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 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.
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 .
作者机构：
[Shaolin Chen] College of Mathematics and Statistics, Hengyang Normal University, Hengyang, Hunan 421008, People’s Republic of China
摘要：
Suppose that f satisfies the following: (1) the polyharmonic equation Δmf=Δ(Δm−1f) =φm (φm∈C(Bn¯,Rn)) , (2) the boundary conditions Δ0f=φ0,Δ1f=φ1,…,Δm−1f=φm−1 on Sn−1 ( φj∈C(Sn−1,Rn) for j∈{0,1,…,m−1} and Sn−1 denotes the boundary of the unit ball Bn ), 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 ‖φj‖∞→0+ for j∈{1,…,m} .
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。
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：
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.
期刊：
Communications in Nonlinear Science and Numerical Simulation,2023年116:106798 ISSN：1007-5704
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.
摘要：
The Roe scheme is known to have high resolution but to be afflicted by the notorious shock anomalies (such as the carbuncle phenomena) and the unphysical expansion shocks. This paper aims to develop a new Roe-type scheme which is robust for strong shock waves and low dissipative for contact waves and shear layers. Based on the mechanism analysis of shock instability, a dissipation-controlling strategy is adopted to adjust the entropy wave viscosity and shear wave viscosity of the transverse numerical flux in the numerical shock layer and the robustness of the Roe scheme is thus enhanced. The violation of entropy condition and the problem of expansion shocks are also fixed to broaden the scheme's application scope. In addition, the THINC reconstruction procedure and a BVD algorithm are implemented to further improve the resolution for contact waves and shear layers. Numerical results of a series of classical one-, two-and three-dimensional test problems fully demonstrate that the proposed new Roe-type scheme has not only better robustness for strong shock waves but also higher resolution for contact waves and shear layers than the original Roe scheme. (C) 2022 Elsevier B.V. All rights reserved.
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.
期刊：
JOURNAL OF GEOMETRIC ANALYSIS,2023年33(6):1-22 ISSN：1050-6926
通讯作者：
Shaolin Chen
作者机构：
[Chen, Shaolin] Hengyang Normal Univ, Coll Math & Stat, Hengyang 421008, 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：
[Shaolin Chen] C;College of Mathematics and Statistics, Hengyang Normal University, Hengyang, People’s Republic of China
关键词：
Lipschitz type space;Harmonic function;Composition operator;Pluriharmonic functions
摘要：
The main purpose of this paper is to develop some methods to study the composition operators between harmonic Lipschitz type spaces. Some characterizations of boundedness and w-compactness of composition operators between the harmonic Lipschitz type spaces will be given. Consequently, the obtained results improve and extend some corresponding known results.
期刊：
Bulletin of the Malaysian Mathematical Sciences Society,2023年46(1):1-19 ISSN：0126-6705
通讯作者：
Junyang Gao
作者机构：
[Gao, Linkui; Gao, Junyang] China Univ Min & Technol, Sch Sci, Beijing 100083, Peoples R China.;[Liu, Gang] Hengyang Normal Univ, Coll Math & Stat, Hengyang 421008, Hunan, Peoples R China.
通讯机构：
[Junyang Gao] S;School of Science, China University of Mining and Technology, Beijing, People’s Republic of China
关键词：
Harmonic trinomials;Harmonic polynomials;Zero inclusion regions
摘要：
In this paper, we mainly determine the zero inclusion regions of certain harmonic trinomials and illustrate our results with several examples. It is considered to be the harmonic version of locating the zeros of harmonic trinomials, compared with the results on the location of the zeros of analytic trinomials obtained by Melman.
