15 May 1994, Volume 37 Issue 3

    

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论文
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  Admissibility of Linear Estimator in Linear Models with Respect to A Incomplete Ellipsoidal Restrictions

  Acta Mathematica Sinica, Chinese Series. 1994, 37(3): 289-300. https://doi.org/10.12386/A1994sxxb0037

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  The admissibility of a linear estimator is characterized in the linear models （Ｙ，Ｘβ，σ２Ｖ，Ｖ≥０） where considered regression parameter varies in a incomplete ellipsoia (β：（β－β０）’Ｎ（β－ β Ｐ０）≤σ２，Ｎ ≥ ０ The results shown that the admissibility of linear estimator among the class of all linear estimators is independent on β0, but the admissibility of homogeneous linear estimator among the class of all homogeneous linear estimators is dependent oil β0.
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  The Determination of the Groups J~(6,k_1,...,K_l)

  Acta Mathematica Sinica, Chinese Series. 1994, 37(3): 296-300. https://doi.org/10.12386/A1994sxxb0038

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  Let Ki be the positive integers and k1 < k2 <... < kl. We have determned the groups J6,k2,...,kl (ki are even and k2 >=12). In this paper, we determine the groups J6,10,k3,...,kl J6,8,k3,...,kl (k3 > 10), J6,8,10,k4...,kl (ki are even).
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  The Position of Boundary Surface for a Sort of Trancendental Equation with Tree Parameters

  Acta Mathematica Sinica, Chinese Series. 1994, 37(3): 301-308. https://doi.org/10.12386/A1994sxxb0039

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  When considering the stability of a differential equation with time lag, one often has to solve the distribute. problem of the roots of a trancedental equation. For the case of the trancendental equation with two parameters, the problem above has been solved completely. For a sort of trancendental equation with three parameters, Bellman and Cooke get a conclusion for partial case: a > 0, b >= 0 in [3]. But it is analytical and inconvenience in application. In this paper, the conditions under which the roots of such equation are in the left half plane, are given in whole parametric space (a, b, c). Furthermore, the roughly shape of the stable region is pointed by figure. The results in this paper are convenient to use, especially in the bifurcation theory.
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  Some Results on Spacelike Surfaces in Minkowski 3-Space

  Acta Mathematica Sinica, Chinese Series. 1994, 37(3): 309-316. https://doi.org/10.12386/A1994sxxb0040

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  In this paper we prove that there exists a Ricci condition such that a 2-dimensional Riemannian manifold can be realized as a spacelike maximal surface in L3, and show that the spacelike surface in L3 whose mean curvature vector h satisfies △ｈ＝λｈ for some λ∈Ｒ is a hyperboloid or a cylinder up to a Lorentz motion in L3.
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  Finite Groups in Whose Second Maximal Subgroups the Cyclic Subgroups of Order 2 and 4 are Quasinarmal

  Acta Mathematica Sinica, Chinese Series. 1994, 37(3): 317-323. https://doi.org/10.12386/A1994sxxb0041

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  The purpose of this paper is to investigate the influence of subgroups of order 2 and 4 on the structure of finite groups. The main result is as follows: If a finite group G satisfies the condition in the tatle, then one of the following holds: (1) G possesses a normal Sylow 2- subgroup; (2) G is 2-nilpotent; (3) G ≌ S4; (4) G = PQ,where P is a generalized quaternion group of order 24 and Q is a cyclic group of order 3; (5) G ≌ A5 or SL(2, 5).
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  Diophantine Inequalities with Mixed Powers (Ⅱ)

  Acta Mathematica Sinica, Chinese Series. 1994, 37(3): 324-331. https://doi.org/10.12386/A1994sxxb0042

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  In the present paper, we consider the analogue of professor Lu Ming-gap's theorem on sums of mixed powers for Diophantine inequalities. More precisely we have the following result. Theorem Suppose that λ１，…，λ７ are non-zero real numbers not all in rational ratio. Then for any real number K and σ < 1/36, the inequality has infinitely many solutions in integers.
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  Classification of A Kind of Irreducible Harish-Chandra Modules over the Algebras of Differential Operators

  Acta Mathematica Sinica, Chinese Series. 1994, 37(3): 332-337. https://doi.org/10.12386/A1994sxxb0043

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  In the present paper, the classification of irreducible Harish-Chandra modules over the associative algebra of differential operators is given, and then the classificiation of irreducible Harish-Chandra modules over the Lie algebra of differential operators with all weight spaces being 1-dimensional is also obtained.
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  n-Approximation Number of Integral Operator

  Acta Mathematica Sinica, Chinese Series. 1994, 37(3): 338-348. https://doi.org/10.12386/A1994sxxb0044

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  This paper is concerned with the study of the error estimate of n-approximation number an (Tk: Lq ~ Lq), where Tk : Lq[0, 1] - Lq[0, 1] (q >=1), (TK)(s) = 1 0 K(s,t)x(t)dt, s E [0, 1], and kernal K(s, t) E W p r ([0, 1]2). When the result of study is applied to optimal error estimate (Bakhvalov [5]) of solving the second linear Fredholm equation (I - TK)x - y using degenerate method, it produces an optimal error estimate which optimizes that in [10] when q = 1.
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  Two Non-Compact Homogeneous Complex Analytic Manifolds

