数学季刊

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1. 关于复几何中的一些新进展—与齐性流形相关的领域

关庄丹

数学季刊 2020, 35 (2): 111-144. DOI: 10.13371/j.cnki.chin.q.j.m.2020.02.001

摘要（440）

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In this article, we give a survey of some progress of the complex geometry, mostly related to the Lie group actions on compact complex manifolds and complex homogeneous spaces in the last thirty years. In particular, we explore some works in the special area in Dierential Geometry, Lie Group and Complex Homogeneous Space. Together with the special area in nonlinear analysis on complex manifolds, they are the two major aspects of my research interests.

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2. 有限元方法的后验误差估计

鄂维南, 穆默, 黄鸿慈

数学季刊 1988, 3 (1): 97-107.

摘要（432）

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有限元的误差分析理论已有丰富的成果,但一般以先验估计为主。这些理论对算法评价和指导计算无疑具有重要意义。但实际计算中常要求给出误差的定量估计,先验估计一般就做不到这一点,因为其中会有如微分方程解的导数等不可计算的量。后验误差估计的研究近年来已开始受到注意。在多重网格技术中基于误差渐近展开的外推可以给出逐点意义下的后验估计。（例如见[1],[2]）另一条途径是通过局部化进行能量模意义下的后验误差估计。其中对一维边值问题的研究已较成熟。[7]就常系数

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3. 楼与群Ⅱ

周国晖 , 黎景辉

数学季刊 2020, 35 (3): 221-254. DOI: 10.13371/j.cnki.chin.q.j.m.2020.03.001

摘要（276）

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This is the second part of a pedagogical introduction to the theory of buildings of Jacques Tits. We define a(B,N) pair and construct a building out of it. Then we give a description of Chevalley groups, their(B,N) pair and the associated buildings. We illustrates this theory with many examples from classical groups.

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4. 楼与群III

黎景辉

数学季刊 2021, 36 (1): 1-31. DOI: 10.13371/j.cnki.chin.q.j.m.2021.01.001

摘要（268）

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This is the third part of a pedagogical introduction to the theory of buildings of Jacques Tits. We describe the construction and properties of the Bruhat-Tits building of a reductive group over a local field.

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5. 一类不确定薛定谔基尔霍夫方程解的存在性和集中性

陈玉松, 常荷洁

数学季刊 2020, 35 (1): 37-45. DOI: 10.13371/j.cnki.chin.q.j.m.2020.01.003

摘要（189）

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This paper is concerned with the nonlinear Schrodinger-Kirchhoff system $-(a+b \int _{R^{3}}|\nabla u|^{2} dx) \triangle u+ \lambda V(x)u=f(x,u)$ in R³, where constants a > 0,b ≥ 0 and λ > 0 is a parameter. We require that V (χ) ∈ C(R³) and has a potential well V ^-1(0). Combining this with other suitable assumptions on K and ƒ, the existence of nontrivisd solutions is obtained via vaxiational methods. Furthermore, the concentration behavior of the nontrivial solution is also explored on the set V ^-1(0) as λ → + ∞ as well. It is worth noting that the (PS )-condition can not be directly got as done in the literature, which makes the problem more complicated. To overcome this difficulty, we adopt different method.

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6. 奇异点附近的复微分方程解的增长性与系数下级的关系

刘元竹, 龙见仁, 曾三桂

数学季刊 2020, 35 (2): 163-170. DOI: 10.13371/j.cnki.chin.q.j.m.2020.02.003

摘要（189）

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We investigate the growth of solutions of the following complex linear differential equation f’’+ A（z）f’+ B（z）f = 0,where A（z） and B（z） are analytic functions in C-{z₀}, z₀∈ C. Some estimations of lower bounded of growth of solutions of the differential equation are obtained by using the concept of lower order.

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7. 关于自然数的方幂和

陈景润, 黎鉴愚

数学季刊 1987, 2 (1): 1-18.

