On the extremal Sombor index of trees with a given diameter
作者：
Li, Shuchao;Wang, Zheng;Zhang, Minjie*
期刊：
Applied Mathematics and Computation ,2022年416:126731 ISSN：0096-3003
通讯作者：
Zhang, Minjie
作者机构：
[Wang, Zheng; Li, Shuchao] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.;[Zhang, Minjie] Hubei Univ Arts & Sci, Sch Math & Stat, Xiangyang 441053, Peoples R China.
通讯机构：
[Zhang, Minjie] H;Hubei Univ Arts & Sci, Sch Math & Stat, Xiangyang 441053, Peoples R China.
关键词：
Diameter;Diametrical path;Sombor index;Tree
摘要：
Based on elementary geometry, Gutman proposed a novel graph invariants called the Sombor index SO(G), which is defined as SO(G)=∑uv∈E(G)dG2(u)+dG2(v), where dG(u) and dG(v) denote the degree of u and v in G, respectively. It has been proved that the Sombor index could predict some physicochemical properties. In this paper, we characterize the extremal graphs with respect to the Sombor index among all the n-order trees with a given diameter. Firstly, we order the trees with respect to the Sombor index among the n-vertex trees with diameter 3. Then, we determine the largest and the second largest Sombor indices of n-vertex trees with a given diameter d≥4 and characterize the corresponding trees. Moreover, for n−d=3, we characterize the extremal n-order trees which reach from the third to the fourth (resp. the sixth, the seventh) largest Sombor indices with d=4 (resp. d=5,d≥6). For n−d≥4, we characterize the extremal n-order trees which reach from the third to the fifth (resp. the eighth, the ninth) largest Sombor indices with d=4 (resp. d=5,d≥6). As consequences, the top four n-order trees with respect to the Sombor index are characterized. © 2021 Elsevier Inc.
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Asymptotic in undirected random graph models with a noisy degree sequence
作者：
Luo Jing;Liu Tour* ;Wu Jing;Ahmed Ali, Sailan Waleed
期刊：
Communications in Statistics - Theory and Methods ,2022年51(3):789-810 ISSN：0361-0926
通讯作者：
Liu Tour
作者机构：
[Luo Jing] South Cent Univ Nationalities, Dept Math & Stat, Wuhan, Peoples R China.;[Liu Tour] Tianjin Normal Univ, Fac Psychol, Tianjin 300387, Peoples R China.;[Wu Jing; Ahmed Ali, Sailan Waleed] Cent China Normal Univ, Dept Math & Stat, Wuhan, Peoples R China.
通讯机构：
[Liu Tour] T;Tianjin Normal Univ, Fac Psychol, Tianjin 300387, Peoples R China.
关键词：
Asymptotic normality;consistency;undirected network data;degree;differential privacy
摘要：
In the case of differential privacy under the Laplace mechanism, the asymptotic properties of parameter estimator have been derived in some special models such as (Formula presented.) model, but under a general noisy mechanism, the results are lacking. In this article, we release the degree sequences of undirected weighted networks under a general noisy mechanism with the discrete Laplace mechanism as a special case. We establish a unified asymptotic result including the consistency and asymptotically normality of the parameter estimator. We apply it to the (Formula presented.) model, (Formula presented.) -linear model, maximum entropy models with discrete weights. © 2020 Taylor & Francis Group, LLC.
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英文
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Non-marginal feature screening for additive hazard model with ultrahigh-dimensional covariates
作者：
Liu, Zili;Xiong, Zikang*
期刊：
Communications in Statistics - Theory and Methods ,2022年51(6):1876-1894 ISSN：0361-0926
通讯作者：
Xiong, Zikang
作者机构：
[Liu, Zili; Xiong, Zikang] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.
通讯机构：
[Xiong, Zikang] C;Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.
