中国科学院数学与系统科学研究院期刊网

28 July 2026, Volume 49 Issue 4
    

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  • Oscillatory and Asymptotic Behaviors of Third-order Dynamic Equations with Nonlinear Neutral Terms and Multiple Time Delays on Time Scales
    ZHAO CHUNRU
    Acta Mathematicae Applicatae Sinica. 2026, 49(4): 665-673. https://doi.org/10.20142/j.cnki.amas.202600064
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    This paper investigates the oscillation and asymptotic behavior of third-order dynamic equations with nonlinear neutral terms and multiple time delays. By applying the generalized Riccati transformation and inequality techniques, several new oscillation criteria are established. These theoretical results generalize and enrich the existing literature. Finally, illustrative example is provided to verify the validity of the obtained theorems.
  • Existence and Uniqueness of Weak Solutions for One-dimensional Semiconductor Equations
    CHEN MIAOCHAO, LIU QILIN
    Acta Mathematicae Applicatae Sinica. 2026, 49(4): 674-679. https://doi.org/10.20142/j.cnki.amas.202600052
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    This paper investigates the time-dependent drift-diffusion semiconductor equations on the one-dimensional torus, aiming to discuss the well-posedness of weak solutions under initial data of lower regularity. By applying appropriate variable transformations to the electron density, hole density and electrostatic potential, the original system is transformed into a coupled parabolic system in terms of sum and difference variables. Using the energy integral method, we obtain the key a priori estimates, and combine the Gagliardo-Nirenberg inequality and Gronwall inequality to prove the existence and uniqueness of weak solutions to the corresponding coupled system. It follows that the one-dimensional semiconductor equations admit a unique weak solution when the initial data \(n_0,p_0\in H^{-1}(\mathbb{T})\). This result improves the weak solution theory of semiconductor equations in the one-dimensional case and supplements the well-posedness results for low-dimensional semiconductor models.
  • Variable Selection and Estimation Method for Non-probability Sample Inference-based on Adaptive LASSO
    YANG JINGBO, ZHOU QI
    Acta Mathematicae Applicatae Sinica. 2026, 49(4): 680-697. https://doi.org/10.20142/j.cnki.amas.202501052
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    In this paper, we propose a method for variable selection in propensity score models for finite population inference using non-probability samples, when relevant auxiliary variables can be obtained from a probability sample. First, we incorporate an $L_1$ penalty term into the pseudo-maximum likelihood equation of the propensity score model to select important auxiliary variables, and prove that this selection method achieves both variable selection consistency and parameter estimation consistency. Next, based on the estimated propensity scores, we introduce an IPW estimator for the population mean, demonstrate the consistency of the estimator, and propose a variance estimation method. Simulation studies indicate that our proposed estimator is more robust and effective compared to methods that do not include variable selection or those using LASSO estimation. We also apply the proposed method to a non-probability sample collected by the Pew Research Center, utilizing relevant auxiliary information from the Current Population Survey dataset.
  • Studies on the Pullback Dynamical Behavior of a Class of Incompressible Non-Newtonian Micropolar Fluid Equations
    HUANG XIAOXIANG, CHEN KAILE, SUN WENLONG
    Acta Mathematicae Applicatae Sinica. 2026, 49(4): 698-718. https://doi.org/10.20142/j.cnki.amas.202600009
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    In this paper, we investigate the pullback dynamical behavior of a class of incompressible non-Newtonian micropolar equations in 2D bounded domains. First different from the classical method, we prove the existence of pullback attractors in $\widehat{V}$ by establishing a-prior estimates of the solutions and verifying that the process generated by the solution operator has pullback flattening property. Then, by slightly improve the regularity of the external force and moment, we apply the semigroup method and the $\varepsilon$-regularity method, combined with the space embedding theory, to prove the compactness of the pullback absorbing family in $\widehat{V}$.
  • A Study of Total Variation Regularization Methods for Option Pricing Inverse Problems
    YANG XINRUI, DENG ZUICHAY
    Acta Mathematicae Applicatae Sinica. 2026, 49(4): 719-738. https://doi.org/10.20142/j.cnki.amas.202600040
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    This paper investigates an inverse problem of determining implied volatility from average option prices. Based on the optimal control framework and total variation regularization, the problem is transformed into a terminal control problem. Due to the total variation term is non-differential, so it is hard to work out the uniqueness of optimal solution. In order to overcome this difficulty, a polished total variation regularization term is introduced. Furthermore, the existence and the necessary conditions of the optimal solution are discussed. Finally, it is proved that the uniqueness, stability of the minimizer is proved successfully when the terminal time is assumed to be relatively small. By introducing appropriate source conditions, the convergence of the minimal elements in the sense of the Bregman distance is proved, and an estimate of the convergence rate is given.
