中国科学院数学与系统科学研究院期刊网

28 November 2024, Volume 47 Issue 6
    

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  • New Oscillation Criteria for Second Order Nonlinear Neutral Delay Differential Equation with Damping Term
    LIU Xi, LIU Jun, YU Yuanhong
    Acta Mathematicae Applicatae Sinica. 2024, 47(6): 855-868. https://doi.org/10.20142/j.cnki.amas.202401072
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    The Oscillation of a class of second order nonlinear neutral delay differential equation with damping term is studied in this paper. By using the generalized Riccati transformation technique and some special techniques, some new oscillation criteria for the equation are obtained in the noncanonical. The oscillation results in several recent literatures are improved, generalized and unified. Finally, some examples demonstrate the applicability of the results of this paper.
  • Monostable Traveling Waves for a Class of Asymmetric System with Nonlocal Diffusion and Delay
    MU Kewang, YANG Yunruiy, LI Xiaowu
    Acta Mathematicae Applicatae Sinica. 2024, 47(6): 869-891. https://doi.org/10.20142/j.cnki.amas.202401050
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    The monostable traveling waves for a class of asymmetric system with nonlocal diffusion and delay(the system can be non-quasimonotone) are investigated. Firstly, the existence of traveling waves is transformed into the fixed point problem of a nonlinear operator by constructing a pair of super-auxiliary system and sub-auxiliary system with quasi-monotonicity, and thus the existence of monostable traveling waves under the non-critical and critical wave speed are established by using Schauder’s fixed point theorem and limiting argument, respectively. Secondly, the non-existence and asymptotic behaviors of monostable waves are discussed by analysis technique and Ikehara’s Tauberian theorem. Finally, concrete examples and numerical simulations for the obtained theoretical results are included.
  • Estimation of Calendar Effect in Microstructure Noise Using High-frequency Financial Data
    SU Tao, ZHANG Zhiyuan
    Acta Mathematicae Applicatae Sinica. 2024, 47(6): 892-906. https://doi.org/10.20142/j.cnki.amas.202401073
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    We build an estimator of calendar effect in market microstructure noise using high-frequency financial data. The associated asymptotic theory and feasible inference are established. This is, to our knowledge, the first (feasible) asymptotic theory ever built for the estimation of calendar effect in market microstructure noise. This research may lead to a better understanding of market microstructure noise and hence the market mechanism.
  • Existence of Positive Periodic Solutions for Singular Rayleigh Equations with Minkowski-curvature Operator
    LI Shaowen, CHENG Zhibo
    Acta Mathematicae Applicatae Sinica. 2024, 47(6): 907-918. https://doi.org/10.20142/j.cnki.amas.202401027
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    In this paper, we consider a singular Rayleigh equation with Minkowski-curvature operator $$ \Big(\frac{u'(t)}{\sqrt{1-(u'(t))^{2}}}\Big)'+f(t,u'(t))+g(u(t))=e(t), $$ $g$ is a continuous function and has a singularity at $u=0$. By using Mawhin continuity theorem and some analytical methods, we obtain the existence of a positive periodic solution for this equation.
  • Hermite Positive Definite Solution of the Matrix Equation Xm-A*X-sA+B*X-tB=Q
    XIONG Hao, HUANG Jingpin
    Acta Mathematicae Applicatae Sinica. 2024, 47(6): 919-935. https://doi.org/10.20142/j.cnki.amas.202401030
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    The nonlinear matrix equation ${{X}^{m}}-{{A}^{*}}{{X}^{-s}}A+{{B}^{*}}{{X}^{-t}}B=Q$ form computational physics and optimal control, etc., the presence of parameters and positive and negative hybrid terms, it is difficult to solve the equation. In this paper, the iterative methods of the Hermite positive definite solution of the equation are discussed under certain conditions. First, the original problem is transformed into an equivalent matrix equation by matrix transformation. Then, the coefficient matrix and its partial order are used to construct the existence interval of the solution of the equation and three iterative schemes. According to the characteristics of each iterative sequence, the residual norm of the solution and the monotonic boundedness of the iterative sequence is used to prove that the given iteration converges to the Hermite positive definite solution of the original equation, and the error estimation formula of the solution is obtained. Finally, two numerical examples demonstrate the effectiveness and feasibility of the proposed method.
  • Calderón-Zygmund Estimates of Weak Solutions of Boundary Value Problems for a Class of Elliptic Equations
    KANG Di, SHEN Yi, XU Xiujuan
    Acta Mathematicae Applicatae Sinica. 2024, 47(6): 936-957. https://doi.org/10.20142/j.cnki.amas.202401017
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    In this paper, the global Calderón-Zygmund estimation of a class of elliptic equation boundary value problems with variable exponential logarithmic growth is concerned. By comparing estimates and utilizing methods such as iterative coverage, we obtain the global Calderón-Zygmund estimates of the problem in non-smooth regions, where operator $\mathbf{a}$ satisfies some appropriate conditions and the given vector function satisfies appropriate growth conditions.
  • Existence of Mild Solutions for Hilfer Fractional Stochastic Evolution Equations with Nonlocal Conditions on the Positive Half-axis
    CUI Haifang, YANG Miny, WANG Qiru
    Acta Mathematicae Applicatae Sinica. 2024, 47(6): 958-974. https://doi.org/10.20142/j.cnki.amas.202401018
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    In this paper, we study the existence of mild solutions for a class of Hilfer fractional stochastic evolution equations with nonlocal conditions on the positive half-axis. Firstly, by applying fractional calculus, semigroup properties of operators, stochastic analysis theory, the generalized Ascoli-Arzela theorem and Krasnoselskii’s fixed point theorem, sufficient conditions for the existence of the mild solutions on the positive half-axis are derived in the case that the associated semigroup is compact. Then relying on the Kuratowski noncompactness measure, we further discuss the existence of the mild solutions on the positive half-axis when associated semigroup is noncompact. At last, an example is provided to illustrate the applicability of the obtained results.
  • Dynamics of a Predator-prey System with Delay of Fear Effect
    SHI Renxiang, HU Zonghai
    Acta Mathematicae Applicatae Sinica. 2024, 47(6): 975-998. https://doi.org/10.20142/j.cnki.amas.202401083
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    In this paper, we study the dynamics of a predator-prey system with delay of fear effect. First we discuss the positivity, boundedness and permanence of the solution, then base on center manifold theorem and normal form, we study Hopf bifurcation caused by delay of fear effect. Furthermore, we discuss the global existence of bifurcated periodic solutions. At last, some simulations are given to support our results.
  • Robust Estimation of Matrix-Valued Time Series Autoregressive Model
    CHEN Yang, ZHANG Xiaomei, ZHU Yingqiu, QIN Leiy
    Acta Mathematicae Applicatae Sinica. 2024, 47(6): 999-1026. https://doi.org/10.20142/j.cnki.amas.202401013
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    In order to solve the problem that the least squares estimation of the matrix autoregressive model (MAR) is easily affected by outliers or thick-tailed distribution errors and deviates from the true value, this paper improves the loss function. Based on the projection method and iterative least squares method, RE-PROJ and RE-ILS methods are proposed to solve the robust estimation of the MAR model. Both methods use the idea of M estimation in the process of constructing estimators, and the simulation data show that the above two methods can better resist the influence of outliers on parameter estimation. This paper further discusses the BIC criterion for order selection of the MAR(p) model and a robust estimation method with the assumption of rank reduction when the matrix observations are correlated. The actual analysis results show that the robust estimation proposed in this paper has more advantages in fitting and prediction than the least squares estimation in the matrix-valued observation data with many outliers or sharp peaks and thick tails.
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