数学季刊

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1. 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（106）

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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.

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2. 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（97）

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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.

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3. 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（96）

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In this paper, an efficient numerical method is proposed to solve the Caputo-Riesz 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.

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4. 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（85）

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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).

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5. 具有奇异势和一般非线性的伪抛物方程解的局部存在性和爆破

江东月, 唐忠华, 房少梅

数学季刊 2024, 39 (2): 111-127. DOI: 10.13371/j.cnki.chin.q.j.m.2024.02.001

摘要（83）

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In this paper, a semilinear pseudo-parabolic equation with a general nonlinearity and singular potential is considered. We prove the local existence of solution by Galerkin method and contraction mapping theorem. Moreover, we prove the blow-up of solution and estimate the upper bound of the blow-up time for J(u0)≤0. Finally, we prove the finite time blow-up and estimate the upper bound of blow-up time for J(u0)>0.

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6. 强乘积图的最小强半径

刘树洋, 李峰

数学季刊 2024, 39 (1): 68-72. DOI: 10.13371/j.cnki.chin.q.j.m.2024.01.006

摘要（70）

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A strong product graph is denoted by G₁ ⊠G₂, where G₁ and G₂ are called its factor graphs. This paper gives the range of the minimum strong radius of the strong product graph. And using the relationship between the cartesian product graph G₁ ×G₂and the strong product graph G₁ ⊠G₂, another different upper bound of the minimum strong radius of the strong product graph is given.

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7. 贝索夫空间中三维布辛涅斯克方程的一些新的正则性准则

邹绵璐, 李强

数学季刊 2024, 39 (1): 73-81. DOI: 10.13371/j.cnki.chin.q.j.m.2024.01.007

摘要（69）

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In this paper, we study the regularity criterion for the three-dimensional Boussinesq equations in Besov spaces. We show that the smooth solution (u,θ) is regular if the horizonal velocity uh holds

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8. 两类四圈图的奇异性

攸晓杰, 马海成, 张斌, 李雅兰

数学季刊 2023, 38 (4): 349-359. DOI: 10.13371/j.cnki.chin.q.j.m.2023.04.002

摘要（62）

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Let G be a finite simple graph and A(G) be its adjacency matrix. Then G is singular if A(G) is singular. The graph obtained by bonding the starting vertices and ending vertices of three paths P_a1, P_a2, P_a3is called θ-graph, represented by θ(a1,a2,a3). The graph obtained by bonding the two end vertices of the path P_s to the vertices of the θ(a₁,a₂,a₃) and θ(b₁,b₂,b₃) of degree three, respectively, is denoted by α(a₁,a₂,a₃,s,b₁,b₂,b₃) and called α-graph. β-graph is denoted when β(a₁,a₂,a₃,b₁,b₂,b₃) =α(a₁,a₂,a₃,1,b₁,b₂,b₃). In this paper, we give the necessary and sufficient conditions for the singularity of α-graph and β-graph, and prove that the probability that a random given α-graph and β-graph is a singular graph is equal to 1423/2048 and 733/1024 , respectively.

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9. 一类包含广义Mittag-Leffler函数的积分算子的从属与超从属结果

王小元, 刘亚娟

数学季刊 2023, 38 (4): 379-391. DOI: 10.13371/j.cnki.chin.q.j.m.2023.04.005

摘要（58）

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In the paper, by making use of the principle of subordination between analytic functions with the multiplier transforms defined by generalized Mittag-Leffler function, the authors investigate subclasses of univalent analytic functions, such as starlike functions, convex functions, close-to-convex functions and quasiconvex functions. Several inclusion relationships, inequality properties, subordination and superordination results associated with the multiplier transforms are proved and the sandwich-type results are also obtained.

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10. 在复二维仿射锥上的完备余齐性一Kähler度量

关庄丹, 梁梦翔

数学季刊 2024, 39 (2): 200-220. DOI: 10.13371/j.cnki.chin.q.j.m.2024.02.008

摘要（58）

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In this paper, we revisit the K¨ahler structures on the affine quadrics M₁={z₁² +z₂² +z₃² = 1} in the paper by Bo Yang and Fang-Yang Zheng. We found that theK¨ahler structures on the complex surface are more complicated than what they havethought. We shall also give some detail calculations and found that our results fit quitewell with earlier papers of the first author, one of them with X. X. Chen.

