期刊：
Results in Mathematics,2024年79(2) ISSN：1422-6383
通讯作者：
Chen, SL
作者机构：
[Chen, Shaolin; Chen, SL] Hengyang Normal Univ, Coll Math & Stat, Hengyang 421002, Hunan, Peoples R China.;[Chen, Shaolin; Chen, SL] Hunan Prov Key Lab Intelligent Informat Proc & App, Hengyang 421002, Peoples R China.;[Hamada, Hidetaka] Kyushu Sangyo Univ, Fac Sci & Engn, 3-1 Matsukadai 2 Chome,Higashi Ku, Fukuoka 8138503, Japan.
通讯机构：
[Chen, SL ] H;Hengyang Normal Univ, Coll Math & Stat, Hengyang 421002, Hunan, Peoples R China.;Hunan Prov Key Lab Intelligent Informat Proc & App, Hengyang 421002, Peoples R China.
关键词：
Bloch type space;complex-valued harmonic function;composition operator;hardy space;pluriharmonic functions
摘要：
The main purpose of this paper is to investigate characterizations of composition operators on Bloch and Hardy type spaces. Initially, we use general doubling weights to study the composition operators from harmonic Bloch type spaces on the unit disc D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {D}}$$\end{document} to pluriharmonic Hardy spaces on the Euclidean unit ball Bn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {B}}<^>n$$\end{document}. Furthermore, we develop some new methods to study the composition operators from harmonic Bloch type spaces on D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {D}}$$\end{document} to pluriharmonic Bloch type spaces on D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {D}}$$\end{document}. Additionally, some application to new characterizations of the composition operators between pluriharmonic Lipschitz type spaces to be bounded or compact will be presented. The obtained results of this paper provide the improvements and extensions of the corresponding known results.
期刊：
Journal of Mathematical Analysis and Applications,2024年534(2):128071 ISSN：0022-247X
通讯作者：
Ponnusamy, S
作者机构：
[Liu, Gang] Hengyang Normal Univ, Coll Math & Stat, Hunan Prov Key Lab Intelligent Informat Proc & App, Hengyang 421002, Hunan, Peoples R China.;[Ponnusamy, S; Ponnusamy, Saminathan] Indian Inst Technol Madras, Dept Math, Chennai 600036, India.;[Ponnusamy, S; Ponnusamy, Saminathan] Lomonosov Moscow State Univ, Moscow Ctr Fundamental & Appl Math, Moscow, Russia.
通讯机构：
[Ponnusamy, S ] I;Indian Inst Technol Madras, Dept Math, Chennai 600036, India.;Lomonosov Moscow State Univ, Moscow Ctr Fundamental & Appl Math, Moscow, Russia.
关键词：
schroder's method;cycle;attracting basin;parabolic basin;siegel disk
摘要：
Let ��,� and ��,� be the functions defined in Schroder's method of the first and second kind for an entire function f with given order n (�>= 2), respectively. Based on unrefined algebra characterizations of ��,� and ��,�, we obtain some sufficient conditions on f such that both ��,� and ��,� possess given finite pairs of extraneous non-repelling cycles. Here, these conditions are a pair of equations, which have infinitely many polynomials or transcendental entire functions as its solutions. For obtaining some solutions f of such equations, we provide a step-by-step method. We start from any solution g in corresponding equations so that the function ��,2 possesses the above finite pairs of extraneous cycles but all are super-attracting, and then f can be obtained by a series of formulas concerning the function g, points and multipliers of those cycles. Note that ��,2=��,2 is identical with Newton's method for f. In a sense, this fact reveals that some extraneous super-attracting cycles of Newton's method imply certain extraneous non-repelling cycles of any method from the two families of methods. More generally, for any given orders n and m, some extraneous non-repelling cycles of ��,� or ��,� imply that of ��,� or ��,� for some entire functions f and F. These give a partial answer for the problem of finding possible link between the two families of methods, which was posed by Steven Smale in 1994.