  • Construction of Supersaturated Design and Its Properties Based on Multiplicative Expansion Method
    LAI XINMIN, LONG KEYU, OU ZUJUN
    Acta Mathematicae Applicatae Sinica. 2026, 49(4): 739-756. https://doi.org/10.20142/j.cnki.amas.202600007
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    Supersaturated designs are frequently utilized in screening experiments for the purpose of identifying critical factors that have a significant impact on the response. This paper presents the construction of a class of supersaturated designs using level permutation and factor multiplication methods. The analytical relationships between these constructed supersaturated designs and their initial designs are discussed under the $E(f_{\rm NOD})$ criterion, the generalized minimum aberration criterion, and the minimum moment aberration criterion. It illustrates that if the initial design is optimal with respect to the $E(f_{\rm NOD})$ criterion, generalized minimum aberration criterion and minimum moment aberration criterion, then the resulting supersaturated design also is optimal under the same criteria and achieves the corresponding lower bounds. Numerical simulation examples show that the constructed supersaturated designs are effective for planning experimental arrangements.
  • Local Search Algorithm and Performance Analysis for Weakly Submodular Function Maximization with p-exchange System Constraint
    SHI MAJUN, WANG JINGJING, QIU LIHONG
    Acta Mathematicae Applicatae Sinica. 2026, 49(4): 757-770. https://doi.org/10.20142/j.cnki.amas.202501050
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    In this paper, we study the maximization problem of a non-negative monotone weakly submodular function under a $p$-exchange system $(p \geq 2)$ constraint, and propose a novel framework aimed at providing provable approximation guarantees for local search algorithms. We find that weak submodularity implies localizability for set function optimization, which can be used to offer theoretical support for local search algorithms. By integrating a partial enumeration technique into the local search algorithm, we prove that this combined approach achieves an approximation ratio of $\frac{\xi^2}{p-1+ \xi^2+\delta}$, where $0<\delta<1$ is a constant and $\xi$ represents the diminishing returns ratio of the set function. Specifically, when $\xi = 1$ (i.e., the objective function is a polymatroid function), our algorithm yields a better approximation ratio of $\frac{1}{p+\delta}$ compared to the greedy approximation ratio of $\frac{1}{p+1}$ provided by Calinescu et al. This work enhances the theoretical understanding and practical applicability of local search algorithms in the context of weakly submodular functions, offering new insights and tools for research in related fields.
  • The Uniformly Strong Consistency of the Generalized Edge Frequency Polygon Density Estimator under WOD Sequences
    LI YONGMING, TAN YALING
    Acta Mathematicae Applicatae Sinica. 2026, 49(4): 771-785. https://doi.org/10.20142/j.cnki.amas.202600010
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    In this paper, we investigate the generalized edge frequency polygon density estimation for widely orthant dependent(WOD) sequences. By using a Bernstein-type inequality, we establish the uniformly strong consistency of the proposed estimator under mild conditions. These results extend some existing ones in the literature. The validity of the results is further illustrated by numerical simulations.
  • Random Attractors for Non-autonomous Stochastic Modified Swift-Hohenberg Lattice Systems in Weighted Spaces
    WANG YAJUN, LI DING-SHI, LI BING
    Acta Mathematicae Applicatae Sinica. 2026, 49(4): 786-803. https://doi.org/10.20142/j.cnki.amas.202600008
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    In this paper, we mainly study the long-time dynamical behaviors of the non-autonomous stochastic modified Swift-Hohenberg lattice system with additive white noise in weighted space $l_{\sigma}^2$. Firstly, we present some the necessary and sufficient conditions for the existence of random attractors on space $l_\sigma^2$. Secondly, establish the well-posedness of solution of such system in weighted space. Then, through the uniform estimation of the solution, and we obtain the pullback asymptotically compact on the absorbing set by estimates on the tails of solutions. Finally, the existence and uniqueness of the pullback random attractor is proved.
