中国科学院数学与系统科学研究院期刊网

15 July 2025, Volume 41 Issue 7
    

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  • Ling Chen
    Acta Mathematica Sinica. 2025, 41(7): 1717-1752. https://doi.org/10.1007/s10114-025-3419-8
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    We study inhomogeneous oscillator representations of the strange Lie superalgebras $P(n)$ on supersymmetric polynomial algebras and on spaces of supersymmetric exponential-polynomial functions. We obtain the composition series for these representations. The obtained irreducible modules are infinite dimensional. Some of them are not of highest-weight type and even not weight modules.
  • Yutao Ma, Yonghua Mao, Siyu Wang
    Acta Mathematica Sinica. 2025, 41(7): 1753-1774. https://doi.org/10.1007/s10114-025-3133-6
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    We consider $\beta$-Jacobi ensembles with parameters $p_1, p_2\ge n.$ We prove that the empirical measure of the rescaled $\beta$-Jacobi ensembles converges weakly to a modified Wachter law via the spectral measure method. We also provide the central limit theorem and the large deviation for the corresponding rescaled spectral measure.
  • Gaohuizi Feng, Pengtong Li
    Acta Mathematica Sinica. 2025, 41(7): 1775-1788. https://doi.org/10.1007/s10114-025-3332-1
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    An operator $T$ on a complex separable infinite dimensional Hilbert space is hypercyclic if there is a vector $y\in\mathcal{H}$ such that the orbit ${\rm Orb}(T,y)=\{y, Ty, T^{2}y, T^{3}y,\ldots\}$ is dense in $\mathcal{H}$. Hypercyclic property and supercyclic proeprty are liable to fail for $2\times 2$ upper triangular operator matrices. In this paper, we aim to explore and characterize the hypercyclicity and the supercyclicity for $2\times 2$ upper triangular operator matrices. We obtain a spectral characterization of the norm-closure of the class of all hypercyclic (supercyclic) operators for $2\times 2$ upper triangular operator matrices.
  • Huaming Wang
    Acta Mathematica Sinica. 2025, 41(7): 1789-1806. https://doi.org/10.1007/s10114-025-4035-3
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    Consider a branching process $\{Z_n\}_{n\ge 0}$ with immigration in varying environments. For $a\in\{0,1,2,\dots\},$ let $C(a)=\{n\ge0:Z_n=a\}$ be the collection of times at which the population size of the process attains level $a.$ We give a criterion to determine whether the set $C(a)$ is finite or not. For the critical Galton–Watson process, based on a moment method, we show that $\frac{|C(a)\cap [1,n]|}{\log n\rightarrow S}$ in distribution, where $S$ is an exponentially distributed random variable with $P(S>t)={\rm e}^{-t},\ t>0.$
  • Meizhong Wang, Jiecheng Chen, Dashan Fan, Ziyao Liu
    Acta Mathematica Sinica. 2025, 41(7): 1807-1831. https://doi.org/10.1007/s10114-025-3294-3
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    In the article we study the solution $u( x,t) $ of the Cauchy problem of linear damped fractional wave equation. We prove that $u( x,t) $ has some sharp boundedness estimates on the Triebel–Lizorkin space. The proof of the necessity part is based on obtaining the precise asymptotic forms of the kernels of operators ${\rm e}^{-t}{\rm cosh}(t\sqrt{L})$ and ${\rm e}^{-t}\frac{{\rm sinh}(t\sqrt{L})}{\sqrt{L}}$ with $L=1-\vert\Delta\vert^{\alpha},$ where $\Delta$ is the Laplacian, as well as the method of stationary phase. Additionally, we study the Riesz mean of the solution and show its convergence in the Triebel–Lizorkin space norm.
  • Hang Chen, Yaru Wang
    Acta Mathematica Sinica. 2025, 41(7): 1832-1854. https://doi.org/10.1007/s10114-025-3379-z
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    In this paper, we study the rigidity of $k(\ge 1)$-extremal submanifolds in a sphere and prove various pinching theorems under different curvature conditions, including sectional and Ricci curvatures in pointwise and integral sense.
