Table of Content

30 March 2024, Volume 39 Issue 1

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Maximal Resonance of {(3,4),4}-Fullerene Graphs

YANG Rui, MA Yan-fei

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.

Implicit Finite Difference Method for Time-Space Caputo-Riesz Fractional Diffusion Equation with Fractional Robin Boundary Conditions

TANG Zhong-hua, FANG Shao-mei

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.

Hopf-Rinow Theorem on Convex Complex Finsler Manifolds

LI Hong-jun

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).

On the Number of F-Points Inside a Convex F-Polygon

GUO Zi-huan, WEI Xiang-lin

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

Boundedness of Integral and Discrete Operators Between Two Types of Weighted Spaces and Estimation of Operator Norm

HONG Yong, ZHAO Qian

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.

Minimum Strong Radius of Strong Product Graphs

LIU Shu-yang, LI Feng

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 ×G2 and the strong product graph G1 ⊠G2, another different upper bound of the minimum strong radius of the strong product graph is given.



Some New Regularity Criteria for the 3D Boussinesq Equations in Homogeneous Besov Spaces

ZOU Mian-lu, LI Qiang

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

A Remark on Equivalence between Two Formulas of the Two-point Witten-Kontsevich Correlators

GUO Jin-dong

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.

The Existence and Uniqueness of Self–Dual Monopole Solutions in Gauge Field Theory

CHEN Xiao

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.

Finite Time Blow-Up and Global Existence for Degenerate Parabolic Equations at High Initial Energy

LIU Gong-wei, YANG Kun

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.