摘要：
We study the spectral property of a class of Sierpinski-type self-affine measures mu(M,D )(.) =1/3 Sigma(d is an element of D) mu(M, D) (M (.) - d) on R-2, where M = [GRAPHICS] . is a real upper triangular expanding matrix and D = {((0)(0)), (d1)((0)), ((d2)(d3))} is a three-element real digit set with d(1)d(3) not equal 0. A necessary and sufficient condition for mu(M,D) to be a spectral measure is established. (C) 2021 Elsevier Inc. All rights reserved.
作者机构：
[Shao Lin CHEN] College of Mathematics and Statistics,Hengyang Normal University,Hengyang 421002,P.R.China;[Shao Lin CHEN] Hunan Provincial Key Laboratory of Intelligent Information Processing and Application,Hengyang 421002,P.R.China;Department of Mathematics,Indian Institute of Technology Madras,Chennai-600 036,India;[Saminathan PONNUSAMY] 马德拉斯理工学院
通讯机构：
[Shao Lin Chen] C;College of Mathematics and Statistics, Hengyang Normal University, Hengyang, P. R. China<&wdkj&>Hunan Provincial Key Laboratory of Intelligent Information Processing and Application, Hengyang, P. R. China
关键词：
Harmonic K-quasiconformal mapping;Koebe type covering theorem;Koebe type distortion theorem;Radial John disk
摘要：
We study the fractional p-Kirchhoff equation (a+b) integral(RN) integral(RN) vertical bar u(x) - u(y)vertical bar(p)/vertical bar x - y vertical bar(N+ps) dx dy (-Delta)(p)(s)u-u vertical bar u vertical bar(p-2)u = vertical bar u vertical bar(q-2)u, x is an element of R-N, where (-Delta)(p)(s) is the fractional p-Laplacian operator, a and b are strictly positive real numbers, s is an element of (0, 1), 1 < p < N/s, and p < q < p(s)* - 2 with p(s)* - Np/N - p(s). By using the variational method, we prove the existence and uniqueness of global minimum or mountain pass type critical points on the L-p-normalized manifold S(c):= {u is an element of W-s,W-p(R-N) : integral(RN) vertical bar u vertical bar(p)dx = c(p)}.
作者：
Li, Liulan;Ponnusamy, Saminathan;Wirths, Karl Joachim
期刊：
Bulletin of the Malaysian Mathematical Sciences Society,2022年45(3):955-972 ISSN：0126-6705
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 & Ap, Hengyang 421002, Hunan, Peoples R China.;[Ponnusamy, S; Ponnusamy, Saminathan] Indian Inst Technol Madras, Dept Math, Chennai 600036, Tamil Nadu, India.;[Ponnusamy, S; Ponnusamy, Saminathan] Petrozavodsk State Univ, Dept Math, Ul Lenina 33, Petrozavodsk 185910, 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, Tamil Nadu, India.;Petrozavodsk State Univ, Dept Math, Ul Lenina 33, Petrozavodsk 185910, Russia.
关键词：
Univalent;Convex;Close-to-convex;Convex in some direction;Subordination;Harmonic convolution
摘要：
In this article, we consider the family of functions f analytic in the unit disk
$$|z|<1$$
with the normalization
$$f(0)=0=f'(0)-1$$
and satisfying the condition
$$\big |\big (z/f(z)\big )^{2}f'(z)-1\big |<\lambda $$
for some
$$0<\lambda \le 1$$
. We denote this class by
$$\mathcal {U}(\lambda )$$
and we are interested in the relations between
$$\mathcal {U}(\lambda )$$
and other families of functions holomorphic or harmonic in the unit disk. Our first example in this direction is the family of functions convex in one direction. Then, we are concerned with the subordinates to the function
$$1/((1-z)(1-\lambda z))$$
. We prove that not all functions f(z)/z
$$(f \in \mathcal {U}(\lambda ))$$
belong to this family. This disproves an assertion from [14]. Further, we disprove a related coefficient conjecture for
$$\mathcal {U}(\lambda )$$
. We consider the intersection of the class of the above subordinates and
$$\mathcal {U}(\lambda )$$
concerning the boundary behaviour of its functions. At last, with the help of functions from
$$\mathcal {U}(\lambda )$$
, we construct functions harmonic and close-to-convex in the unit disk.
