中国科学院数学与系统科学研究院期刊网

15 March 2026, Volume 69 Issue 2
    

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  • A Weak Invariance Principle for Branching Process in a Random Environment
    Xulan Huang, Yingqiu Li, Chunhua Ma
    Acta Mathematica Sinica, Chinese Series. 2026, 69(2): 145-156. https://doi.org/10.12386/A20240125
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    In this paper, we study the supercritical branching process $(Z_{n})$ in an independent and identically distributed random environment $\xi=(\xi_{n})$. We first establish the weak invariance principle of $(\log Z_{n})_n$ under annealing distribution. Then we present a version of the almost everywhere central limit theorem.
  • Elliptic Gradient Estimates of Lu=∂u/∂t on Conformal Solitons
    Jingjing Yang, Guangwen Zhao
    Acta Mathematica Sinica, Chinese Series. 2026, 69(2): 157-165. https://doi.org/10.12386/A20240099
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    This paper proves elliptic gradient estimates for positive bounded solutions of the parabolic equation $\mathcal{L}u=\frac{\partial u}{\partial t}$ on conformal solitons given by general conformal vector fields. As a corollary, a Liouville type theorem is obtained. We also apply our main results to self-shrinkers, self-expanders and translating solitons.
  • Regular Wavelets and Characterization of Q Type Spaces via Caffarelli-Silvestre Extensions
    Jingsi Yang, Kai Zhao, Shujuan Zhou
    Acta Mathematica Sinica, Chinese Series. 2026, 69(2): 166-184. https://doi.org/10.12386/A20240124
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    In this paper, by the aid of regular wavelets, we extend the functions in the Q type spaces $\mathscr{Q}_{p,\lambda}^{\alpha}(\mathbb{R}^{n})$ to fractional harmonic functions on $\mathbb R^{n+1}_{+}$. Conversely, we introduce a trace operator to characterize the boundary value of solutions to Caffarelli-Silvestre extensions.
  • Global Well-Posedness of Classical Solutions to the Isentropic Compressible Navier-Stokes Equations with Anisotropic Viscous-Stress Tensor
    Hui Bai, Zhenhua Guo, Lei Xu
    Acta Mathematica Sinica, Chinese Series. 2026, 69(2): 185-226. https://doi.org/10.12386/A20240059
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    In this paper, the initial boundary value problem of isentropic compressible Navier-Stokes equations with anisotropic viscous stress tensors in a two-dimensional simply connected bounded domain is studied under slip boundary conditions. By means of energy analysis and compactness analysis, the existence and uniqueness of the global classical solution are proved under some small assumptions of the initial value and small perturbation of the viscous stress tensor. In addition, some exponential decay estimates of solutions are obtained.
  • Isolated Toughness Condition for Fractional (a, b, m)-covered Graphs
    Wei Gao, Weifan Wang, Yaojun Chen
    Acta Mathematica Sinica, Chinese Series. 2026, 69(2): 227-241. https://doi.org/10.12386/A20240147
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    A graph $G$ is called a fractional $(a, b, m)$-covered graph if for any $H\subseteq E(G)$ satisfying $|H|=m$, there exists a fractional $[a, b]$-factor (the corresponding fractional indicator function is denoted by $h$) such that $h(e)=1$ holds for any $e\in H$. This paper gives the bounds of isolated toughness and its variant for fractional $(a, b, m)$-covered graphs, and by counterexamples we show that the bounds are tight.
  • The Existence of Even Symmetric Periodic Solutions in the Comb-drive MEMS Model with Cubic Stiffness
    Xuhua Cheng, Rui Zhao
    Acta Mathematica Sinica, Chinese Series. 2026, 69(2): 242-254. https://doi.org/10.12386/A20240133
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    In this paper, we study the existence of the families of even symmetric periodic solutions in the Comb-drive MEMS model with a cubic nonlinear stiffness term. Based on the properties of the period of the solution of the corresponding autonomous system ($\delta=0$) and the Leray-Schauder continuation theorem, we derive that there are even periodic solutions emanating from parabolic periodic solutions of the corresponding autonomous system for all positive values of the $\delta\in(0,\widetilde{\Delta}_*]$.
  • Characterizing Line Graphs of Triangle-free Mixed Graphs
    Juan Liu, Hong Yang, Xindong Zhang, Hongjian Lai
    Acta Mathematica Sinica, Chinese Series. 2026, 69(2): 255-269. https://doi.org/10.12386/A20240159
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    The characterization of line graphs helps to simplify the structure of (di) graphs, explore graph isomorphism, study matching and covering problems in graphs, analyze connectivity, and compute graph properties. The characterization of line graphs is significant for graph theory and its applications in various fields. As two special cases of mixed graphs, graphs and digraphs have many existing results on the characterization of their line (di)graphs. This paper mainly focuses on the characterization of line graphs for mixed graphs. The main results obtained in this paper are as follows: Let $H$ be a connected mixed graph with at least four vertices. $H$ is the line graph of a triangle-free mixed graph if and only if the edges of $H$ can be divided into a $T_{F} $-set or $H^{U} $ is $\{K_{1,3}, K_{1,1,2}\} $-free and $H$ is $\mathcal{Q}$-free; Furthermore, for bipartite mixed graphs and tree mixed graphs, the characterization of their line graphs is obtained.
  • Complex Linear Differential Equations with Solutions in Average Radial Integrability Spaces
    Huayou Xie, Qingze Lin
    Acta Mathematica Sinica, Chinese Series. 2026, 69(2): 270-278. https://doi.org/10.12386/A20240071
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    In this paper, we first give a sufficient condition for all solutions of the $n$th-order complex linear differential equation $$ f^{(n)}+A_{n-1}(z)f^{(n-1)}+\cdots+A_1(z)f'+A_0(z)f=A_n(z) $$ to lie in average radial integrability spaces $RM(p,q)$, where $A_i(z) \, (i=1,\ldots,n)$ are analytic functions in the unit disc. In addition, we present a different sufficient condition for determining that all solutions of this equation lie in the weighted Bergman spaces.
  • A Note on T. Asai & T. Yoshida’s Conjecture
    Baijun Gao, Jinke Hai
    Acta Mathematica Sinica, Chinese Series. 2026, 69(2): 279-286. https://doi.org/10.12386/A20240105
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    Let $H$ be the direct product of a $2$-group $P_{2^m}$ of maximal class and the modular group $M_{p^n}$, and let $G$ be a finite group. Then the number of homomorphisms from $H$ to $G$ is divisible by the greatest common divisor of $|H/H'|$ and $|G|$, i.e., T. Asai & T. Yoshida's conjecture holds for $H$ and $G$.
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