中国科学院数学与系统科学研究院期刊网

15 September 1994, Volume 10 Issue 3
    

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  • Tong Wenting
    Acta Mathematica Sinica. 1994, 10(3): 225-230. https://doi.org/10.1007/BF02560713
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    Let R be a ring with an identity element. R∈IBN means that RmRn implies m=n, R∈IBN1 means that RmRnK implies m≥n, and R∈IBN2 means that RmRmK implies K=0. In this paper we give some characteristic properties of IBN1 and IBN2, with orderings on the Grothendieck groups. In addition, we obtain the following results: (1) If R∈IBN1 and all finitely generated projective left R-modules are stably free, then the Grothendieck group K0(R) is a totally ordered abelian group. (2) If the pre-ordering of the Grothendieck group K0(R) of a ring R is a partial ordering, then R∈IBN1 or K0(R)=0.
  • Liu Bin, You Jiangong
    Acta Mathematica Sinica. 1994, 10(3): 231-242. https://doi.org/10.1007/BF02560714
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    In this paper, we study the existence of quasi-periodic solutions and the boundedness of solutions for a wide class nonlinear differential equations of second order. Using the KAM theorem of reversible systems and the theory of transformations we obtain the existence of quasi-periodic solutions and the boundedness of solutions under some reasonable conditions.
  • Pan Jianzhong
    Acta Mathematica Sinica. 1994, 10(3): 243-248. https://doi.org/10.1007/BF02560715
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    In this paper we investigate whether a polynomial algebra can be realized as a cohomology ring of a topological space. Our main results are that we can split the realizable polynomial algebra into a tensor product of certain simple factors and that these factors are given explicitly when p>7. What is worth mentioning is that most of these factors are known to be realizable.
  • Ma Jigang, He Yuzan
    Acta Mathematica Sinica. 1994, 10(3): 249-259. https://doi.org/10.1007/BF02560716
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    In this paper, the Bers-Orlicz spaces on the automorphic form Aαφ (G) (or EAαφ (G)) and Lαφ(G) on the product Riemann surfaces are studied. We prove that each fAαφ (G) is a cusp form. For fAαφ (G), we give the reproducing formula. And, we give the projective operator Pa from Lαφ (G) to Aαφ (G) to EAαφ (G)). After giving some fundamental properties of the Poincaré series, we prove a dual theorem Aαφ* (G)=(EAαφ(G))*.
  • Chen Mufa
    Acta Mathematica Sinica. 1994, 10(3): 260-275. https://doi.org/10.1007/BF02560717
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    This paper is devoted to studying a new topic: optimal Markovian couplings, mainly for time-continuous Markov processes. The study emphasizes the analysis of the coupling operators rather than the processes. Some constructions of optimal Markovian couplings for Markov chains and diffusions are presented, which are often unexpected. Then, the results are applied to study the L2-convergence for Markov chains and for a diffusion on compact manifold. The estimate of the convergent rate provided by this method can be sharp.
  • Shi Peide, Cheng Ping
    Acta Mathematica Sinica. 1994, 10(3): 276-288. https://doi.org/10.1007/BF02560718
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    Consider the nonparametric regression model Y= g0(T)+ u, where Y is real-valued, u is a random error, T ranges over a nondegenerate compact interval, say [0,1], and g0(·) is an unknown regression function, which is m(m≥0) times continuously differentiable and its mth derivative, g0(m), satisfies a Hölder condition of order γ(m+γ>1/2). A piecewise polynomial L1-norm estimator of g0 is proposed. Under some regularity conditions including that the random errors are independent but not necessarily have a common distribution, it is proved that the rates of convergence of the piecewise polynomial L1-norm estimator are almost surely and in probability, which can arbitrarily approach the optimal rates of convergence for nonparametric regression, where σ is any number in (0, min((m+γ-1/2)/3,γ)).
  • Xiao Yimin, Lin Huonan
    Acta Mathematica Sinica. 1994, 10(3): 289-300. https://doi.org/10.1007/BF02560719
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    The Hausdorff dimensions of the image and the graph of random fields are given under general conditions. The results can be used to a wider class of self-similar random fields and processes, including Brownian motion, Brownian sheet, fractional Brownian motion, processes with stable or (α, β)-fractional stable components.
  • R. W. Kieboom, Chen Jixiang
    Acta Mathematica Sinica. 1994, 10(3): 301-307. https://doi.org/10.1007/BF02560720
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    This paper introduced a new homotopy extension property called the fairly weak homotopy extension property (FWHEP) and showed some its characterizations and properties. The FWHEP is strictly between the WHEP and the VWHEP (RWHEP).
  • Zhang Xuelian
    Acta Mathematica Sinica. 1994, 10(3): 308-314. https://doi.org/10.1007/BF02560721
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    This paper is to study the characteristic functions of meromorphic functions for an angular domain. We show an inequality which is similar to the inequality in the second fundamental theorem of Nevanlinna, and estimate its remainder. Finally, as an application we obtain a sufficient and necessary condition of Borel directions.
  • Chen Dirong
    Acta Mathematica Sinica. 1994, 10(3): 315-324. https://doi.org/10.1007/BF02560722
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    This paper discusses some problems on the cardinal spline interpolation corresponding to infinite order differential operators. The remainder formulas and a dual theorem are established for some convolution classes, where the kernels are PF densities. Moreover, the exact error of approximation of a convolution class with interpolation cardinal splines is determined. The exact values of average n-Kolmogorov widths are obtained for the convolution class.
  • Chen Shaohua
    Acta Mathematica Sinica. 1994, 10(3): 325-335. https://doi.org/10.1007/BF02560723
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    We discuss the existence of global classical solution for the uniformly parabolic equation

    Where a is strongly nonlinear with respect to uxx and φ is not necessarily small. We also deal with nonuniform case.
  • Jiang Jiahe
    Acta Mathematica Sinica. 1994, 10(3): 336-336. https://doi.org/10.1007/BF02560724
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