数学季刊

Select

1. 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）

PDF（pc）（330KB）（93）

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.

相关文章 | 多维度评价

Select

2. 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）

PDF（pc）（356KB）（230）

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.

相关文章 | 多维度评价

Select

3. 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）

PDF（pc）（322KB）（194）

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.

相关文章 | 多维度评价

Select

4. 扰动双扩散方程周期波的全局存在唯一性

廖笑照, 黄文韬, 杨素敏

数学季刊 2022, 37 (2): 124-131. DOI: 10.13371/j.cnki.chin.q.j.m.2022.02.002

摘要（146）

PDF（pc）（534KB）（80）

In this paper, we study the periodic wave propagation phenomenon in elastic waveguides modeled by a combined double-dispersive partial differential equation (PDE). The traveling wave ansazt transforms the PDE model into a perturbed integrable ordinary differential equation (ODE). The global bifurcation theory is applied for the perturbed ODE model to establish the existence and uniqueness of the limit cycle, which corresponds
the periodic traveling wave for the PDE model. The main tool is the Abelian integral taken from Poincar´ e bifurcation theory. Simulation is carried out to verify the theoretical result.

相关文章 | 多维度评价

Select

5. 非对称凸体的截面与投影体积不等式

曹子昕, 李爱军

数学季刊 2022, 37 (2): 178-188. DOI: 10.13371/j.cnki.chin.q.j.m.2022.02.007

摘要（142）

PDF（pc）（346KB）（75）

In this paper, we establish volume inequalities for k-dimensional sections and projections of convex bodies (not necessarily symmetric) and their polars in a more general position than John’s position.

相关文章 | 多维度评价

Select

6. 高阶变系数非线性发展方程的Painlev\'{e} 分析

王媛

数学季刊 2021, 36 (2): 196-203. DOI: 10.13371/j.cnki.chin.q.j.m.2021.02.008

摘要（142）

PDF（pc）（266KB）（189）

There is a close relationship between the Painlev´e integrability and other
integrability of nonlinear evolution equation. By using the Weiss-Tabor-Carnevale (WTC)
method and the symbolic computation of Maple, the Painlev´e test is used for the higher
order generalized non-autonomous equation and the third order Korteweg-de Vries equation
with variable coefficients. Finally the Painlev´e integrability condition of this equation is
gotten.

相关文章 | 多维度评价

Select

7.

带有时滞和热扩散效应的 Timoshenko 系统的适定性

秦玉明, 韩宁

数学季刊 2022, 37 (1): 1-9. DOI: 10.13371/j.cnki.chin.q.j.m.2022.01.001

摘要（141）

PDF（pc）（293KB）（349）

In this paper, we study the well-posedness for the thermoelastic Timoshenko system with a constant delay and mass diffusion effects. Heat and mass exchange with the environment during thermodiffusion in Timoshenko beam. The C₀ -semigroup theory will be used to prove the well-posedness of the considered problem.

相关文章 | 多维度评价

Select

8. 一类具有导数型非线性记忆项的半线性波动方程的爆破结果

欧阳柏平, 肖胜中

数学季刊 2021, 36 (3): 235-243. DOI: 10.13371/j.cnki.chin.q.j.m.2021.03.002

摘要（130）

PDF（pc）（330KB）（241）

In this paper, we study the blow-up of solutions to a semi-linear wave equation with a nonlinear memory term of derivative type. By using methods of an iteration argument and differential inequalities, we obtain the blow-up result for the semi-linear wave equation when the exponent of p is under certain conditions. Meanwhile, we derive an upper bound of the lifespan of solutions to the Cauchy problem for the semi-linear wave equation.

相关文章 | 多维度评价

Select

9. 哈林图的导出匹配可扩性

张庆楠, 惠志昊, 杨雨, 王安

数学季刊 2022, 37 (4): 380-385. DOI: 10.13371/j.cnki.chin.q.j.m.2022.04.005

摘要（130）

PDF（pc）（344KB）（80）

Let G be a connected graph having a perfect matching. The graph G is said to be induced matching (IM) extendable if every induced matching M of G is contained in a perfect matching of G. In this paper, we show that Halin graph G =T ∪C is IMextendable if and only if its characteristic tree T is isomorphic to K_1,3, K_1,5, K_1,7or S_2,2.

