数学季刊

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

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.

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

2022, 37(2): 124-131. doi:10.13371/j.cnki.chin.q.j.m.2022.02.002

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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.

关于一类有限 p-群的因子分解数

王玉雷, 白雪, 张元峰

2022, 37(2): 132-141. doi:10.13371/j.cnki.chin.q.j.m.2022.02.003

摘要 ( 77 )

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Let G be a group and A and B be subgroups of G. If G = AB, then G is said
to be factorized by A and B. Let p be a prime number. The factorization numbers of
a 2-generators abelian p-group and a modular p-group have been determined. Further,
suppose that G is a finite p-group as follows G = <a,b|_apⁿ= _bp^m=1 , a^b =_apⁿ⁻¹⁺¹>, where n≥ 2, m≥ 1. In this paper, the factorization number of G is computed completely, which
is a generalization of the result of Saeedi and Farrokhi.

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

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.

Orbifold 基本群和 Deck 变换群

林奕武

2022, 37(2): 147-161. doi:10.13371/j.cnki.chin.q.j.m.2022.02.005

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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.

薄膜外延生长的四阶抛物模型解的渐近性质

孙安琪, 李锋杰

2022, 37(2): 162-177. doi:10.13371/j.cnki.chin.q.j.m.2022.02.006

摘要 ( 60 )

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This paper deals with a homogeneous Neumann initial-boundary problem of
a 4th-order parabolic equation modeling epitaxial growth of thin film. We determine the
classification of initial energy on the existence of blow-up, global existence and extinction
of solutions by using the potential well method and the auxiliary function method.
Moreover, asymptotic estimates on global solution and extinction solution are studied,
respectively.

非对称凸体的截面与投影体积不等式

曹子昕, 李爱军

2022, 37(2): 178-188. doi:10.13371/j.cnki.chin.q.j.m.2022.02.007

摘要 ( 142 )

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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.

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

2022, 37(2): 189-202. doi:10.13371/j.cnki.chin.q.j.m.2022.02.008

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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.

多线性交换子在变指数Herz空间上的有界性

彭姗姗, 陈纪莉

2022, 37(2): 203-213. doi:10.13371/j.cnki.chin.q.j.m.2022.02.009

摘要 ( 82 )

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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.

混合范数乘积空间上的奇异积分

王潇

2022, 37(2): 214-220. doi:10.13371/j.cnki.chin.q.j.m.2022.02.010

摘要 ( 73 )

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In this paper, we prove the boundedness of the singular integral operators on
product spaces with mixed norms and obtain the endpoint weak-type estimates.

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