关键词：
Additive hazard model;non-marginal independent screening;survival data;ultrahigh dimensionality;sure screening property
摘要：
Survival data with ultrahigh-dimensional covariates have been frequently encountered in medical studies and other fields. In this article, we propose a non-marginal feature screening procedure for the additive hazard model with ultrahigh-dimensional covariates. The proposed method utilizes the joint effects between covariates, which can effectively identify active covariates that are jointly dependent but marginally independent of the response. We develop an iterative hard-thresholding (IHT) algorithm to effectively implement the proposed procedure. Its convergence properties were investigated rigorously and further proved that the proposed procedure possesses the sure screening property. We conduct Monte Carlo simulation to evaluate the finite sample performance of the proposed procedure, and demonstrate the proposed procedure through an empirical analysis of a real data example. © 2020 Taylor & Francis Group, LLC.
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英文
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Weighted symmetrized centered discrepancy for uniform design
作者：
He, Lanlan;Qin, Hong;Ning, Jianhui*
期刊：
Communications in Statistics - Simulation and Computation ,2022年51(8):4509-4519 ISSN：0361-0918
通讯作者：
Ning, Jianhui
作者机构：
[Qin, Hong; He, Lanlan; Ning, Jianhui] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Ning, Jianhui] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
关键词：
Cover volume;Uniform design;Variable selection;Weighted symmetrized centered discrepancy
摘要：
Uniformity and projection uniformity are very important criteria in space-filling design and studied by many authors. In this paper, a new criterion, called weighted symmetrized centered discrepancy (WSCD), is put forwarded for measuring the uniformity of design array. Firstly, a new kernel function is deduced by symmetrizing the reproducing kernel of centered L 2 discrepancy (CD). The new criterion WSCD is generated from the symmetrized the reproducing kernel, which make it avoid the well-known shortcomings of CD. Secondly, the customized weights are set to all the sub-dimensions to conform with the Effect Hierarchy principle. The WSCD has similar computation formula with the popularly used discrepancies, hence all the construction methods for uniform design still work. Thirdly, the weights choice is also discussed, and a practical suggestion is made. A naive empirical comparison is also conducted to show that the new criterion performs better than those existed discrepancies in the variable screening. © 2020 Taylor & Francis Group, LLC.
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Weighted directed networks with a differentially private bi-degree sequence
作者：
Wang, Qiuping* ;Zhang, Xiao;Luo, Jing* ;Ouyang, Yang;Wang, Qian
期刊：
Communications in Statistics - Theory and Methods ,2022年51(2):285-300 ISSN：0361-0926
通讯作者：
Wang, Qiuping;Luo, Jing
作者机构：
[Zhang, Xiao; Wang, Qiuping; Wang, Qian; Ouyang, Yang] Cent China Normal Univ, Dept Stat, Wuhan 430079, Peoples R China.;[Luo, Jing] South Cent Univ Nationalities, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Wang, Qiuping] C;[Luo, Jing] S;Cent China Normal Univ, Dept Stat, Wuhan 430079, Peoples R China.;South Cent Univ Nationalities, Sch Math & Stat, Wuhan 430079, Peoples R China.
关键词：
Asymptotic normality;bi-degree;consistency;differential privacy
摘要：
The p 0 model is an exponential random graph model for directed networks with the bi-degree sequence as the exclusively sufficient statistic. It captures the network feature of degree heterogeneity. The consistency and asymptotic normality of a differentially private estimator of the parameter in the private p 0 model has been established. However, the p 0 model only focuses on binary edges. In many realistic networks, edges could be weighted, taking a set of finite discrete values. In this article, we further show that the moment estimators of the parameters based on the differentially private bi-degree sequence in the weighted p 0 model are consistent and asymptotically normal. Numerical studies demonstrate our theoretical findings. © 2022 Taylor & Francis Group, LLC.