相关文章 | 多维度评价

Select

10. 涉及分担解析函数的亚纯函数的正规族

杨祺, 袁文俊, 田宏跟

数学季刊 2022, 37 (1): 26-36. DOI: 10.13371/j.cnki.chin.q.j.m.2022.01.003

摘要（122）

PDF（pc）（330KB）（136）

In this paper, we study the normal criterion of meromorphic functions concerning shared analytic function. We get some theorems concerning shared analytic function, which improves some earlier related results.

相关文章 | 多维度评价

Select

11. 具退化非局部阻尼和源项的非线性耦合粘弹性波方程组解的指数增长性

刘烁, 张宏伟, 呼青英

数学季刊 2021, 36 (2): 210-220. DOI: 10.13371/j.cnki.chin.q.j.m.2021.02.010

摘要（121）

PDF（pc）（298KB）（192）

This paper is concerned with a system of nonlinear viscoelastic
wave equations with degenerate nonlocal damping and memory terms. We will
prove that the energy associated to the system is unbounded. In fact, it will
be proved that the energy will grow up as an exponential function as time goes
to infinity, provided that the initial data are positive initial energy.

相关文章 | 多维度评价

Select

12. 基于固有时间尺度分解和自适应Huber损失的脑电特征学习模型

杨利军, 蒋淑月, 魏小鸽, 肖运海

数学季刊 2022, 37 (3): 281-300. DOI: 10.13371/j.cnki.chin.q.j.m.2022.03.006

摘要（120）

PDF（pc）（538KB）（316）

According to the World Health Organization, about 50 million people world-
wide suffer from epilepsy. The detection and treatment of epilepsy face great challenges.
Electroencephalogram (EEG) is a significant research object widely used in diagnosis and
treatment of epilepsy. In this paper, an adaptive feature learning model for EEG signals
is proposed, which combines Huber loss function with adaptive weight penalty term.
Firstly, each EEG signal is decomposed by intrinsic time-scale decomposition. Secondly,
the statistical index values are calculated from the instantaneous amplitude and frequency
of every component and fed into the proposed model. Finally, the discriminative features
learned by the proposed model are used to detect seizures. Our main innovation is to
consider a highly flexible penalization based on Huber loss function, which can set different
weights according to the influence of different features on epilepsy detection. Besides, the
new model can be solved by proximal alternating direction multiplier method, which can
effectively ensure the convergence of the algorithm. The performance of the proposed
method is evaluated on three public EEG datasets provided by the Bonn University,
Childrens Hospital Boston-Massachusetts Institute of Technology, and Neurological and
Sleep Center at Hauz Khas, New Delhi(New Delhi Epilepsy data). The recognition
accuracy on these two datasets is 98% and 99.05%, respectively, indicating the application
value of the new model.

相关文章 | 多维度评价

Select

13. 耦合Lyapunov 矩阵方程的AOR迭代法

张士君, 王世恒, 王珂

数学季刊 2021, 36 (2): 141-148. DOI: 10.13371/j.cnki.chin.q.j.m.2021.02.003

摘要（117）

PDF（pc）（285KB）（224）

An AOR (Accelerated Over-Relaxation) iterative method is suggested by
introducing one more parameter than SOR (Successive Over-Relaxation) method for
solving coupled Lyapunov matrix equations (CLMEs) that come from continuous-time
Markovian jump linear systems. The proposed algorithm improves the convergence rate,
which can be seen from the given illustrative examples. The comprehensive theoretical
analysis of convergence and optimal parameter needs further investigation.

相关文章 | 多维度评价

Select

14. 一个新的无参数填充函数及其在最小二乘法中的应用

李硕, 尚有林, 屈德强

数学季刊 2021, 36 (3): 263-274. DOI: 10.13371/j.cnki.chin.q.j.m.2021.03.005

摘要（117）

PDF（pc）（289KB）（132）

The filled function algorithm is an important method to solve global optimization problems. In this paper, a parameter-free filled function is proposed for solving general global optimization problem, discuss the theoretical properties of this function and give the corresponding algorithm. The numerical experiments on some typical test problems using the algorithm and the numerical results show that the algorithm is effective. Applying the filled function method to the parameter solving problem in the logical population growth model, and then can be effectively applied to Chinese population prediction. The experimental results show that the algorithm has good practicability in practical application.