通讯机构：
[Zengbo Wang] C;College of Mathematics and Statistics, Hengyang Normal University, Hengyang 421002, China
关键词：
mobile laser scanning;individual tree detection;MLS point clouds;outdoor scene
摘要：
Abstract: The automatic extraction of individual tree from mobile laser scanning (MLS) scenes has important applications in tree growth monitoring, tree parameter calculation and tree modeling. However, trees often grow in rows and tree crowns overlap with varying shapes, and there is also incompleteness caused by occlusion, which makes individual tree extraction a challenging problem. In this paper, we propose a trunk-constrained and tree structure analysis method to extract trees from scanned urban scenes. Firstly, multi-feature enhancement is performed via PointNet to segment the tree points from raw urban scene point clouds. Next, the candidate local tree trunk clusters are obtained by clustering based on the intercepted local tree trunk layer, and the real local tree trunk is obtained by removing noise data. Then, the trunk is located and extracted by combining circle fitting and region growing, so as to obtain the center of the tree crown. Further, the points near the tree’s crown (core points) are segmented through distance difference, and the tree crown boundary (boundary points) is distinguished by analyzing the density and centroid deflection angle. Therefore, the core and boundary points are deleted to obtain the remaining points (intermediate points). Finally, the core, intermediate and boundary points, as well as the tree trunks, are combined to extract individual tree. The performance of the proposed method was evaluated on the Pairs-Lille-3D dataset, which is a benchmark for point cloud classification, and data were produced using a mobile laser system (MLS) applied to two different cities in France (Paris and Lille). Overall, the precision, recall, and F1-score of instance segmentation were 90.00%, 98.22%, and 99.08%, respectively. The experimental results demonstrate that our method can effectively extract trees with multiple rows of occlusion and improve the accuracy of tree extraction. Keywords: mobile laser scanning; individual tree detection; MLS point clouds; outdoor scene
作者机构：
[Yang, Yufei; Hu, Boxia] Hunan Univ, Sch Math, Changsha 410082, Peoples R China.;[Hu, Boxia] Hengyang Normal Univ, Coll Math & Stat, Hengyang 421002, Peoples R China.;[Ouyang, Ze; Sun, Yaqi; Zhang, Feng] Hengyang Normal Univ, Coll Comp Sci & Technol, Hengyang 421002, Peoples R China.;[Yang, Yufei] Changsha Univ, Sch Math, Changsha 410022, Peoples R China.
关键词：
Rain removal;edge optimization;robust;Unet plus plus
摘要：
Image deraining has become a hot topic in the field of computer vision. It is the process of removing rain streaks from an image to reconstruct a high-quality background. This study aims at improving the performance of image rain streak removal and reducing the disruptive effects caused by rain. To better fit the rain removal task, an innovative image deraining method is proposed, where a kernel prediction network with Unet++ is designed and used to filter rainy images, and rainy-day images are used to estimate the pixel-level kernel for rain removal. To minimize the gap between synthetic and real data and improve the performance in real rainy image handling, a loss function and an effective data optimization method are suggested. In contrast with other methods, the loss function consists of Structural Similarity Index loss, edge loss, and L1 loss, and it is adopted to improve performance. The proposed algorithm can improve the Peak Signal-to-Noise ratio by 1.3% when compared to conventional approaches. Experimental results indicate that the proposed method can achieve a better efficiency and preserve more image structure than several classical methods.
摘要：
Brown planthopper Nilaparvata lugens is a serious rice damaging pest and can transmit rice ragged stunt virus. A new biological control method for Nilaparvata lugens by using Wolbachia wStri has been successful in the laboratory. No matter using the strategy of population replacement or the strategy of population suppression to release Nilaparvata lugens infected with wStri, theoretical analysis shows that Nilaparvata lugens infected with wStri may eventually disappear after interacting with the wild Nilaparvata lugens, so the Nilaparvata lugens infected with wStri should be released several times. The question is when and how much to release. In this paper, we propose a population replacement model and a population suppression model with state-dependent impulse release. The existence and stability conditions of the corresponding periodic solutions for these two systems are obtained by applying the theory of semi-continuous dynamical system. We found that the defined evaluation index of wStri release time determines the property of the solutions of the systems. The growth period of Nilaparvata lugens infected with wStri is divided into several stages according to the evaluation index of wStri release time, and the release measures for different stages are put forward, especially the release strategy to make the wild Nilaparvata lugens extinct is discussed. Based on the concept of control degree, a more realistic control goal is also discussed, which is to keep the wild Nilaparvata lugens under a lower level within a finite time. Numerical simulation shows that the effective control has good robustness to the biological parameters of insect, and both strategies can effectively control the wild Nilaparvata lugens.(c) 2022 Elsevier B.V. All rights reserved.