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英文
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Asymptotics in a probit model for directed networks
作者：
Wang, Qian* ;Wang, Qiuping;Luo, Jing
期刊：
Communications in Statistics - Theory and Methods ,2022年51(11):1-17 ISSN：0361-0926
通讯作者：
Wang, Qian
作者机构：
[Wang, Qiuping; Wang, Qian] Cent China Normal Univ, Dept Stat, Wuhan 430079, Peoples R China.;[Luo, Jing] South Cent Univ Nationalities, Dept Stat, Wuhan, Peoples R China.
通讯机构：
[Wang, Qian] C;Cent China Normal Univ, Dept Stat, Wuhan 430079, Peoples R China.
关键词：
Asymptotical normality;consistency;directed networks;moment estimators;probit model
摘要：
In this paper, we use the probit distribution to model the degree heterogeneity of the directed networks. We refer this model as the Probit Network Model, in which each edge is independently distributed as a Bernoulli random variable with a success probability measured by the probit function with a set of degree parameters. By using the moment equation to estimate the degree parameters, we establish the uniform consistency and the asymptotic normality of the moment estimator when the number of nodes goes to infinity. Simulation studies are provided to illustrate the asymptotic results. © 2020, © 2020 Taylor & Francis Group, LLC.
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英文
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Variable screening for varying coefficient models with ultrahigh-dimensional survival data
作者：
Qu, Lianqiang;Wang, Xiaoyu;Sun, Liuquan
期刊：
Computational Statistics & Data Analysis ,2022年172:107498 ISSN：0167-9473
通讯作者：
Sun, Liuquan(slq@amt.ac.cn)
作者机构：
[Qu, Lianqiang] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.;[Sun, Liuquan; Wang, Xiaoyu] Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing 100190, Peoples R China.
通讯机构：
[Liuquan Sun] I;Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, PR China
关键词：
Kernel smoothing;Survival data;Ultrahigh dimensionality;Variable screening;Varying coefficient
摘要：
In this article, we develop a variable screening method for varying coefficient hazards models of single-index form. The proposed method can be viewed as a natural survival extension of conditional correlation screening. An appealing feature of the proposed method is that it is applicable to many popularly used survival models, including the varying coefficient additive hazards model and the varying coefficient Cox model. The proposed method enjoys the sure screening property, and the number of the selected covariates can be bounded by a moderate order. Simulation studies demonstrate that our method performs well, and an empirical example is also presented. © 2022 Elsevier B.V.
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英文
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Two Solutions for Fractional Elliptic Systems
作者：
Aissaoui, Narimane;Li, Benniao;Long, Wei
期刊：
Acta Applicandae Mathematicae ,2022年178(1):1-21 ISSN：0167-8019
通讯作者：
Li, BN
作者机构：
[Aissaoui, Narimane] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Li, Benniao; Li, BN; Long, Wei] Jiangxi Normal Univ, Sch Math & Stat, Nanchang 330022, Jiangxi, Peoples R China.
通讯机构：
[Li, BN ] J;Jiangxi Normal Univ, Sch Math & Stat, Nanchang 330022, Jiangxi, Peoples R China.
