数学季刊

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1.

带有时滞和热扩散效应的 Timoshenko 系统的适定性

秦玉明, 韩宁

数学季刊 2022, 37 (1): 1-9. DOI: 10.13371/j.cnki.chin.q.j.m.2022.01.001

摘要（141）

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In this paper, we study the well-posedness for the thermoelastic Timoshenko system with a constant delay and mass diffusion effects. Heat and mass exchange with the environment during thermodiffusion in Timoshenko beam. The C₀ -semigroup theory will be used to prove the well-posedness of the considered problem.

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2. 基于固有时间尺度分解和自适应Huber损失的脑电特征学习模型

杨利军, 蒋淑月, 魏小鸽, 肖运海

数学季刊 2022, 37 (3): 281-300. DOI: 10.13371/j.cnki.chin.q.j.m.2022.03.006

摘要（120）

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According to the World Health Organization, about 50 million people world-
wide suffer from epilepsy. The detection and treatment of epilepsy face great challenges.
Electroencephalogram (EEG) is a significant research object widely used in diagnosis and
treatment of epilepsy. In this paper, an adaptive feature learning model for EEG signals
is proposed, which combines Huber loss function with adaptive weight penalty term.
Firstly, each EEG signal is decomposed by intrinsic time-scale decomposition. Secondly,
the statistical index values are calculated from the instantaneous amplitude and frequency
of every component and fed into the proposed model. Finally, the discriminative features
learned by the proposed model are used to detect seizures. Our main innovation is to
consider a highly flexible penalization based on Huber loss function, which can set different
weights according to the influence of different features on epilepsy detection. Besides, the
new model can be solved by proximal alternating direction multiplier method, which can
effectively ensure the convergence of the algorithm. The performance of the proposed
method is evaluated on three public EEG datasets provided by the Bonn University,
Childrens Hospital Boston-Massachusetts Institute of Technology, and Neurological and
Sleep Center at Hauz Khas, New Delhi(New Delhi Epilepsy data). The recognition
accuracy on these two datasets is 98% and 99.05%, respectively, indicating the application
value of the new model.

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3. 带有异常点检测的稀疏降秩回归

梁冰洁

数学季刊 2021, 36 (3): 275-287. DOI: 10.13371/j.cnki.chin.q.j.m.2021.03.006

摘要（84）

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Based on the multivariate mean-shift regression model, we propose a new
sparse reduced-rank regression approach to achieve low-rank sparse estimation and outlier
detection simultaneously. A sparse mean-shift matrix is introduced in the model to indicate
outliers. The rank constraint and the group-lasso type penalty for the coefficient matrix
encourage the low-rank row sparse structure of coefficient matrix and help to achieve
dimension reduction and variable selection. An algorithm is developed for solving our
problem. In our simulation and real-data application, our new method shows competitive
performance compared to other methods.

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4. 一类具有导数型非线性记忆项的半线性波动方程的爆破结果

欧阳柏平, 肖胜中

数学季刊 2021, 36 (3): 235-243. DOI: 10.13371/j.cnki.chin.q.j.m.2021.03.002

摘要（130）

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In this paper, we study the blow-up of solutions to a semi-linear wave equation with a nonlinear memory term of derivative type. By using methods of an iteration argument and differential inequalities, we obtain the blow-up result for the semi-linear wave equation when the exponent of p is under certain conditions. Meanwhile, we derive an upper bound of the lifespan of solutions to the Cauchy problem for the semi-linear wave equation.

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5. 与 Mittag-Leffler 函数有关的多叶亚纯函数的优化和 Fekete-Szegö 问题

龙品红, 甘加达兰•穆鲁古桑德拉莫西, 韩惠丽, 汪文帅

数学季刊 2022, 37 (2): 111-123. DOI: 10.13371/j.cnki.chin.q.j.m.2022.02.001

摘要（164）

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The main object of this present paper is to investigate the problem of majorization of certain class of multivalent meromorphic functions of complex order involving Mittag-Leffler function. Meanwhile, for this subclass the corresponding coefficient estimates and some Fekete-Szeg¨ o type inequalities are obtained. Moreover we point out some new or known consequences of our main results.

