中国科学院数学与系统科学研究院期刊网

15 March 2025, Volume 41 Issue 2
    

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    ARTICLES
  • The Local Poincaré Inequality of Stochastic Dynamic and Application to the Ising Model
    Kai-yuan CUI, Fu-zhou GONG
    Acta Mathematicae Applicatae Sinica(English Series). 2025, 41(2): 305-336. https://doi.org/10.1007/s10255-025-0001-1
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    Inspired by the idea of stochastic quantization proposed by Parisi and Wu, we reconstruct the transition probability function that has a central role in the renormalization group using a stochastic differential equation. From a probabilistic perspective, the renormalization procedure can be characterized by a discrete-time Markov chain. Therefore, we focus on this stochastic dynamic, and establish the local Poincaré inequality by calculating the Bakry-Émery curvature for two point functions. Finally, we choose an appropriate coupling relationship between parameters $K$ and $T$ to obtain the Poincaré inequality of two point functions for the limiting system. Our method extends the classic Bakry-Émery criterion, and the results provide a new perspective to characterize the renormalization procedure.
  • Some New Results on Majority Coloring of Digraphs
    Jian-sheng CAI, Wei-hao XIA, Gui-ying YAN
    Acta Mathematicae Applicatae Sinica(English Series). 2025, 41(2): 337-343. https://doi.org/10.1007/s10255-025-0002-0
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    A majority coloring of a directed graph is a vertex-coloring in which every vertex has the same color as at most half of its out-neighbors. Kreutzer et al. conjectured that every digraph is majority 3-colorable. For an integer $k\geq 2$, $\frac{1}{k}$-majority coloring of a directed graph is a vertex-coloring in which every vertex $v$ has the same color as at most $\frac{1}{k}d^+(v)$ of its out-neighbors. a $\frac{1}{k}$-majority coloring of a digraph is a coloring of the vertices such that each vertex receives the same color as at most a $\frac{1}{k}$ proportion of its out-neighbors. Girão et al. proved that every digraph admits a $\frac{1}{k}$-majority $2k$-coloring. In this paper, we prove that Kreutzer's conjecture is true for digraphs under some conditions, which improves Kreutzer's results, also we obtained some results of $\frac{1}{k}$-majority coloring of digraphs. Moreover, we discuss the majority 3-coloring of random digraphs with some conditions.
  • Blow up, Growth and Decay of Solutions for Class of a Coupled Nonlinear Viscoelastic Kirchhoff Equations with Variable Exponents and Fractional Boundary Conditions
    Abdelbaki CHOUCHA, Salah BOULAARAS, Djamel OUCHENANE, Rashid JAN
    Acta Mathematicae Applicatae Sinica(English Series). 2025, 41(2): 344-374. https://doi.org/10.1007/s10255-024-1150-3
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    We examine a quasilinear system of viscoelastic equations in this study that have fractional boundary conditions, dispersion, source, and variable-exponents. We discovered that the solution of the system is global and constrained under the right assumptions about the relaxation functions and initial conditions. After that, it is demonstrated that the blow-up has negative initial energy. Subsequently, the growth of solutions is demonstrated with positive initial energy, and the general decay result in the absence of the source term is achieved by using an integral inequality due to Komornik.
  • Constrained Stochastic Recursive Linear Quadratic Optimal Control Problems and Application to Finance
    Liang-quan ZHANG, Qing ZHOU
    Acta Mathematicae Applicatae Sinica(English Series). 2025, 41(2): 375-399. https://doi.org/10.1007/s10255-024-1157-9
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    In this paper, we focus on a control-constrained stochastic LQ optimal control problem via backward stochastic differential equation (BSDE in short) with deterministic coefficients. One of the significant features in this framework, in contrast to the classical LQ issue, embodies that the admissible control set needs to satisfy more than the square integrability. By introducing two kinds of new generalized Riccati equations, we are able to announce the explicit optimal control and the solution to the corresponding H-J-B equation. A linear quadratic recursive utility portfolio optimization problem in the financial engineering is discussed as an explicitly illustrated example of the main result with short-selling prohibited. Feasibility of the mean-variance portfolio selection problem via BSDE for a financial market is characterized, and associated efficient portfolios are given in a closed form.
