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. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 远程制备任意赤道态的简单通用协议

马松雅, 李翔, 李琦

数学季刊 2022, 37 (3): 260-273. DOI: 10.13371/j.cnki.chin.q.j.m.2022.03.004

摘要（106）

PDF（pc）（348KB）（135）

We first put forward a deterministic protocol to realize the remote preparation
of arbitrary multi-qubit equatorial states via EPR pairs. A set of useful measurement
basis is constructed which plays a key role. The receiver just needs to perform Pauli Z
operations to recover the target state. Comparing with the previous protocols, the recovery
operation is simplified and expressed by a general formula. As there are no universal
protocols for high-dimensional systems, we further generalize to the case of multi-qudit
equatorial states by means of Fourier transformation. It is worth mentioning that the
proposed schemes can be extended to multi-party controlled remote state preparation.
Moreover, we consider the effect of two-type decoherence noises.

相关文章 | 多维度评价

Select

10. 具有特定独立的罗马2-控制数的树

李贝贝, 尚卫苹

数学季刊 2022, 37 (4): 386-393. DOI: 10.13371/j.cnki.chin.q.j.m.2022.04.006

摘要（104）

PDF（pc）（336KB）（110）

For a graph G = (V,E), a Roman {2}-dominating function f :V → {0,1,2} has the property that for every vertex v ∈V with f(v) = 0, either v is adjacent to at least one vertex u for which f(u) = 2, or at least two vertices u₁and u₂ for which f(u₁) =f(u₂) = 1. A Roman {2}-dominating function f = (V₀,V₁,V₂) is called independent if V₁∪V₂ is an independent set. The weight of an independent Roman {2}-dominating function f is the value ω(f) =\sum_v∈V f(v), and the independent Roman {2}-domination number i_{R2}(G) is the minimum weight of an independent Roman {2}-dominating function on G. In this paper, we characterize all trees with i_{R2}(T) =γ(T)+ 1, and give a linear time algorithm to compute the value of i_{R2}(T) for any tree T.

相关文章 | 多维度评价

Select

11. 有向图的加权解析挠率

任世全, 王冲

数学季刊 2023, 38 (1): 30-49. DOI: 10.13371/j.cnki.chin.q.j.m.2023.01.003

摘要（100）

PDF（pc）（389KB）（107）

In 2020, Alexander Grigor’yan, Yong Lin and Shing-Tung Yau [6] introduced
the Reidemeister torsion and the analytic torsion for digraphs by means of the path
complex and the path homology theory. Based on the analytic torsion for digraphs
introduced in [6], we consider the notion of weighted analytic torsion for vertex-weighted
digraphs. For any non-vanishing real functions f and g on the vertex set, we consider the
vertex-weighted digraphs with the weights ( f,g ). We calculate the ( f,g )-weighted analytic
torsion by examples and prove that the ( f,g )-weighted analytic torsion only depend on
the ratio f/g . In particular, if the weight is of the diagonal form ( f,f ), then the weighted
analytic torsion equals to the usual (un-weighted) torsion.

相关文章 | 多维度评价

Select

12. Orbifold 基本群和 Deck 变换群

林奕武

数学季刊 2022, 37 (2): 147-161. DOI: 10.13371/j.cnki.chin.q.j.m.2022.02.005

摘要（96）

PDF（pc）（332KB）（101）

In this paper, we define the notions of orbifold loop and orbifold road, with which, we reformulate the definition of orbifold fundamental group and deck translation group. We show that, for each orbifold, the orbifold fundamental group is isomorphic to the deck translation group.

相关文章 | 多维度评价

Select

13. 一类具有时滞的生态流行病模型的稳定性与 Hopf 分支

白宏芳

数学季刊 2023, 38 (2): 157-183. DOI: 10.13371/j.cnki.chin.q.j.m.2023.02.005

摘要（96）

PDF（pc）（1289KB）（150）

In this paper, an eco-epidemiological model with time delay is studied. The
local stability of the four equilibria, the existence of stability switches about the predation-
free equilibrium and the coexistence equilibrium are discussed. It is found that Hopf
bifurcations occur when the delay passes through some critical values. Formulae are
obtained to determine the direction of bifurcations and the stability of bifurcating periodic
solutions by using the normal form theory and center manifold theorem. Some numerical
simulations are carried out to illustrate the theoretical results.

相关文章 | 多维度评价

Select

14. 工件允许拆分加工的单机排序问题

申惠军, 耿志超

数学季刊 2022, 37 (4): 412-421. DOI: 10.13371/j.cnki.chin.q.j.m.2022.04.009

摘要（92）

PDF（pc）（295KB）（43）

The single-machine lot scheduling problem with splittable jobs to minimize the number of tardy jobs has been showed to be weakly NP-hard in the literature. In this paper, we show that a generalized version of this problem in which jobs have deadlines is strongly NP-hard, and also present the results of some related scheduling problems.