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6. T2SVNSs 的熵和相似性度量及其应用

耿娟娟, 叶万红, 张菊, 徐东胜

数学季刊 2021, 36 (2): 160-175. DOI: 10.13371/j.cnki.chin.q.j.m.2021.02.005

摘要（101）

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The objective of this paper is to present a new approach for solving the multicriteria group decision-making (MCGDM) problems in type-2 single valued neutrosophic
set (T2SVNS) environment. Firstly, we give the concepts SVNS, T2SVNS and tangent
similarity measure with T2SVN information. Secondly, we define a new entropy function
for determining unknown attribute weights. In addition, a MCGDM method is developed
based on entropy and tangent similarity measure of T2SVNSs. Finally, an illustrative
example and comparative analysis are given to confirm the rationality and feasibility of
the proposed method.

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7. 耦合Lyapunov 矩阵方程的AOR迭代法

张士君, 王世恒, 王珂

数学季刊 2021, 36 (2): 141-148. DOI: 10.13371/j.cnki.chin.q.j.m.2021.02.003

摘要（117）

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An AOR (Accelerated Over-Relaxation) iterative method is suggested by
introducing one more parameter than SOR (Successive Over-Relaxation) method for
solving coupled Lyapunov matrix equations (CLMEs) that come from continuous-time
Markovian jump linear systems. The proposed algorithm improves the convergence rate,
which can be seen from the given illustrative examples. The comprehensive theoretical
analysis of convergence and optimal parameter needs further investigation.

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8. 求解全局优化问题的一种新的非参数填充函数

刘金赞, 屈德强

数学季刊 2021, 36 (2): 188-195. DOI: 10.13371/j.cnki.chin.q.j.m.2021.02.007

摘要（91）

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In the paper, to solve the global optimization problems, we propose a novel
parameter-free filled function. Based on the non-parameter filled function, a new filled
function algorithm is designed. In the algorithm, the selection and adjustment of parameters can be ignored by the characteristic that the filled function is parameter-free. In
addition, in the region lower than the current local minimizer of the objective function, the
filled function is continuously differentiable which enables any gradient descent method
to be used as a local search method in the algorithm. Through numerical experiments by
solving two test problems, the effectiveness of the algorithm is verified.

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9. 一类具有状态依赖脉冲影响的捕食者-食饵模型动力学分析

李永凤, 朱城志, 刘艳伟

数学季刊 2023, 38 (1): 1-19. DOI: 10.13371/j.cnki.chin.q.j.m.2023.01.001

摘要（82）

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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.

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10. 随机变量的共轭梯度方法

许铭修, 黎景辉

数学季刊 2021, 36 (2): 111-121. DOI: 10.13371/j.cnki.chin.q.j.m.2021.02.001

摘要（153）

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We study the conjugate gradient method for solving a system of linear
equations with coefficients which are measurable functions and establish the rate of
convergence of this method.

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11. 具退化非局部阻尼和源项的非线性耦合粘弹性波方程组解的指数增长性

刘烁, 张宏伟, 呼青英

数学季刊 2021, 36 (2): 210-220. DOI: 10.13371/j.cnki.chin.q.j.m.2021.02.010

摘要（121）

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This paper is concerned with a system of nonlinear viscoelastic
wave equations with degenerate nonlocal damping and memory terms. We will
prove that the energy associated to the system is unbounded. In fact, it will
be proved that the energy will grow up as an exponential function as time goes
to infinity, provided that the initial data are positive initial energy.

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12. 高阶变系数非线性发展方程的Painlev\'{e} 分析

王媛

数学季刊 2021, 36 (2): 196-203. DOI: 10.13371/j.cnki.chin.q.j.m.2021.02.008

摘要（142）

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There is a close relationship between the Painlev´e integrability and other
integrability of nonlinear evolution equation. By using the Weiss-Tabor-Carnevale (WTC)
method and the symbolic computation of Maple, the Painlev´e test is used for the higher
order generalized non-autonomous equation and the third order Korteweg-de Vries equation
with variable coefficients. Finally the Painlev´e integrability condition of this equation is
gotten.