  • Adapted Runge-Kutta Methods for Nonlinear First-Order Delay BVPs with Time-variable Delay
    Cheng-jian ZHANG, Yang WANG, Hao HAN
    Acta Mathematicae Applicatae Sinica(English Series). 2025, 41(2): 400-413. https://doi.org/10.1007/s10255-024-1145-0
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    This paper deals with numerical solutions for nonlinear first-order boundary value problems (BVPs) with time-variable delay. For solving this kind of delay BVPs, by combining Runge-Kutta methods with Lagrange interpolation, a class of adapted Runge-Kutta (ARK) methods are developed. Under the suitable conditions, it is proved that ARK methods are convergent of order $\min\{p,\mu\!+\!\nu\!+\!1\}$, where $p$ is the consistency order of ARK methods and $\mu,\nu$ are two given parameters in Lagrange interpolation. Moreover, a global stability criterion is derived for ARK methods. With some numerical experiments, the computational accuracy and global stability of ARK methods are further testified.
  • Uniqueness and Nondegeneracy of Positive Solutions of General Kirchhoff Type Equations
    Yu-ting KANG, Peng LUO, Chang-lin XIANG, Xue-xiu ZHONG
    Acta Mathematicae Applicatae Sinica(English Series). 2025, 41(2): 414-424. https://doi.org/10.1007/s10255-023-1062-7
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    In the present paper, we study uniqueness and nondegeneracy of positive solutions to the general Kirchhoff type equations $$-M\Big(\int_{ R^N}|\nabla v|^2 dx\Big)\Delta v=g(v) \qquad \hbox{in} R^N, $$ where $M:[0,+\infty)\mapsto R$ is a continuous function satisfying some suitable conditions and $v\in H^1(R^N)$. Applying our results to the case $M(t)=at+b$, $a,b>0$, we make it clear all the positive solutions for all dimensions $N\geq 1$. Our results can be viewed as a generalization of the corresponding results of Li et al. [JDE, 2020, 268, Section 1.2].
  • Ramsey and Gallai-Ramsey Numbers of Cycles and Books
    Mei-qin WEI, Ya-ping MAO, Ingo SCHIERMEYER, Zhao WANG
    Acta Mathematicae Applicatae Sinica(English Series). 2025, 41(2): 425-440. https://doi.org/10.1007/s10255-025-0009-6
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    Given two non-empty graphs $G,H$ and a positive integer $k$, the Gallai-Ramsey number $\operatorname{gr}_k(G:H)$ is defined as the minimum integer $N$ such that for all $n\geq N$, every exact $k$-edge-coloring of $K_n$ contains either a rainbow copy of $G$ or a monochromatic copy of $H$. Denote $\operatorname{gr}'_k(G:H)$ as the minimum integer $N$ such that for all $n\geq N$, every edge-coloring of $K_n$ using at most $k$ colors contains either a rainbow copy of $G$ or a monochromatic copy of $H$. In this paper, we get some exact values or bounds for $\operatorname{gr}_k(P_5:H)$ and $\operatorname{gr}'_k(P_5:H)$, where $H$ is a cycle or a book graph. In addition, our results support a conjecture of Li, Besse, Magnant, Wang and Watts in 2020.
  • General Minimum Lower-order Confounding Split-plot Designs with Important Subplot Factors
    Tao SUN, Sheng-li ZHAO
    Acta Mathematicae Applicatae Sinica(English Series). 2025, 41(2): 441-455. https://doi.org/10.1007/s10255-024-1027-5
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    In this paper, we consider the regular $s$-level fractional factorial split-plot (FFSP) designs when the subplot (SP) factors are more important. The idea of general minimum lower-order confounding criterion is applied to such designs, and the general minimum lower-order confounding criterion of type SP (SP-GMC) is proposed. Using a finite projective geometric formulation, we derive explicit formulae connecting the key terms for the criterion with the complementary set. These results are applied to choose optimal FFSP designs under the SP-GMC criterion. Some two- and three-level SP-GMC FFSP designs are constructed.