相关文章 | 多维度评价

Select

15. Born-Infeld理论中的多项式函数模型

代兵兵, 张瑞凤

数学季刊 2022, 37 (3): 221-236. DOI: 10.13371/j.cnki.chin.q.j.m.2022.03.001

摘要（115）

PDF（pc）（413KB）（88）

Based on the Lagrangian action density under Born-Infeld type dynamics and
motivated by the one-dimensional prescribed mean curvature equation, we investigate the
polynomial function model in Born-Infeld theory in this paper with the form of
−([1−a(ϕ')² ]ϕ' )' =λf(ϕ(x)),
where λ> 0 is a real parameter, f ∈C² (0 , + ∞ ) is a nonlinear function. We are interested
in the exact number of positive solutions of the above nonlinear equation. We specifically
develop for the problem combined with a careful analysis of a time-map method.

相关文章 | 多维度评价

Select

16. Auslander范畴和自由正规化扩张

谷勤勤, 卓远帆

数学季刊 2021, 36 (2): 204-209. DOI: 10.13371/j.cnki.chin.q.j.m.2021.02.009

摘要（114）

PDF（pc）（299KB）（139）

相关文章 | 多维度评价

Select

17. 具有一般非线性项的半线性抛物方程解的有限时间爆破和爆破时间上界

李娜, 房少梅

数学季刊 2022, 37 (1): 103-110. DOI: 10.13371/j.cnki.chin.q.j.m.2022.01.011

摘要（113）

PDF（pc）（315KB）（162）

In this paper, we consider a semilinear parabolic equation with a general nonlinearity. We establish a new finite time blow-up criterion and also derive the upper bound for the blow-up time. The results partially generalize some recent ones obtained by He Ma et al.

相关文章 | 多维度评价

Select

18. 具有勢壘的Sturm-Liouville算子的特徵值和特徵函數

SARWAR Qanitah 黄振友 ZAHID Abdul Hannan

数学季刊 2023, 38 (1): 50-61. DOI: 10.13371/j.cnki.chin.q.j.m.2023.01.004

摘要（112）

PDF（pc）（279KB）（131）

We aim to find the eigenvalues and eigenfunctions of the barrier potential
case for Strum-Liouville operator on the finite interval [0 ,π ] when λ> 0. Generally, the
eigenvalue problem for the Sturm-Liouville operator is often solved by using integral
equations, which are sometimes complex to solve, and difficulties may arise in computing
the boundary values. Considering the said complexity, we have successfully developed
a technique to give the asymptotic formulae of the eigenvalue and the eigenfunction for
Sturm-Liouville operator with barrier potential. The results are of significant interest in
the field of quantum mechanics and atomic systems to observe discrete energy levels.

相关文章 | 多维度评价

Select

19. 一种求解未知噪音水平的低秩矩阵恢复问题有效算法

靳正芬, 王朵, 尚有林, 律金曼

数学季刊 2021, 36 (4): 356-368. DOI: 10.13371/j.cnki.chin.q.j.m.2021.04.002

摘要（110）

PDF（pc）（363KB）（115）

Recovering an unknown high dimensional low rank matrix from a small set of entries is widely spread in the fields of machine learning, system identification and image restoration, etc. In many practical applications, the few observations are always corrupted by noise and the noise level is also unknown. A novel model with nuclear norm and square root type estimator has been proposed, which does not rely on the knowledge or on an estimation of the standard deviation of the noise. In this paper, we firstly reformulate the problem to an equivalent variable separated form by introducing an auxiliary variable. Then we propose an efficient alternating direction method of multipliers(ADMM) for solving it. Both of resulting subproblems admit an explicit solution, which makes our algorithm have a cheap computing. Finally, the numerical results show the benefits of the model and the efficiency of the proposed method.

相关文章 | 多维度评价

Select

20. 一类高维组内相关结构的检验

汤平, 肖南南, 解俊山

数学季刊 2022, 37 (1): 10-25. DOI: 10.13371/j.cnki.chin.q.j.m.2022.01.002

摘要（107）

PDF（pc）（462KB）（163）

The paper considers a high-dimensional likelihood ratio (LR) test on the intraclass correlation structure of the multivariate normal population. When the dimension p and sample size N satisfy N − 1 >p→∞ , it is proved that the logarithmic LR statistic asymptotically obeys Gaussian distribution, and the explicit expressions of the mean and the variance are also obtained. The simulations demonstrate that our high-dimensional LR test method outperforms the traditional Chi-square approximation method or F-approximation method, and performs as efficient as the accurate high-dimensional Edgeworth expansion method and the more accurate high-dimensional Edgeworth expansion method in analyzing the intraclass covariance structure of highdimensional data.

相关文章 | 多维度评价

摘要点击排行