期刊：
Complex Variables and Elliptic Equations,2024年:08 ISSN：1747-6933
通讯作者：
Li, LL
作者机构：
[Li, Liulan; Li, LL] Hengyang Normal Univ, Coll Math & Stat, Hengyang, Hunan, Peoples R China.;[Qian, Tao] Macau Univ Sci & Technol, Macao Ctr Math Sci, Macau, Peoples R China.;[Wang, Shilin] Unitedhlth Grp, Med Informat Dept, Cypress, CA USA.
通讯机构：
[Li, LL ] H;Hengyang Normal Univ, Coll Math & Stat, Hengyang, Hunan, Peoples R China.
摘要：
In this paper, we introduce a new member to the universal families, called universal quotient Blaschke product, which is a formal quotient of two formal infinite Blaschke products. A formal infinite Blaschke product is of the form B(z)=Pi(infinity)(k=1) z-z(k)/1-(z) over bar (k)z' where {zk}(k=1)(infinity) is a sequence of points in the unit disk but may not satisfy the Blaschke condition: Sigma(infinity)(k=1)(1 - vertical bar z(k vertical bar)) < infinity. A partial quotient of a universal quotient Blaschke product is the quotient of two finite Blaschke products. We show that the set of partial quotients of a universal quotient Blaschke product is dense in the set of continuous self-mappings on the unit circle in the complex plane. Meanwhile, subsequences of the partial quotients of a universal quotient Blaschke product can be used to approximate any holomorphic functions bounded by one on the unit disk. Moreover, we prove that the set of universal quotient Blaschke products is huge in the sense of Baire category.
期刊：
Communications in Nonlinear Science and Numerical Simulation,2024年128:107602 ISSN：1007-5704
通讯作者：
Hu, LJ
作者机构：
[Hu, LJ; Hu, Lijun] Hengyang Normal Univ, Sch Math & Stat, Hengyang 421002, Hunan, Peoples R China.;[Wang, Xiaohui] Univ Texas Rio Grande Valley, Sch Math & Stat Sci, Edinburg, TX 78539 USA.
通讯机构：
[Hu, LJ ] H;Hengyang Normal Univ, Sch Math & Stat, Hengyang 421002, Hunan, Peoples R China.
关键词：
3D compressible flows;Roe scheme;Shock instability;Contact discontinuities;High accuracy
摘要：
The low-dissipation Roe scheme is a popular shock capturing scheme but the shock instability, such as the infamous carbuncle phenomenon, seriously affects its application in high Mach number flows. Although considerable research has been undertaken in two dimensions, mechanism analysis of the three-dimensional shock instability is relatively scarce. Numerical simulations of the Sedov blast wave indicate that the shock instability is more prominent in three dimensions, so it has theoretical and practical significance to analyze and heal the numerical instability. The mechanism for three-dimensional shock instability has been thoroughly studied by means of the linearized stability analysis and the dissipation-controlling approach which introduces the required transverse dissipation in the numerical shock layer and is adopted to enhance the Roe scheme's shock stability. Furthermore, the unphysical expansion shock resulting from the violation of entropy condition is eliminated by a simple modification of numerical signal speed. For the improvement of the resolution for contact discontinuities and shear waves, an algebraic method which combines the THINC reconstruction scheme and the BVD algorithm is employed to minimize the density difference in the numerical diffusion term. A series of benchmark numerical experiments fully demonstrate that the proposed scheme is endowed with excellent robustness against the shock instability and high accuracy for contact discontinuities and shear waves.
作者机构：
[Chen, Shaolin; Chen, SL] Hengyang Normal Univ, Coll Math & Stat, Hengyang 421008, Hunan, Peoples R China.
通讯机构：
[Chen, SL ] H;Hengyang Normal Univ, Coll Math & Stat, Hengyang 421008, Hunan, Peoples R China.
