中国科学院数学与系统科学研究院期刊网

28 September 2025, Volume 48 Issue 5
    

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  • Ridge Estimators of Lognormal Mode Regression Model
    ZHANG Jiaming, WU Liucang
    Acta Mathematicae Applicatae Sinica. 2025, 48(5): 675-691. https://doi.org/10.20142/j.cnki.amas.202401079
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    With the continuous prosperity of the national economy and social progress, more and more economic and engineering data have multicollinearity and skewed thick tail characteristics. Traditional models cannot solve this type of data and are prone to instability. This paper proposes the lognormal mode regression model for the first time and studies ridge estimators statistical inference. The Gauss-Newton iteration method, fixed point iteration method, and mutual iteration method are used to solve the maximum likelihood estimations of parameters. Monte Carlo simulations show the effectiveness of the model and algorithm, and the Gauss-Newton iteration has the best solution effect, and example analysis shows that the lognormal mode regression model has high accuracy and robustness, superior to the mean regression model.
  • Tolerance Interval for the Mixture Gamma Distribution
    JIAO Junjun, CHENG Weihuy, ZHAO Xu
    Acta Mathematicae Applicatae Sinica. 2025, 48(5): 692-708. https://doi.org/10.20142/j.cnki.amas.202501037
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    Gamma mixture distribution has wide applications in reliability, hydrology and finance fields. Constructing a tolerance interval for the mixture distribution is a challenging task owing to the complexity the mixture structure. In this study, the wilson-Hilferty(WH) normal-based approximation combined with the popular clustering algorithm for Gaussian mixtures namely, model-based clustering(MCLUST) is used to obtain the maximum likelihood estimation(MLE) for the parameters of the Gamma mixture distribution, and then construct the tolerance intervals for the mixture gamma distribution based on the asymptotic normality of the MLE of the quantile. In addition, The accuracy of the tolerance intervals is improved by Bootstrap calibration. At the end, using various simulation studies and real datasets, we compare alternative tolerance intervals and show that the new tolerance interval is highly competitive.
  • Moment Estimates for a Linear Mean-field Stochastic Differential Equation
    PEI Bochao, WANG Yan
    Acta Mathematicae Applicatae Sinica. 2025, 48(5): 709-720. https://doi.org/10.20142/j.cnki.amas.202501041
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    The paper investigates a class of linear mean-field stochastic differential equations (SDE), where the driving process is a Brownian motion, and its drift and diffusion coefficients are linear functionals of the system state and its mathematical expectation. Utilizing theoretical tools such as Itô's formula, Hölder's inequality, Jensen's inequality, etc., we derive moment estimates for the solutions of the SDE. In the context of stochastic control theory, this result plays a crucial role in establishing the maximum principle for mean-field stochas-tic optimal control problems.
  • Two Classes of Asymptotically Optimal Codebooks Based on Hybrid Character Sums
    YANG Mengjie, HENG Zilingy, LI Xiaoru
    Acta Mathematicae Applicatae Sinica. 2025, 48(5): 721-736. https://doi.org/10.20142/j.cnki.amas.202401060
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    Codebooks with small correlation values have important applications in CDMA communication, coding theory, compressed sensing and many other fields. A codebook whose parameters achieve the Welch bound with equality is called an optimal codebook. However, there are only a few known optimal codebooks in the literature whose parameters are not flexible enough. Recently, Ziling Heng and Fuling Chen studied some classes of hybrid character sums in (Journal of Algebra, 2023, 634: 790-831). Based on the hybrid character sums in this reference, two families of complex codebooks asymptotically achieve the Welch bound are constructed in this paper. Compared with known codebooks, these two families of codebooks have new parameters.
  • Random Uniform Attractors for Non-autonomous Stochastic p-Laplacian Lattice Equation
    ZENG Tianhao, HE Manlu, LI Ding-shi
    Acta Mathematicae Applicatae Sinica. 2025, 48(5): 737-750. https://doi.org/10.20142/j.cnki.amas.202401082
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    In this paper, we mainly consider the existence of uniform random attractors on space $l^2$ for nonautonomous stochastic $p$-Laplacian lattice equation driven by multiplicative noise. Firstly, we present some the necessary and sufficient conditions for the existence of uniform random attractors on space $l^2$. Secondly, by using the Ornstein-Uhlenbeck process, a reversible variable substitution is constructed to transform the non-autonomous stochastic $p$-Laplacian lattice equation (SDE) with multiplicative noise into a non-autonomous random $p$-Laplacian lattice equation (RDE) without multiplicative noise. It is proved that the solution of the RDE system can define a jointly continuous non-autonomous random dynamical system. Then, through the uniform estimation of the solution, we obtain that the equation has a closed uniformly pullback absorbing set with respect to the symbol space, and the solution is uniformly pullback asymptotically compact on the absorbing set. Finally, the existence and uniqueness of the uniform random attractor is proved by using the existence theorem of the uniform random attractor.
