期刊：
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE,2021年38(6):1841-1867 ISSN：0294-1449
通讯作者：
Zi, Ruizhao
作者机构：
[Zi, Ruizhao] Cent China Normal Univ, Sch Math, Wuhan 430079, Peoples R China.;[Zi, Ruizhao] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Zi, Ruizhao] C;Cent China Normal Univ, Sch Math, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
关键词：
Global well-posedness;Inviscid limit;Oldroyd-B model
期刊：
Advances in Applied Mathematics,2021年127:102164 ISSN：0196-8858
通讯作者：
Li, Shuchao(lscmath@mail.ccnu.edu.cn)
作者机构：
[Yu, Yuantian; Li, Shuchao] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Shuchao Li] F;Faculty of Mathematics and Statistics, Central China Normal University, Wuhan 430079, PR China
关键词：
Wiener index;Closed walk;Adjacency polynomial;Laplacian polynomial;Edge cover polynomial;Independence polynomial
摘要：
This contribution gives an extensive study on the Wiener indices, the number of closed walks, the coefficients of some graph polynomials (the adjacency polynomial, the Laplacian polynomial, the edge cover polynomial and the independence polynomial) of trees. Csikv?ri (2010) [4] introduced the generalized tree shift, which keeps the number of vertices of trees. Applying the generalized tree shifts and recurrence relation, we extend the works of Csikv?ri (2010) [4] and Csikv?ri (2013) [5]. Using a unified approach, we obtain the following main results: Firstly, for all n and 8, we characterize the unique tree having the maximum (resp. minimum) Wiener index and the unique tree having the maximum (resp. minimum) number of closed walks of length $ among the trees of order n which are neither a path nor a star. Secondly, we characterize the unique tree whose adjacency polynomial (resp. Laplacian polynomial, independence polynomial) has the maximum (resp. minimum) coefficients in absolute value among the trees of order n which are neither a path nor a star, respectively. At last, we identify all the n-vertex trees whose edge cover polynomial has the minimum coefficients in absolute value and we also determine the unique tree having This contribution gives an extensive study on the Wiener indices, the number of closed walks, the coefficients of some graph polynomials (the adjacency polynomial, the Laplacian polynomial, the edge cover polynomial and the independence polynomial) of trees. Csikv & aacute;ri (2010) [4] introduced the generalized tree shift, which keeps the number of vertices of trees. Applying the generalized tree shifts and recurrence relation, we extend the works of Csikv & aacute;ri (2010) [4] and Csikv & aacute;ri (2013) [5]. Using a unified approach, we obtain the following main results: Firstly, for all n and 8, we characterize the unique tree having the maximum (resp. minimum) Wiener index and the unique tree having the maximum (resp. minimum) number of closed walks of length $ among the trees of order n which are neither a path nor a star. Secondly, we characterize the unique tree whose adjacency polynomial (resp. Laplacian polynomial, independence polynomial) has the maximum (resp. minimum) coefficients in absolute value among the trees of order n which are neither a path nor a star, respectively. At last, we identify all the n-vertex trees whose edge cover polynomial has the minimum coefficients in absolute value and we also determine the unique tree having the maximum coefficients in absolute value among the trees of order n which are neither a path nor a star. (c) 2021 Elsevier Inc. All rights reserved.
