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1. 关于数论函数值分布的研究 邵品琮 数学季刊    1987, 2 (2): 27-43.   摘要 （170）      PDF（pc） （895KB）（395）    可视化    收藏 对于数义在自然数集 N 上的数论函数（Arithmetical function）f（n）, n\inN,取值可以是实数, 也可以是复数（一般为实数）, 例如著名的 Euler 函数 \varphi(n)=\Sigma_{(a,n)=1,a<n}1,  除数函数τ（n）=\Sigma_{d/n}1,以及除数和函数σ（n）=\Sigma_{d/n}d  相关文章 | 多维度评价

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2. 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 （139）      PDF（pc） （427KB）（376）    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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3. 关于复几何中的一些新进展—与齐性流形相关的领域 关庄丹 数学季刊    2020, 35 (2): 111-144.   DOI: 10.13371/j.cnki.chin.q.j.m.2020.02.001 摘要 （434）      PDF（pc） （1154KB）（366）    可视化    收藏 In this article, we give a survey of some progress of the complex geometry, mostly related to the Lie group actions on compact complex manifolds and complex homogeneous spaces in the last thirty years. In particular, we explore some works in the special area in Dierential Geometry, Lie Group and Complex Homogeneous Space. Together with the special area in nonlinear analysis on complex manifolds, they are the two major aspects of my research interests. 相关文章 | 多维度评价

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4. 楼与群III 黎景辉 数学季刊    2021, 36 (1): 1-31.   DOI: 10.13371/j.cnki.chin.q.j.m.2021.01.001 摘要 （265）      PDF（pc） （533KB）（361）    可视化    收藏 This is the third part of a pedagogical introduction to the theory of buildings of Jacques Tits. We describe the construction and properties of the Bruhat-Tits building of a reductive group over a local field. 相关文章 | 多维度评价

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5. 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 （134）      PDF（pc） （293KB）（338）    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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6. 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 （51）      PDF（pc） （609KB）（321）    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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7. 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 （418）      PDF（pc） （588KB）（318）    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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8. 具非局部非线性阻尼和源项的波方程解的能量衰减估计 张宏伟, 李栋浩, 呼青英 数学季刊    2020, 35 (3): 302-310.   DOI: 10.13371/j.cnki.chin.q.j.m.2020.03.005 摘要 （138）      PDF（pc） （473KB）（308）    可视化    收藏 We consider a wave equation with nonlocal nonlinear damping and source terms. We prove a general energy decay property for solutions by constructing a stable set and using the multiplier technique. The main difficult is how to handle with the nonlocal nonlinear damping term. Our result extends and improves the result in the literature such as the work by Jorge Silva and Narciso（Evolution Equation and Control Theory, 2017（6）:437-470） and Narciso（Evolution Equations and Control Theory, 2020, 9（2）: 487-508）. 相关文章 | 多维度评价

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9. 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 （91）      PDF（pc） （559KB）（298）    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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10. 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 （115）      PDF（pc） （538KB）（296）    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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11. 楼与群Ⅱ 周国晖 , 黎景辉 数学季刊    2020, 35 (3): 221-254.   DOI: 10.13371/j.cnki.chin.q.j.m.2020.03.001 摘要 （270）      PDF（pc） （1238KB）（283）    可视化    收藏 This is the second part of a pedagogical introduction to the theory of buildings of Jacques Tits. We define a(B,N) pair and construct a building out of it. Then we give a description of Chevalley groups, their(B,N) pair and the associated buildings. We illustrates this theory with many examples from classical groups.  相关文章 | 多维度评价

