期刊：
Rendiconti del Circolo Matematico di Palermo,2024年:1-12 ISSN：0009-725X
通讯作者：
Shaolin Chen
作者机构：
[Shaolin Chen] College of Mathematics and Statistics, Hengyang Normal University, Hengyang, People’s Republic of China;[Hidetaka Hamada] Faculty of Science and Engineering, Kyushu Sangyo University, Fukuoka, 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：
Harmonic function;Linear measure;Non-iterative dynamic system
摘要：
The main purpose of this paper is to determine the linear measure of non-iterative dynamic system of some classes of harmonic functions.
摘要：
It is known that the inverse of a quasiconformal homeomorphism of domains in R n is also quasiconformal. This paper focuses on the inverse problem for free quasiconformality in Banach spaces. We first show that the inverse of a fully semisolid homeomorphism is fully semisolid under an additional coarsely Lipschitz condition in the quasihyperbolic metric. This gives several partial answers to two open problems posed by V & auml;is & auml;l & auml;. Next, we prove that the inverse of a locally quasisymmetric homeomorphism is also locally quasisymmetric. As applications, we obtain new characterizations of freely quasiconformal mappings in Banach spaces, and study the relation between freely quasiconformal mappings and quasisymmetric mappings between uniform domains.
期刊：
Frontiers in Public Health,2024年12:1288262 ISSN：2296-2565
通讯作者：
Yin, L
作者机构：
[Li, Fang; Luo, Wanhong] Hunan First Normal Univ, Sch Phys Educ, Changsha, Peoples R China.;[Yin, Long; Yin, L] Hunan Normal Univ, Coll Phys Educ, Changsha, Peoples R China.;[Gao, Zan] Univ Tennessee, Dept Kinesiol Recreat & Sport Studies, Knoxville, TN USA.;[Ryu, Suryeon] Univ Minnesota Twin Cities, Sch Kinesiol, Minneapolis, MN USA.;[Sun, Mingyun] Hengyang Normal Univ, Sch Math & Stat, Hengyang, Peoples R China.
通讯机构：
[Yin, L ] H;Hunan Normal Univ, Coll Phys Educ, Changsha, Peoples R China.
关键词：
24-h movement behavior;isotemporal substitution;mental health;non-screen-based sedentary behavior;screen-based sedentary behavior
摘要：
The 24-h movement behavior of preschoolers comprises a spectrum of activities, including moderate-to-vigorous intensity physical activity (MVPA), light-intensity physical activity (LPA), screen-based sedentary behavior (SCSB), non-screen-based sedentary behavior (NSCSB), and sleep. While previous research has shed light on the link between movement behaviors and children's mental health, the specific impacts on the unique demographic of Chinese preschoolers remain underexplored. This study significantly contributes to the literature by exploring how 24-h movement behavior affects the mental health of preschoolers in a Chinese context. The study involved205 Chinese preschool children (117 boys and 88 girls) between the ages of 3 and 6 years wore accelerometers to measure their LPA, MVPA, and sedentary behavior (SB), while their parents reported the time spent on sleep and SCSB. The parents also completed the Strength and Difficulties Questionnaire to assess their children's mental health. The study used compositional regression and isotemporal substitution models to examine the relationship between the various components of 24-h movement behavior and mental health. The results showed that greater NCSSB compared to MVPA, LPA, sleep, and SCSB was associated with good prosocial behavior and lower scores on externalizing problems. This highlights the potential of NSCSB as a beneficial component in the daily routine of preschoolers for fostering mental well-being. Replacing 15 min of sleep and SCSB with 15 min of NSCSB was associated with a decrease of 0.24 and 0.15 units, respectively, in externalizing problems. Reallocating 15 min of sleep to NSCSB was linked to an increase of 0.11 units in prosocial behavior. There were no significant substitution effects between LPA and MVPA time with any other movement behavior on prosocial behavior and externalizing problems. Given the positive associations observed, further longitudinal studies are necessary to explore the link between 24-h movement behavior and mental health in preschool children.