期刊：
IMA JOURNAL OF APPLIED MATHEMATICS,2021年86(4):662-687 ISSN：0272-4960
通讯作者：
Yan, Guozheng(yangz@mail.ccnu.edu.cn)
作者机构：
[Xiang, Jianli; Yan, Guozheng] School of Mathematics and Statistics, Central China Normal University, Wuhan;430079, China;College of Science, China Three Gorges University, Yichang;443002, China;[Xiang, Jianli] 430079, China<&wdkj&>College of Science, China Three Gorges University, Yichang
通讯机构：
[Guozheng Yan] S;School of Mathematics and Statistics , Central China Normal University, Wuhan 430079, China
关键词：
Factorization method;Far field operator;Inverse acoustic scattering;Mixed inhomogeneous medium;Variational method
作者机构：
[Yang, Xiaolong] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Yang, Xiaolong] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Xiaolong Yang] S;School of Mathematics and Statistics and Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, People’s Republic of China
关键词：
Fractional Laplacian;Choquard equation;bound state solutions
摘要：
In this paper, we study the following nonlinear Choquard equation
0.1
$$\begin{aligned} (-\Delta )^{s}u+V(x)u=(I_{\alpha }*|u|^{2^{*}_{\alpha ,s}})|u|^{2^{*}_{\alpha ,s}-2}u, \quad u\in \mathcal {D}^{s,2}(\mathbb {R}^N), \end{aligned}$$
where
$$s\in (0,1)$$
,
$$N>2s$$
,
$$0<\alpha <N$$
and
$$2^{*}_{\alpha ,s}=\frac{N+\alpha }{N-2s}$$
is the critical exponent in the sense of Hardy–Littlewood–Sobolev inequality. We showed that Eq. (0.1) has at least one bound state solution if
$$\Vert V(x)\Vert _{L^{\frac{N}{2s}}}$$
is suitably small, by proving a version to the Fractional operator in
$$\mathbb {R}^N$$
of the Global Compactness result due to Struwe (see Struwe 1984)
期刊：
Applied Mathematics and Computation,2021年390:125598 ISSN：0096-3003
通讯作者：
Li, Shuchao
作者机构：
[Deng, Kecai] Huaqiao Univ, Sch Math Sci, Quanzhou 362000, Fujian, Peoples R China.;[Li, Shuchao] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Li, Shuchao] C;Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
摘要：
For a given graph G, the Mostar index Mo(G) is the sum of absolute values of the differences between n(u)(e) and n(v)(e) over all edges e = uv of G, where n(u)(e) and n(v)(e) are, respectively, the number of vertices of G lying closer to u than to v and the number of vertices of G lying closer to v than to u. The degree sequence of a tree is the sequence of the degrees (in descending order) of the non-leaf vertices. This paper determines those trees with a given degree sequence which have the greatest Mostar index. Consequently, all extremal trees with the greatest Mostar index are obtained in the sets of all trees of order n with the maximum degree, the number of leaves, the independence number and the matching number, respectively. On the other hand, some properties of trees with a given degree sequence which have the least Mostar index are given. We also determine those trees with exactly n - 3 or n - 4 leaves when the degree sequence is given, which have the least Mostar index. At last some numerical results are discussed, in which we calculate the Mostar indices of two sets of molecular graphs: octane isomers and benzenoid hydrocarbons; We compare their Mostar indices with some other distance-based topological indices through their correlations with the chemical properties. The linear model for the Mostar index is better than or as good as the models corresponding to the other distance-based indices. (C) 2020 Elsevier Inc. All rights reserved.
期刊：
Communications in Statistics - Theory and Methods,2021年50(21):4963-4976 ISSN：0361-0926
通讯作者：
Luo, Jing
作者机构：
[Luo, Jing; Wang, Zhenghong] Department of Mathematics and Statistics, South-Central University for Nationalities, Wuhan, China;[Chen, Qianqian; Zeyneb, Laala] Department of Mathematics and Statistics, Central China Normal University, Wuhan, China
通讯机构：
[Jing Luo] D;Department of Mathematics and Statistics, South-Central University for Nationalities, Wuhan, China
关键词：
Approximate likelihood-based estimation;directed network data;generalized linear model;null model;sparse random graph
期刊：
Applied and Computational Harmonic Analysis,2021年52:63-81 ISSN：1063-5203
通讯作者：
Yan, Zhi-Hui
作者机构：
[Dai, Xin-Rong; Yan, Zhi-Hui] Sun Yat Sen Univ, Sch Math, Guangzhou 510275, Peoples R China.;[Fu, Xiao-Ye] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Yan, Zhi-Hui] S;Sun Yat Sen Univ, Sch Math, Guangzhou 510275, Peoples R China.