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12. 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 （66）      PDF（pc） （445KB）（261）    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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13. 楼与群I 黎景辉, 梁志斌 数学季刊    2020, 35 (1): 1-28.   DOI: 10.13371/j.cnki.chin.q.j.m.2020.01.001 摘要 （149）      PDF（pc） （913KB）（259）    可视化    收藏 This is a pedagogical introduction to the theory of buildings of Jacques Tits and to some applications of this theory.This paper has 4 parts.In the first part we discuss incidence geometry,Coxeter systems and give two definitions of buildings.We study in the second part the spherical and affine buildings of Chevalley groups.In the third part we deal with Bruhat-Tits theory of reductive groups over local fields.Finally we discuss the construction of the p-adic flag manifolds.  相关文章 | 多维度评价

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14. 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 （81）      PDF（pc） （622KB）（256）    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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15. 带有分数阶Robin边界条件的Riesz空间分数阶对流-扩散方程的有限差分方法 林海欣 , 房少梅, 数学季刊    2020, 35 (3): 278-289.   DOI: 10.13371/j.cnki.chin.q.j.m.2020.03.003 摘要 （147）      PDF（pc） （611KB）（252）    可视化    收藏 In this paper, a Riesz space fractional advection-dispersion equation with fractional Robin boundary condition is considered. By applying the fractional central difference formula and the weighted and shifted Gru¨nwald-Letnikov formula, we derive a weighted implicit finite difference scheme with accuracy O（?t2+ h2）. The solvability,stability, and convergence of the proposed numerical scheme are proved. A numerical example is presented to confirm the accuracy and efficiency of the scheme.  相关文章 | 多维度评价

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16. 一维等熵流气体力学方程组的真空问题 李大潜, 赵彦淳 数学季刊    1986, 1 (1): 41-46.   摘要 （85）      PDF（pc） （373KB）（250）    可视化    收藏 相关文章 | 多维度评价

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17. 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 （93）      PDF（pc） （306KB）（249）    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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18. 有限体积方法非结构网格方法解分数阶Allen-Cahn程 陈爱敏, 刘发旺 数学季刊    2017, 32 (4): 345-354.   DOI: 10.13371/j.cnki.chin.q.j.m.2017.04.002 摘要 （75）      PDF（pc） （761KB）（245）    可视化    收藏 Fractional-in-space Allen-Cahn equation containing a very strong nonlinear source term and small perturbation shows metastability and a quartic double well potential.Using a finite volume unstructured triangular mesh method, the present paper solves the twodimensional fractional-in-space Allen-Cahn equation with homogeneous Neumann boundary condition on different irregular domains. The efficiency of the method is presented through numerical computation of the two-dimensional fractional-in-space Allen-Cahn equation on different domains.  相关文章 | 多维度评价

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19. 一 维动力系统 周作领 数学季刊    1988, 3 (1): 42-65.   摘要 （116）      PDF（pc） （1556KB）（245）    可视化    收藏  前言一维动力系统是指一维紧致连通流形即线段和圆周上的动力系统,也就是线段和圆周自映射理论,是最简单的动力系统。这种动力系统就是差分方程,而利用一阶差分方程这样一个简单的数学模型描述具体问题早在四十年代就已开始,并已经发现了某些复杂的性状。但从纯数学的角度进行理论研究那还是近代微分动力系统——大范围结构稳定性理论这一新兴大型综合性数学分支出现并接受其影响以后的事情。简而言之,近代微分动力系统研究的是微分流形上常微系统（向量场或流,包括微分自同胚）的大范围结构稳定性问题。在国外,这方面最早的观念在Andronov和Pon-  相关文章 | 多维度评价

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20. 奇异点附近的复微分方程解的增长性与系数下级的关系 刘元竹, 龙见仁, 曾三桂 数学季刊    2020, 35 (2): 163-170.   DOI: 10.13371/j.cnki.chin.q.j.m.2020.02.003 摘要 （184）      PDF（pc） （495KB）（239）    可视化    收藏 We investigate the growth of solutions of the following complex linear differential equation f’’+ A（z）f’+ B（z）f = 0,where A（z） and B（z） are analytic functions in C-{z0}, z0 ∈ C. Some estimations of lower bounded of growth of solutions of the differential equation are obtained by using the concept of lower order.  相关文章 | 多维度评价