关键词：
Fractional Laplacian;Critical exponent;Multiplicity
摘要：
In this paper, we are concerned with the following system linearly coupled by nonlinear fractional elliptic equations {(-Delta)su+lambda su=|u|2s*-2u+beta v, in omega, (-Delta)tv+lambda tv=|v|2t*-2v+beta u, in omega, u=v=0, on partial differential partial derivative Omega ,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left \{ \textstyle\begin{array}{l@{\quad }l} (-\Delta )<^>{s} u+\lambda _{s} u = |u|<^>{2_{s}<^>{*}-2}u+\beta v, & \hspace{1cm} \text{ in } \Omega , \\ (- \Delta )<^>{t} v+\lambda _{t} v= |v|<^>{2_{t}<^>{*}-2}v+ \beta u,& \hspace{1cm} \text{ in } \Omega , \\ u=v=0, & \hspace{1cm} \text{ on }\partial \Omega , \end{array}\displaystyle \right . where, for alpha{-69pt} \begin{document}$t$\end{document}) in (0,1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(0,1)$\end{document}, (-Delta)alpha\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(-\Delta )<^>{\alpha }$\end{document} is the fractional Laplacian, lambda alpha>-lambda 1,alpha(omega)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\lambda _{\alpha }> - \lambda _{1,\alpha }(\Omega )$\end{document}, lambda 1,alpha(omega)\documentclass frac{2N}{N-2\alpha }$\end{document} is a fractional Sobolev exponent, N>max{2s,2t}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$N> \max \{2s, 2t\}$\end{document}, beta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\beta $\end{document} is a coupling parameter, and omega\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Omega $\end{document} is a smooth bounded domain in RN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb{R}<^>{N}$\end{document}. By the classical variational method, we prove that (P) has a positive ground state solution for beta>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\beta >0$\end{document}. On the other hand, we also show that (P) admits a positive higher energy solution for small |beta|\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$| \beta |$\end{document} through the perturbation argument. Moreover, we study the asymptotic behaviors of the positive ground state and higher solutions as beta -> 0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\beta \rightarrow 0$\end{document}.
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Spectral determination of graphs with one positive anti-adjacency eigenvalue
作者：
Lei, Xingyu;Wang, Jianfeng
期刊：
Applied Mathematics and Computation ,2022年422:126995 ISSN：0096-3003
通讯作者：
Wang, JF
作者机构：
[Lei, Xingyu; Wang, Jianfeng] Shandong Univ Technol, Sch Math & Stat, Zibo 255049, Peoples R China.;[Lei, Xingyu] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Wang, JF ] S;Shandong Univ Technol, Sch Math & Stat, Zibo 255049, Peoples R China.
摘要：
The anti-adjacency matrix (or eccentricity matrix) of a graph is obtained from its distance matrix by retaining for each row and each column only the largest distances. This matrix can be viewed as the opposite of the adjacency matrix, which is, on the contrary, obtained from the distance matrix of a graph by keeping for each row and each column only the distances being 1. In this paper, we prove that the graphs with exactly one positive anti-adjacency eigenvalue are determined by the anti-adjacency spectra. As corollaries, the well-known (generalized) friendship graphs and windmill graphs are shown to be determined by their anti-adjacency spectra. © 2022 Elsevier Inc.
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英文
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Galois self-orthogonal constacyclic codes over finite fields
作者：
Fu, Yuqing;Liu, Hongwei*
期刊：
DESIGNS CODES AND CRYPTOGRAPHY ,2022年90(11):2703-2733 ISSN：0925-1022
通讯作者：
Liu, Hongwei
作者机构：
[Liu, Hongwei; Fu, Yuqing] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Liu, Hongwei] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
关键词：
Constacyclic code;Galois self-orthogonal code;Galois self-dual code;Enumeration;Weight distribution;MDS code
摘要：
Let
$${\mathbb {F}}_{q}$$
be a finite field with
$$q=p^{e}$$
elements, where p is a prime and e is a positive integer. In 2017, Fan and Zhang introduced
$$\ell $$
-Galois inner products on the n-dimensional vector space
$${\mathbb {F}}_{q}^{n}$$
for
$$0\le \ell <e$$
, which generalized the Euclidean inner product and Hermitian inner product.
