中国科学院数学与系统科学研究院期刊网

15 January 2025, Volume 68 Issue 1
    

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  • A Projection-Based Feature Screening Method for Multiple Responses
    Feng Zou, Hengjian Cui
    Acta Mathematica Sinica, Chinese Series. 2025, 68(1): 1-29. https://doi.org/10.12386/A20230182
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    In this paper, a nonnegative projection correlation coefficient (NPCC) is proposed to measure the dependence between two random vectors, where the projection direction comes from the standard multivariate normal distribution. The NPCC is nonnegative and is zero if and only if the two random vectors are independent. Also, its estimation is free of tuning parameters and does not require any moment conditions on the random vectors. Based on the NPCC, we further propose a novel feature screening procedure for ultrahigh dimensional data, which is robust, model-free and enjoys both sure screening and rank consistency properties under weak assumptions. Monte Carlo simulation studies indicate that the NPCC-based screening procedure have strong competitive advantages over the existing methods. Lastly, we also use a real data example to illustrate the application of the proposed procedure.
  • Globally Exponential Decay and Inviscid Limit of the Incompressible Oldroyd-B Model on Torus
    Yuying Chen, Xinghong Pan
    Acta Mathematica Sinica, Chinese Series. 2025, 68(1): 30-44. https://doi.org/10.12386/B20230321
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    In this paper, we first prove the global existence and exponential decay of small-data analytical solutions to the three-dimensional incompressible Oldroyd-B model in torus. An a priori estimate of viscosity independence will be obtained. Based on such a priori estimate, we then show validity of the inviscid limit of the Oldroyd-B system. The nonlinear quadratic terms have one more order derivative than the linear part and no good structure is found to overcome this derivative loss problem. So we can only build the global-in-time result in the analytical energy functional space rather than the Sobolev space with finite order derivatives.
  • Aubry Sets in Discounted Hamiltonian Systems Defined by PDE
    Yiwen Yuan, Xia Li
    Acta Mathematica Sinica, Chinese Series. 2025, 68(1): 45-55. https://doi.org/10.12386/A20230151
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    It is important to study the discounted Hamilton—Jacobi (H-J) equation, because it is a special form of the contact H-J equation. In this article, we provide a definition of the Aubry set in a discounted Hamilton system under certain conditions in the sense of viscosity solution, which is similar to the definition of Aubry set in classical Hamilton systems, and the Aubry set defined by this definition has the properties of minimal action and recurrence in a variational sense.
  • Bifurcation Analysis of a General Predator-prey Model with Nonlocal Fear Effect
    Xiuli Sun
    Acta Mathematica Sinica, Chinese Series. 2025, 68(1): 56-66. https://doi.org/10.12386/B20230418
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    It has been well established that the predator-induced fear has indirect impact on prey but can have comparable effects on prey population as direct killing. In this paper, a diffusive predator-prey system with nonlocal fear effect is formulated and investigated. We firstly study the existence and boundedness of solutions and then discuss the stability of constant steady states. Steady-state bifurcations are carried out in detail by using the Lyapunov—Schmidt method. Finally, numerical simulations are showed to verify our theoretical results.
  • A New Extragradient Method with Bregman Distance for Solving Variational Inequality Problems in Hilbert Spaces
    Yuelu Zhang, Gang Cai, Vu Tien Dung
    Acta Mathematica Sinica, Chinese Series. 2025, 68(1): 67-80. https://doi.org/10.12386/B20230422
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    In this paper, we introduce a new Bregman extragradient projection method for solving monotone variational inequalities in real Hilbert spaces. Moreover, we prove a weak convergence theorem for our suggested algorithm under some reasonable assumptions imposed on the parameters. Finally, we give some numerical examples to demonstrate how our algorithm outperforms earlier findings in the literature in terms of convergence performance.
  • Geometric Classifications of Quasi-sum Production Functions in Economics
    Yanru Luo, Yu Fu
    Acta Mathematica Sinica, Chinese Series. 2025, 68(1): 81-98. https://doi.org/10.12386/A20230084
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    Production function is one of the core concepts of neoclassical economics and an important tool for economic analysis. This paper studies quasi-sum production functions from the perspective of geometric invariants. By discussing the constant Gauss curvature equation and the constant mean curvature equation of the corresponding surfaces of quasi-sum production functions, a series of interesting classification results are obtained. The results of this paper not only have certain significance for the study of surface theory in differential geometry, but also provide more alternative types of production models in economic analysis, and promote the development of the theory of production function to a certain extent.
