数学季刊

江东月, 唐忠华, 房少梅

2024, 39(2): 111-127. doi:10.13371/j.cnki.chin.q.j.m.2024.02.001

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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.

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

2024, 39(2): 128-143. doi:10.13371/j.cnki.chin.q.j.m.2024.02.002

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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.

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

2024, 39(2): 144-160. doi:10.13371/j.cnki.chin.q.j.m.2024.02.003

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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.

非正则赋权有向图 A_a谱半径的上界

席维鸽, 许涛

2024, 39(2): 161-170. doi:10.13371/j.cnki.chin.q.j.m.2024.02.004

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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.

重复齐次化问题的强收敛率

赵杰, 吴喜民, 王娟

2024, 39(2): 171-179. doi:10.13371/j.cnki.chin.q.j.m.2024.02.005

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In this paper, we study the reiterated homogenization operators L_ε=−div(A(x/ε,x/ε2)∇). We establish the homogenized problem and representation equation by introducing the two correctors. As a consequence, we obtain the H₀¹and L²convergence estimates of solutions.

紧黎曼曲面上锥度量的高斯博内公式

方晗兵, 许斌, 杨百瑞

2024, 39(2): 180-184. doi:10.13371/j.cnki.chin.q.j.m.2024.02.006

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We prove a generalization of the classical Gauss-Bonnet formula for a conical metric on a compact Riemann surface provided that the Gaussian curvature is Lebesgue integrable with respect to the area form of the metric. We also construct explicitly some conical metrics whose curvature is not integrable.

Bouw-M¨oler曲面的Minkowski常数

许云龙, 钟裕民

2024, 39(2): 185-199. doi:10.13371/j.cnki.chin.q.j.m.2024.02.007

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We consider the Bouw-M¨oller surfaces with two parameters m,n when they are not both even or m=n, n is even. We computer the e-Minkowski constant of them.

在复二维仿射锥上的完备余齐性一Kähler度量

关庄丹, 梁梦翔

2024, 39(2): 200-220. doi:10.13371/j.cnki.chin.q.j.m.2024.02.008

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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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