$$\ell $$
-Galois self-orthogonal codes are generalizations of Euclidean self-orthogonal codes and Hermitian self-orthogonal codes, and can be used to construct entanglement-assisted quantum error-correcting codes. In this paper, we study
$$\ell $$
-Galois self-orthogonal constacyclic codes of length n over the finite field
$${\mathbb {F}}_{q}$$
. Sufficient and necessary conditions for constacyclic codes of length n over
$${\mathbb {F}}_{q}$$
being
$$\ell $$
-Galois self-orthogonal and
$$\ell $$
-Galois self-dual are characterized. A sufficient and necessary condition for the existence of nonzero
$$\ell $$
-Galois self-orthogonal constacyclic codes of length n over
$${\mathbb {F}}_{q}$$
is obtained. Formulae to enumerate the number of
$$\ell $$
-Galois self-orthogonal and
$$\ell $$
-Galois self-dual constacyclic codes of length n over
$${\mathbb {F}}_{q}$$
are found. In particular, formulae to enumerate the number of Hermitian self-orthogonal and Hermitian self-dual constacyclic codes of length n over
$${\mathbb {F}}_{q}$$
are obtained. Weight distributions of two classes of
$$\ell $$
-Galois self-orthogonal constacyclic codes are calculated. A family of MDS
$$\ell $$
-Galois self-orthogonal constacyclic codes over
$${\mathbb {F}}_{q}$$
is constructed.
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英文
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Some further results on the maximal hitting times of trees with some given parameters
作者：
Li, Shuchao;Xu, Yangyang;Zhang, Huihui
期刊：
Discrete Applied Mathematics ,2022年313:115-134 ISSN：0166-218X
通讯作者：
Zhang, Huihui(zhanghhmath@163.com)
作者机构：
[Xu, Yangyang; Li, Shuchao] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.;[Zhang, Huihui] Luoyang Normal Univ, Dept Math, Luoyang 471934, Peoples R China.
通讯机构：
[Huihui Zhang] D;Department of Mathematics, Luoyang Normal University, Luoyang 471934, PR China
关键词：
Diameter;Hitting time;Matching number;Segment sequence;Tree
摘要：
Given a connected graph G with vertex set VG, the hitting time HG(u,v) of vertices u and v in G is defined as the expected number of steps that a random walk takes to go from u to v. Then the ZZ index of G, denoted by ψ(G), is defined as ψ(G)=max{u,v}⊆VGHG(u,v). This hitting-time-based invariant was first proposed by Zhu and Zhang (2021). In this paper, some further extremal problems on the ZZ index of trees with some given parameters are considered. Firstly, the extremal graphs with the second largest and the third largest ZZ indices are characterized among all the trees with given diameter (resp. matching number, domination number, vertex bipartition, the number of leaves). Secondly, the unique graph with the largest ZZ index is determined among all the trees with given segment sequence (resp. the number of segments). © 2022 Elsevier B.V.
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英文
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MDS symbol-pair codes from repeated-root cyclic codes
作者：
Ma, Junru;Luo, Jinquan*
期刊：
DESIGNS CODES AND CRYPTOGRAPHY ,2022年90(1):121-137 ISSN：0925-1022
通讯作者：
Luo, Jinquan
作者机构：
[Ma, Junru] Hubei Univ, Fac Math & Stat, Hubei Key Lab Appl Math, Wuhan 430062, Hubei, Peoples R China.;[Luo, Jinquan] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.;[Luo, Jinquan] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Hubei, Peoples R China.
通讯机构：
[Luo, Jinquan] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.;Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Hubei, Peoples R China.
