15 December 2021, Volume 37 Issue 12

    

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  Empirical Likelihood of Quantile Difference with Missing Response When High-dimensional Covariates Are Present

  Cui Juan KONG, Han Ying LIANG

  Acta Mathematica Sinica. 2021, 37(12): 1803-1825. https://doi.org/10.1007/s10114-021-0570-8

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  We, in this paper, investigate two-sample quantile difference by empirical likelihood method when the responses with high-dimensional covariates of the two populations are missing at random. In particular, based on sufficient dimension reduction technique, we construct three empirical loglikelihood ratios for the quantile difference between two samples by using inverse probability weighting imputation, regression imputation as well as augmented inverse probability weighting imputation, respectively, and prove their asymptotic distributions. At the same time, we give a test to check whether two populations have the same distribution. A simulation study is carried out to investigate finite sample behavior of the proposed methods too.
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  Packing Dimension of Space-time Anisotropic Gaussian Random Fields

  Zhen Long CHEN, Jun WANG, Dong Sheng WU

  Acta Mathematica Sinica. 2021, 37(12): 1826-1840. https://doi.org/10.1007/s10114-021-0307-8

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  Let X={X(t) ∈ R^d, t ∈ R^N } be a centered space-time anisotropic Gaussian random field whose components are independent and satisfy some mild conditions. We study the packing dimension of range X(E) under the anisotropic (time variable) metric space (R^N, ρ) and (space variable) metric space (R^d, τ), where E ⊂ R^N is a Borel set. Our results generalize the corresponding results of Estrade, Wu and Xiao (Commun. Stoch. Anal., 5, 41-64 (2011)) for time-anisotropic Gaussian random fields to space-time anisotropic Gaussian fields.
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  A Characterization of T_2g+1,2 among Alternating Knots

  Yi NI

  Acta Mathematica Sinica. 2021, 37(12): 1841-1846. https://doi.org/10.1007/s10114-021-0408-4

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  Let K be a genus g alternating knot with Alexander polynomial Δ_K(T)=Σ_i=-g^g a_iTⁱ. We show that if|a_g|=|a_g-1|, then K is the torus knot T_2g+1,±2. This is a special case of the Fox Trapezoidal Conjecture. The proof uses Ozsváth and Szabó's work on alternating knots.
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  Topological Multiple Recurrence of Weakly Mixing Minimal Systems for Generalized Polynomials

  Rui Feng ZHANG, Jian Jie ZHAO

  Acta Mathematica Sinica. 2021, 37(12): 1847-1874. https://doi.org/10.1007/s10114-021-1053-7

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  Let (X, T) be a weakly mixing minimal system, p₁,..., p_d be integer-valued generalized polynomials and (p₁, p₂,..., p_d) be non-degenerate. Then there exists a residual subset X₀ of X such that for all x ∈ X₀, {(T ^p₁(n)x,..., T^p_d(n)x):n ∈ Z} is dense in X^d.
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  On the Chern-Simons-Schrödinger Equation with Critical Exponential Growth

  Si Tong CHEN, Xian Hua TANG, Shuai YUAN

  Acta Mathematica Sinica. 2021, 37(12): 1875-1895. https://doi.org/10.1007/s10114-021-0534-z

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  This paper is concerned with the following Chern-Simons-Schrödinger equation -Δu + V (|x|)u +(∫_|x|^∞h(s)/su²(s)ds + h²(|x|)/|x|²)u=a(|x|)f(u) in R², where h(s)=∫₀^sl/2u²(l)dl, V, a:R⁺ → R are radially symmetric potentials and the nonlinearity f:R → R is of subcritical or critical exponential growth in the sense of Trudinger-Moser. We give some new sufficient conditions on f to obtain the existence of nontrivial solutions or ground state solutions. In particular, some new estimates and techniques are used to overcome the difficulty arising from the critical growth of Trudinger-Moser type.
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  A Kenmotsu Metric as a ∗-conformal Yamabe Soliton with Torse Forming Potential Vector Field

  Soumendu ROY, Arindam BHATTACHARYYA

  Acta Mathematica Sinica. 2021, 37(12): 1896-1908. https://doi.org/10.1007/s10114-021-1008-z

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  The purpose of the present paper is to deliberate ∗-conformal Yamabe soliton, whose potential vector field is torse-forming on Kenmotsu manifold. Here, we have shown the nature of the soliton and find the scalar curvature when the manifold admitting ∗-conformal Yamabe soliton on Kenmotsu manifold. Next, we have evolved the characterization of the vector field when the manifold satisfies ∗-conformal Yamabe soliton. Also we have embellished some applications of vector field as torse-forming in terms of ∗-conformal Yamabe soliton on Kenmotsu manifold. We have developed an example of ∗-conformal Yamabe soliton on 3-dimensional Kenmotsu manifold to prove our findings.
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  The Commutators of Strongly Singular Integral Operators on the Weighted Hardy Spaces

  Yan Yan HAN, Huo Xiong WU

  Acta Mathematica Sinica. 2021, 37(12): 1909-1920. https://doi.org/10.1007/s10114-021-1069-z

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  Let T be a strongly singular Calderón-Zygmund operator and b ∈ L_loc(Rⁿ). This article finds out a class of non-trivial subspaces BMOω,p,u(Rⁿ) of BMO(Rⁿ) for certain ω ∈ A₁, 0 < p ≤ 1 and 1 < u ≤ ∞, such that the commutator[b, T] is bounded from weighted Hardy space H_ω^p(Rⁿ) to weighted Lebesgue space L_ω^p(Rⁿ) if b ∈ BMOω,p,∞(Rⁿ), and is bounded from weighted Hardy space H_ω^p(Rⁿ) to itself if T^∗1=0 and b ∈ BMOω,p,u(Rⁿ) for 1 < u < 2.
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  Laplacian Perfect State Transfer in Extended Neighborhood Coronas

  Yi Peng LI, Xiao Gang LIU, Sheng Gui ZHANG

  Acta Mathematica Sinica. 2021, 37(12): 1921-1932. https://doi.org/10.1007/s10114-021-0582-4

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  In this paper, we give some sufficient conditions for extended neighborhood coronas to have Laplacian perfect state transfer. We also give some conditions for extended neighborhood coronas to be periodic.
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  Stronger Versions of Sensitivity for Minimal Group Actions

  Jian LI, Yi Ni YANG

  Acta Mathematica Sinica. 2021, 37(12): 1933-1946. https://doi.org/10.1007/s10114-021-0511-6

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  We study several stronger versions of sensitivity for minimal group actions, including n-sensitivity, thick n-sensitivity and blockily thick n-sensitivity, and characterize them by the regionally proximal relation.
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  Relative Entropy and Mean Li-Yorke Chaos Along Some Good Sequences

  Pei WANG, Er Cai CHEN, Xiu Xiu LIU, Xiao Yao ZHOU

  Acta Mathematica Sinica. 2021, 37(12): 1947-1954. https://doi.org/10.1007/s10114-021-0604-2

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  In this article, we showed that positive relative entropy implies mean Li-Yorke chaos along some good sequences in the fiber. Our result extended Li and Qiao's result in[Monatsh. Math., 186 (2018), 153-173].