关键词：
Heinz type inequality;Lipschitz continuous;Polyharmonic mapping;Quasiconformal mapping
摘要：
Suppose that f satisfies the following: (1) the polyharmonic equation triangle(m) f = triangle(triangle(m-1) f ) = phi(m) (phi(m) is an element of C((B-n) over bar, R-n)), (2) the boundary conditions triangle(0) f = phi(0), triangle(1) f = phi 1, ..., triangle(m-1) f = phi(m-1 )on Sn-1 (phi (j) is an element of C(Sn-1, R-n) for j is an element of {0, 1, ... , m - 1} and Sn-1 denotes the boundary of the unit ball B-n), and (3) f (0) = 0, where n >= 3 and m >= 1 are integers. Initially, we prove a Schwarz type lemma and use it to obtain a Heinz type inequality of mappings satisfying the polyharmonic equation with the above Dirichlet boundary value conditions. Furthermore, we establish a Bloch type theorem of mappings satisfying the above polyharmonic equation, which gives an answer to an open problem in Chen and Ponnusamy, (2019). Additionally, we show that if f is a K-quasiconformal self-mapping of Bn satisfying the above polyharmonic equation, then f is Lipschitz continuous, and the Lipschitz constant is asymptotically sharp as K -> 1(+) and parallel to phi(j) parallel to infinity -> 0(+) for j is an element of {1, ... , m}.(c) 2023 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.
作者：
Liu, Gang;Ponnusamy, Saminathan;V. Starkov, Victor
期刊：
BULLETIN DES SCIENCES MATHEMATIQUES,2023年184:103256 ISSN：0007-4497
通讯作者：
Ponnusamy, S
作者机构：
[Liu, Gang] Hengyang Normal Univ, Coll Math & Stat, Hunan Prov Key Lab Intelligent Informat Proc & App, Hengyang 421002, Hunan, Peoples R China.;[Ponnusamy, S; Ponnusamy, Saminathan] Indian Inst Technol Madras, Dept Math, Chennai 600036, India.;[Ponnusamy, S; Ponnusamy, Saminathan] Lomonosov Moscow State Univ, Moscow Ctr Fundamental & Appl Math, Moscow, Russia.;[V. Starkov, Victor] Univ Petrozavodsk, Dept Math, ul Lenina 33, Petrozavodsk 185910, Russia.
通讯机构：
[Ponnusamy, S ] I;Indian Inst Technol Madras, Dept Math, Chennai 600036, India.;Lomonosov Moscow State Univ, Moscow Ctr Fundamental & Appl Math, Moscow, Russia.
关键词：
Bohr inequality;Convex;Harmonic mapping;Linear and affine invariant family;Subordination;Univalent
摘要：
Let 710 denote the set of all sense-preserving harmonic mappings f = h + g in the unit disk D, normalized with h(0) = g(0) = g'(0) = 0 and h'(0) = 1. In this paper, we mainly investigate some properties of certain subclasses of 710, including inclusion relations and stability analysis by precise examples, coefficient bounds, growth, covering and distortion theorems. As applications, we build some Bohr inequalities for these subclasses by means of subordination. Among these subclasses, six classes consist of functions f = h +g E 710 such that h + eg is univalent (or convex) in D for each |e| = 1 (or for some |e| = 1, or for some |e| < 1). Simple analysis shows that if the function f = h + g belongs to a given class from these six classes, then the functions h + eg belong to corresponding class for all |e| = 1. We call these classes as stable classes. (c) 2023 Elsevier Masson SAS. All rights reserved.
期刊：
Computational Methods and Function Theory,2023年:1-11 ISSN：1617-9447
通讯作者：
Ponnusamy, S
作者机构：
[Li, Liulan] Hengyang Normal Univ, Coll Math & Stat, Hunan Prov Key Lab Intelligent Informat Proc & App, Hengyang 421002, Hunan, Peoples R China.;[Ponnusamy, S; Ponnusamy, Saminathan] Indian Inst Technol Madras, Dept Math, Chennai 600036, India.;[Ponnusamy, S; Ponnusamy, Saminathan] Lomonosov Moscow State Univ, Moscow Ctr Fundamental & Appl Math, Moscow, Russia.;[Wirths, Karl-Joachim] Tech Univ Carolo Wilhelmina Braunschweig, Inst Algebra & Anal, D-38106 Braunschweig, Germany.