关键词：
MDS symbol-pair codes;AMDS symbol-pair codes;Minimum symbol-pair distance;Constacyclic codes;Repeated-root cyclic codes
摘要：
Symbol-pair codes are proposed to protect against pair-errors in symbol-pair read channels. The research of symbol-pair codes with the largest possible minimum symbol-pair distance is of great significance since such codes have the best error-correcting capability. A symbol-pair code meeting the Singleton bound is called a maximum distance separable (MDS) symbol-pair code. In this paper, two new classes of MDS symbol-pair codes are proposed by utilizing repeated-root cyclic codes over finite fields with odd characteristic. It should be noted that these codes have minimum symbol-pair distance ten or twelve. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
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英文
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On the eccentricity spectra of complete multipartite graphs
作者：
Wei, Wei;Li, Shuchao
期刊：
Applied Mathematics and Computation ,2022年424:127036 ISSN：0096-3003
通讯作者：
Li, Shuchao(lscmath@ccnu.edu.cn)
作者机构：
[Wei, Wei] Shanghai Univ Engn Sci, Ctr Intelligent Comp & Appl Stat, Sch Math Phys & Stat, Shanghai 201620, Peoples R China.;[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, China
关键词：
Eccentricity matrix;epsilon-spectrum;Majorization;Multiplicity
摘要：
The eccentricity matrix E(G) of a graph G is derived from the corresponding distance matrix by keeping only the largest non-zero elements for each row and each column and leaving zeros for the remaining ones. The E-eigenvalues of a graph G are those of its eccentricity matrix, in which the maximum modulus is called the E-spectral radius. In this paper, we first establish the relationship between the majorization and E-spectral radii of complete multipartite graphs. As applications, the extremal complete multipartite graphs having the minimum and maximum E-spectral radii are determined. Furthermore, we study the multiplicities of E-eigenvalues among complete multipartite graphs and identify all complete multipartite graphs with distinct E-eigenvalues. © 2022 Elsevier Inc.
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英文
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Inference in a probit model for affiliation networks
作者：
Wang, Qian;Zhao, Chen;Luo, Jing*
期刊：
Communications in Statistics - Theory and Methods ,2022年51(21):7528-7546 ISSN：0361-0926
通讯作者：
Luo, Jing
作者机构：
[Zhao, Chen; Wang, Qian] Cent China Normal Univ, Dept Stat, Wuhan, Peoples R China.;[Luo, Jing] South Cent Univ Nationalities, Dept Stat, Wuhan 430074, Peoples R China.
通讯机构：
[Luo, Jing] S;South Cent Univ Nationalities, Dept Stat, Wuhan 430074, Peoples R China.
关键词：
Affiliation networks;asymptotic normality;consistency;the probit model;moment estimators
摘要：
Affiliation network is a two-mode social network composed of two different groups of nodes (a group of actors and a group of social events) and the edge between nodes to represent the affiliation relationship between actors and social events. Although a number of statistical models are proposed to analyze affiliation networks, the probit distribution to model the degree heterogeneity of the affiliation networks are still unknown or have not been properly explored. In this paper, we use the probit distribution to model the degree heterogeneity of the affiliation networks and establish the uniform consistency and the asymptotic normality of the moment estimator when the number of actors and events both go to infinity. Simulation studies and a real data example demonstrate our theoretical results. © 2021 Taylor & Francis Group, LLC.
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英文
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Some new constructions of MDS self-dual codes over finite fields
作者：
Lebed, Khawla* ;Liu, Hongwei
期刊：
Finite Fields and Their Applications ,2022年77:101934 ISSN：1071-5797
通讯作者：
Lebed, Khawla
作者机构：
[Liu, Hongwei; Lebed, Khawla] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
通讯机构：
[Lebed, Khawla] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
关键词：
Extended Reed-Solomon code;Generalized Reed-Solomon code;MDS code;Self-dual code
摘要：
In this paper, for some fixed q, we construct some new classes of maximum distance separable (MDS) self-dual codes over Fq by using (extended) generalized Reed-Solomon codes. Our constructions utilize the additive and/or multiplicative structures of the finite field Fq. It reveals that by choosing suitable subsets of Fq, more MDS self-dual codes with new parameters can be found. © 2021 Elsevier Inc.
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英文
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Comprehensive Evaluation on Teachers’ Knowledge Sharing Behavior Based on the Improved TOPSIS Method
作者：
Yu, Xiaojuan;Hu, Dianshun;Li, Na;Xiao, Yan
期刊：
Computational Intelligence and Neuroscience ,2022年2022 ISSN：1687-5265
通讯作者：
Hu, DS;Xiao, Y
作者机构：
[Hu, Dianshun; Hu, DS; Yu, Xiaojuan; Li, Na] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Xiao, Yan; Xiao, Y] Chongqing Univ Technol, Coll Mech Engn, Chongqing 400054, Peoples R China.;[Xiao, Yan; Xiao, Y] Macau Univ Sci & Technol, Sch Business, Macau 999078, Peoples R China.