  • Large Deviations for a Critical Galton-Watson Branching Process
    Dou-dou LI, Wan-lin SHI, Mei ZHANG
    Acta Mathematicae Applicatae Sinica(English Series). 2025, 41(2): 456-478. https://doi.org/10.1007/s10255-024-1058-y
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    In this paper, a critical Galton-Watson branching process $\{Z_{n}\}$ is considered. Large deviation rates of $S_{Z_n}:=\sum\limits_{i=1}^{Z_n} X_i$ are obtained, where $\{X_i, \ i\geq 1\}$ is a sequence of independent and identically distributed random variables and $X_1$ is in the domain of attraction of an $\alpha$-stable law with $\alpha\in(0,2)$. One shall see that the convergence rate is determined by the tail index of $X_1$ and the variance of $Z_1$. Our results can be compared with those ones of the supercritical case.
  • Quantile Regression under Truncated, Censored and Dependent Assumptions
    Chang-sheng LIU, Yun-jiao LU, Si-li NIU
    Acta Mathematicae Applicatae Sinica(English Series). 2025, 41(2): 479-497. https://doi.org/10.1007/s10255-024-1034-6
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    In this paper, we focus on the problem of nonparametric quantile regression with left-truncated and right-censored data. Based on Nadaraya-Watson (NW) Kernel smoother and the technique of local linear (LL) smoother, we construct the NW and LL estimators of the conditional quantile. Under strong mixing assumptions, we establish asymptotic representation and asymptotic normality of the estimators. Finite sample behavior of the estimators is investigated via simulation, and a real data example is used to illustrate the application of the proposed methods.
  • Time-dependent Global Attractors for the Nonclassical Diffusion Equations with Fading Memory
    Yu-ming QIN, Xiao-ling CHEN
    Acta Mathematicae Applicatae Sinica(English Series). 2025, 41(2): 498-512. https://doi.org/10.1007/s10255-024-1036-4
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    In this paper, we discuss the long-time behavior of solutions to the nonclassical diffusion equation with fading memory when the nonlinear term $f$ satisfies critical exponential growth and the external force $ g(x)\in L^{2}(\Omega)$. In the framework of time-dependent spaces, we verify the existence of absorbing sets and the asymptotic compactness of the process, then we obtain the existence of the time-dependent global attractor $\mathscr{A}=\{A_t\}_{t\in \mathbb{R}}$ in $\mathcal{M}_t$. Furthermore, we achieve the regularity of $\mathscr{A}$, that is, $A_t$ is bounded in $\mathcal{M}_t^1$ with a bound independent of $t$.
  • Global Existence and Boundedness for the Attraction-repulsion Keller-Segel Model with Volume Filling Effect
    Jian DENG
    Acta Mathematicae Applicatae Sinica(English Series). 2025, 41(2): 513-524. https://doi.org/10.1007/s10255-025-0020-y
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    This paper is concerned with the attraction-repulsion Keller-Segel model with volume filling effect. We consider this problem in a bounded domain $\Omega\subset \mathbb R^3$ under zero-flux boundary condition, and it is shown that the volume filling effect will prevent overcrowding behavior, and no blow up phenomenon happen. In fact, we show that for any initial datum, the problem admits a unique global-in-time classical solution, which is bounded uniformly. Previous findings for the chemotaxis model with volume filling effect were derived under the assumption $0\le u_0(x)\le 1$ with $\rho(x,t)\equiv 1$. However, when the maximum size of the aggregate is not a constant but rather a function $\rho(x,t)$, ensuring the boundedness of the solutions becomes significantly challenging. This introduces a fundamental difficulty into the analysis.