摘要：
In this paper, we study the spectral property of a class of self-affine measures mu(R,D) on R-2 generated by the iterated function system {phi(d) (.) = R-1 (.+d)}(d is an element of D) associated with the real expanding matrix R= (graphics) and the digit set D = {((0)(0)), ((1)(0)), ((0)(1))}. We show that mu(R,D) is a spectral measure if and only if 3 vertical bar b(i, )i = 1, 2. This extends the result of Deng and Lau [J. Funct. Anal., 2015], where they considered the case b(1) = b(2). And we also give a tree structure for any spectrum of mu(R,D) by providing a decomposition property on it. (C) 2020 Elsevier Inc. All rights reserved.
作者机构：
[Yu, Gexin; Li, Xiangwen] Cent China Normal Univ, Dept Math & Stat, Wuhan 430079, Peoples R China.;[Liu, Runrun] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Zhejiang, Peoples R China.;[Yu, Gexin] Coll William & Mary, Dept Math, Williamsburg, VA 23185 USA.
通讯机构：
[Runrun Liu] D;Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China
期刊：
Cryptography and Communications,2021年13(1):1-14 ISSN：1936-2447
通讯作者：
Luo, Jinquan
作者机构：
[Fang, Xiaolei; Luo, Jinquan; Liu, Meiqing] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Fang, Xiaolei; Luo, Jinquan; Liu, Meiqing] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Fang, Xiaolei] Wuhan Polytech Univ, Sch Math & Comp Sci, Wuhan 430048, Peoples R China.
通讯机构：
[Luo, Jinquan] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
摘要：
In this paper, we propose a mechanism for the construction of MDS codes with arbitrary dimensions of Euclidean hulls. Precisely, we construct (extended) generalized Reed-Solomon (GRS) codes with assigned dimensions of Euclidean hulls from self-orthogonal GRS codes. It turns out our constructions are more general than previous works on Euclidean hulls of (extended) GRS codes.
期刊：
Cryptography and Communications,2021年13(1):101-115 ISSN：1936-2447
通讯作者：
Luo, Jinquan
作者机构：
[Ma, Junru; Luo, Jinquan] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Ma, Junru; Luo, Jinquan] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Luo, Jinquan] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
关键词：
Central limit theorem;network data;increasing number of parameters;maximum likelihood estimator
摘要：
The asymptotic normality of a fixed number of the maximum likelihood estimators in a network model with degree heterogeneity and homophily has been established recently. In this paper, we further derive a central limit theorem for a linear combination of all the maximum likelihood estimators of degree parameter with degree heterogeneity and homophily when the number of nodes goes to infinity. Simulation studies are provided to illustrate the asymptotic results.
作者：
Dinh, Hai Q.;Wang, Xiaoqiang*;Liu, Hongwei;Yamaka, Woraphon
期刊：
Finite Fields and Their Applications,2021年70:101794 ISSN：1071-5797
通讯作者：
Wang, Xiaoqiang
作者机构：
[Dinh, Hai Q.] Ton Duc Thang Univ, Inst Computat Sci, Div Computat Math & Engn, Ho Chi Minh City, Vietnam.;[Wang, Xiaoqiang] Hubei Univ, Fac Math & Stat, Hubei Key Lab Appl Math, Wuhan 430062, Peoples R China.;[Dinh, Hai Q.] Ton Duc Thang Univ, Fac Math & Stat, Ho Chi Minh City, Vietnam.;[Liu, Hongwei] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.;[Yamaka, Woraphon] Chiang Mai Univ, Fac Econ, Ctr Excellence Econometr, Chiang Mai 52000, Thailand.
通讯机构：
[Wang, Xiaoqiang] H;Hubei Univ, Fac Math & Stat, Hubei Key Lab Appl Math, Wuhan 430062, Peoples R China.
