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1. 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 （240）      PDF（pc） （2367KB）（316）    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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2. 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 （217）      PDF（pc） （404KB）（305）    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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3. 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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4. 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 （156）      PDF（pc） （319KB）（212）    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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5. 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 （174）      PDF（pc） （307KB）（208）    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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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 （200）      PDF（pc） （1289KB）（204）    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. 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 （220）      PDF（pc） （279KB）（180）    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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8. Stokes 现象与量子群的表示 徐晓濛 数学季刊    2023, 38 (3): 311-330.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.03.005 摘要 （145）      PDF（pc） （458KB）（177）    可视化    收藏 This is a survey paper that lists our research works in the study of Stokes phenomenon of meromorphic ordinary differential equations and its relation with representation theory of quantum groups 相关文章 | 多维度评价

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9. 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 （113）      PDF（pc） （358KB）（170）    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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10. 凸复Finsler流形上的Hopf-Rinow定理 李鸿军 数学季刊    2024, 39 (1): 31-45.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.01.003 摘要 （161）      PDF（pc） （365KB）（158）    可视化    收藏 Suppose (M,F) is a convex complex Finsler manifold. We prove that geodesics of (M,F) are locally minimizing. Hence, F introduces a distance function d such that (M,d) is a metric space from topology. Next, we prove the classical Hopf-Rinow Theorem holds on (M,F). 相关文章 | 多维度评价

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11. 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 （223）      PDF（pc） （389KB）（155）    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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12. 规范场论中自对偶磁单极子解的存在唯一性 陈筱 数学季刊    2024, 39 (1): 86-96.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.01.009 摘要 （100）      PDF（pc） （316KB）（147）    可视化    收藏 Magnetic monopoles stand for the static solution arising from a (1+ 3)– dimensional theory describing the interaction between a real scalar triplet and non–Abelian gauge field. In this paper, we obtain a two–point boundary value problem of a first–order ordinary differential equations from the self–dual monopole model. Then we establish the existence and uniqueness theorem for the problem by using a dynamical shooting method, we also obtain sharp asymptotic estimates for the solutions at infinity. 相关文章 | 多维度评价

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13. 曲面上的曲率在理论物理中的一些应用 杨亦松 数学季刊    2023, 38 (3): 221-253.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.03.001 摘要 （537）      PDF（pc） （496KB）（146）    可视化    收藏 In this survey article, we present two applications of surface curvatures in theoretical physics. The first application arises from biophysics in the study of the shape of cell vesicles involving the minimization of a mean curvature type energy called the Helfrich bending energy. In this formalism, the equilibrium shape of a cell vesicle may present itself in a rich variety of geometric and topological characteristics. We first show that there is an obstruction, arising from the spontaneous curvature, to the existence of a minimizer of the Helfrich energy over the set of embedded ring tori. We then propose a scale-invariant anisotropic bending energy, which extends the Canham energy, and show that it possesses a unique toroidal energy minimizer, up to rescaling, in all parameter regime. Furthermore, we establish some genus-dependent topological lower and upper bounds, which are known to be lacking with the Helfrich energy, for the proposed energy. We also present the shape equation in our context, which extends the Helfrich shape equation. The second application arises from astrophysics in the search for a mechanism for matter accretion in the early universe in the context of cosmic strings. In this formalism, gravitation may simply be stored over a two-surface so that the Einstein tensor is given in terms of the Gauss curvature of the surface which relates itself directly to the Hamiltonian energy density of the matter sector. This setting provides a lucid exhibition of the interplay of the underlying geometry, matter energy, and topological characterization of the system. In both areas of applications, we encounter highly challenging nonlinear partial differential equation problems. We demonstrate that studies on these equations help us to gain understanding of the theoretical physics problems considered. 相关文章 | 多维度评价

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14. 单层圆柱形网格图的独立多项式和Merrifield-Simmons指数 季琳星, 张 科, 胡文军 数学季刊    2024, 39 (4): 379-387.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.04.004 摘要 （80）      PDF（pc） （490KB）（137）    可视化    收藏 Research on the independence polynomial of graphs has been very active. However, the computational complexity of determining independence polynomials for general graphs remains NP-hard. Let α(G) be the independence number of G and i(G; k) be the number of independent sets of order k in G, then the independence polynomial is defined as ...... 相关文章 | 多维度评价