  Acta Mathematica Sinica, Chinese Series. 1994, 37(3): 349-361. https://doi.org/10.12386/A1994sxxb0045

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  In this paper, two non-compact homogeneous complex analytic manifolds are presented. We first discuss the structure of the two complex analytic manifolds and give some homogeneous complex analytic submanifolds. We apply the results obtained to the extended spaces of the two exceptional symmetric domains. Secondly, we obtain analytic flexhomeomohpism groups of the two exceptional symmetric domains from affine flexhomeomorhpism groups on the complex manifolds, and we prove that they are closed symelectic subgroups.
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  Covariates Selection and Parameter Estimation in Growth Curve Models

  Acta Mathematica Sinica, Chinese Series. 1994, 37(3): 362-372. https://doi.org/10.12386/A1994sxxb0046

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  This paper studies the Potthoff-Roy transformation in growth curve models and obtains the best Potthoff-Roy transformation under the criterion of minimum matrix norm. The paper proposes further an approach to improve the Potthoff-Roy transformation by using the covariates. The selection of covariates and its influence on the estimation of parameters in also studied.
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  Group Inverses and Drazin Inverse of Matrices over Rings

  Acta Mathematica Sinica, Chinese Series. 1994, 37(3): 373-380. https://doi.org/10.12386/A1994sxxb0047

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  In this paper, we give necessary and sufficient conditions for the existence of group inverses, (1, 5)-inverses, Drazin inverses of a class of matrices over rings and new formulas for these inverses if they exist. We also generalize the Cline theorem of group inverses over division rings.
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  On the Inclusion Regions of.Numerical Field of a Complex Matrix

  Acta Mathematica Sinica, Chinese Series. 1994, 37(3): 381-386. https://doi.org/10.12386/A1994sxxb0048

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  In this paper, we discuss equivalent representations of smallest inclusion region, improve and generalized corresponding results of [1]--[3], moreover give an new inclusion region
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  geometry and nonlinear differential equations (Brunswich Maine, 1984); contemporary Math., 49 (1986), 51--61. Harmonic Maps from the Two-Sphere to a Complex Grassmann Manifold

  Acta Mathematica Sinica, Chinese Series. 1994, 37(3): 387-392. https://doi.org/10.12386/A1994sxxb0049

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  We show: let φ：Ｓ２－Ｇｔ（ＣＮ）（ｔ＞１） be a harmonic map. Its isotropic order Ｉ（φ）≥ ｋ for some integer k. If energy density of φ ｅ（φ） ≤ ２πｋ (for canonical metric ds2 -- dadz on S2), then φ be isotropic. As a corollary, we obtain: let φ: S2 - Gt(CN) (t > 1) be a harmonic map, if e(φ) ≤ ２π (for canonical metric ds2 = dzdz on S2), then φ is isotropic.
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  Strong Consistency of a Semiparametric Regression Estimate Under Fixed Design

  Acta Mathematica Sinica, Chinese Series. 1994, 37(3): 393-401. https://doi.org/10.12386/A1994sxxb0050

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  For semiparametric regression modelｙｉ（Ｔ）＝βｘｉ（Ｔ）＋ｇ（ｔｉ（Ｔ））＋εｉ（Ｔ），we use the least squares and usual nonparametric method to define the estimates βT and gT for β and g, and obtain its strong consistency under suitable conditions.
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  The Root Properties on (D)~m-Class of Operators

  Acta Mathematica Sinica, Chinese Series. 1994, 37(3): 402-408. https://doi.org/10.12386/A1994sxxb0051

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  In this paper, we discuss the problems on the base perturbation of (D)m-class of operators. Our results are extended to the related ones in [8, 9], and so on. In the same time the problem posed in [14] is partly solved.
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  Periodic Solutions to a Class of Differential Equations with Deviating Arguments

  Acta Mathematica Sinica, Chinese Series. 1994, 37(3): 409-413. https://doi.org/10.12386/A1994sxxb0052

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  In this paper we consider the existence, uniqueness, stability, unstability of periodic solutions to a class of differential equations with deviating aguments. New results are obtained.
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  The Conjugate Points in a Complete Riemann Manifold

  Acta Mathematica Sinica, Chinese Series. 1994, 37(3): 414-419. https://doi.org/10.12386/A1994sxxb0053

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  In the paper, We get a necessary and sufficient condition about a geodesic without conjugate points in a complete manifold with nonnegative sectional currature, then we prove that the sectional curvature must be zero if the section contains the tangent of a geodesic without conjugate points.
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  A Problem on MHR-Rings

  Acta Mathematica Sinica, Chinese Series. 1994, 37(3): 420-422. https://doi.org/10.12386/A1994sxxb0054

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  By an MHR-ring, we mean a ring with minimum condition on principal right ideals. In this note, we prove that, the MHR-ring is satisfy the minimum condition for finitely generated right ideal. So give a complete answer to the 31th problem of szasz.
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  Type I C-F Formula of Holomorphic Funrtions on Bounded Domain in C~n

  Acta Mathematica Sinica, Chinese Series. 1994, 37(3): 423-429. https://doi.org/10.12386/A1994sxxb0055

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  An Cauchy-Fantappie formula of holomorphic functions on bounded domain in Cn whose density function contains derivatives of holomorphic functions is obtained, it is called to be type I C-F formula, using this formula, by suitable chosing its vector function, one can obtain the corresponding type I integral representations of holomorphic functions on various domains.