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13. 具有导数型非线性项的半线性双波动方程解的全局非存在性

欧阳柏平, 林奕武

数学季刊 2021, 36 (2): 149-159. DOI: 10.13371/j.cnki.chin.q.j.m.2021.02.004

摘要（75）

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In this paper, we study the blow-up of solutions to a semilinear double-wave
equation with nonlinearity of derivative type. By using the iteration method and the
differential inequality techniques, we can get the estimates of the lifespan and the blow-up
of solutions in the subcritical case under some assumptions.

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14. 一类非凸优化问题的邻近拟牛顿方法的复杂性

金玲子

数学季刊 2023, 38 (1): 62-84. DOI: 10.13371/j.cnki.chin.q.j.m.2023.01.005

摘要（68）

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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.

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15. Korteweg-de Vries方程的 Legendre 时空谱配置方法

王川, 乔炎

数学季刊
录用日期: 2023-04-12

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16. 邻域集值双量化粗糙集

李文涛, 李璋, 朱春龙, 徐伟华

数学季刊 2021, 36 (2): 122-140. DOI: 10.13371/j.cnki.chin.q.j.m.2021.02.002

摘要（89）

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Double-quantitative rough approximation, containing two types of quan-
titative information, indicated stronger generalization ability and more accurate data
processing capacity than the single-quantitative rough approximation. In this paper,
the neighborhood-based double-quantitative rough set models are firstly presented in a
set-valued information system. Secondly, the attribute reduction method based on the
lower approximation invariant is addressed, and the relevant algorithm for the approx-
imation attribute reduction is provided in the set-valued information system. Finally,
to illustrate the superiority and the effectiveness of the proposed reduction approach,
experimental evaluation is performed using three datasets coming from the University of
California-Irvine (UCI) repository.

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17. 局部共形拟 Kähler Finsler 流形

李鸿军

数学季刊 2021, 36 (3): 244-251. DOI: 10.13371/j.cnki.chin.q.j.m.2021.03.003

摘要（95）

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In this paper, we give a necessary and sufficient condition for a strongly pseudoconvex complex Finsler metric to be locally conformal pseudo-Kähler Finsler. As an application, we find any complete strongly convex and locally conformal pseudo-Kähler Finsler manifold, which is simply connected or whose fundamental group contains elements of finite order only, can be given a Kähler metric.

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18. 一类高维组内相关结构的检验

汤平, 肖南南, 解俊山

数学季刊 2022, 37 (1): 10-25. DOI: 10.13371/j.cnki.chin.q.j.m.2022.01.002

摘要（107）

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The paper considers a high-dimensional likelihood ratio (LR) test on the intraclass correlation structure of the multivariate normal population. When the dimension p and sample size N satisfy N − 1 >p→∞ , it is proved that the logarithmic LR statistic asymptotically obeys Gaussian distribution, and the explicit expressions of the mean and the variance are also obtained. The simulations demonstrate that our high-dimensional LR test method outperforms the traditional Chi-square approximation method or F-approximation method, and performs as efficient as the accurate high-dimensional Edgeworth expansion method and the more accurate high-dimensional Edgeworth expansion method in analyzing the intraclass covariance structure of highdimensional data.

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19. 具有一般非线性项的半线性抛物方程解的有限时间爆破和爆破时间上界

李娜, 房少梅

数学季刊 2022, 37 (1): 103-110. DOI: 10.13371/j.cnki.chin.q.j.m.2022.01.011

摘要（113）

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In this paper, we consider a semilinear parabolic equation with a general nonlinearity. We establish a new finite time blow-up criterion and also derive the upper bound for the blow-up time. The results partially generalize some recent ones obtained by He Ma et al.

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20.

具有非齐次核的半离散 Hilbert 型多重积分不等式的最佳搭配参数及其应用

洪勇, 和炳

数学季刊 2021, 36 (3): 252-262. DOI: 10.13371/j.cnki.chin.q.j.m.2021.03.004

摘要（77）

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By using the weight function method, the matching parameters of the half discrete Hilbert type multiple integral inequality with a non-homogeneous kernel K ( n,||x|| _ρ,m ) = G ( n^{λ 1} ||x|| ^{λ 2}_ρ,m) are discussed, some equivalent conditions of the optimal matching parameter are established, and the expression of the optimal constant factor is obtained. Finally, their applications in operator theory are considered.

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