中国科学院数学与系统科学研究院期刊网

28 March 2026, Volume 49 Issue 2
    

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  • Predictive Expectile Regression Models under Possible High Persistence and Conditional Heteroskedasticity
    LIU Xiaohui, CAO Yang, FAN Yawen, PENG Ling
    Acta Mathematicae Applicatae Sinica. 2026, 49(2): 203-231. https://doi.org/10.20142/j.cnki.amas.202600015
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    Traditional mean regression models have been widely applied in forecasting; however, they often fail to capture the tail behaviors of data, especially in the presence of skewness and heavy-tailed distributions. Expectile regression, as an extension of the mean regression model, provides a more flexible framework that adapts to different data distributions and quantiles, offering a more detailed perspective on predictability. This paper proposes a unified predictability test for expectile predictive regression models, accounting for high persistence and conditional heteroscedasticity in financial time series. The asymptotic distribution of the test statistic is derived, and the method is robust against different persistences of the predictor. The empirical analysis re-examines the predictability of monthly returns on the S&P 500 index using 11 macroeconomic indicators, revealing significant variations in predictive power across different expectiles. This study highlights the effectiveness of expectile regression in capturing the complexities of financial data and improving predictive accuracy under challenging conditions.
  • An Overdetermined Problem for Fourth Order Elliptic Operator in Convex Cones
    DENG Haiyun, JIANG Xuyong
    Acta Mathematicae Applicatae Sinica. 2026, 49(2): 232-237. https://doi.org/10.20142/j.cnki.amas.202600012
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    In this paper, we investigate an overdetermined problem involving a fourth order elliptic operator defined within convex cones. The primary objective is to establish the radial symmetry of solutions under specified boundary conditions. Our approach entails the construction of a $P$-function and the application of the maximum principle, leading to a proof that any smooth solution in a bounded sector-like domain with a mean-convex boundary portion necessitates the domain being a spherical sector—the intersection of the cone with a ball. A major contribution is overcoming the challenge of deriving precise boundary estimates for the $P$-function on the cone, a setting with more intricate geometry than classical bounded domains. We also present the solution's explicit form and the relation between the Neumann data and the sphere's radius, thereby extending several classical rigidity results to the context of convex cones.
  • Optimal Reinsurance Based on Inside Information of Claim and Competition Between an Insurer and Multiple Reinsurers
    YANG Peng
    Acta Mathematicae Applicatae Sinica. 2026, 49(2): 238-258. https://doi.org/10.20142/j.cnki.amas.202501055
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    This paper studies the optimal reinsurance decision-making problem between an insurer and $n$ reinsurers based on competition under the influence of inside information of claims. The insurer and $n$ reinsurers joint share claims, the competition between the insurer and reinsurers is quantified by relative performance. Inside information of claims refers to partial information about future claims, which is modeled by filtration expansion theory. The insurer's aim is to maximize his expected relative surplus while minimizing the variance of his relative surplus at the time of reinsurance termination. By using stochastic control and stochastic analysis theory, we establish the Hamilton-Jacobi-Bellman (HJB) equation and verification theorem. By solving the HJB equation and constructing Lagrange function, we obtain the explicit solutions for the optimal reinsurance strategy and the corresponding optimal value function. Finally, the influence of key model features such as inside information of claim, competition and the number of reinsurers on the optimal reinsurance strategy is examined by numerical experiments, and the insurance and economic significance behind the influence is also analyzed.
  • Statistical Estimation for Dividend Problems Under Threshold Dividend Strategy
    LIU Shuangyang, ZHANG Zhimin, XIE Jiayi
    Acta Mathematicae Applicatae Sinica. 2026, 49(2): 259-276. https://doi.org/10.20142/j.cnki.amas.202501028
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    Research on dividend problems has always been a core focus in the field of risk theory. In real situations, insurance companies do not fully know the specific distribution of claims and can only obtain information related to claims before a specific time. Therefore, It would be more meaningful to study the statistical estimation of dividend functions using the data. This paper studied the expected present value of dividend payments before ruin of the perturbed compound Poisson model under the threshold dividend strategy. Based on the available observation data of claims and dividends, the Fourier cosine series expansion method (COS method) was used to obtain the statistical estimator of the expected present value of dividend payments before ruin and analyzed its convergence speed in a large sample environment. Finally, numerical results were given to further prove the effectiveness of the estimation method.
  • Time-Dependent Asymptotic Behavior of The Beam Equation with Rotational Inertia and Strong Damping
    WANG Wei, WANG Xuan
    Acta Mathematicae Applicatae Sinica. 2026, 49(2): 277-303. https://doi.org/10.20142/j.cnki.amas.202501029
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    In this paper, the asymptotic behavior of the solutions to the beam equation with rotational inertia and strong damping: $\varepsilon(t)(1+(-\Delta) ^{\alpha})\partial^{2}_tu+\Delta^2 u-\gamma\Delta\partial_tu+f(u)=g(x),$ where $\alpha\in[0,1)$ is discussed. When the growth exponent of nonlinear terms satisfies $1\leqslant p< p^{*}=\frac{N+2}{N-4},$ $N\geqslant5,$ firstly, by using the Faedo-Galerkin approximation method and the asymptotic regular estimate technique, the well-posedness and regularity of solutions are established; secondly, the asymptotic compactness of the solution process is proved via the method of contraction function; finally, the existence of a time-dependent global attractor is obtained in the time-dependent space $\mathcal{H}_{t}^{\alpha}$.
