数学季刊

Select

1. 一类对数p-Laplace抛物型方程中的爆破和衰减估计

李平, 李锋杰

数学季刊 2024, 39 (4): 331-354. DOI: 10.13371/j.cnki.chin.q.j.m.2024.04.001

摘要（247）

PDF（pc）（462KB）（114）

This paper deals with an initial-boundary value problem of a fourth-order parabolic equation involving Logarithmic type p-Laplacian, which could be proposed as a model for the epitaxial growth of thin films. By using the variational method and the
logarithmic type Sobolev inequality, we give some threshold results for blow-up solutions and global solutions, which could be classified by the initial energy. The asymptotic estimates about blow-up time and decay estimate of weak solutions are obtained.

相关文章 | 多维度评价

Select

2. 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（173）

PDF（pc）（366KB）（126）

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.

相关文章 | 多维度评价

Select

3. 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（162）

PDF（pc）（387KB）（55）

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.

相关文章 | 多维度评价

Select

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（161）

PDF（pc）（365KB）（158）

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

Select

5. 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）（135）

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

Select

6. 具有指数临界增长的薛定谔方程的高能正规化解

张小藏, 许丽萍

数学季刊 2025, 40 (1): 1-19. DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.001

摘要（153）

PDF（pc）（417KB）（47）

In this paper, we study high energy normalized solutions for the following Schrödinger equation ……

相关文章 | 多维度评价

Select

7. 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（151）

PDF（pc）（465KB）（109）

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.

相关文章 | 多维度评价

Select

8. 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（140）

PDF（pc）（267KB）（67）

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.

相关文章 | 多维度评价

Select

9. 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（138）

PDF（pc）（355KB）（124）

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

相关文章 | 多维度评价

Select

10. 水沙输运模型的间断有限元方法

张任鹏, 王波, 王强

数学季刊 2024, 39 (4): 355-365. DOI: 10.13371/j.cnki.chin.q.j.m.2024.04.002

摘要（132）

PDF（pc）（1085KB）（72）

In this article, we propose and research a first-order, linearized discontinuous Galerkin method for the approximation of the hydrodynamic and sediment transport model. The method is decoupled and fully discrete, and is shown to be unconditionally
stable. Furthermore, error estimates are proved. Finally, the theoretical analysis is confirmed by numerical examples.

相关文章 | 多维度评价

Select

11. 具有食饵避难所的离散捕食者-食饵模型的余维二分支分析

庞茹一, 陈巧玲

数学季刊 2024, 39 (2): 128-143. DOI: 10.13371/j.cnki.chin.q.j.m.2024.02.002

摘要（129）

PDF（pc）（842KB）（83）

In this paper, a discrete predator-prey model with prey refuge is investigated. It is proved that the model undergoes codimension-2 bifurcations associated with 1:2 and 1:3 resonances. The bifurcation diagrams and phase portraits show that the model has some interesting complex dynamical behaviors, such as limit cycle, periodic solutions, chaos and codimension-1 bifurcations.

相关文章 | 多维度评价

Select

12. 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（128）

PDF（pc）（393KB）（71）

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.

相关文章 | 多维度评价

Select

13. 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（125）

PDF（pc）（330KB）（87）

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.

相关文章 | 多维度评价

Select

14. 非齐次Riemann-Hilbert边值问题的求解

张雯雯, 李平润

数学季刊 2024, 39 (3): 262-269. DOI: 10.13371/j.cnki.chin.q.j.m.2024.03.004

摘要（125）

PDF（pc）（321KB）（48）

This paper studies the non-homogeneous generalized Riemann-Hilbert (RH) problems involving two unknown functions. Using the uniformization theorem, such problems are transformed into the case of homogeneous type. By the theory of classical boundary value problems, we adopt a novel method to obtain the sectionally analytic solutions of problems in strip domains, and analyze the conditions of solvability and properties of solutions in various domains.

相关文章 | 多维度评价

Select

15. 具有Riemann-Liouville分数阶积分的强阻尼波动方程的爆破现象

向常永, 段霁松, 龙群飞

数学季刊 2025, 40 (3): 304-312. DOI: 10.13371/j.cnki.chin.q.j.m.2025.03.006

摘要（120）

PDF（pc）（354KB）（44）

We investigate the blow-up effect of solutions for a non-homogeneous wave equation
u_tt−∆u−∆u_t=I₀^α+ (|u|^p)+ω(x),
where p >1, 0≤α<1 and ω(x) with \int_{\mathbb{R}^{N}} ω(x)dx >0. By a way of combining the argument by contradiction with the test function techniques, we prove that not only any non-trivial solution blows up in finite time under 0< α <1, N ≥1 and p >1, but also any non-trivial solution blows up in finite time under α= 0, 2≤ N ≤4 and p being the Strauss exponent.

相关文章 | 多维度评价

Select

16. 涉及调和数的组合恒等式

陈玉磊, 郭东威

数学季刊 2024, 39 (3): 307-314. DOI: 10.13371/j.cnki.chin.q.j.m.2024.03.008

摘要（118）

PDF（pc）（295KB）（57）

In this paper, we firstly establish a combinatorial identity with a free parameter x, and then by means of derivative operation, several summation formulae concerning classical and generalized harmonic numbers, as well as binomial coefficients are derived.

相关文章 | 多维度评价

Select

17. 秩为1的偶格顶点算子代数上的半共形向量簇

楚彦军, 高艺博

数学季刊 2025, 40 (1): 36-48. DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.004

摘要（116）

PDF（pc）（430KB）（31）

In this paper, we shall study structures of even lattice vertex operator algebras by using the geometry of the varieties of their semi-conformal vectors. We first give the varieties of semi-conformal vectors of a family of vertex operator algebras……

相关文章 | 多维度评价

Select

18. 非正则赋权有向图 A_a谱半径的上界

席维鸽, 许涛

数学季刊 2024, 39 (2): 161-170. DOI: 10.13371/j.cnki.chin.q.j.m.2024.02.004

摘要（115）

PDF（pc）（345KB）（37）

Let D be a weighted digraph with n vertices in which each arc has been assigned a positive number. Let A(D) be the adjacency matrix of D and W(D) = diag(w₁⁺,w₂⁺,...,w_n⁺). In this paper, we study the matrix A_α(D), which is defined as A_α(D) =αW(D)+ (1−α)A(D), 0≤α≤1. The spectral radius of Aα(D) is called the Aα spectral radius of D, denoted by λα(D). We obtain some upper bounds on the Aα spectral radius of strongly connected irregular weighted digraphs.

相关文章 | 多维度评价

Select

19. w-(b,c)-核逆

方莉, 赵良

数学季刊 2025, 40 (1): 26-35. DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.003

摘要（114）

PDF（pc）（308KB）（72）

We introduce and study a new kind of generalized inverses named w-(b,c)-core inverses, which is a generalization of the (b,c)-core inverse. An example is given to show that w-(b,c)-core inverses need not be (b,c)-core inverses. In addition, the dual version of the w-(b,c)-core inverse is studied. Some results on (b,c)-core inverses and e-(b,c)-core
inverses are unified and generalized.

相关文章 | 多维度评价

Select

20. 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（113）

PDF（pc）（348KB）（55）

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.

相关文章 | 多维度评价

摘要点击排行