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1. 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 （188）      PDF（pc） （306KB）（831）    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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2. 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 （129）      PDF（pc） （534KB）（773）    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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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 （134）      PDF（pc） （1147KB）（681）    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. 全平面上Laplace-Stieltjes变换所表示整函数的增长性 宁菊红, 宋文佩, 黄文平 数学季刊    2020, 35 (4): 363-369.   DOI: 10.13371/j.cnki.chin.q.j.m.2020.04.004 摘要 （163）      PDF（pc） （315KB）（514）    可视化    收藏  In the paper, the α-order of the Laplace-Stieltjes Transform is introduced firstly, then we get the relationship between  α-order represented by the maximum modulus and α-order represented by A∗n, λn. Lastly, we obtain the relationship between type τ represented by the maximum modulus and type τ represented by A∗n, λn. 相关文章 | 多维度评价

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5. 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 （958）      PDF（pc） （588KB）（485）    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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6. 常微分方程双曲不动点结构稳定性的证明 王琪, 张硕 数学季刊    2018, 33 (1): 93-97.   DOI: 10.13371/j.cnki.chin.q.j.m.2018.01.011 摘要 （203）      PDF（pc） （254KB）（476）    可视化    收藏 In ordinary differential equations, structural stability of hyperbolic fixed points is a classical result, but the proof of this result in [2] has same small mistake. In this paper,we will correct the above mistake by using the Hartman theorem and its idea.  相关文章 | 多维度评价

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7. 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 （324）      PDF（pc） （895KB）（469）    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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8. 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 （542）      PDF（pc） （427KB）（468）    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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9. 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 （242）      PDF（pc） （293KB）（441）    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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10. 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 （181）      PDF（pc） （559KB）（432）    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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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 （381）      PDF（pc） （1238KB）（426）    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. 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 （459）      PDF（pc） （533KB）（426）    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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13. 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 （279）      PDF（pc） （473KB）（421）    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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14. r-正则有向图的多数染色 夏伟皓, 石美, 肖明月, 蔡建生, 王纪辉 数学季刊    2022, 37 (2): 142-146.   DOI: 10.13371/j.cnki.chin.q.j.m.2022.02.004 摘要 （301）      PDF（pc） （330KB）（417）    可视化    收藏  A majority k-coloring of a digraph D with k colors is an assignment c: V ( D ) →{ 1,2,···,k} , such that for every v∈V (D), we have c(w)=c(v) for at most half of all out-neighbors w∈N+( v ). For a natural number k≥2, a 1/k-majority coloring of a digraph is a coloring of the vertices such that each vertex receives the same color as at most a 1/k proportion of its out-neighbours. Kreutzer, Oum, Seymour, van der Zypen and Wood proved that every digraph has a majority 4-coloring and conjectured that every digraph admits a majority 3-coloring. Gir$\widetilde{a}$o, Kittipassorn and Popielarz proved that every digraph has a 1/k-majority 2k-coloring and conjectured that every digraph admits a 1\k-majority (2k−1)-coloring. We showed that every r -regular digraph D with r>36ln(2n) has a majority 3-coloring and proved that every digraph D with minimum outdegree $\delta^+>\frac{2k^2(2k-1)^2}{(k-1)^2}\ln{[(2k-1)n]}$ has a 1/k-majority (2k−1)-coloring. And we also proved that every r-regular digraph D with  $r>\frac{3k^2(2k-1)}{(k-1)^2} \ln(2n)$ has a 1/k-majority (2k−1)-coloring. 相关文章 | 多维度评价

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15. n-倾斜挠类与n-余倾斜挠自由类 何东林, 李煜彦 数学季刊    2019, 34 (2): 196-203.   DOI: 10.13371/j.cnki.chin.q.j.m.2019.02.007 摘要 （145）      PDF（pc） （326KB）（409）    可视化    收藏 In this paper, we consider some generalizations of tilting torsion classes and cotilting torsion-free classes, give the definition and characterizations of n-tilting torsion classes and n-cotilting torsion-free classes, and study n-tilting preenvelopes and n-cotilting precovers.  相关文章 | 多维度评价

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16. 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 （205）      PDF（pc） （538KB）（401）    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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17. 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 （698）      PDF（pc） （1154KB）（400）    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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18. 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 （216）      PDF（pc） （439KB）（389）    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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19. 3-正则无爪图的导出匹配覆盖 董丽, 汤京永, 宋新宇 数学季刊    2011, 26 (3): 355-359.   摘要 （71）      PDF（pc） （271KB）（384）    可视化    收藏 The induced matching cover number of a graph G without isolated vertices, denoted by imc(G), is the minimum integer k such that G has k induced matchings {M1,M2,···,Mk} such that, V(M1)∪V(M2)∪···∪V(Mk) covers V(G). This paper shows that, if G is a 3-regular claw-free graph, then imc(G)∈{2,3}. 相关文章 | 多维度评价

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20. 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 （216）      PDF（pc） （913KB）（375）    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