通讯机构：
[Hu, DS ; Xiao, Y ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;Chongqing Univ Technol, Coll Mech Engn, Chongqing 400054, Peoples R China.;Macau Univ Sci & Technol, Sch Business, Macau 999078, Peoples R China.
摘要：
Knowledge sharing among teachers is one of the important ways to improve their teaching and research ability. From the perspectives of teachers' knowledge sharing willingness, knowledge sharing ability, knowledge sharing environment, knowledge sharing technology support, knowledge sharing effect, and so forth, this paper constructs a teacher knowledge sharing behavior evaluation model, develops a knowledge sharing behavior evaluation index system, and proposes a comprehensive teacher's knowledge sharing behavior evaluation method based on the improved entropy-TOPSIS method. This is a comprehensive evaluation method combining subjective and objective weights, which avoids the subjectivity of traditional expert evaluation methods and other multilevel and multi-index weight determination methods and makes the evaluation results more objective, accurate, and more realistic. Finally, by taking the example of evaluating knowledge sharing behavior of teachers in a university of Chongqing, China, this paper verifies the feasibility and practicability of the proposed comprehensive teachers' knowledge sharing behavior evaluation system and method. © 2022 Xiaojuan Yu et al.
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英文
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Anti-Ramsey numbers for cycles in n-prisms
作者：
Li, Yibo;Liu, Huiqing;Hu, Xiaolan
期刊：
Discrete Applied Mathematics ,2022年322:1-8 ISSN：0166-218X
通讯作者：
Hu, Xiaolan(xlhu@ccnu.edu.cn)
作者机构：
[Li, Yibo; Liu, Huiqing] Hubei Univ, Fac Math & Stat, Hubei Key Lab Appl Math, Wuhan 430062, Peoples R China.;[Hu, Xiaolan] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Hu, Xiaolan] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Xiaolan Hu] S;School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan 430079, PR China
关键词：
Anti-Ramsey number;Cycle;n-prism
摘要：
An edge colored graph is called rainbow if all the colors on its edges are distinct. A rainbow copy of a graph H in an edge colored graph G is a subgraph of G isomorphic to H such that the coloring restricted to H is rainbow. Let G and H be two graphs. The anti-Ramsey number Ar(G,H) is the maximum number of colors in an edge coloring of G which has no rainbow copy of H. For n≥3, the n-prism is the cartesian product Cn□K2. In this paper, we determine the anti-Ramsey numbers for cycles in n-prisms. © 2022 Elsevier B.V.
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英文
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Coefficient inverse problem for variable order time-fractional diffusion equations from distributed data
作者：
Jiang, Daijun;Li, Zhiyuan
期刊：
Calcolo ,2022年59(4):1-28 ISSN：0008-0624
通讯作者：
Li, Zhiyuan(lizhiyuan@nbu.edu.cn)
作者机构：
[Jiang, Daijun] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Jiang, Daijun] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Li, Zhiyuan] Ningbo Univ, Sch Math & Stat, 818 Fenghua Rd, Ningbo 315211, Peoples R China.
通讯机构：
[Zhiyuan Li] S;School of Mathematics and Statistics, Ningbo University, Ningbo, People’s Republic of China
关键词：
Inverse problem;Variable order time-fractional diffusion equation;Uniqueness;Distributed observation
摘要：
This paper deals with an inverse problem on determining a time dependent potential in a diffusion equation with temporal fractional derivative of variable order from a distributed observation. We shall study the existence, uniqueness and regularity estimates of the solution for the forward problem by utilizing the Freldhom alternative principle for compact operators. Based on a newly established coercivity for fractional derivatives of variable order, we prove a uniqueness result for the inverse potential problem. Numerically, we transform the inverse potential problem into an optimization problem with Tikhonov regularization. An iterative thresholding algorithm is proposed to find the minimizers by a newly constructed adjoint system, whose wellposedness is also verified. Several numerical experiments are presented to show the accuracy and efficiency of the proposed algorithm. © 2022, The Author(s) under exclusive licence to Istituto di Informatica e Telematica (IIT).
