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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. 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）      PDF（pc） （356KB）（230）    可视化    收藏 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. 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. 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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5. 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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6. 一类具有时滞的生态流行病模型的稳定性与 Hopf 分支 白宏芳 数学季刊    2023, 38 (2): 157-183.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.02.005 摘要 （96）      PDF（pc） （1289KB）（150）    可视化    收藏  In this paper, an eco-epidemiological model with time delay is studied. The local stability of the four equilibria, the existence of stability switches about the predation- free equilibrium and the coexistence equilibrium are discussed. It is found that Hopf bifurcations occur when the delay passes through some critical values. Formulae are obtained to determine the direction of bifurcations and the stability of bifurcating periodic solutions by using the normal form theory and center manifold theorem. Some numerical simulations are carried out to illustrate the theoretical results. 相关文章 | 多维度评价

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7. Bihom-李代数的同调 程永胜, 王梦平 数学季刊    2022, 37 (3): 237-247.   DOI: 10.13371/j.cnki.chin.q.j.m.2022.03.002 摘要 （71）      PDF（pc） （286KB）（139）    可视化    收藏  The purpose of this paper is to define Hochschild type homology of Bihom- associative algebras and Chevalley-Eilenberg type homology of Bihom-Lie algebras with non-trivial coefficients in their bimodules respectively. In particular, we give their low order homology in detail. 相关文章 | 多维度评价

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8. 顶点算子, 广义辛Schur函数的Littlewood-Richardson规则 黄芳, 楚彦军 数学季刊    2022, 37 (3): 301-316.   DOI: 10.13371/j.cnki.chin.q.j.m.2022.03.007 摘要 （73）      PDF（pc） （375KB）（136）    可视化    收藏  Littlewood-Richardson rule gives the expansion formula for decomposing a product of two Schur functions as a linear sum of Schur functions, while the decomposition formula for the multiplication of two symplectic Schur function is also given by the combinatorial method. In this paper, we will construct the algebraic forms of the decomposition formula for the product of two symplectic Schur functions by using the generating functions and vertex operator realizations, and then extend these results to generalized symplectic Schur functions. 相关文章 | 多维度评价

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9. 远程制备任意赤道态的简单通用协议 马松雅, 李翔, 李琦 数学季刊    2022, 37 (3): 260-273.   DOI: 10.13371/j.cnki.chin.q.j.m.2022.03.004 摘要 （106）      PDF（pc） （348KB）（135）    可视化    收藏  We first put forward a deterministic protocol to realize the remote preparation of arbitrary multi-qubit equatorial states via EPR pairs. A set of useful measurement basis is constructed which plays a key role. The receiver just needs to perform Pauli Z operations to recover the target state. Comparing with the previous protocols, the recovery operation is simplified and expressed by a general formula. As there are no universal protocols for high-dimensional systems, we further generalize to the case of multi-qudit equatorial states by means of Fourier transformation. It is worth mentioning that the proposed schemes can be extended to multi-party controlled remote state preparation. Moreover, we consider the effect of two-type decoherence noises. 相关文章 | 多维度评价

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10. 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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11. 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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12. 时间尺度上具有泄漏时滞的一般BAM神经网络概周期解的存在性和指数稳定性 董延寿, 韩艳, 代婷婷 数学季刊    2022, 37 (2): 189-202.   DOI: 10.13371/j.cnki.chin.q.j.m.2022.02.008 摘要 （81）      PDF（pc） （885KB）（129）    可视化    收藏  In this paper, the existence of almost periodic solutions to general BAM neural networks with leakage delays on time scales is first studied, by using the exponential dichotomy method of linear differential equations and fixed point theorem. Then, the exponential stability of almost periodic solutions to such BAM neural networks on time scales is discussed by utilizing differential inequality. Finally, an example is given to support our results in this paper and the results are up-to-date. 相关文章 | 多维度评价

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13. Allen-Cahn方程的虚拟元方法 王培珍, 田旭 数学季刊    2023, 38 (1): 20-29.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.01.002 摘要 （84）      PDF（pc） （307KB）（112）    可视化    收藏  In this article, the virtual element method of the Allen-Cahn equation on a polygon grid is discussed in the fully discrete formulation. With the help of the energy projection operator, we give the corresponding error estimates in the L2 norm and H1 norm. 相关文章 | 多维度评价

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14. 具有特定独立的罗马2-控制数的树 李贝贝, 尚卫苹 数学季刊    2022, 37 (4): 386-393.   DOI: 10.13371/j.cnki.chin.q.j.m.2022.04.006 摘要 （104）      PDF（pc） （336KB）（110）    可视化    收藏 For a graph G = (V,E), a Roman {2}-dominating function f :V → {0,1,2} has the property that for every vertex v ∈V with f(v) = 0, either v is adjacent to at least one vertex u for which f(u) = 2, or at least two vertices u1 and u2 for which f(u1) =f(u2) = 1. A Roman {2}-dominating function f = (V0,V1,V2) is called independent if V1∪V2 is an independent set. The weight of an independent Roman {2}-dominating function f is the value ω(f) =\sumv∈V f(v), and the independent Roman {2}-domination number i{R2}(G) is the minimum weight of an independent Roman {2}-dominating function on G. In this paper, we characterize all trees with i{R2}(T) =γ(T)+ 1, and give a linear time algorithm to compute the value of i{R2}(T) for any tree T.  相关文章 | 多维度评价

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15. 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

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16. 关于一类有限 p-群的因子分解数 王玉雷, 白雪, 张元峰 数学季刊    2022, 37 (2): 132-141.   DOI: 10.13371/j.cnki.chin.q.j.m.2022.02.003 摘要 （77）      PDF（pc） （353KB）（105）    可视化    收藏 Let G be a group and A and B be subgroups of G. If G = AB, then G is said to be factorized by A and B. Let p be a prime number. The factorization numbers of a 2-generators abelian p-group and a modular p-group have been determined. Further, suppose that G is a finite p-group as follows  G = <a,b|apn= bpm=1 , ab = apn−1+1>, where n≥ 2, m≥ 1. In this paper, the factorization number of G is computed completely, which is a generalization of the result of Saeedi and Farrokhi. 相关文章 | 多维度评价

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17. 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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18. Orbifold 基本群和 Deck 变换群 林奕武 数学季刊    2022, 37 (2): 147-161.   DOI: 10.13371/j.cnki.chin.q.j.m.2022.02.005 摘要 （96）      PDF（pc） （332KB）（101）    可视化    收藏 In this paper, we define the notions of orbifold loop and orbifold road, with which, we reformulate the definition of orbifold fundamental group and deck translation group. We show that, for each orbifold, the orbifold fundamental group is isomorphic to the deck translation group. 相关文章 | 多维度评价

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19. 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 （179）      PDF（pc） （330KB）（93）    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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20. 利用莫尔斯指标理论求解一类薛定谔方程解的存在性 李佳洋, 王琪 数学季刊    2022, 37 (3): 274-280.   DOI: 10.13371/j.cnki.chin.q.j.m.2022.03.005 摘要 （65）      PDF（pc） （338KB）（93）    可视化    收藏  In this paper, with the relative Morse index, we will study the existence of solutions of (1.1) under the assumptions that V satisfies some weaker conditions than those in [2]. 相关文章 | 多维度评价