  • Turing Pattern Dynamics Analysis of Oregonator Model with Cross-diffusion Terms
    LI Hongliang, XIAO Min, ZHOU Ying, DING Jie
    Acta Mathematicae Applicatae Sinica. 2026, 49(2): 304-319. https://doi.org/10.20142/j.cnki.amas.202501030
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    At present, there have been many achievements in the study of Turing instability of reaction-diffusion models, but the study of Turing pattern formation and evolution process of reaction-diffusion system pattern formation is still in the early stage, especially under the drive of cross diffusion. Therefore, the Turing pattern dynamics of a class of Oregonator reaction-diffusion models with cross-diffusion terms are analyzed. First, the conditions of Turing instability induced by cross-diffusion term are obtained when self-diffusion term drives the system to be stable. Secondly, the effect of the cross-diffusion term of the reactants on the pattern formation and evolution process of the system is studied, and whether the cross-diffusion term can change the Turing unstable state caused by the self-diffusion term and whether the different cross-diffusion coefficients can affect the stability rate of the system is discussed. Finally, the simulation results show that the cross-diffusion term plays a significant role in Turing instability and pattern evolution.
  • Dynamic Analysis of a Predator-prey Model with Nonlinear Harvesting
    JIA Zijie, ZHAO Ming
    Acta Mathematicae Applicatae Sinica. 2026, 49(2): 320-333. https://doi.org/10.20142/j.cnki.amas.202501031
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    In this paper, we propose and explore a modified Leslie-Gower with nonlinear harvesting in prey. Through an examination of the existence and stability of all possible equilibria, we find the system may exhibit complex bifurcation phenomena. Using Sotomayor's theorem, the rigorous proof of the occurrence of saddle-node bifurcation is derived. To investigate the stability of the limit cycle of Hopf bifurcation, the Lyapunov coefficient is calculated, and a numerical example is conducted to illustrate this visually. By computing a universal unfolding near the cusp, we show that the system experiences a codimension 2 Bogdanov-Takens bifurcation and provide its bifurcation diagram. At the same time, the dynamic behavior of the model is demonstrated in detail by numerical simulation. Our findings enhance the understanding of Leslie-type predator-prey dynamics.
  • Analysis of a Free Boundary Problem for Tumor Growth with Angiogenesis and Periodic Nutrient Supply
    XU Shihe, WU Junde
    Acta Mathematicae Applicatae Sinica. 2026, 49(2): 334-348. https://doi.org/10.20142/j.cnki.amas.202600014
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    In this paper, a mathematical model for a solid spherically symmetric vascular tumor growth with nutrient periodic supply is studied. The external radius of the tumor $R(t)$ changes with time, so the model is a free boundary problem. The cells inside the tumor obtain nutrient $\sigma(r,t)$ through blood vessels, and the tumor attracts blood vessels at a rate proportional to $\alpha(t)$. Thus, the boundary value condition \begin{equation*} \sigma_r(R(t),t)+\alpha(t)(\sigma(R(t),t)-\psi(t))=0 \end{equation*} holds on the boundary, where the function $\psi(t)$ is the concentration of nutrient externally supplied to the tumor. Considering that the nutrients provided by the outside world are often periodic, the research in this paper assumes that $\psi(t)$ is a periodic function. $\alpha(t)$ is a uniformly bounded function with a positive lower bound. The purpose of this study is to investigate the impact of periodic nutrient supply on the growth of vascularized tumors. Sufficient and necessary conditions for the global stability of zero steady state (i.e., tumor free equilibrium) are provided. Under the condition that the zero steady state is unstable, if $\lim\limits_{t\rightarrow\infty}(\alpha(t)-\bar{\alpha}(t))=0,$ where $\bar{\alpha}(t)$ is a periodic function, by using the Brouwer fixed-point theorem, we prove that there exists a unique periodic solution which is the global attractor of all solutions of the problem. The results are illustrated by computer simulations.
