摘要：
In this paper, we will give new characterizations of Lipschitz-type spaces, and establish related growth theorems for Bloch-type spaces. Then we will present applications to certain PDEs. We will also consider the Dirichlet-type energy integrals and their applications.
作者机构：
[胡立军] College of Mathematics and Statistics, Hengyang Normal University, Hengyang, 421002, China;[吴世枫] School of Mathematics and System Sciences, Guangdong Polytechnic Normal University, Guangzhou, 510665, China;[Zhai J.] Dawning Information Industry Co., Ltd., Beijing, 100193, China
摘要：
When using the conventional direction splitting method to calculate multidimensional high speed gas-dynamical flows, Riemann solvers capable of resolving contact surface and shear wave accurately will suffer from different forms of shock instability, such as the notorious carbuncle phenomenon. The stability analysis shows that the lack of dissipation in the direction transverse to the shock front leads to the shock instability of low-dissipation HLLEM solver. To overcome this defect, an accurate and carbuncle-free genuinely two-dimensional HLL-type Riemann solver is proposed. Using Zha-Bilgen splitting method, the flux vector of two-dimensional Euler equations is split into the convective flux and pressure flux. An algorithm similar to AUSM+ scheme is adopted to calculate the convective flux and the pressure flux is calculated by the low-dissipation HLLEM scheme. Following Balsara's idea, the genuinely two-dimensional properties of the new solver are achieved by solving the two-dimensional Riemann problem that considers transversal features of the flow at each vertex of the cell interface. Numerical results of benchmark tests demonstrate that the new solver has higher resolution and better robustness than the conventional HLLEM solver implemented in dimension by dimension. (C) 2020 Elsevier Ltd. All rights reserved.
期刊：
JOURNAL OF INEQUALITIES AND APPLICATIONS,2020年2020(1):1-8 ISSN：1029-242X
通讯作者：
Sung, Soo Hak
作者机构：
[Yi, Yanchun] Hengyang Normal Univ, Coll Math & Stat, Hengyang, Peoples R China.;[Chen, Pingyan] Jinan Univ, Dept Math, Guangzhou, Peoples R China.;[Sung, Soo Hak] Pai Chai Univ, Dept Appl Math, Daejeon, South Korea.
通讯机构：
[Sung, Soo Hak] P;Pai Chai Univ, Dept Appl Math, Daejeon, South Korea.
关键词：
Strong law of large numbers;Weighted sum;Widely orthant dependent random variable
摘要：
Let $1\le p<2$ and $0<\alpha , \beta <\infty $ with $1/p=1/\alpha +1/\beta $. Let $\{X_{n}, n\ge 1\}$ be a sequence of random variables satisfying a generalized Rosenthal type inequality and stochastically dominated by a random variable X with $E|X|^{\beta }< \infty $. Let $\{a_{nk}, 1\le k\le n, n\ge 1\}$ be an array of constants satisfying $\sum_{k=1}^{n} |a_{nk}|^{\alpha }=O(n)$. Marcinkiewicz–Zygmund type strong laws for weighted sums of the random variables are established. Our results generalize or improve the corresponding ones of Wu (J. Inequal. Appl. 2010:383805, 2010), Huang et al. (J. Math. Inequal. 8:465–473, 2014), and Wu et al. (Test 27:379–406, 2018).
期刊：
Journal of Computational and Applied Mathematics,2020年368:112549 ISSN：0377-0427
通讯作者：
Ponnusamy, Saminathan
作者机构：
[Liu, Gang] Hengyang Normal Univ, Coll Math & Stat, Hunan Prov Key Lab Intelligent Informat Proc & Ap, Hengyang 421002, Hunan, Peoples R China.;[Ponnusamy, Saminathan] Indian Inst Technol Madras, Dept Math, Chennai 600036, Tamil Nadu, India.
通讯机构：
[Ponnusamy, Saminathan] I;Indian Inst Technol Madras, Dept Math, Chennai 600036, Tamil Nadu, India.
关键词：
Konig's method;Steffensen's method;Cycle;Attracting basin;Parabolic basin;Siegel disk
摘要：
The aim of this paper is to reveal some complex dynamical properties of Konig's and Steffensen's methods for entire functions. Two procedures are presented for constructing infinite entire functions simultaneously so that any given finite pairs of prescribed cycles occur when the two methods are applied, respectively. Furthermore, these functions can be chosen by polynomials or transcendental entire functions. (C) 2019 Elsevier B.V. All rights reserved.
作者机构：
[Xiao, Juan] Hengyang Normal Univ, Sch Math & Stat, Hengyang 421008, Peoples R China.;[Qiu, De-hua] Guangdong Univ Finance & Econ, Sch Math & Stat, Guangzhou 510320, Peoples R China.
通讯机构：
[Qiu, De-hua] G;Guangdong Univ Finance & Econ, Sch Math & Stat, Guangzhou 510320, Peoples R China.
关键词：
pairwise negative quadrant dependent (PNQD) random variable;strong law of large numbers;complete convergence;general moment condition
摘要：
Let {X, X-n,n >= 1} be a sequence of identically distributed pairwise negative quadrant dependent (PNQD) random variables and {a(n),n >= 1} be a sequence of positive constants witha(n)=f(n) andf(theta(k))/f(theta(k-1)) >=beta for all large positive integersk, where 1 <theta <=beta andf(x) > 0 (x >= 1) is a non-decreasing function on [b, +infinity) for someb >= 1. In this paper, we obtain the strong law of large numbers and complete convergence for the sequence {X, X-n,n >= 1}, which are equivalent to the general moment condition n-ary sumation Sigma P-infinity(n=1)(vertical bar X vertical bar>a(n))<infinity. Our results extend and improve the related known works in Baum and Katz [1], Chen at al. [3], and Sung [14].
