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1. 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）      PDF（pc） （538KB）（316）    可视化    收藏 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. 相关文章 | 多维度评价

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2. 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）      PDF（pc） （2367KB）（222）    可视化    收藏  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. 相关文章 | 多维度评价

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3. 离散动力系统的稳定性 王慕秋, 王联 数学季刊    1987, 2 (3): 12-30.   摘要 （41）      PDF（pc） （1147KB）（218）    可视化    收藏  随着高速数字计算机的出现, 对于控制理论家,经济学家以及生物学家来说, 差分方程（离散时间系统）已经成为一个重要且有用的数学模型. 因此, 在文献中, 差分方程理论已经得到了迅速地发展. 到目前为止, 大量的这方面的研究是平行于常微分方程进行的,特别地,对于差分方程稳定性理论的研究也是如此. 有关微分方程系统的稳定性理论方面的一些处理方法（例如李雅普诺夫函数法）及重要结果, 已被成功地平行地运用到差分方程上来. 众所周知, 关于由常微分方程所描述的系统的稳定性, 自上世纪末, 由A.M.  相关文章 | 多维度评价

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4. 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）      PDF（pc） （293KB）（349）    可视化    收藏 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 C 0 -semigroup theory will be used to prove the well-posedness of the considered problem. 相关文章 | 多维度评价

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5. 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）      PDF（pc） （330KB）（241）    可视化    收藏  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. 相关文章 | 多维度评价

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6. 带有对合的素环的微分恒等式 黄述亮 数学季刊    2023, 38 (2): 134-144.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.02.003 摘要 （53）      PDF（pc） （319KB）（132）    可视化    收藏  Let R be a prime ring of characteristic different from two with the sec- ond involution ∗ and α an automorphism of R . An additive mapping F of R is called a generalized ( α,α )-derivation on R if there exists an ( α,α )-derivation d of R such that F ( xy )= F ( x ) α ( y )+ α ( x ) d ( y ) holds for all x,y∈R. The paper deals with the s- tudy of some commutativity criteria for prime rings with involution. Precisely, we describe the structure of R admitting a generalized ( α,α )-derivation F satisfying any one of the following properties: ( i ) F ( xx∗) −α ( xx∗) ∈Z ( R ). ( ii ) F ( xx∗ )+ α ( xx∗ ) ∈ Z ( R ). ( iii ) F ( x ) F ( xx∗) −α ( xx∗) ∈Z ( R ). ( iv ) F ( x ) F (x∗)+ α ( xx∗) ∈Z ( R ). ( v ) F ( xx∗) − F ( x ) F (x∗ ) ∈Z ( R ). ( vi ) F ( xx∗) −F (x∗) F ( x )=0 for all x∈R . Also, some examples are given to demonstrate that the restriction of the various results is not superfluous. In fact, our results unify and extend several well known theorems in literature. 相关文章 | 多维度评价

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7. 时间分数阶对流-扩散方程的有限差分解法 马燕, MUSBAH F.S. 数学季刊    2019, 34 (3): 259-273.   DOI: 10.13371/j.cnki.chin.q.j.m.2019.03.004 摘要 （98）      PDF（pc） （559KB）（302）    可视化    收藏 In this paper, three implicit finite difference methods are developed to solve one dimensional time fractional advection-diffusion equation. The fractional derivative is treated by applying right shifted Gr¨unwald-Letnikov formula of order α∈(0, 1). We investigate the stability analysis by using von Neumann method with mathematical induction and prove that these three proposed methods are unconditionally stable. Numerical results are presented to demonstrate the effectiveness of the schemes mentioned in this paper. 相关文章 | 多维度评价

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8. 代数曲线的相交重数 梁宏昌 数学季刊    2019, 34 (1): 14-20.   DOI: 10.13371/j.cnki.chin.q.j.m.2019.01.002 摘要 （100）      PDF（pc） （306KB）（250）    可视化    收藏 In this paper, we study the intersection multiplicity of algebraic curves at a point both in R2 and in real projective plane P2. We introduce the fold point of curves and provide conditions for the relations between the intersection multiplicity of curves at a point and the folds of the point.  相关文章 | 多维度评价

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9. 幺半群上的强α-自反环 彭宅铭 , 谷勤勤 , 张蕊蕊 数学季刊    2018, 33 (3): 260-271.   DOI: 10.13371/j.cnki.chin.q.j.m.2018.03.004 摘要 （69）      PDF（pc） （445KB）（264）    可视化    收藏 For a monoid M and an endomorphism α of a ring R, we introduce the notion of strongly M-α-reflexive rings and study its properties. For an u.p.-monoid M and a right Ore ring R with its classical right quotient ring Q, we prove that R is strongly M-α-reflexive if and only if Q is strongly M-α-reflexive, where R is α-rigid, α is an epimorphism of R. The relationship between some special subrings of upper triangular matrix rings and strongly M-α-reflexive rings is also investigated. Several known results similar to strongly M-α-reversible rings are obtained.  相关文章 | 多维度评价

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10. 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）      PDF（pc） （404KB）（182）    可视化    收藏 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. 相关文章 | 多维度评价

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11. 有限元方法的后验误差估计 鄂维南, 穆默, 黄鸿慈 数学季刊    1988, 3 (1): 97-107.   摘要 （432）      PDF（pc） （588KB）（326）    可视化    收藏 有限元的误差分析理论已有丰富的成果,但一般以先验估计为主。这些理论对算法评价和指导计算无疑具有重要意义。但实际计算中常要求给出误差的定量估计,先验估计一般就做不到这一点,因为其中会有如微分方程解的导数等不可计算的量。后验误差估计的研究近年来已开始受到注意。在多重网格技术中基于误差渐近展开的外推可以给出逐点意义下的后验估计。（例如见[1],[2]）另一条途径是通过局部化进行能量模意义下的后验误差估计。其中对一维边值问题的研究已较成熟。[7]就常系数  相关文章 | 多维度评价