期刊：
Computational Methods and Function Theory,2024年24(1):229-239 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：
MATHEMATICAL BIOSCIENCES AND ENGINEERING,2024年21(2):2344-2365 ISSN：1547-1063
作者机构：
[Haihua Zhou] School of Mathematics and Statistics, Hengyang Normal University, Hengyang 421010, China;[Yaxin Liu; Zejia Wang; Huijuan Song] School of Mathematics and Statistics, Jiangxi Normal University, Nanchang 330022, China
摘要：
<jats:p xml:lang="fr"><abstract><p>This paper was concerned with a free boundary problem modeling the growth of tumor cord with a time delay in cell proliferation, in which the cell location was incorporated, the domain was bounded in $ \mathbb{R}^2 $, and its boundary included two disjoint closed curves, one fixed and the other moving and a priori unknown. A parameter $ \mu $ represents the aggressiveness of the tumor. We proved that there exists a unique radially symmetric stationary solution for sufficiently small time delay, and this stationary solution is linearly stable under the nonradially symmetric perturbations for any $ \mu &gt; 0 $. Moreover, adding the time delay in the model leads to a larger stationary tumor. If the tumor aggressiveness parameter is bigger, the time delay has a greater effect on the size of the stationary tumor, but it has no effect on the stability of the stationary solution.</p></abstract></jats:p>
摘要：
As digital images are widely used in social media, medical, military and other fields, ensuring the privacy and security of image data has become a critical concern. Firstly, we propose a novel four-dimensional hyperchaotic system and validate that it exhibits a broad chaotic range, as demonstrated by bifurcation diagrams and Lyapunov exponent experiments. Additionally, simulated circuit diagrams verify the hardware feasibility of the proposed system. Secondly, we design a dynamic iterative scrambling (DIS) scheme that dynamically divides the image into multiple matrices for spatially indexed scrambling. Excellent substitution performance can be ensured by multiple iterations. In the diffusion stage, a multidirectional bit-level L-shaped (MDBL) scheme is proposed. Diffusion is conducted on the bit plane using a designed cross-multiplanar selection algorithm, which fuses the high and low bit planes, thereby enhancing the diffusion performance of MDBL. Thirdly, Based on the above concepts, a novel four-dimensional hyperchaotic system and an encryption algorithm based on bit-level diffusion are proposed. Finally, experimental results and security analyses demonstrate the effectiveness of the novel 4D hyperchaotic system and image encryption scheme. The proposed encryption scheme exhibits robust anti-interference capabilities and effectively safeguards image security.
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.
摘要：
Although the genuinely two-dimensional HLL-CPS solver holds the inherent multidimensionality property and capability of resolving contact discontinuities, the conventional low-order (second-order and below) reconstruction methods still limits its application in the two-dimensional complex flows involving shock waves and shear layers. A fifth-order reconstruction method is proposed for the genuinely two-dimensional HLL-CPS solver. The conserved variable vectors at the midpoints of interfaces are approximated by the fifth-order 1D WENO reconstruction. Meanwhile, variables at the corners are evaluated by a dimension-by-dimension reconstruction method consisting of a number of 1D fifth-order WENO sweeps. To avoid introducing spurious oscillations, each reconstruction is carried out in the corresponding local characteristic fields. Numerical results of several benchmark tests indicate the higher-order accuracy and the multidimensionality property of the proposed scheme. Compared with the 1D HLLE, HLLC and HLL-CPS schemes, the proposed high-order genuinely two-dimensional HLL-CPS solver provides higher resolution for contact discontinuities and presents better robustness against the shock anomalies.
期刊：
Neural Computing and Applications,2024年:1-23 ISSN：0941-0643
通讯作者：
Tiejun Zhou
作者机构：
College of Mathematics and Statistics, Hengyang Normal University, Hengyang, China;[Xiangyu Xu] College of Information and Intelligence Science, Hunan Agricultural University, Changsha, China;Hunan Province Key Laboratory of Intelligent Agriculture Equipment, Changsha, China;[Zhiguang Liu] College of Mathematics and Statistics, Hengyang Normal University, Hengyang, China<&wdkj&>College of Information and Intelligence Science, Hunan Agricultural University, Changsha, China;[Tiejun Zhou] College of Information and Intelligence Science, Hunan Agricultural University, Changsha, China<&wdkj&>Hunan Province Key Laboratory of Intelligent Agriculture Equipment, Changsha, China
通讯机构：
[Tiejun Zhou] C;College of Information and Intelligence Science, Hunan Agricultural University, Changsha, China<&wdkj&>Hunan Province Key Laboratory of Intelligent Agriculture Equipment, Changsha, China
摘要：
Let M = ( [GRAPHICS] ) be a real upper triangular expanding matrix and.. = {(0 0), (d(1) 0), (d(2) d(3))} be a three-element real digit set with d(1)d(3) not equal 0, and let {n(k)}(k=1)(infinity) be a sequence of positive integers with upper bound. The infinite convolutions mu(M,D,{nk}) = delta(M-n1 D) * delta(M-(n1 + n2) D) * center dot center dot center dot * delta(M-(n1 +center dot center dot center dot+ nk) D) * center dot center dot center dot converges weakly to a Borel probability measure (homogeneous Moran measure). In this paper, we study the existence of exponential orthonormal basis for L-2(mu(M,D,{nk})). A necessary and sufficient condition for mu(M,D,{nk}) to be a spectral measure is established.
期刊：
Complex Variables and Elliptic Equations,2024年:1-15 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.
作者机构：
[Wang, Keyan] Hengyang Normal Univ, Sch Math & Stat, Hengyang 421008, Hunan, Peoples R China.
通讯机构：
[Wang, KY ] H;Hengyang Normal Univ, Sch Math & Stat, Hengyang 421008, Hunan, Peoples R China.