摘要（185）

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求自然数的方幂和是一个经典问题，设 S_k(n) 表示 \sigma_m-1ⁿ m⁴, Schwlts 和Scott 都通过复杂的计算给出了当1 \leq k \leq 6 及 7 \leq k \leq 13时 S_k(n) 的计算公式。本文用初等的方法给出了1 \leq k \leq 30时 S_k(n) 的计算公式。

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8. r-正则有向图的多数染色

夏伟皓, 石美, 肖明月, 蔡建生, 王纪辉

数学季刊 2022, 37 (2): 142-146. DOI: 10.13371/j.cnki.chin.q.j.m.2022.02.004

摘要（179）

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A majority k-coloring of a digraph D with k colors is an assignment c: V ( D ) →{ 1,2,···,k} , such that for every v∈V (D), we have c(w)=c(v) for at most half of all out-neighbors w∈N⁺( v ). For a natural number k≥2, a
1/k-majority coloring of a digraph is a coloring of the vertices such that each vertex receives the same color as at
most a 1/k proportion of its out-neighbours. Kreutzer, Oum, Seymour, van der Zypen and
Wood proved that every digraph has a majority 4-coloring and conjectured that every
digraph admits a majority 3-coloring. Gir$\widetilde{a}$o, Kittipassorn and Popielarz proved that every
digraph has a 1/k-majority 2k-coloring and conjectured that every digraph admits a
1\k-majority (2k−1)-coloring. We showed that every r -regular digraph D with r>36ln(2n)
has a majority 3-coloring and proved that every digraph D with minimum outdegree
$\delta^+>\frac{2k^2(2k-1)^2}{(k-1)^2}\ln{[(2k-1)n]}$ has a 1/k-majority (2k−1)-coloring. And we also proved that
every r-regular digraph D with $r>\frac{3k^2(2k-1)}{(k-1)^2} \ln(2n)$ has a 1/k-majority (2k−1)-coloring.

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9. n*n非负整数矩阵的极大子群

杨琳, 任苗苗

数学季刊 2020, 35 (2): 186-193. DOI: 10.13371/j.cnki.chin.q.j.m.2020.02.006

摘要（176）

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In this paper we study the subgroup structure of the semigroup Mn(Z+) of all n * n nonnegative integral matrices under multiplication. We prove that every maximal subgroup of Mn(Z+) containing an idempotent element of rank r is isormorphic to Sr.

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10. 关于数论函数值分布的研究

邵品琮

数学季刊 1987, 2 (2): 27-43.

摘要（175）

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对于数义在自然数集 N 上的数论函数（Arithmetical function）f（n）, n\inN,取值可以是实数, 也可以是复数（一般为实数）, 例如著名的 Euler 函数 \varphi(n)=\Sigma_{(a,n)=1,a<n}1, 除数函数τ（n）=\Sigma_{d/n}1,以及除数和函数σ（n）=\Sigma_{d/n}d

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11. 广义的Orlicz空间上的Korn不等式与散度方程

吴芮民, 王松柏

数学季刊 2020, 35 (4): 344-353. DOI: 10.13371/j.cnki.chin.q.j.m.2020.04.002

摘要（167）

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Let ϕ be a generalized Orlicz function satisfying (A0), (A1), (A2), (aInc) and (aDec). We prove that the mapping

f →f ^#:=sup_B 1/\int_|B||f(x)-f_B|dx is continuous on L^ϕ(·)(Rⁿ) by extrapolation. Based on this result we generalize Korn’s inequality to the setting of generalized Orlicz spaces, i.e., ||\triangledown f||_{L^{ϕ(·)}(Ω)}\lesssim||DF|||_L^{ϕ}(Ω) . Using the Calder´on–Zygmund theory on generalized Orlicz spaces, we obtain that the divergence equation divu=f has a solution u∈(W0^1,ϕ(·)(Ω))ⁿsuch that ||\triangledown u||_L^{_ϕ(·)}(Ω) \lesssim ||f||_L^{ϕ}(Ω).

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12. Ladder图和Mbius Ladder图的彩虹点连通数

刘慧敏, 毛亚平

数学季刊 2016, 31 (4): 399-405. DOI: 10.13371/j.cnki.chin.q.j.m.2016.04.008

摘要（165）

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A vertex-colored graph G is said to be rainbow vertex-connected if every two vertices of G are connected by a path whose internal vertices have distinct colors, such a path is called a rainbow path. The rainbow vertex-connection number of a connected graph G, denoted by rvc（G）, is the smallest number of colors that are needed in order to make G rainbow vertex-connected. If for every pair u, v of distinct vertices, G contains a rainbow u-v geodesic, then G is strong rainbow vertex-connected. The minimum number k for which there exists a k-vertex-coloring of G that results in a strongly rainbow vertex-connected graph is called the strong rainbow vertex-connection number of G, denoted by srvc（G）. Observe that rvc（G） ≤ srvc（G） for any nontrivial connected graph G. In this paper, for a Ladder Ln,we determine the exact value of srvc（L_n） for n even. For n odd, upper and lower bounds of srvc（L_n） are obtained. We also give upper and lower bounds of the（strong） rainbow vertex-connection number of Mbius Ladder.