  • Yanyue Shi, Yunpeng Li, Bo Zhang, Yufeng Lu
    Acta Mathematica Sinica. 2025, 41(7): 1855-1867. https://doi.org/10.1007/s10114-025-3195-5
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    On the classical Bergman space, Toeplitz operators with radial symbols are diagonal and those operators commute. However, on the $n$-analytic Bergman space $A^{2}_{n}(\mathbb{D})$ when $n\geq 2$, the case is different. In this paper, our focus is on the problem of commuting Toeplitz operators with quasihomogeneous symbols, specifically in the context of the function space $A^{2}_{2}(\mathbb{D})$. We show a kind of block matrice expression of Toeplitz operators on $A^{2}_{2}(\mathbb{D})$. Based on the block expression, we give several important properties. Our results indicate that in some cases, two Toeplitz operators are commutative if and only if both operators are analytic or differ by a constant multiple.
  • Tianqi Feng, Jun Zhao, Liangyun Chen, Chenrui Yao
    Acta Mathematica Sinica. 2025, 41(7): 1868-1890. https://doi.org/10.1007/s10114-025-3220-8
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    Perfect and complete Lie conformal algebras will be discussed in this paper. We give the characterizations of complete Lie conformal algebras. We demonstrate that every perfectly complete Lie conformal algebra can be uniquely decomposed to a direct sum of indecomposable perfectly complete ideals. And we show the existence of a sympathetic decomposition in every perfect Lie conformal algebra. Finally, we study a class of ideals of Lie conformal algebras such that the quotients are perfectly complete Lie conformal algebras.
  • Chengbin Xu
    Acta Mathematica Sinica. 2025, 41(7): 1891-1905. https://doi.org/10.1007/s10114-025-4015-7
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    In this paper, we study the long-time behavior of global solutions to the Schrödinger–Choquard equation $${\rm i}\partial_tu+\Delta u=-(I_\alpha\ast|\cdot|^b|u|^{p})|\cdot|^b|u|^{p-2}u.$$ Inspired by Murphy who gave a simple proof of scattering for the non-radial INLS, we find that the inhomogeneous term $|x|^b$ can replace the radial Sobolev embedding theorem, which allows us to prove scattering theory below the ground state for the intercritical case in energy space without radial assumption.
  • Yong Chen
    Acta Mathematica Sinica. 2025, 41(7): 1906-1922. https://doi.org/10.1007/s10114-025-3217-3
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    In this paper, we discuss the concept of HN-semipositive,(HN-positive) vector bundle and also introduce strongly HN-semipositive vector bundle over compact complex manifold. Let $M$ be a projective manifold with HN-semipositive tangent bundle. If $M$ is rationally connected, we show that $T^{1,0}M$ is strongly HN-positive. We give a characterization of rationally connected compact Kähler manifolds with strongly HN-semipositive tangent bundle. In the second part, we show that a uniformly RC $k$-positivity implies mean curvature positivity.
  • Xianfa Hu, Yonglei Fang, Bin Wang
    Acta Mathematica Sinica. 2025, 41(7): 1923-1943. https://doi.org/10.1007/s10114-025-4348-2
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    In this paper, we formulate two new families of fourth-order explicit exponential Runge–Kutta (ERK) methods with four stages for solving first-order differential systems $y^{\prime}(t)+My(t)=f(y(t))$. The order conditions of these ERK methods are derived by comparing the Taylor series of the exact solution, which are exactly identical to the order conditions of explicit Runge–Kutta methods, and these ERK methods reduce to classical Runge–Kutta methods once $M\rightarrow \mathbf{0}$. Moreover, we analyze the stability properties and the convergence of these new methods. Several numerical examples are implemented to illustrate the accuracy and efficiency of these ERK methods by comparison with standard exponential integrators.
  • Jiaqun Wei
    Acta Mathematica Sinica. 2025, 41(7): 1944-1952. https://doi.org/10.1007/s10114-025-4309-9
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    Let $A$ be an Artin algebra and $M$ be a presilting radical complex. We show that $M$ is silting provided its some left part or some right part is silting.