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1. 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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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）      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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3. 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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4. 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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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. 代数微分方程组的分量允许解 李国望, 高凌云 数学季刊    2011, 26 (3): 457-461.   摘要 （30）      PDF（pc） （261KB）（25）    可视化    收藏 Using the Nevanlinna value distribution theory of meromorphic function, we investigate the existence problem of admissible solutions of higher-order algebraic differential equations systems, and obtain a result concerning admissible components of solution. 相关文章 | 多维度评价

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7. 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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8. 集值映射向量优化的ε-强有效解 王其林 数学季刊    2010, 25 (1): 104-109.   摘要 （19）      PDF（pc） （277KB）（27）    可视化    收藏 In locally convex Hausdorff topological vector spaces, ε-strongly efficient solutions for vector optimization with set-valued maps are discussed. Firstly, ε-strongly efficient point of set is introduced. Secondly, under the nearly cone-subconvex like set-valued maps, the theorem of scalarization for vector optimization is obtained. Finally, optimality conditions of ε-strongly efficient solutions for vector optimization with generalized inequality constraints and equality constraints are obtained. 相关文章 | 多维度评价

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9. 具有环境容纳量和成熟双时滞的有毒食饵-捕食者收获模型 钟颖, 韦煜明 数学季刊    2023, 38 (4): 331-348.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.04.001 摘要 （53）      PDF（pc） （589KB）（45）    可视化    收藏  In this paper, a model of predator-prey with dual delay in maturation and carrying capacity is discussed, in which the past activity of the prey should have an impact on the carrying capacity, the mature prey initiates defense mechanisms to release toxins when subjected to predation, and a commercial harvest of the prey is performed. The stability of the equilibrium of the system in the absence of delay is examined and the optimal harvesting strategy of the model is proven. By investigating the roots of the characteristic equation and applying normalized theory, the properties of the coexistence equilibrium of the system and the conditions for the occurrence of the Hopf bifurcation in the neighborhood of the positive equilibrium are described for various combinations of delays. In the end, numerical simulations are used to verify theoretical analysis results. 相关文章 | 多维度评价

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10. 带分数阶Robin边界条件的时间-空间分数阶扩散方程的有限差分方法 唐忠华, 房少梅 数学季刊    2024, 39 (1): 18-30.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.01.002 摘要 （31）      PDF（pc） （366KB）（27）    可视化    收藏 In this paper, an efficient numerical method is proposed to solve the CaputoRiesz fractional diffusion equation with fractional Robin boundary conditions. We approximate the Riesz space fractional derivatives using the fractional central difference scheme with second-order accurate. A priori estimation of the solution of the numerical scheme is given, and the stability and convergence of the numerical scheme are analyzed. Finally, a numerical example is used to verify the accuracy and efficiency of the numerical method. 相关文章 | 多维度评价

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11. 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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12. 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 （143）      PDF（pc） （473KB）（315）    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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13. 弱Hopf群余代数的Maschke型定理 贾玲, 陈笑缘 数学季刊    2015, 30 (1): 144-152.   DOI: 10.13371/j.cnki.chin.q.j.m.2015.01.015 摘要 （32）      PDF（pc） （358KB）（111）    可视化    收藏 In this paper, we mainly generalize a Maschke type theorem to the setting of a weak Hopf group coalgebra. First we introduce the notion of a weak Hopf group coalgebra as a generalization of Hopf group coalgebra introduced in [7] and a weak Hopf algebra introduced in [2]. And we study some basic properties of weak Hopf group coalgebras. Next we aim at finding some sufficient conditions under which an epimorphism of weak（H, A）Hopf π-comodule splits if it splits as an A-module morphism and give an application of our results.  相关文章 | 多维度评价

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14. 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）      PDF（pc） （285KB）（224）    可视化    收藏  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. 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. 一个Schwarz引理的推广 赵连坤 , 李红裔 数学季刊    2017, 32 (1): 1-6.   DOI: 10.13371/j.cnki.chin.q.j.m.2017.01.001 摘要 （41）      PDF（pc） （291KB）（221）    可视化    收藏 In this paper, we establish a boundary Schwarz Lemma for holomorphic mapping on the generalized complex ellipsoid in C~n.  相关文章 | 多维度评价

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17. 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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18. 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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19. 由Frobenius对产生的Hovey三元组 刘硕 数学季刊    2021, 36 (2): 176-187.   DOI: 10.13371/j.cnki.chin.q.j.m.2021.02.006 摘要 （78）      PDF（pc） （420KB）（114）    可视化    收藏 We revisit Auslander-Buchweitz approximation theory and fifind some relations with cotorsion pairs and model category structures. From the notion of weak-cogenerators, we introduce the concept of Frobenius pair (X ,ω) in a triangulated category T . We show how to construct from a Frobenius pair (X ,ω) a triangulated model structure on X ∧. 相关文章 | 多维度评价

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20. 有向图的加权解析挠率 任世全, 王冲 数学季刊    2023, 38 (1): 30-49.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.01.003 摘要 （100）      PDF（pc） （389KB）（107）    可视化    收藏  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. 相关文章 | 多维度评价