关键词：
hyperbolic equation;expanded mixed finite element method;two-grid method;error estimate
摘要：
In this article, we present a scheme for solving two-dimensional hyperbolic equation using an expanded mixed finite element method. To solve the resulting nonlinear expanded mixed finite element system more efficiently, we propose a two-step two-grid algorithm. Numerical stability and error estimate are proved on both the coarse grid and fine grid. It is shown that the two-grid method can achieve asymptotically optimal approximation as long as the coarse grid size H and the fine grid size h satisfy h = O(H(2k+1)/(k+ 1)) (k >= 1), where k is the degree of the approximating space for the primary variable. Numerical experiment is presented to demonstrate the accuracy and the efficiency of the proposed method.
摘要：
The primary goal of this paper is to develop methods for investigating equivalent norms and Hardy-Littlewood-type theorems on Lipschitz-type spaces of analytic and complex-valued harmonic functions. First, we provide characterizations of equivalent norms on these spaces. Furthermore, we establish Hardy-Littlewood-type theorems for complex-valued harmonic functions. These results improve and extend the main findings of Dyakonov (1997) and Dyakonov (2005). Additionally, we apply the derived equivalent norms and Hardy-Littlewood-type theorems to the study of composition operators between Lipschitz-type spaces.
期刊：
Bulletin of the Malaysian Mathematical Sciences Society,2024年47(4):1-17 ISSN：0126-6705
通讯作者：
Hamada, H
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：
[Hamada, H ] K;Kyushu Sangyo Univ, Fac Sci & Engn, 3-1 Matsukadai 2-Chome,Higashi Ku, Fukuoka 8138503, Japan.
关键词：
Bloch space;Bounded symmetric domains;Composition operator;JB*-triple;The Kobayashi metric;Pluriharmonic function
摘要：
Let BX\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {B}_X$$\end{document} be a bounded symmetric domain realized as the open unit ball of a JB*-triple X. First, we extend the definition for pluriharmonic Bloch functions to BX\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {B}_X$$\end{document} by using the infinitesimal Kobayashi metric. Next, we develop some methods to investigate Bloch functions, and composition operators of pluriharmonic Bloch spaces on bounded symmetric domains. The obtained results provide the improvements and extensions of the corresponding known results.
摘要：
In this paper, we introduce a class of Moran measures generated by quasi periodic sequences, and consider power decay of the Fourier transforms of this kind of measures.
摘要：
In this paper, we propose a color image compression and encryption algorithm that combines compressed sensing, Sudoku matrix, and hyperchaotic map to ensure the security of image data and improve transmission and storage efficiency. Firstly, we design a novel two-dimensional sine-logistic coupled hyperchaotic map that exhibits a more continuous and broader chaotic range and more complex hyperchaotic behavior compared to some existing known chaotic maps. Secondly, to mitigate the impact of compression thresholds on image reconstruction quality, we employ multiple optimization strategies to improve the dung beetle optimization algorithm, enhancing its global exploration and local exploitation capabilities, thereby making it more efficient and accurate in handling complex optimization problems. Based on this, we optimize the compression threshold using the improved algorithm to find the optimal threshold for the best image reconstruction quality. Finally, to further enhance the security of the algorithm, we introduce Sudoku matrices in the permutation stage. By using randomly generated Sudoku matrices to permute the image pixel positions, the original image structure is effectively disrupted, increasing the complexity and randomness of the encryption. In the diffusion stage, we employ a bidirectional diffusion operation to ensure that pixel information is effectively spread throughout the image, and we dynamically update the diffusion keys in each round, making the key sequence highly random and unpredictable. Experimental results demonstrate that the proposed algorithm can resist various illegal attacks and offers high security.
期刊：
JOURNAL OF GEOMETRIC ANALYSIS,2024年34(9):1-23 ISSN：1050-6926
通讯作者：
Hamada, H
作者机构：
[Chen, Shaolin; Xie, Dou] 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：
[Hamada, H ] K;Kyushu Sangyo Univ, Fac Sci & Engn, 3-1 Matsukadai 2-Chome,Higashi Ku, Fukuoka 8138503, Japan.
关键词：
Hardy-Littlewood type Theorem;Hopf type lemma;Differential operator;Dirichlet solution
摘要：
The main aim of this paper is to investigate Hardy-Littlewood type Theorems and a Hopf type lemma on functions induced by a differential operator. We first prove more general Hardy-Littlewood type theorems for the Dirichlet solution of a differential operator which depends on
$$\alpha \in (-1,\infty )$$
over the unit ball
$$\mathbb {B}^n$$
of
$$\mathbb {R}^n$$
with
$$n\ge 2$$
, related to the Lipschitz type space defined by a majorant which satisfies some assumption. We find that the case
$$\alpha \in (0,\infty )$$
is completely different from the case
$$\alpha =0$$
due to Dyakonov (Adv. Math. 187 (2004), 146–172). Then a more general Hopf type lemma for the Dirichlet solution of a differential operator will also be established in the case
$$\alpha >n-2$$
.
