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Table of Content

    30 March 2023, Volume 38 Issue 1
    Dynamic Analysis of a Predator-Prey Model with State-Dependent Impulsive Effects
    LI Yong-feng, ZHU Cheng-zhi, LIU Yan-wei
    2023, 38(1):  1-19.  doi:10.13371/j.cnki.chin.q.j.m.2023.01.001
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     In this paper, a pest-dependent model and integrated pest management
    strategy is proposed, that is, when pest populations reach levels that impair economic
    development, we will use a combination of strategies, such as biological, cultural and
    chemical control strategies reduce pests to a reasonable level. First, we investigated the
    system without control measures, and discussed the existence and stability of equilibria,
    we also proved the system has no limit cycle. Then, a state feedback impulsive model is
    constructed, the existence and uniqueness of the order-one periodic solution are proved
    by means of the successor function method to confirm the feasibility of the biological and
    chemical control strategy of pest management. Secondly, the stability of system is proved
    by the analogue of the Poincar ´ e criterion. Finally, we give an example and numerical
    simulations to explain the mathematical conclusions.
    Virtual Element Method of the Allen-Cahn Equation
    WANG Pei-zhen, TIAN Xu
    2023, 38(1):  20-29.  doi:10.13371/j.cnki.chin.q.j.m.2023.01.002
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     In this article, the virtual element method of the Allen-Cahn equation on a
    polygon grid is discussed in the fully discrete formulation. With the help of the energy
    projection operator, we give the corresponding error estimates in the L2 norm and H1
    norm.
    Weighted Analytic Torsion for Weighted Digraphs
    REN Shi-quan, WANG Chong
    2023, 38(1):  30-49.  doi:10.13371/j.cnki.chin.q.j.m.2023.01.003
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     In 2020, Alexander Grigor’yan, Yong Lin and Shing-Tung Yau [6] introduced
    the Reidemeister torsion and the analytic torsion for digraphs by means of the path
    complex and the path homology theory. Based on the analytic torsion for digraphs
    introduced in [6], we consider the notion of weighted analytic torsion for vertex-weighted
    digraphs. For any non-vanishing real functions f and g on the vertex set, we consider the
    vertex-weighted digraphs with the weights ( f,g ). We calculate the ( f,g )-weighted analytic
    torsion by examples and prove that the ( f,g )-weighted analytic torsion only depend on
    the ratio f/g . In particular, if the weight is of the diagonal form ( f,f ), then the weighted
    analytic torsion equals to the usual (un-weighted) torsion.
    On the Eigenvalues and Eigenfunctions of the Sturm-Liouville Operator with the Barrier Potential
    SARWAR Qanitah, HUANG Zhen-you, ZAHID Abdul Hannan, XU Xin-Jian
    2023, 38(1):  50-61.  doi:10.13371/j.cnki.chin.q.j.m.2023.01.004
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    We aim to find the eigenvalues and eigenfunctions of the barrier potential
    case for Strum-Liouville operator on the finite interval [0 ,π ] when λ> 0. Generally, the
    eigenvalue problem for the Sturm-Liouville operator is often solved by using integral
    equations, which are sometimes complex to solve, and difficulties may arise in computing
    the boundary values. Considering the said complexity, we have successfully developed
    a technique to give the asymptotic formulae of the eigenvalue and the eigenfunction for
    Sturm-Liouville operator with barrier potential. The results are of significant interest in
    the field of quantum mechanics and atomic systems to observe discrete energy levels.
    Complexity on Proximal Quasi-Newton Methods for a Class of Nonconvex Composite Optimization
    JIN Ling-Zi
    2023, 38(1):  62-84.  doi:10.13371/j.cnki.chin.q.j.m.2023.01.005
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    This paper studies a class of nonconvex composite optimization, whose
    objective is a summation of an average of nonconvex (weakly) smooth functions and a
    convex nonsmooth function, where the gradient of the former function has the Hölder
    continuity. By exploring the structure of such kind of problems, we first propose a
    proximal (quasi-)Newton algorithm wPQN (Proximal quasi-Newton algorithm for weakly
    smooth optimization) and investigate its theoretical complexities to find an approximate
    solution. Then we propose a stochastic variant algorithm wPSQN (Proximal stochastic
    quasi-Newton algorithm for weakly smooth optimization), which allows a random subset
    of component functions to be used at each iteration. Moreover, motivated by recent
    success of variance reduction techniques, we propose two variance reduced algorithms,
    wPSQN-SVRG and wPSQN-SARAH, and investigate their computational complexity
    separately.
    Worst-Case Optimization on Mean-CVaR Ratio with Returns Distribution Ellipsoidal Uncertainty
    QING Nai-qiao
    2023, 38(1):  85-96.  doi:10.13371/j.cnki.chin.q.j.m.2023.01.006
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    The article explores a mean-CVaR ratio model with returns distribution
    uncertainty. To describe the uncertainty of returns distribution, a mixture ellipsoidal
    distribution absorbing some typical distributions such as the mixture distribution and
    and ellipsoidal distribution is introduced. Then, by using robust technique with some
    assumptions, the original robust mean-CVaR ratio model can be formulated as a second-
    order cone optimization model where the underlying random returns have a mixture
    ellipsoidal distribution. As an illustration, the corresponding robust optimization models
    are applied to allocations of assets in securities market. Numerical simulations are
    presented to illustrate the relation between robustness and optimality and to compare
    mixture ellipsoidal distribution to some typical distributions as well.
    Estimates of the Parameter and Reliability Function for the Topp-Leone Distribution under Type-I Left Censoring
    LONG Qin-yi, XU Li-ping
    2023, 38(1):  97-110.  doi:10.13371/j.cnki.chin.q.j.m.2023.01.007
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     Firstly, the maximum likelihood estimate and asymptotic confidence interval
    of the unkown parameter for the Topp-Leone distribution are obtained under Type-I left
    censored samples, furthermore, the asymptotic confidence interval of reliability function
    is obtained based on monotonicity. Secondly, under different loss functions, the Bayesian
    estimates of the unkown parameter and reliability function are obtained, and the expected
    mean square errors of Bayesian estimates are calculated. Monte-Carlo method is used to
    calculate the mean values and relative errors of the estimates. Finally, an example of life
    data is analyzed by using the statistical method in this paper.