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11. 一类退化抛物方程高初始能量下解的有限时刻爆破及整体存在性

刘功伟, 杨坤

数学季刊 2024, 39 (1): 97-110. DOI: 10.13371/j.cnki.chin.q.j.m.2024.01.010

摘要（57）

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We consider the initial-boundary value problem for finitely degenerate parabolic equation. We first give sufficient conditions for the blow-up and global existence of the parabolic equation at high initial energy level. Then, we establish the existence of solutions blowing up in finite time with initial data at arbitrary energy level. Finally, we estimate the upper bound of the blow-up time under certain conditions.

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12. 一类 Gerstenhaber 代数的构造

侯波, 扣雯

数学季刊 2023, 38 (4): 370-378. DOI: 10.13371/j.cnki.chin.q.j.m.2023.04.004

摘要（57）

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For any K-algebra A, based on Hochschild complex and Hochschild cohomology of A, we construct a new Gerstenhaber algebra, and give Gerstenhaber algebra epimorphism from the new Gerstenhaber algebra to the Gerstenhaber algebra of the Hochschild cohomology of A.

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13. 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（56）

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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.

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14. 两类加权空间间的积分算子与离散算子的有界性及算子范数估计

洪勇, 赵茜

数学季刊 2024, 39 (1): 59-67. DOI: 10.13371/j.cnki.chin.q.j.m.2024.01.005

摘要（53）

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Using the weight coefficient method, we first discuss semi-discrete Hilbert-type inequalities, and then discuss boundedness of integral and discrete operators and operator norm estimates based on Hilbert-type inequalities in weighted Lebesgue space and weighted normed sequence space.

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15. 一个一维二阶拟线性双曲组的精确边界能控性

王珂, 潘盼盼

数学季刊 2023, 38 (4): 424-440. DOI: 10.13371/j.cnki.chin.q.j.m.2023.04.010

摘要（52）

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In this paper, we propose a second-order quasilinear hyperbolic system. By means of the theory on semi-global C¹solution to first-order quasilinear hyperbolic systems, we establish the existence and uniqueness of semi-global C²solution to this second-order quasilinear hyperbolic system. After then, the general constructive framework is utilized to obtain the local exact boundary controllability for this second-order system. Keywords: First-order quasilinear hyperbolic system; Second-order quasilinear hyperbolic system; Semi-global solution; Exact boundary controllability

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16. 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（51）

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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.

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17. 一个2×2块矩阵的Moore-Penrose逆的显式公式

曾敏, 袁永新

数学季刊 2023, 38 (4): 401-409. DOI: 10.13371/j.cnki.chin.q.j.m.2023.04.007

摘要（49）

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The representation for the Moore-Penrose inverse of the matrix
A B
C D
is derived by using the solvability theory of linear equations, where A∈C^m×n, B∈C^m×p, C∈C^q×nand D∈C^q×p, with which some special cases are discussed.

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18. 基于半参数Copula学习的确定性独立筛选研究

辛欣, 谢博易, 刘科科

数学季刊 2024, 39 (2): 144-160. DOI: 10.13371/j.cnki.chin.q.j.m.2024.02.003

摘要（46）

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This paper is concerned with ultrahigh dimensional data analysis, which has become increasingly important in diverse scientific fields. We develop a sure independence screening procedure via the measure of conditional mean dependence based on Copula (CC-SIS, for short). The CC-SIS can be implemented as easily as the sure independence screening procedures which respectively based on the Pearson correlation, conditional mean and distance correlation (SIS, SIRS and DC-SIS, for short) and can significantly improve the performance of feature screening. We establish the sure screening property for the CC-SIS, and conduct simulations to examine its finite sample performance. Numerical comparison indicates that the CC-SIS performs better than the other two methods in various models. At last, we also illustrate the CC-SIS through a real data example.

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19. 关于两个两点Witten-Kontsevich关联子公式等价的一个注记

郭晋东

数学季刊 2024, 39 (1): 82-85. DOI: 10.13371/j.cnki.chin.q.j.m.2024.01.008

摘要（45）

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We prove the equivalence between two explicit expressions for two-point Witten-Kontsevich correlators obtained by Bertola-Dubrovin-Yang and by Zograf, respec-tively.

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20. 凸F-多边形内部的F-点数

郭自欢, 魏祥林

数学季刊 2024, 39 (1): 46-58. DOI: 10.13371/j.cnki.chin.q.j.m.2024.01.004

摘要（44）

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An F-polygon is a simple polygon whose vertices are F-points, which are points of the set of vertices of a tiling of R² by regular triangles and regular hexagons of unit edge. Let f(v) denote the least possible number of F-points in the interior of a convex F-polygon K with v vertices. In this paper we prove that f(10) = 10, f(11) = 12, f(12) = 12

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