通讯机构：
[Ponnusamy, S ] I;Indian Inst Technol Madras, Dept Math, Chennai 600036, India.;Lomonosov Moscow State Univ, Moscow Ctr Fundamental & Appl Math, Moscow, Russia.
关键词：
Meromorphic functions;Taylor coefficients;Laurent series
摘要：
In this article, we consider the family of functions f meromorphic in the unit disk
$${\mathbb D}=\{z:\,|z| < 1\}$$
with a pole at the point
$$z=p$$
, a Taylor expansion
$$\begin{aligned} f(z)= z+\sum _{k=2}^{\infty } a_kz^k, \quad |z|<p, \end{aligned}$$
and satisfying the condition
$$\begin{aligned} \left| \left( \frac{z}{f(z)}\right) -z\left( \frac{z}{f(z)}\right) '-1\right| <\lambda \qquad \text {for all }z\in {\mathbb D}, \end{aligned}$$
for some
$$\lambda $$
,
$$0<\lambda < 1$$
. We denote this class by
$$\mathcal {U}_p(\lambda )$$
and we shall prove a representation theorem for the functions in this class. As consequences, we get a simple proof for the estimates of
$$|a_2|$$
and obtain inequalities for the initial coefficients of the Laurent series of
$$f\in \mathcal {U}_p(\lambda )$$
at its pole. In [8] it had been conjectured that for
$$f\in \mathcal {U}_p(\lambda )$$
the inequalities
$$\begin{aligned} |a_n|\le \frac{1}{p^{n-1}}\sum _{k=0}^{n-1}(\lambda p^2)^k, \quad n\ge 2, \end{aligned}$$
are valid. We provide a counterexample to this conjecture for the case
$$n=3$$
.
期刊：
Journal of Mathematical Analysis and Applications,2023年518(2):126702 ISSN：0022-247X
作者机构：
[Deng YiHua] College of Mathematics and Statistics, Hengyang Normal University, Hengyang, Hunan 421002, China
摘要：
In this paper, we discuss the rigidity of gradient generalized m-quasi-Einstein manifolds and gradient shrinking Ricci solitons. We get some useful equations for the potential function of gradient generalized m-quasi-Einstein manifolds. Using these equations, we obtain some rigid properties for gradient generalized m-quasi-Einstein manifolds. Furthermore, we prove that some complete gradient shrinking Ricci solitons with pinching condition on the Weyl tensor are finite quotients of Rn or Sn.
摘要：
目的 应用成分数据分析方法研究幼儿24 h活动行为（24-hour Movement Behavior）与基本动作技能（Fundamental Movement Skills,FMS）之间的关联，以及各活动行为间等时替代后幼儿FMS的预期变化。方法 采用ActiGraph wGT3-BT加速度计测量323名3～6岁幼儿（男童181名，女童142名）的身体活动（Physical Activity,PA)、静态行为（Sedentary Behaviour,SB)数据，采用美国大肌肉动作发展测试第3版工具（Test of Gross Motor Development,TGMD-3）测量FMS，睡眠时间由父母报告，成分数据的描述性统计分析、多元线性模型和等时替代均采用R软件完成。结果 (1)幼儿24 h活动时间分布与动作发展关联紧密，中高强度身体活动（Moderate-to-Vigorous Physical Activity,MVPA）在成分之间分布相对稳定，与低强度身体活动（Light Physical Activity,LPA）转换的可能性更大；(2)幼儿MVPA对移动技能和总动作技能（Total Motor Skill, Total MS）的影响最大，MVPA等时替代其他行为均具有积极效益，其中替换LPA效果最为明显，其他行为等时替代MVPA预示着更低的动作能力，而且预测具有不对称性。结论 虽然MVPA对幼儿动作发展影响最大，但更需要从整体视角平衡24 h活动行为对动作发展的影响；在幼儿园、家庭和社区环境中，强调将幼儿的LPA转换为MVPA，以更好地促进其FMS发展。
期刊：
Journal of Mathematics,2023年2023 ISSN：2314-4629
作者机构：
[Wang, Keyan; Hu, Boxia] Hengyang Normal Univ, Sch Math & Stat, Hengyang 421008, Hunan, Peoples R China.;[Hu, Boxia] Hunan Univ, Sch Math, Changsha 410082, Hunan, Peoples R China.