相关文章 | 多维度评价

Select

15. 带位势的基尔霍夫方程规范解的存在性

梁艳霞

数学季刊 2023, 38 (2): 196-209. DOI: 10.13371/j.cnki.chin.q.j.m.2023.02.007

摘要（88）

PDF（pc）（378KB）（60）

In this paper we discuss the following Kirchhoff equation

\left\{
\begin{array}{lr}
-\left(a+b \int_{\mathbb{R}^3}|\nabla u|^{2} d x\right) \Delta u+V(x)u+\lambda u=\mu|u|^{q-2}u+|u|^{p-2}u \ {\rm in}\ \mathbb{R}^3,&\\
\int_{\mathbb{R}^{3}}u^{2}dx=c^2,
\end{array}
\right.
where a, b, µ and c are positive numbers, λ is unknown and appears as a Lagrange multiplier,

14/3<q<p<6 and V is a continuous non-positive function vanishing at infinity.
Under some mild assumptions on V , we prove the existence of a mountain pass normalized solution. To the author’s knowledge, it is the first time to study the existence of
normalized solution to Kirchhoff equation with potential via the minimax principle.

相关文章 | 多维度评价

Select

16. Allen-Cahn方程的虚拟元方法

王培珍, 田旭

数学季刊 2023, 38 (1): 20-29. DOI: 10.13371/j.cnki.chin.q.j.m.2023.01.002

摘要（84）

PDF（pc）（307KB）（112）

In this article, the virtual element method of the Allen-Cahn equation on a
polygon grid is discussed in the fully discrete formulation. With the help of the energy
projection operator, we give the corresponding error estimates in the L² norm and H¹
norm.

相关文章 | 多维度评价

Select

17. 最大净收益指标及其应用

杨晓慧, 白欣宇, 李子欣, 黄昆

数学季刊 2022, 37 (3): 248-259. DOI: 10.13371/j.cnki.chin.q.j.m.2022.03.003

摘要（83）

PDF（pc）（6924KB）（29）

Receiver operating characteristics (ROC) curve and the area under the curve
(AUC) value are often used to illustrate the diagnostic ability of binary classifiers.
However, both ROC and AUC focus on high accuracy in theory, which may not be
effective for practical applications. In addition, it is difficult to judge which one is better
when the ROC curves are intersect and the AUC values are equal. Decision curve analysis
(DCA) methods improve ROC by incorporating accuracy and consequences. However,
similar to ROC, DCA requires a quantitative indicator to objectively determine which
one is better when DCA curves intersect. A DCA-based statistical indicator named
maximum net benefit (MNB) is constructed for evaluating clinical treatment regimens
rather than just accuracy as in ROC and AUC. As a simple and effective statistical
indicator, the construction process of MNB is given theoretically. Moreover, the MNB
can still provide effective identification when the AUC values are equal, which is proved
by theory. Furthermore, the feasibility and effectiveness of the proposed MNB are verified
by gene selection and classifier performance comparison on actual data.

相关文章 | 多维度评价

Select

18. 一类具有状态依赖脉冲影响的捕食者-食饵模型动力学分析

李永凤, 朱城志, 刘艳伟

数学季刊 2023, 38 (1): 1-19. DOI: 10.13371/j.cnki.chin.q.j.m.2023.01.001

摘要（82）

PDF（pc）（2367KB）（222）

In this paper, a pest-dependent model and integrated pest management
strategy is proposed, that is, when pest populations reach levels that impair economic
development, we will use a combination of strategies, such as biological, cultural and
chemical control strategies reduce pests to a reasonable level. First, we investigated the
system without control measures, and discussed the existence and stability of equilibria,
we also proved the system has no limit cycle. Then, a state feedback impulsive model is
constructed, the existence and uniqueness of the order-one periodic solution are proved
by means of the successor function method to confirm the feasibility of the biological and
chemical control strategy of pest management. Secondly, the stability of system is proved
by the analogue of the Poincar ´ e criterion. Finally, we give an example and numerical
simulations to explain the mathematical conclusions.

相关文章 | 多维度评价

Select

19. 多线性交换子在变指数Herz空间上的有界性

彭姗姗, 陈纪莉

数学季刊 2022, 37 (2): 203-213. DOI: 10.13371/j.cnki.chin.q.j.m.2022.02.009

摘要（82）

PDF（pc）（381KB）（76）

We consider multilinear commutators of singular integrals defined by $T_{\vec{b}}f(x) =\int_{\mathbb{R}^n}\prod^m_{i=1}(b_i(x)-b_i(y))K(x, y)f(y)dy,$

where K is a standard Calder\'{o}n-Zygmund kernel, m is a positive integer and \vec{b} b =(b₁,b₂,...,b_m) is a family of m locally integrable functions. Based on the theory of
variable exponent and on generalization of the BMO norm, we prove the boundedness of
multilinear commutators T_{\vec{b}} on grand variable Herz spaces. The result is still new even in
the special case of m=1.

相关文章 | 多维度评价

Select

20. 时间尺度上具有泄漏时滞的一般BAM神经网络概周期解的存在性和指数稳定性

董延寿, 韩艳, 代婷婷

数学季刊 2022, 37 (2): 189-202. DOI: 10.13371/j.cnki.chin.q.j.m.2022.02.008

摘要（81）

PDF（pc）（885KB）（129）

In this paper, the existence of almost periodic solutions to general BAM neural
networks with leakage delays on time scales is first studied, by using the exponential
dichotomy method of linear differential equations and fixed point theorem. Then, the
exponential stability of almost periodic solutions to such BAM neural networks on time
scales is discussed by utilizing differential inequality. Finally, an example is given to
support our results in this paper and the results are up-to-date.

相关文章 | 多维度评价

摘要点击排行