1/2) .Then we determine coefficient bounds and distortion th eorems for these classes .All results are sharp. Finally, we discuss the relations hips between these classes and known classes of functions.     

正态分布方差SPRT的maxE(n)

In this paper the explicit formulae of ASN's maximum are derived for SPRT under normal distribution N(μ₀,σ²), where σ² is an unknown parameter. And under the same condition we have obtained the size of sample of single samp-ling inspection plan.     

悖论与数学基础问题(Ⅰ)

This expository article is motivated by two well-known antinomies. The first is the extended Zeno paradox concerning two persons playing at a ball, passing theball to and fro within 1/2,1/4,1/8,…, minutes successively, and questioning the place of the ball at the end of one minute. The second antinomy is that of Engels concerning the real infinitude of successively generated finite ordinals. In order to explain away or give answer to these two antinomies, we have constructed a kind of non-Cantorian model for the sequence of natural numbers by the aid of Van Osdol-Takahashi's ultrapower (extended real number field) ^*R. In what follows are a few definitions and some propositions discussed in this article.     

周期点集为闭集的圆周自映射周期点的周期

Let S¹ denote the circle. In this paper, we show the following.Theorem. Let f: S¹→S¹ be a continuous map and suppose f has a fixed point and the set of periodic points of f is closed, then the period of each periodic point of f is a power of 2.Corollary. Let f: S¹→S¹ be a continuous map and suppose the set of periodic points of f is closed, then there exists an odd integer m such that the set of periods of periodic points of f is contained in the set {m·2ⁿ; n = 0,1,2,…}.     

黎曼流形上某些微分方程的通解

Let (Mⁿ,g) be a Riemannian manifold of dimension n and let ▽ denote the Riemannian connection defined by g. In this paper we study the following systems of differential equations.     

用2-块AOR方法求解最小二乘问题的收敛域

In this paper , we consided the 2-block AOR method for solving large sparse least-squares problems, and gave the convergence domains of its by the functional relation (λ-ω-1)²=ωλrμ².     

A Characterization of the Standard Tori in C2 as Compact Lagrangian ξ-Submanifolds*

In this paper, the authors give a characterization theorem for the standard tori S¹(a) × S¹(b), a, b > 0, as the compact Lagrangian ξ-submanifolds in the two-dimensional complex Euclidean space C² , and obtain the best version of a former rigidity theorem for compact Lagrangian ξ-submanifold in C² . Furthermore, their argument in this paper also proves a new rigidity theorem which is a direct generalization of a rigidity theorem by Li and Wang for Lagrangian self-shrinkers in C².