摘要：
In this paper, two efficient two-grid algorithms for the convection-diffusion problem with a modified characteristic finite element method are studied. We present an optimal error estimate in L-p-norm for the characteristic finite element method unconditionally, while all previous works require certain time-step restrictions. To linearize the characteristic method equations, two-grid algorithms based on the Newton iteration approach and the correction method are applied. The error estimate and the convergence result of the two-grid method are derived in detail. It is shown that the coarse space can be extremely coarse and achieve asymptotically optimal approximations as long as the mesh sizes H=Oh(1/3) in the first algorithm and H=Oh(1/4) in the second algorithm, respectively. Finally, two numerical examples are presented to demonstrate the theoretical analysis.
作者机构：
[Shi, Xiulian] Zhaoqing Univ, Sch Math & Stat, Zhaoqing 526061, Peoples R China.;[Wang, Keyan] Hengyang Normal Univ, Sch Math & Stat, Hengyang 421008, Peoples R China.;[Sun, Hui] Xinyang Normal Univ, Sch Math & Stat, Xinyang 464000, Peoples R China.
通讯机构：
[Shi, XL ] Z;Zhaoqing Univ, Sch Math & Stat, Zhaoqing 526061, Peoples R China.
摘要：
In this paper, we propose and analyze a spectral collocation method for the numerical solutions of fractional multipantograph delay differential equations. The fractional derivatives are described in the Caputo sense. We present that some suitable variable transformations can convert the equations to a Volterra integral equation defined on the standard interval [-1, 1]. Then the Jacobi-Gauss points are used as collocation nodes, and the Jacobi-Gauss quadrature formula is used to approximate the integral equation. Later, the convergence analysis of the proposed method is investigated in the infinity norm and weighted L(2 )norm. To perform the numerical simulations, some test examples are investigated, and numerical results are presented. Further, we provide the comparative study of the proposed method with some existing numerical methods.
期刊：
JOURNAL OF GEOMETRIC ANALYSIS,2023年33(7):1-45 ISSN：1050-6926
通讯作者：
Chen, SL
作者机构：
[Huang, Manzi; Chen, Jiaolong; Zheng, Huaqing] Hunan Normal Univ, Sch Math & Stat, MOE LCSM, Changsha 410081, Hunan, Peoples R China.;[Chen, Shaolin; Chen, SL] Hengyang Normal Univ, Coll Math & Stat, Hengyang 421002, Hunan, Peoples R China.;[Chen, Shaolin; Chen, SL] Hunan Prov Key Lab Intelligent Informat Proc & App, Hengyang 421002, Peoples R China.
通讯机构：
[Chen, SL ] H;Hengyang Normal Univ, Coll Math & Stat, Hengyang 421002, Hunan, Peoples R China.;Hunan Prov Key Lab Intelligent Informat Proc & App, Hengyang 421002, Peoples R China.
关键词：
Isoperimetric type inequality;Poisson type integral;Hardy type space;Bergman type space;\((K,K')\)-elliptic mapping
摘要：
The main purpose of this paper is to establish some isoperimetric type inequalities for mappings induced by the weighted Laplace differential operators. The obtained results of this paper provide improvements and extensions of the corresponding known results.
作者机构：
[Liu, ZS; Liu, Z. -S] Hengyang Normal Univ, Coll Math & Stat, Hengyang 421002, Hunan, Peoples R China.