  • Gradual Change Point Test of Trend Terms in Heavy-Tailed Financial Series
    JIANG DONG, XU TIANMING
    Acta Mathematicae Applicatae Sinica. 2026, 49(4): 804-826. https://doi.org/10.20142/j.cnki.amas.202501053
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    Trend characteristics are widespread in financial time series, and detecting change points in trend terms is a core problem in statistical inference. To address the challenge of detecting gradual structural changes in financial data, this study distinguishes the directions of trend changes and constructs two types of gradual change-point models, thereby overcoming the limitations of existing abrupt change-point models. To reduce the dependence of conventional cumulative sum (CUSUM) tests on variance estimation and improve their applicability, we propose ratio-type test statistics based on CUSUM functionals. We derive their limiting distributions under the null hypothesis and establish consistency under the alternative. Monte Carlo simulations show that, when the error terms follow infinite-variance heavy-tailed distributions, the ratio statistics have high testing power; the effects of different parameters on testing power are also compared. Finally, an empirical analysis of the 2020-2024 stock-price series of PetroChina and Sinopec confirms significant gradual changes in trend and demonstrates the effectiveness of the proposed method.
  • Credibility Estimation and Statistical Analysis of the Gini Coefficient
    WEN LIMIN, LIU YU, ZHANG YI
    Acta Mathematicae Applicatae Sinica. 2026, 49(4): 827-846. https://doi.org/10.20142/j.cnki.amas.202600047
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    The Gini coefficient is an important measure of income inequality. To improve the estimation accuracy of the Gini coefficient, this paper develops a Bayesian credibility estimation framework by combining sample information with prior information. By introducing a linearization approach for the population survival function and minimizing the expected weighted integrated loss function, we obtain the credibility estimator of the survival function, and then construct the credibility estimator of the Gini coefficient based on the “Plug-in” principle. Theoretical results show that the proposed estimator is consistent and asymptotically normal under large samples. In addition, simulation studies demonstrate its desirable mean squared error convergence performance in small-sample settings. Furthermore, using data from the China Household Income Project (CHIP), this paper proposes estimation methods for the hyperparameters and conducts an empirical analysis of the Gini coefficient in China. Compared with traditional estimators of the Gini coefficient, the proposed credibility estimator possesses favorable statistical properties, does not rely on specific prior distribution assumptions, and exhibits stronger robustness.
  • The Relaxed two-sweep Modulus-based Matrix Splitting Iteration Methods for Extended Second-order Cone Vertical Linear Complementarity Problem
    YU DONGMEIY, ZHANG YIMING, WEI HUILING
    Acta Mathematicae Applicatae Sinica. 2026, 49(4): 847-866. https://doi.org/10.20142/j.cnki.amas.202600065
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    In this paper, we propose a new class of relaxed two-sweep modulus-based matrix splitting (NRTMMS) iteration methods for solving the extended second-order cone vertical linear complementarity problem (ESOCVLCP) by reformulating the ESOCVLCP into a new implicit fixed-point iteration equation. The convergence results of the proposed methods are proved under the globally uniquely solvable (GUS) property of the ESOCVLCP. Numerical experiments are given to demonstrate the feasibility and effectiveness of the NRTMMS iteration methods.
  • Variational Bayesian Regularization Quantile Regression
    WANG WEIXIAN, ZHANG JUANJUAN, TIAN MAOZAI
    Acta Mathematicae Applicatae Sinica. 2026, 49(4): 867-893. https://doi.org/10.20142/j.cnki.amas.202600063
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    Regularization methods in quantile regression can improve the predictive capability of the model, and Bayesian estimation is generally superior to frequentist estimation. For the three common regularization quantile regression models: Lasso quantile regression, Elastic Net quantile regression, and Fused Lasso quantile regression, they can all be obtained through specific priors in the Bayesian framework. This article presents a hierarchical representation of these three Bayesian quantile regression models, assuming that the posterior of the model parameters is independent, and uses the Variational Bayesian (VB) algorithm to obtain the unconditional posterior of each parameter. Simulation studies show that there is little difference in estimation accuracy between VB algorithm's regularized quantile regression and MCMC algorithm's regularized quantile regression, and the running time of the VB algorithm is much shorter than that of the MCMC algorithm in high-dimensional settings. Therefore, the algorithm proposed in this article is more suitable for high-dimensional quantile regression models.
  • Nonparametric Estimates Based on Laguerre Polynomials
    JIANG YONGSHENG, REN XIUMEI, DONG CHAOHUA
    Acta Mathematicae Applicatae Sinica. 2026, 49(4): 894-910. https://doi.org/10.20142/j.cnki.amas.202501054
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    This paper studies the nonparametric model $y_t=g(x_t)+e_t, t=1,\cdots,n,$ where ${x_t}$ is a stationary time series with support on a semi-infinite interval, and the conditional mean function $g(\cdot)$ is defined on the same restricted domain. Based on Laguerre orthogonal polynomial expansions, we develop an orthogonal series estimator for $g(\cdot)$ and establish its associated central limit theorem. The Monte Carlo simulations demonstrate that the proposed nonparametric estimator performs well in finite samples.
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