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13. 与 Mittag-Leffler 函数有关的多叶亚纯函数的优化和 Fekete-Szegö 问题

龙品红, 甘加达兰•穆鲁古桑德拉莫西, 韩惠丽, 汪文帅

数学季刊 2022, 37 (2): 111-123. DOI: 10.13371/j.cnki.chin.q.j.m.2022.02.001

摘要（164）

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The main object of this present paper is to investigate the problem of majorization of certain class of multivalent meromorphic functions of complex order involving Mittag-Leffler function. Meanwhile, for this subclass the corresponding coefficient estimates and some Fekete-Szeg¨ o type inequalities are obtained. Moreover we point out some new or known consequences of our main results.

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14. 经典Hilbert不等式的p进制版本

金建军, 李春华

数学季刊 2020, 35 (4): 431-440. DOI: 10.13371/j.cnki.chin.q.j.m.2020.04.012

摘要（160）

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In this note, we introduce and study a p-adic Hilbert-type integral operator and obtain its sharp norm estimate. As applications, we establish a p-adic Hilbert-type inequality with the best constant and its equivalent form.

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15. 求解箱式约束全局优化问题的新的填充函数

屈德强, 吴丹, 尚有林

数学季刊 2020, 35 (4): 354-362. DOI: 10.13371/j.cnki.chin.q.j.m.2020.04.003

摘要（159）

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本文考虑利用辅助函数法求解箱式约束全局优化问题。首先，提出了一个新的与目标函数具有相同局部极小点的无参数填充函数。该填充函数的局部极小点是目标函数更优的局部极小点，基于这一特征设计的填充函数方法，目标函数只需要被极小化一次。改变了传统填充函数法目标函数和填充函数交替极小化的算法框架，能有效减少算法的迭代次数，加快寻找全局极小点的速度。随后进一步讨论了填充函数的理论性质，并建立了相应的算法。最后，通过数值实验验证了算法的可行性和有效性。

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16. 黎曼球上n点组的模空间奇点

吴悦, 许斌

数学季刊 2020, 35 (2): 145-162. DOI: 10.13371/j.cnki.chin.q.j.m.2020.02.002

摘要（154）

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We classify the finite groups associated to the orbifold singularities of the moduli space of n ≥ 5 unordered points on the Riemann sphere.

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17. 随机变量的共轭梯度方法

许铭修, 黎景辉

数学季刊 2021, 36 (2): 111-121. DOI: 10.13371/j.cnki.chin.q.j.m.2021.02.001

摘要（153）

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We study the conjugate gradient method for solving a system of linear
equations with coefficients which are measurable functions and establish the rate of
convergence of this method.

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18. 楼与群I

黎景辉, 梁志斌

数学季刊 2020, 35 (1): 1-28. DOI: 10.13371/j.cnki.chin.q.j.m.2020.01.001

摘要（152）

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This is a pedagogical introduction to the theory of buildings of Jacques Tits and to some applications of this theory.This paper has 4 parts.In the first part we discuss incidence geometry,Coxeter systems and give two definitions of buildings.We study in the second part the spherical and affine buildings of Chevalley groups.In the third part we deal with Bruhat-Tits theory of reductive groups over local fields.Finally we discuss the construction of the p-adic flag manifolds.

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19. 带有分数阶Robin边界条件的Riesz空间分数阶对流-扩散方程的有限差分方法

林海欣 , 房少梅,

数学季刊 2020, 35 (3): 278-289. DOI: 10.13371/j.cnki.chin.q.j.m.2020.03.003

摘要（151）

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In this paper, a Riesz space fractional advection-dispersion equation with fractional Robin boundary condition is considered. By applying the fractional central difference formula and the weighted and shifted Gru¨nwald-Letnikov formula, we derive a weighted implicit finite difference scheme with accuracy O（?t²+ h²）. The solvability,stability, and convergence of the proposed numerical scheme are proved. A numerical example is presented to confirm the accuracy and efficiency of the scheme.

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20. 一类具有耦合项的 Kirchhoff 型双调和方程组正解的存在性和多解性

李振辉, 许丽萍

数学季刊 2021, 36 (1): 49-66. DOI: 10.13371/j.cnki.chin.q.j.m.2021.01.004

摘要（151）

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In this paper, we study a coupled fourth-order system of Kirchhoff type. Under appropriate hypotheses of Vi(x) for i=1,2, f and g, we obtained two main existence theorems of weak solutions for the problem by variational methods. Some recent results
are extended.

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