通讯机构：
[Liu, ZS ] H;Hengyang Normal Univ, Coll Math & Stat, Hengyang 421002, Hunan, Peoples R China.
关键词：
spectral measure;orthonormal basis;spectrum;Moran measure;Moran set
摘要：
Let
$$\{(R_k,D_k)\}_{k=1}^\infty$$
be a sequence of pairs, where
$$D_k=\{0,1,\ldots,q_k-1\}(1,1)^T$$
is an integer vector set and
$$R_k$$
is an integer diagonal matrix or upper triangular matrix, i.e.,
$$R_k={\begin{pmatrix} s_k & 0\\ 0 & t_k \end{pmatrix}}$$
or
$$R_k={\begin{pmatrix} u_k & 1\\ 0 & v_k \end{pmatrix}}$$
.
Associated with the sequence
$$\{(R_k,D_k)\}_{k=1}^\infty$$
, Moran measure
$$\mu_{\{R_k\},\{D_k\}}$$
is defined by
$$\mu_{\{R_k\},\{D_k\}}=\delta_{R_{1}^{-1}D_{1}}\ast\delta_{R_{1}^{-1}R_{2}^{-1}D_{2}}\ast\cdots\ast \delta_{R_{1}^{-1}R_{2}^{-1}\cdots R_{k}^{-1}D_{k}}\ast \cdots.$$
In this paper, we consider the spectrality of
$$\mu_{\{R_k\},\{D_k\}}$$
. We prove that
$$\mu_{\{R_k\},\{D_k\}}$$
is a spectral measure under certain conditions in terms of
$$(R_k,D_k)$$
, i.e., there exists a Fourier basis for
$$L^2(\mu_{\{R_k\},\{D_k\}})$$
.
期刊：
Communications in Nonlinear Science and Numerical Simulation,2023年116:106798 ISSN：1007-5704
通讯作者：
Hu, Lijun(hulijun@lsec.cc.ac.cn)
作者机构：
[Hu, Lijun] Hengyang Normal Univ, Sch Math & Stat, Hengyang 421002, Hunan, Peoples R China.;Univ Texas Rio Grande Valley, Sch Math & Stat Sci, Edinburg, TX 78539 USA.
通讯机构：
[Lijun Hu] S;School of Mathematics and Statistics, Hengyang Normal University, Hengyang, Hunan 421002, China
期刊：
Bulletin of the Malaysian Mathematical Sciences Society,2023年46(4):1-19 ISSN：0126-6705
通讯作者：
Chen, SL
作者机构：
[Chen, Shaolin; Chen, SL] Hengyang Normal Univ, Coll Math & Stat, Hengyang 421002, Hunan, Peoples R China.;[Chen, Shaolin; Chen, SL] Hunan Prov Key Lab Intelligent Informat Proc & App, Hengyang 421002, Hunan, Peoples R China.;[Hamada, Hidetaka] Kyushu Sangyo Univ, Fac Sci & Engn, 3-1 Matsukadai 2 Chome,Higashi Ku, Fukuoka 8138503, Japan.
通讯机构：
[Chen, SL ] H;Hengyang Normal Univ, Coll Math & Stat, Hengyang 421002, Hunan, Peoples R China.;Hunan Prov Key Lab Intelligent Informat Proc & App, Hengyang 421002, Hunan, Peoples R China.
关键词：
Bergman type class;Complex-valued harmonic function;Elliptic mapping;Hardy type space
摘要：
The main purpose of this paper is to discuss Hardy type spaces and Bergman type classes of complex-valued harmonic functions. We first establish a Hardy-Littlewood type theorem on complex-valued harmonic functions. Next, the relationships between the Bergman type classes and the Hardy type spaces of complex-valued harmonic functions or the relationships between the Bergman type classes and the Hardy type spaces of harmonic
$$(K,K')$$
-elliptic mappings will be discussed, where
$$K\ge 1$$
and
$$K'\ge 0$$
are constants.