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12. 求解低秩列稀疏矩阵恢复问题的嵌套交替方向乘子法 沈楠, 靳正芬, 王秋雨 数学季刊    2021, 36 (1): 90-110.   DOI: 10.13371/j.cnki.chin.q.j.m.2021.01.007 摘要 （143）      PDF（pc） （427KB）（379）    可视化    收藏 The task of dividing corrupted-data into their respective subspaces can be well illustrated, both theoretically and numerically, by recovering low-rank and sparse-column components of a given matrix. Generally, it can be characterized as a matrix and a `2,1-norm involved convex minimization problem. However, solving the resulting problem is full of challenges due to the non-smoothness of the objective function. One of the earliest solvers is an 3-block alternating direction method of multipliers (ADMM) which updates each variable in a Gauss-Seidel manner. In this paper, we present three variants of ADMM for the 3-block separable minimization problem. More preciously, whenever one variable is derived, the resulting problems can be regarded as a convex minimization with 2 blocks, and can be solved immediately using the standard ADMM. If the inner iteration loops only once, the iterative scheme reduces to the ADMM with updates in a Gauss-Seidel manner. If the solution from the inner iteration is assumed to be exact, the convergence can be deduced easily in the literature. The performance comparisons with a couple of recently designed solvers illustrate that the proposed methods are effective and competitive. 相关文章 | 多维度评价

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13. 考虑毛管形状的幂律流体等效渗透率计算方法 杨二龙, 李欢, 高慧娟, 谷婷婷 数学季刊    2015, 30 (3): 420-428.   DOI: 10.13371/j.cnki.chin.q.j.m.2015.03.013 摘要 （27）      PDF（pc） （534KB）（158）    可视化    收藏 While studying the flow of oil and gas in the reservoir, it is not realistic that capillary with circular section is only used to express the pores. It is more representative to simulate porous media pore with kinds of capillary with triangle or rectangle section etc. In the condition of the same diameter, when polymer for oil displacement flows in the porous medium, there only exists shear flow which can be expressed with power law model. Based on fluid flow-pressure drop equation in single capillary, this paper gives a calculation method of equivalent permeability of power law fluid of single capillary and capillary bundles with different sections. 相关文章 | 多维度评价

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14. 具有对数非线性项的伪抛物型 p-Laplacian 型方程的初边值问题 潘嘉慧, 房少梅 数学季刊    2023, 38 (4): 360-369.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.04.003 摘要 （37）      PDF（pc） （358KB）（104）    可视化    收藏  In this paper, we study the initial boundary value problem of pseudo-parabolic p-Laplacian type equation, which be use to model some important physical and biological phenomena. By using the potential well method, we obtain the global existence, asymptotic behavior and blow up results of weak solution with subcritical initial energy. Then we also extend these results to the critical initial energy. 相关文章 | 多维度评价

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15. 规范场中Skyrme模型单位拓扑电荷的双荷子 吴忠林, 李东亚 数学季刊    2019, 34 (2): 152-170.   DOI: 10.13371/j.cnki.chin.q.j.m.2019.02.004 摘要 （57）      PDF（pc） （609KB）（328）    可视化    收藏 Dyons are an important family of topological solitons carrying both electric and magnetic charges and the presence of a nontrivial temporal component of the gauge field essential for the existence of electricity often makes the analysis of the underlying nonlinear equations rather challenging since the governing action functional assumes an indefinite form. In this work, developing a constrained variational technique, We establish an existence theorem for the dyon solitons in a Skyrme model coupled with SO(3)-gauge fields, formulated by Brihaye, Kleihaus, and Tchrakian. These solutions carry unit monopole and Skyrme charges.  相关文章 | 多维度评价

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16. 关于3-正则哈密尔顿图的围长的一个注记 赵秋兰, 原晋江 数学季刊    2022, 37 (4): 430-431.   DOI: 10.13371/j.cnki.chin.q.j.m.2022.04.011 摘要 （52）      PDF（pc） （226KB）（69）    可视化    收藏 It is well-known that the Petersen graph is nonhamiltonian. A very short proof for this result was presented in [2] due to D. B. West. In this note, by extending the proof technique in [2], we briefly show that the girth of every 3-regular hamiltonian graph on n≥10 vertices is at most (n+ 4)/3. 相关文章 | 多维度评价

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17. 具有勢壘的Sturm-Liouville算子的特徵值和特徵函數 SARWAR Qanitah 黄振友 ZAHID Abdul Hannan 数学季刊    2023, 38 (1): 50-61.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.01.004 摘要 （112）      PDF（pc） （279KB）（131）    可视化    收藏 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. 相关文章 | 多维度评价

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18. 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）      PDF（pc） （622KB）（257）    可视化    收藏  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. 相关文章 | 多维度评价

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19. 关于二重Ore扩张的一点注释 李启宁 数学季刊    2019, 34 (1): 99-110.   DOI: 10.13371/j.cnki.chin.q.j.m.2019.01.011 摘要 （97）      PDF（pc） （439KB）（229）    可视化    收藏 The aim of this article is to summarize the relationship between double Ore extensions and iterated Ore extensions, and mainly describe the lifting of properties from an algebra A to a(right) double Ore extension B of A which can not be presented as iterated Ore extensions.  相关文章 | 多维度评价

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20. 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）      PDF（pc） （283KB）（164）    可视化    收藏 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. 相关文章 | 多维度评价