  • Analogy of Fan-type Condition on Weak Cycle Partition of Graphs
    Xiao-dong CHEN, Qing JI, Zhi-quan HU
    Acta Mathematicae Applicatae Sinica(English Series). 2025, 41(2): 525-535. https://doi.org/10.1007/s10255-025-0008-7
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    For a graph $G$ of order $n$ and a positive integer $k,$ a $k$-weak cycle partition of $G$, called $k$-WCP, is a sequence of vertex disjoint subgraphs $H_1,H_2,\cdots,H_k$ of $G$ with $\bigcup_{i=1}^{k}V(H_i)=V(G),$ where $H_i$ is isomorphic to $K_1,K_2$ or a cycle. Let $\sigma_2(G)=\min\{d(x)+d(y):xy\notin E(G),x,y\in V(G)\}.$ Hu and Li [Discrete Math. 307(2007)] proved that if $G$ is a graph of order $n\ge k+12$ with a $k$-WCP and $\sigma_2(G)\ge \frac{2n+k-4}{3},$ then $G$ contains a $k$-WCP with at most one subgraph isomorphic to $K_2.$ In this paper, we generalize their result on the analogy of Fan-type condition that $\max\{d(x),d(y)\}\ge \frac{2n+k-4}{6}$ for each pair of nonadjacent vertices $x,y\in V(G).$
  • Inverse Scattering Transform and Multi-soliton Solutions for the Sextic Nonlinear Schrödinger Equation
    Xin WU, Shou-fu TIAN, Jin-Jie YANG
    Acta Mathematicae Applicatae Sinica(English Series). 2025, 41(2): 536-555. https://doi.org/10.1007/s10255-025-0004-y
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    In this work, we consider the inverse scattering transform and multi-soliton solutions of the sextic nonlinear Schrödinger equation. The Jost functions of spectral problem are derived directly, and the scattering data with $t=0$ are obtained accordingly to analyze the symmetry and other related properties of the Jost functions. Then we make use of translation transformation to get the relation between potential and kernel, and recover potential according to Gel'fand-Levitan-Marchenko (GLM) integral equations. Furthermore, the time evolution of scattering data is considered, on the basis of that, the multi-soliton solutions are derived. In addition, some solutions of the equation are analyzed and revealed its dynamic behavior via graphical analysis, which could enrich the nonlinear phenomena of the sextic nonlinear Schrödinger equation.
  • A Regularization Smoothing Newton Method for the Symmetric Cone Complementarity Problem with the Cartesian P0-property
    Xiang-jing LIU, San-yang LIU
    Acta Mathematicae Applicatae Sinica(English Series). 2025, 41(2): 556-572. https://doi.org/10.1007/s10255-025-0007-8
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    In this paper, we consider the symmetric cone linear complementarity problem with the Cartesian $P_0$-property and present a regularization smoothing method with a nonmonotone line search to solve this problem. It has been demonstrated that the proposed method exhibits global convergence under the condition that the solution set of the complementarity problem is nonempty. This condition is less stringent than those that have appeared in some existing literature. We also show that the method has locally quadratic convergence under appropriate conditions. Some experimental results are reported to illustrate the efficiency of the proposed method.
  • Central Limit Theorem, Moderate Deviation and an Upper Bound of Large Deviation for Multivariate Marked Hawkes Processes
    Ming-zhou XU, Kun CHENG, Yun-zheng DING
    Acta Mathematicae Applicatae Sinica(English Series). 2025, 41(2): 573-587. https://doi.org/10.1007/s10255-025-0006-9
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    We study a multivariate linear Hawkes process with random marks. In this paper, we establish that a central limit theorem, a moderate deviation principle and an upper bound of large deviation for multivariate marked Hawkes processes hold.
  • The Lindley-Weibull Distribution
    Jun-mei JIA, Zai-zai YAN, Xiu-yun PENG
    Acta Mathematicae Applicatae Sinica(English Series). 2025, 41(2): 588-600. https://doi.org/10.1007/s10255-025-0003-z
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    In this paper, a new distribution named the Lindley-Weibull distribution which combines Lindley and Weibull distributions by using the method of T-X family is introduced. This distribution offers a more flexible model for lifetime data. We study its statistical properties include the shapes of density and hazard rate, residual and reversed residual lifetime, moment, moment generating functions, conditional moment, conditional moment generating, quantiles functions, mean deviations, Rényi entropy, Bonferroni and Loren curves. The distribution is capable of modeling increasing, decreasing, upside-down bathtub and decreasing-increasing-decreasing hazard rate functions. The method of maximum likelihood is adopted for estimating the model parameters. The potentiality of the new model is illustrated by means of one real data set.
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