  • Chaotic Properties of Nonautonomous Fuzzy Coupled Map Lattices
    CHEN Yuanlin, ZHOU Jie, LU Tianxiu, ZHAO Jiazheng
    Acta Mathematicae Applicatae Sinica. 2026, 49(2): 349-362. https://doi.org/10.20142/j.cnki.amas.202600011
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    The fuzzy mappings are led into a class of coupled map lattices related to chaotic cryptographic algorithm. It is proved that the $\mathcal{P}_1$-chaos of fuzzy coupled systems means that the initial value mappings also have the same chaotic properties. Where $\mathcal{P}_1$-chaos includes $({{\mathcal{F}}_{1}},{{\mathcal{F}}_{2}})$-chaos, Li-Yorke chaos, distributional chaos, spatio-temporal chaos, densely $\delta $-chaos, densely chaos, Ruelle-Takens chaos and Kato chaos. In particular, by limiting the initial value mappings to the diagonal of the space, a sufficient condition for the fuzzy system to has $\mathcal{P}_2$-chaos is obtained. Where $\mathcal{P}_2$-chaos is one of the followings: initial value sensitive dependence, Li-Yorke sensitive, densely Li -Yorke sensitive, infinite sensitive, synthetically sensitive, cofinitely sensitive, $({{\mathcal{F}}_{1}},{{\mathcal{F}}_{2}})$-sensitive, $\mathcal{F}$-sensitive, transitive, exact, or accessible.
  • A (3,1)*-choosability of Plane Graphs with Neither Adjacent Short Cycles nor 7-cycles
    ZHANG Jufeng, CHEN Min, WANG Yiqiao
    Acta Mathematicae Applicatae Sinica. 2026, 49(2): 363-376. https://doi.org/10.20142/j.cnki.amas.202600019
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    Let $G=(V,E)$ be a graph. Let $k$ and $d$ be positive integers. If we can color these vertices with $k$ colors such that at most $d$ neighbors of $v$ receive the same color as $v$, then $G$ is called to be $(k,d)^{*}$-colorable. A list assignment of $G$ is a function $L$ that assigns a color list $L(v)$ to each vertex $v\in V(G)$. An $(L,d)^{*}$-coloring of $G$ is a mapping $\pi$ that assigns a color $\pi(v)\in L(v)$ to each vertex $v\in V(G)$ so that at most $d$ neighbors of $v$ receive the color $\pi(v)$. If there exists an $(L,d)^{*}$-coloring for every list assignment $L$ with $|L(v)|\ge k$ for all $v\in V(G)$, then $G$ is called to be $(k,d)^{*}$-choosable. In this paper, we prove every planar graph $G$ without adjacent $i$-cycles and $7$-cycles is $(3,1)^{*}$-choosable, for all $i\in\{3,4\}$.
  • A Conjugate Gradient Method and Its Application in Deep Learning
    YUAN Gonglin, MA Xinyan, Deng Wei, Liu Ke-Jun
    Acta Mathematicae Applicatae Sinica. 2026, 49(2): 377-391. https://doi.org/10.20142/j.cnki.amas.202600018
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    As a new research direction in the field of artificial intelligence, deep learning has received widespread attention in recent years and has made significant progress in many application areas. Conjugate gradient method, as an effective optimization method, achieves excellent numerical performance by iteratively approximating the optimal solution. Compared to other methods, the conjugate gradient method does not require the computation of the Hessian matrix, thereby greatly reducing the computational and storage requirements. Therefore, this paper aims to investigate the application of the conjugate gradient method in deep learning and proposes a new conjugate gradient method, demonstrating its sufficient descent property and trust region characteristics. In addition, we introduce the stochastic subspace algorithm and an improved version of it with variance reduction techniques, providing detailed steps for the new algorithm to facilitate a better understanding of its purpose and significance. Through theoretical analysis, we prove that the new algorithm exhibits good convergence properties and high iteration efficiency, with a complexity of $O(\epsilon^{-\frac{1}{1-\beta}})$. Furthermore, experimental results demonstrate the favorable numerical performance of this method.
  • Measure-theoretic Invariance Pressure for Control Systems
    ZHONG Xingfu
    Acta Mathematicae Applicatae Sinica. 2026, 49(2): 392-403. https://doi.org/10.20142/j.cnki.amas.202600021
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    We introduce a new notion of measure-theoretic invariance pressure for control systems and present an inverse variational principle for this invariance pressure. Moreover, we obtain two characterizations of this invariance pressure for nonsingular measures: Bowen measure-theoretic invariance pressure and measure-theoretic feedback pressure.
  • Sparse Huber Regression Incorporating Graphical Structure Among Predictors
    PAN Yingli, ZHAO Xiaoluo, LIU Zhan
    Acta Mathematicae Applicatae Sinica. 2026, 49(2): 404-418. https://doi.org/10.20142/j.cnki.amas.202600020
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    With the rapid development of high technology, the influx of high dimensional data brings new challenges to the existing statistical methods and theories. Huber regression is a statistical analysis method that uses regression analysis in mathematical statistics to determine the interdependent quantitative relationship between two or more variables. Existing methods in Huber regression treat all the predictors equally with the same priori, we take advantage of the graphical structure among predictors to improve the performance of parameter estimation, model selection and prediction in sparse Huber regression. In order to overcome the difficulty of solving Huber regression with graphic structure, we propose an alternating direction method of multipliers (ADMM) algorithm with a linearization technique. The simulation and empirical results show that the Huber regression method combining graphical structure among predictors is superior to the adaptive Lasso penalty Huber regression without graphical structure in estimation accuracy and prediction performance.
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