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15. 矩阵方程的最小二乘{P,Q,k+1}-自反解 董昌州, 李浩雪 数学季刊    2023, 38 (2): 210-220.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.02.008 摘要 （148）      PDF（pc） （383KB）（136）    可视化    收藏  Let P ∈C m×m and Q∈C n×n be Hermitian and {k +1 } -potent matrices, i.e., P k+1 = P = P ∗ , Q k+1 = Q = Q ∗ , where ( · ) ∗ stands for the conjugate transpose of a matrix. A matrix X ∈C m×n is called {P,Q,k +1 } -reflexive (anti-reflexive) if PXQ = X ( PXQ = −X ). In this paper, the least squares solution of the matrix equation AXB = C subject to {P,Q,k +1 } -reflexive and anti--reflexive constraints are studied by converting into two simpler cases: k=1 and k=2. 相关文章 | 多维度评价

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16. 富勒烯图的极大共振性 杨瑞, 马燕菲 数学季刊    2024, 39 (1): 1-17.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.01.001 摘要 （159）      PDF（pc） （551KB）（134）    可视化    收藏 A {(3,4),4}-fullerene graph S is a 4-regular map on the sphere whose faces are of length 3 or 4. It follows from Euler’s formula that the number of triangular faces is eight. A set H of disjoint quadrangular faces of S is called resonant pattern if S has a perfect matching M such that every quadrangular face in H is M-alternating. Let k be a positive integer, S is k-resonant if any i≤k disjoint quadrangular faces of S form a resonant pattern. Moreover, if graph S is k-resonant for any integer k, then S is called maximally resonant. 相关文章 | 多维度评价

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17. 带位势的基尔霍夫方程规范解的存在性 梁艳霞 数学季刊    2023, 38 (2): 196-209.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.02.007 摘要 （238）      PDF（pc） （378KB）（133）    可视化    收藏  In this paper we discuss the following Kirchhoff equation \left\{ \begin{array}{lr} -\left(a+b \int_{\mathbb{R}^3}|\nabla u|^{2} d x\right) \Delta u+V(x)u+\lambda u=\mu|u|^{q-2}u+|u|^{p-2}u \ {\rm in}\ \mathbb{R}^3,&\\ \int_{\mathbb{R}^{3}}u^{2}dx=c^2, \end{array} \right. where a, b, µ and c are positive numbers, λ is unknown and appears as a Lagrange multiplier, 14/3<q<p<6 and V is a continuous non-positive function vanishing at infinity. Under some mild assumptions on V , we prove the existence of a mountain pass normalized solution. To the author’s knowledge, it is the first time to study the existence of normalized solution to Kirchhoff equation with potential via the minimax principle. 相关文章 | 多维度评价

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18. 奇异鞍点问题中广义位移分裂迭代方法的半收敛性分析 黄卓红 数学季刊    2023, 38 (2): 145-156.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.02.004 摘要 （140）      PDF（pc） （300KB）（133）    可视化    收藏 Recently, some authors (Shen and Shi, 2016) studied the generalized shift- splitting (GSS) iteration method for singular saddle point problem with nonsymmetric positive definite (1,1)-block and symmetric positive semidefinite (2,2)-block. In this paper, we further apply the GSS iteration method to solve singular saddle point problem with nonsymmetric positive semidefinite (1,1)-block and symmetric positive semidefinite (2,2)-block, prove the semi-convergence of the GSS iteration method and analyze the spectral properties of the corresponding preconditioned matrix. Numerical experiment is given to indicate that the GSS iteration method with appropriate iteration parameters is effective and competitive for practical use. 相关文章 | 多维度评价

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19. 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 （194）      PDF（pc） （589KB）（130）    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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20. 关于全局吸引子的一个新的存在性定理以及它对于非经典扩散方程的应用 秦玉明, 陈家乐, 姜慧特 数学季刊    2023, 38 (3): 276-289.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.03.003 摘要 （168）      PDF（pc） （364KB）（128）    可视化    收藏 In this paper, we first survey existed theorems and propose all 46 related open problems of the existence of global attractors for autonomous dynamical systems, then establish a new existence theorem of global attractors which will be applied to a nonclassical diffusion equation for the norm-to-weak continuous, weakly compact semigroup on H01(Ω) and H2(Ω)∩H01(Ω) respectively. As an application of this new existence theorem of global attractors, we obtain the existence of the global attractors onH01(Ω) and H2(Ω)∩ H01(Ω) respectively for a nonclassical-diffusion equation. 相关文章 | 多维度评价