  • Global Dynamics Analysis of a Delayed Discrete Model with Nonlinear Incidence
    XU Jinhu, HUANG Guokun
    Acta Mathematicae Applicatae Sinica. 2025, 48(5): 751-764. https://doi.org/10.20142/j.cnki.amas.202501040
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    Since some classical numerical discrete methods are not often successfully in preserving the quantitative properties of corresponding continuous model. Thus, it is necessary to find a suitable numerical scheme for keeping the main dynamical properties of the corresponding continuous model. In this paper, a numerical method for a delayed model with nonlinear incidence rate was investigated by utilizing non-standard finite difference scheme. The positivity and boundedness of solutions were carried out, then by constructing discrete Lyapunov functionals, it shown that the global stabilities of equilibria are completely determined by the basic reproduction number for viral infection and for immune response. The results indicate that dynamical consistency between the discrete model and its corresponding continuous model.
  • Last Passage Percolation with Bounded Edge Passage Time on Complete Graph
    GUO Yameng, WANG Feng, WU Xianyuan
    Acta Mathematicae Applicatae Sinica. 2025, 48(5): 765-778. https://doi.org/10.20142/j.cnki.amas.202401087
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    Let $G_{n}=\big([n],E_{n}\big)$ be the complete graph. Denoted by $W_n$ the largest passage time among all self-avoiding paths from vertex 1 to vertex $n$. Let $\mu$ be the time constant of the model. $i.e.$ the essential supremum of the edge passage time $X_{e}$ (in the present paper we consider the case of $ \mu<\infty $, without loss of generality, assume that $ \mu=1 $). This paper focuses on the problem for the divergence rate of $n-W_n$ while $n$ tends to infinity. Actually, for three cases of the decay rate of the tail probability of $X_e$ respectively, we first give the upper and lower bounds to $n-\mathbb E(W_n)$, then by estimating the variance of $W_n$ appropriately, we give upper bounds to $n-W_n$.
  • Transmission Dynamics of an Aids Model with Heterogeneity of Infection Risk: Protective Effects of Condom Among Gay Men
    MA Xia, GUO Zunguang, LUO Xiaofeng
    Acta Mathematicae Applicatae Sinica. 2025, 48(5): 779-798. https://doi.org/10.20142/j.cnki.amas.202501038
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    This paper mainly investigated the transmission dynamics of AIDS model with heterogeneity of infection risk and the protective effect of condoms among gay men. Firstly, the basic reproduction number $R_0$ was defined by the method of Next generation matrix, and the threshold dynamics of the model were analyzed. Secondly, the least squares and Monte Carlo methods were utilized to fit the actual data of HIV/AIDS in China from 2012 to 2019, and the basic reproduction number was estimated to be $R_0 = 1.4386$, and the epidemic transmission trend of HIV/AIDS in China in the next ten years was predicted. Finally, the effect of publicity and education and the usage coverage of condoms among gay men on the risk of HIV transmission were demonstrated. The results illustrated that when the coverage rate of condom reached 0.71 or the propaganda and education level was greater than 0.3, the outbreak of HIV/AIDS could be effectively controlled. The sensitivity analysis of $R_0$ discovered that expanding the level of publicity and education for the susceptible population and gay men, increasing the usage of condoms for gay men, popularizing HIV screening and testing could reduce the basic reproduction number, thereby delaying the transmit speed of AIDS. The research findings could provide suggestions for the control of AIDS to the public health department.
  • Learning Performance of the Perceptron Model Based on Markov Sampling
    HU Shulan, QIAN Zhiyong, WANG Renhe, WANG Xinyu
    Acta Mathematicae Applicatae Sinica. 2025, 48(5): 799-813. https://doi.org/10.20142/j.cnki.amas.202501042
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    The perceptron model is an essential algorithm in machine learning and artificial intelligence, functioning as a linear classifier for binary classification tasks. This paper investigates the learning performance of the perceptron model based on Markov sampling, which builds upon the traditional framework with independent and identically distributed samples. Initial efforts establish the constraints on the perceptron model's learning performance with uniformly ergodic Markov chain samples and validates its consistent behavior. Furthermore, the paper introduces a ueMC-PM algorithm. Numerical investigations undertaken on benchmark repositories reveal that the perceptron model utilizing ueMC samples yields fewer misclassification rates.
  • Determining Nodes of 2D Non-autonomous Micropolar Fluid Flows with Infinite Delay
    HUANG Xiaoxiang, SUN Wenlong, GE Huanzhi, LIANG Yunyun
    Acta Mathematicae Applicatae Sinica. 2025, 48(5): 814-828. https://doi.org/10.20142/j.cnki.amas.202501033
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    In this paper, the asymptotic behavior of a non-autonomous micropolar fluid flows with infinite delay term is studied in 2D bounded domains, precisely, the number of determining nodes to the system is estimated. The results show that the long time behavier of the strong solution can be determined by its values on a finite number of points.
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