语种：
英文
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Constructions of MDS symbol-pair codes with minimum distance seven or eight
作者：
Ma, Junru;Luo, Jinquan
期刊：
DESIGNS CODES AND CRYPTOGRAPHY ,2022年90(10):2337-2359 ISSN：0925-1022
通讯作者：
Luo, Jinquan(luojinquan@mail.ccnu.edu.cn)
作者机构：
[Ma, Junru] Hubei Univ, Fac Math & Stat, Hubei Key Lab Appl Math, Wuhan 430062, Hubei, Peoples R China.;[Luo, Jinquan] Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Hubei, Peoples R China.
通讯机构：
[Jinquan Luo] S;School of Mathematics and Statistics, Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, China
关键词：
MDS symbol-pair codes;Minimum symbol-pair distance;Constacyclic codes;Repeated-root cyclic codes
摘要：
Symbol-pair codes are proposed to guard against pair-errors in symbol-pair read channels. The minimum symbol-pair distance plays a vital role in determining the error-correcting capability and the constructions of symbol-pair codes with largest possible minimum symbol-pair distance is of great importance. Maximum distance separable (MDS) symbol-pair codes are optimal in the sense that such codes can acheive the Singleton bound. In this paper, for length 5p, two new classes of MDS symbol-pair codes with minimum symbol-pair distance seven or eight are constructed by utilizing repeated-root cyclic codes over Fp, where p is a prime. In addition, we derive a class of MDS symbol-pair codes with minimum symbol-pair distance seven and length 4p. © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
语种：
英文
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New global dynamical results and application of several SVEIS epidemic models with temporary immunity
作者：
Wang, Lianwen;Liu, Zhijun* ;Guo, Caihong;Li, Yong;Zhang, Xinan
期刊：
Applied Mathematics and Computation ,2021年390:125648 ISSN：0096-3003
通讯作者：
Liu, Zhijun
作者机构：
[Liu, Zhijun; Wang, Lianwen] Hubei Minzu Univ, Dept Math, Enshi 445000, Peoples R China.;[Guo, Caihong] Enshi Special Care Hosp, Enshi 445000, Peoples R China.;[Li, Yong] Yangtze Univ, Sch Informat & Math, Jingzhou 434023, Peoples R China.;[Zhang, Xinan] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Liu, Zhijun] H;Hubei Minzu Univ, Dept Math, Enshi 445000, Peoples R China.
关键词：
Global stability;Vaccination;Temporary immunity;Nonlinear incidence;Li-Muldowney geometric criterion;Parameter estimation
摘要：
This work applies a novel geometric criterion for global stability of nonlinear autonomous differential equations generalized by Lu and Lu (2017) to establish global threshold dynamics for several SVEIS epidemic models with temporary immunity, incorporating saturated incidence and nonmonotone incidence with psychological effect, and an SVEIS model with saturated incidence and partial temporary immunity. Incidentally, global stability for the SVEIS models with saturated incidence in Cai and Li (2009), Sahu and Dhar (2012) is completely solved. Furthermore, employing the DEDiscover simulation tool, the parameters in Sahu and Dhar'model are estimated with the 2009-2010 pandemic H1N1 case data in Hong Kong China, and it is validated that the vaccination programme indeed avoided subsequent potential outbreak waves of the pandemic. Finally, global sensitivity analysis reveals that multiple control measures should be utilized jointly to cut down the peak of the waves dramatically and delay the arrival of the second wave, thereinto timely vaccination is particularly effective. (C) 2020 Elsevier Inc. All rights reserved.
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英文
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