期刊：
Journal of Clinical Medicine,2022年11(19):5623- ISSN：2077-0383
通讯作者：
Long Yin
作者机构：
[Yin, Long; Li, Fang] Hengyang Normal Univ, Sch Phys Educ, Hengyang 421002, Peoples R China.;[Sun, Mingyun] Hengyang Normal Univ, Sch Math & Stat, Hengyang 421002, Peoples R China.;[Gao, Zan] Univ Minnesota Twin Cities, Sch Kinesiol, Minneapolis, MN 55455 USA.
通讯机构：
[Long Yin] S;School of Physical Education, Hengyang Normal University, Hengyang 421002, China<&wdkj&>Author to whom correspondence should be addressed.
关键词：
locomotor skills;object control skills;physical activity;sleep duration;screen time
摘要：
Background: Few studies have investigated associations between meeting 24-Hour Movement Guidelines and preschool children's fundamental movement skills (FMS). This study aimed to investigate the associations between Chinese preschoolers meeting various combinations of the Guidelines and FMS, as well as examining gender differences across those outcomes. Methods: A total of 322 preschool children (181 boys and 141 girls) aged 3-6 years old were recruited from five early-childhood education and care services in China. Children's 7-day physical activity (PA) was assessed using accelerometry, and screen time (ST) and sleep duration were reported by their parents. FMS were assessed by Test of Gross Motor Development 3. Descriptive statistics and gender differences in children's meeting the Guidelines and FMS were calculated using t-tests for continuous variables and Chi-square tests for categorical variables. Results: Most preschoolers met the sleep and ST guidelines, but only 22.3% met the PA guidelines; 4% of preschoolers did not meet any of the recommendations, while 9.3% met all three recommendations. Boys reported significantly higher compliance with all combined recommendations. There were positive associations between meeting the PA guidelines and both locomotor (beta = 0.49; p < 0.001) and object control skills (beta = 0.21; p < 0.001). A significantly positive relationship was identified between meeting PA + sleep guidelines and locomotor skills (beta = -0.16; p = 0.02). A significantly negative association was observed between preschoolers' meeting sleep + ST guidelines and locomotor skills (beta = 0.31; p = 0.001). Conclusion: Few preschoolers met all three movement behavior guidelines. The findings suggest that PA levels, especially MVPA, are important for the promotion of FMS. Meanwhile, the impacts of ST and sleep on motor development cannot be neglected.
摘要：
In this article, we study a complete convergence theorem for weighted sums in sublinear expectations space. We establish a complete convergence theorem for weighted sums under the optimal moment conditions in sub-linear expectations space. Our result extends and improves the corresponding result of Cai (Metrika, 68:323-331, 2008) in some extent.
摘要：
In this paper, we discuss the lower diameter estimate for a class of compact generalized quasi-Einstein manifolds which are closely related to the conformal geometry. Using the Bochner formula and the Hopf maximum principle, we get a gradient estimate for the potential function of the manifold. Based on the gradient estimate, we get the lower diameter estimate for this class of generalized quasi-Einstein manifolds.
期刊：
BULLETIN DES SCIENCES MATHEMATIQUES,2021年173:103054 ISSN：0007-4497
通讯作者：
Saminathan Ponnusamy
作者机构：
[Liu, Gang] Hengyang Normal Univ, Hunan Prov Key Lab Intelligent Informat Proc & Ap, Coll Math & Stat, Hengyang 421002, Hunan, Peoples R China.;[Liu, Zhihong] Guilin Univ Technol, Coll Sci, Guilin 541004, Guangxi, Peoples R China.;[Ponnusamy, Saminathan] Indian Inst Technol Madras, Dept Math, Chennai 600036, Tamil Nadu, India.
通讯机构：
[Saminathan Ponnusamy] D;Department of Mathematics, Indian Institute of Technology Madras, Chennai-600 036, India
关键词：
Bohr inequality;Bohr radius;Bohr-Rogosinski inequality;Bounded analytic function;Symmetric function
摘要：
In this article, by combining appropriate refined Bohr's inequalities with some techniques concerning bounded analytic functions defined in the unit disk, we generalize and improve several Bohr-type inequalities for such functions. (C) 2021 Elsevier Masson SAS. All rights reserved.
