15 June 1994, Volume 10 Issue 2

    

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  On Indecomposable Definite Unimodular Hermitian Forms

  Zhu Fuzu

  Acta Mathematica Sinica. 1994, 10(2): 113-120. https://doi.org/10.1007/BF02580417

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  For any natural numbers m and n≥17 we can construct explicitly indecomposable definite unimodular normal Hermitian lattices of rank n over the ring of algebraic integers R_m in an imaginary quadratic field Q(√-m. It is proved that for any n (in case m=11, there is one exception n=3) there exist indecomposable definite unimodular normal Hermitian R₁₅(R₁₁)-lattices of rank n, and we exhibit representatives for each class. In the exceptional case there are no lattices with the desired properties. The method given in this paper can solve completely the problem of constructing indecomposable definite unimodular normal Hermitian R_m -lattices of any rank n for each m.
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  Unicity Theorems for Entire or Meromorphic Functions

  Yi Hongxun

  Acta Mathematica Sinica. 1994, 10(2): 121-131. https://doi.org/10.1007/BF02580418

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  In this paper, we deal with the problem of uniqueness of entire or meromorphic functions and obtain some results that are improvements over those of M. Ozawa, H. Ueda, K. Shibazaki and Yi Hongxun. An example shows that the results in this paper are sharp.
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  Normal Operators Similar to Irreducible Operators

  Fong Chekao, Jiang Chunlan

  Acta Mathematica Sinica. 1994, 10(2): 132-135. https://doi.org/10.1007/BF02580419

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  A complete characterization of normal operators which are similar to irreducible operators and some related results are given.
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  A Polyhedral Theory on Graphs

  Liu Yanpei

  Acta Mathematica Sinica. 1994, 10(2): 136-142. https://doi.org/10.1007/BF02580420

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  This paper provides a polyhedral theory on graphs from which the criteria of Whitney and MacLane for the planarity of graphs are unified, and a brief proof of the Gauss crossing conjecture is obtained.
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  Remark on the Weierstrass Points on Curves

  Xu Mingwei

  Acta Mathematica Sinica. 1994, 10(2): 143-148. https://doi.org/10.1007/BF02580421

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  We give a treatment of the Weiertrass points of curves which is a little different from the treatment by Laksov. We introduce the notion of the ith weight which makes the treatment easier and gives an algorithm for computing the gap sequence of an effective divisor and the weight at a point.
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  Infinite Steinberg Groups

  Li Fuan

  Acta Mathematica Sinica. 1994, 10(2): 149-157. https://doi.org/10.1007/BF02580422

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  The Steinberg group over a ring along an arbitrary set is defined. Its properties, structure, and isomorphism theory are studied.
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  The View-Obstruction Problem for 3-Dimensional Spheres

  Chen Yonggao

  Acta Mathematica Sinica. 1994, 10(2): 158-167. https://doi.org/10.1007/BF02580423

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  Let C be an n-dimensional sphere with diameter 1 and center at the origin in Eⁿ . The view-obstruction problem for n-dimensional spheres is to determine a constant ν(n) to be the lower bound of those α for which any half-line L, given by x_{em = aem} t (em=1,2,…, n) where parameter t≥0 and a_em (em=1,2,……, n) are positive real numbers, intersects
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  In this paper, for n=3, the following result is proved. For α > we have that any half-line L, given by x_em = a_em t(em=1,2,3), intersects Δ(C,α), where parameter t≥0 and a_em (em=1,2,3) are positive real numbers such that |a|+|b|+|c|≠3 whenever aa₁+ba₂+ca₃=0 for three integers a,b,c.
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  Some Results on Entire Functions of Finite Lower Order

  Wu Shengjian

  Acta Mathematica Sinica. 1994, 10(2): 168-178. https://doi.org/10.1007/BF02580424

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  Let f(z) be an entire function of order λ and of finite lower order μ. If the zeros of f(z) accumulate in the vicinity of a finite number of rays, then
  (a) λ is finite;
  (b) for every arbitrary number k₁>1, there exists k₂>1 such that T(k₁ r,f)≤k₂ T(r,f) for all r≥ r₀.
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  Refined Convergents to the Associated Continued Fractions for Binary Sequences

  Dai Zongduo, Zeng Kencheng

  Acta Mathematica Sinica. 1994, 10(2): 179-191. https://doi.org/10.1007/BF02580425

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  The relation between continued fractions and Berlekamp's algorithm was studied by some researchers. The latter is an iterative procedure proposed for decoding BCH codes. However, there remains an unanswered question wheter each of the iterative steps in the algorithm can be interpreted in terms of continued fractions. In this paper, we first introduce the so-called refined convergents to the continued fraction expansion of a binary sequence S, and then give a thorough answer to the question in the context of Massey's linear feedback shift register synthesis algorithm which is equivalent to that of Berlekamp, and at last we prove that there exists a one-to-one correspondence between the n-th refined convergents and the length n segments.
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  Dual Space, Carleson Measure and Sequence Interpolation on A^p(ψ)(O<p<1)

  Xiao Jie

  Acta Mathematica Sinica. 1994, 10(2): 192-201. https://doi.org/10.1007/BF02580426

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  Let D={z∈Σ:|z|<1} and ψ be a normal function on [0,1). For p∈(0,1) such a function ψ is used to define a Bergman space A^p (ψ) on D with weight ψ^p (|·|)/(1-|·|²). In this paper, the dual space of A^p (ψ) is given, four characteristics of Carleson measure on A^p (ψ) are obtained. Moreover, as an application, three sequence interpolation theorems in A^p (ψ) are derived.
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  On the Linear Representations of Circle Expanding Maps

  Cui Guizhen

  Acta Mathematica Sinica. 1994, 10(2): 202-208. https://doi.org/10.1007/BF02580427

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  In this paper, it is proved that the two real analytic expanding endomorphisms of the unit circle are equivalent if and only if they have equal eigenvalues along corresponding cycles. A sufficient and necessary condition that a real analytic solution of Cvitanovic-Feigenbaum equation induces a real analytic expanding map is given.
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  Spectra of Composition Operators on Lummer-Hardy Spaces

  Yuan Jinyong

  Acta Mathematica Sinica. 1994, 10(2): 209-214. https://doi.org/10.1007/BF02580428

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  In this paper, we completely determine the spectrum of a compact composition operator on lummer-Hardy space.
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  Differential Polynomials and Normal Families

  Xu Wansong

  Acta Mathematica Sinica. 1994, 10(2): 215-218. https://doi.org/10.1007/BF02580429

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  This paper continues the researches of Yang Lo and others, and gives a further generalization of Gu's criterion for the normality of a family of meromorphic functions.
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  Local Continuity Modulus for Wiener and Infinite Dimensional OU Processes

  Lu Chuanrong, Shen Siwei, Wang Xiuyun

  Acta Mathematica Sinica. 1994, 10(2): 219-224. https://doi.org/10.1007/BF02580430

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  In this paper, we gave a proof for the local continuity modulus theorem of the Wiener process, i.e.,
  a.s.
  This result was given by Csérgé and Révész (1981), but the proof gets them nowhere. We also gave a similar local continuity modulus result for the infinite dimensional OU processes.