数学季刊

杨瑞, 马燕菲

2024, 39(1): 1-17. doi:10.13371/j.cnki.chin.q.j.m.2024.01.001

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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.

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

2024, 39(1): 18-30. doi:10.13371/j.cnki.chin.q.j.m.2024.01.002

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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.

凸复Finsler流形上的Hopf-Rinow定理

李鸿军

2024, 39(1): 31-45. doi:10.13371/j.cnki.chin.q.j.m.2024.01.003

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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).

凸F-多边形内部的F-点数

郭自欢, 魏祥林

2024, 39(1): 46-58. doi:10.13371/j.cnki.chin.q.j.m.2024.01.004

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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

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

2024, 39(1): 59-67. doi:10.13371/j.cnki.chin.q.j.m.2024.01.005

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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.

强乘积图的最小强半径

刘树洋, 李峰

2024, 39(1): 68-72. doi:10.13371/j.cnki.chin.q.j.m.2024.01.006

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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.

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

2024, 39(1): 73-81. doi:10.13371/j.cnki.chin.q.j.m.2024.01.007

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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

关于两个两点Witten-Kontsevich关联子公式等价的一个注记

郭晋东

2024, 39(1): 82-85. doi:10.13371/j.cnki.chin.q.j.m.2024.01.008

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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.

规范场论中自对偶磁单极子解的存在唯一性

陈筱

2024, 39(1): 86-96. doi:10.13371/j.cnki.chin.q.j.m.2024.01.009

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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.

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

2024, 39(1): 97-110. doi:10.13371/j.cnki.chin.q.j.m.2024.01.010

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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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