中国科学院数学与系统科学研究院期刊网

15 May 2020, Volume 36 Issue 5
    

  • Select all
    |
    Articles
  • Jin Fa CHENG
    Acta Mathematica Sinica. 2020, 36(5): 487-511. https://doi.org/10.1007/s10114-020-9258-8
    Abstract ( ) Download PDF ( )   Knowledge map   Save

    In this article, we obtain a new fundamental theorems for Nikiforov-Uvarov-Suslov complex difference equation of hypergeometric type by the method of Euler integral transformation, its expression is different from Suslov's Theorem. We also establish the adjoint equation for Nikiforov-Uvarov-Suslov difference equation of hypergeometric type on non-uniform lattices, and prove it to be a difference equation of hypergeometric type on non-uniform lattices as well. The particular solutions of the adjoint equation are then obtained. As an appliction of these particular solutions, we use them to obtain the particular solutions for the original difference equation of hypergeometric type on non-uniform lattices and other important results.

  • Jing Yu BAO, Fei YE, Ying YANG
    Acta Mathematica Sinica. 2020, 36(5): 512-534. https://doi.org/10.1007/s10114-020-7300-5
    Abstract ( ) Download PDF ( )   Knowledge map   Save

    The screening effect is the phenomenon that optimal linear prediction of a spatial process on an unobserved location mostly depends on nearby observations. That is, the optimal predictor based on just nearby observations yields a good approximation of which based on the whole large dataset. However, the approximation does not always perform well since the screening effect may not hold in all situations. To determine when the screening effect holds is an important issue in spatial statistics. This paper provides some sufficient conditions for ensuring an asymptotic screening effect in Rd based on the spectral density of the underlying isotropic Gaussian process and the geometries of nearby observations. These results apply to isotropic processes with an arbitrary degree of differentiability. Assuming we are predicting at origin, the conditions are (1) the spectral density is nearly a constant in balls of finite radius far from the origin, (2) the positions of nearby observations do not fall on a curve with non-zero intercept whose degree is less or equal to the order of mean square differentiability of the process. These conditions are easy to verify in practice. Convergence rates of the asymptotic screening effect are also obtained. These rates depend on the rate of decrease of the spectral density. Simulation studies on the screening effect for finite samples are also provided.

  • Dong Li LIU, Ji Man ZHAO
    Acta Mathematica Sinica. 2020, 36(5): 535-558. https://doi.org/10.1007/s10114-020-8324-6
    Abstract ( ) Download PDF ( )   Knowledge map   Save

    In this paper, on homogeneous groups, we study the Littlewood-Paley operators in variable exponent spaces. First, we prove that the weighted Littlewood-Paley operators are controlled by the weighted Hardy-Littlewood maximal function, and obtain the vector-valued inequalities of the Littlewood-Paley operators, including the Lusin function, Littlewood-Paley g function and gλ* function. Second, we prove the boundedness of multilinear Littlewood-Paley gψ* function.

  • Xing Xiao LI, Yang Yang LIU, Rui Na QIAO
    Acta Mathematica Sinica. 2020, 36(5): 559-577. https://doi.org/10.1007/s10114-020-9078-x
    Abstract ( ) Download PDF ( )   Knowledge map   Save

    In this paper we study the complete space-like λ-surfaces in the three dimensional Minkowski space R13. As the result, we obtain a complete classification theorem for all the complete space-like λ-surfaces x:M2→R13 with the second fundamental form of constant length. This is a natural extension to the λ-surfaces in 13 of a recent interesting classification theorem by Cheng and Wei for λ-surfaces in the Euclidean space R3.

  • Da XU, Yong ZHOU
    Acta Mathematica Sinica. 2020, 36(5): 578-596. https://doi.org/10.1007/s10114-020-8079-0
    Abstract ( ) Download PDF ( )   Knowledge map   Save

    Length-biased data are encountered in many fields, including economics, engineering and epidemiological cohort studies. There are two main challenges in the analysis of such data:the assumption of independent censoring is violated and the assumed model for the underlying population is no longer satisfied for the observed data. In this paper, a proportional mean residual life varyingcoefficient model for length-biased data is considered and a local pseudo likelihood method is proposed for estimating the coefficient functions in the model. Asymptotic properties are investigated for the proposed estimators. The finite sample performance of the proposed methodology is demonstrated by simulation studies. Finally, the method is applied to a real data set concerning the Academy Awards.

  • Bo Wen LIU
    Acta Mathematica Sinica. 2020, 36(5): 597-604. https://doi.org/10.1007/s10114-020-8252-5
    Abstract ( ) Download PDF ( )   Knowledge map   Save

    In this paper, we obtain the existence of non-planar circular homographic solutions and non-circular homographic solutions of the (2 + N)- and (3 + N)-body problems of the Lennard-Jones system. These results show the essential difference between the Lennard-Jones potential and the Newton's potential of universal gravitation.

  • Guang Ming HU, Yi QI
    Acta Mathematica Sinica. 2020, 36(5): 605-619. https://doi.org/10.1007/s10114-020-8096-z
    Abstract ( ) Download PDF ( )   Knowledge map   Save

    It is known that every finitely unbranched holomorphic covering π:SS of a compact Riemann surface S with genus g ≥ 2 induces an isometric embedding Φπ:Teich(S)→Teich(S). By the mutual relations between Strebel rays in Teich(S) and their embeddings in Teich(S), we show that the 1st-strata space of the augmented Teichmüller space Teich (S) can be embedded in the augmented Teichmüller space Teich (S) isometrically. Furthermore, we show that Φπ induces an isometric embedding from the set Teich(S)B(∞) consisting of Busemann points in the horofunction boundary of Teich(S) into Teich(S)B(∞) with the detour metric.

  • Li Juan ZHOU
    Acta Mathematica Sinica. 2020, 36(5): 620-630. https://doi.org/10.1007/s10114-020-8036-y
    Abstract ( ) Download PDF ( )   Knowledge map   Save

    In this note, we consider the stability of geodesics on volume-preserving diffeomorphism groups with one-side invariant metric. We showed that for non-Beltrami fields on a three-dimensional compact manifold, there does not exist Eulerian stable flow which is Lagrangian exponential unstable. We noticed that a stationary flow corresponding to the KdV equation can be Eulerian stable while the corresponding motion of the fluid is at most exponentially unstable.