  • Periodic Solutions and KAM Invariant Tori in the Nosé—Hoover System
    Shengqing Hu, Jing Zhang
    Acta Mathematica Sinica, Chinese Series. 2025, 68(1): 99-112. https://doi.org/10.12386/B20230071
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    In this paper, we consider a one-dimensional Nosé—Hoover system: $\dot{q}=p^{2m+1},$ $\dot{p}=-q^{2n+1}-\frac{\xi}{Q} p,$ $\dot{\xi}=p^{2m+2}-\beta^{-1},$ where $p, q, \xi\in \mathbb{R}$ are one-dimensional variables, $m,n\geq 0$ are integers and $Q, \beta$ are parameters. For $Q$ large enough, by using the averaging method we prove the existence of a linearly stable periodic solution. In addition, based on Moser's twist theorem we give a proof for the existence of invariant tori surrounding the periodic orbit for large $Q$.
  • The Generators and Relations for Affine q-Schur Algebra SΔ(2,3)
    Mingqiang Liu, Qian Yang
    Acta Mathematica Sinica, Chinese Series. 2025, 68(1): 113-125. https://doi.org/10.12386/A20230024
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    In terms of the generators and relations of affine $q$-Schur algebra $\mathcal{S}_{\Delta}(n, r)$, Doty et al. provided a presentation for $n>r$. Deng—Du—Fu gave the presentations for affine $q$-Schur algebra $\mathcal{S}_{\Delta}(r, r)$. The presentation of the affine $q$-Schur algebra $\mathcal{S}_{\Delta}(n, r)$ is more complicated in the case of $n < r$. In this paper, we obtain the monomial basis of affine $q$-Schur algebra $\mathcal{S}_{\Delta}(2, 3)$ and present a new set for generators and relations of $q$-Schur algebra $\mathcal{S}_{\Delta}(2, 3)$ by monomial basis.
  • Some Problems Related to Sun Zhiwei's Conjectures
    Xingxing LÜ, Wenpeng Zhang
    Acta Mathematica Sinica, Chinese Series. 2025, 68(1): 126-134. https://doi.org/10.12386/A20220007
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    In this paper, we study the computational problems of one kind congruent equation modulo $p$, and give some exact computational formulae for them.
  • Quadratic Transportation Cost Inequalities for a Space-time Fractional Stochastic Heat Equation with Fractional Noise
    Xinyu Wang, Ruinan Li, Shulan Hu
    Acta Mathematica Sinica, Chinese Series. 2025, 68(1): 135-144. https://doi.org/10.12386/A20230011
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    In this paper, we prove a Talagrand's ${\bf T_2}$ transportation cost-information inequality for the law of the space-time fractional stochastic heat equation with fractional noise on the continuous path space with respect to the weighted $L^2$-norm.
  • Limit Properties of Exceedances Point Processes for Stationary Random Fields Subject to Random Missing
    Huiyan Liu, Zhongquan Tan
    Acta Mathematica Sinica, Chinese Series. 2025, 68(1): 145-164. https://doi.org/10.12386/A20220103
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    This paper studied the limit properties of exceedances point processes for weakly dependent stationary random fields subject to random missing. By using the obtained results, this paper got the limit properties of extreme order statistics for the random fields and the limit properties of exceedances point processes for Gaussian order random fields and $\chi$ random fields.
  • Complex Dynamical Properties of Solutions of Second Order Differential Equations
    Xiubi Wu, Xue Li
    Acta Mathematica Sinica, Chinese Series. 2025, 68(1): 165-172. https://doi.org/10.12386/A20220104
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    Research on the Julia sets of meromorphic functions has been one of the hot problems in complex dynamical systems. In the paper, we gave some more accurate estimations of the lower bound of the radial distribution of Julia sets by investigating the growth of solutions of second-order differential equations.
  • Bias Correction Estimation for Partially Linear Varying Coefficient Spatial Autoregressive Panel Model with Fixed Effects
    Feipeng Ding
    Acta Mathematica Sinica, Chinese Series. 2025, 68(1): 173-196. https://doi.org/10.12386/A20220056
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    In this paper, we construct an efficient estimation method for partially linear varying coefficient spatial autoregressive panel model with fixed effects by combining bias correction, variable transformation and quadratic inference functions. Moreover, under some regularity conditions, asymptotic normality of parameter estimators is proved and convergence rate of the estimators of coefficient functions is derived. Lastly, the performance of the proposed method under the finite samples is evaluated by Monte Carlo simulation and real data analysis.
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