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.
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.
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.
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).
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].
作者机构：
[Li, Linyan; Huang, Haiwu] Hengyang Normal Univ, Coll Math & Stat, Hengyang 421002, Peoples R China.;[Huang, Haiwu] Hunan Prov Key Lab Intelligent Informat Proc & Ap, Hengyang 421002, Peoples R China.;[Lu, Xuewen] Univ Calgary, Dept Math & Stat, Calgary, AB T2N 1N4, Canada.
通讯机构：
[Huang, Haiwu] H;Hengyang Normal Univ, Coll Math & Stat, Hengyang 421002, Peoples R China.;Hunan Prov Key Lab Intelligent Informat Proc & Ap, Hengyang 421002, Peoples R China.
关键词：
negatively orthant dependent random variables;the tail probability;strong convergence
摘要：
In this research, strong convergence properties of the tail probability for weighted sums of negatively orthant dependent random variables are discussed. Some sharp theorems for weighted sums of arrays of rowwise negatively orthant dependent random variables are established. These results not only extend the corresponding ones of Cai [4], Wang et al. [19] and Shen [13], but also improve them, respectively.
期刊：
Physica A-Statistical Mechanics and its Applications,2020年546:123765 ISSN：0378-4371
通讯作者：
Jin, Zhen
作者机构：
[Song, Haitao; Jin, Jun; Jin, Zhen; Zhou, Zhidong] Shanxi Univ, Complex Syst Res Ctr, Taiyuan 030006, Peoples R China.;[Zhou, Zhidong] Hengyang Normal Univ, Coll Math & Stat, Hengyang 421002, Peoples R China.;[Song, Haitao; Jin, Jun; Jin, Zhen; Zhou, Zhidong] Shanxi Univ, Shanxi Key Lab Math Tech & Big Data Anal Dis Cont, Taiyuan 030006, Peoples R China.
通讯机构：
[Jin, Zhen] S;Shanxi Univ, Complex Syst Res Ctr, Taiyuan 030006, Peoples R China.
关键词：
Complex network;Hypernetwork;Stationary average hyperdegree distribution;Degree distribution;Scale-free;Power-law distribution
摘要：
Based on hypernetwork theory, we construct a new evolving hypernetwork, which incorporating new nodes and new hyperedges growing, old nodes and old hyperedges disappearing, or rewiring of hyperedges from some nodes to anothers. Besides the growth of hyperedges by adding new nodes, it is also possible that a new hyperedge can be constructed between old nodes in hypernetworks. This evolving hypernetwork model with both increasing and decreasing is more realistic than the evolving model only with increasing. By employing Poisson process theory and continuous method, we obtain stationary average hyperdegree distribution and degree distribution of the hypernetwork. Analytical result shows that the evolving hypernetwork following a generalized power-law distribution, has a phenomenon of "the rich get richer'' and a wide range of universality. The theoretical prediction of the stationary average hyperdegree distribution and degree distribution are in good agreement with the real numerical simulation results. (C) 2020 The Authors. Published by Elsevier B.V.
作者机构：
[Li, Long; Long, Zuqiang] Hengyang Normal Univ, Coll Math & Stat, Hengyang 421008, Hunan, Peoples R China.;[Qiao, Zhijun] Univ Texas Rio Grande Valley, Dept Math, Edinburg, TX 78539 USA.
通讯机构：
[Li, Long] H;Hengyang Normal Univ, Coll Math & Stat, Hengyang 421008, Hunan, Peoples R China.
摘要：
In this paper, a smoothing algorithm with constant learning rate is presented for training two kinds of fuzzy neural networks (FNNs): max-product and max-min FNNs. Some weak and strong convergence results for the algorithm are provided with the error function monotonically decreasing, its gradient going to zero, and weight sequence tending to a fixed value during the iteration. Furthermore, conditions for the constant learning rate are specified to guarantee the convergence. Finally, three numerical examples are given to illustrate the feasibility and efficiency of the algorithm and to support the theoretical findings.
摘要：
The purpose of this paper is to study the properties of the solutions to the inhomogeneous biharmonic equations:
$$\Delta (\Delta f)=g$$
, where g :
$$\overline{\mathbb {D}}\rightarrow \mathbb {C}$$
is a continuous function and
$$\overline{\mathbb {D}}$$
denotes the closure of the unit disk
$$\mathbb {D}$$
in the complex plane
$$\mathbb {C}$$
. In fact, we establish the following properties for those solutions: Firstly, we establish the Schwarz-type lemma. Secondly, by using the obtained results, we get a Landau-type theorem. Thirdly, we discuss their Lipschitz-type property.
摘要：
In this paper, we are concerned with the following Schrodinger-Poisson-Slater problem with critical growth: -Delta u + (u(2) * 1/vertical bar 4 pi x vertical bar)u = mu k(x)vertical bar u vertical bar(p-2) u + vertical bar u vertical bar(4) u in R-3.( ) We use a measure representation concentration-compactness principle of Lions to prove that the (PS), condition holds locally. Via a truncation technique and Krasnoselskii genus theory, we further obtain infinitely many solutions for mu is an element of (0, mu*) with some mu* > 0.
