摘要：
Let G be a graph and let k 2 be an integer. A {K1,j : 1 S j S k}-factor of G is a spanning subgraph of G, in which each component is isomorphic to a member in {K1,j : 1 S j S k}. In this paper, we first establish a lower bound on the size (resp. the spectral radius) of G to guarantee that G contains a {K1,j : 1 S j S k}-factor. Then we determine an upper bound on the distance spectral radius of G to ensure that G has a {K1,j : 1 S j S k}-factor. Furthermore, we construct some extremal graphs to show all the bounds obtained in this contribution are best possible.(c) 2022 Elsevier B.V. All rights reserved.
期刊：
Linear Algebra and its Applications,2023年662:110-135 ISSN：0024-3795
通讯作者：
Shuchao Li
作者机构：
[Yu, Yuantian; Li, Shuchao] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Yu, Yuantian; Li, Shuchao] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.;[Tam, Bit-Shun] Tamkang Univ, Dept Math, New Taipei City 25137, Taiwan.;[Zhao, Qin] Hubei Univ, Fac Math & Stat, Hubei Key Lab Appl Math, Wuhan 430062, Peoples R China.
通讯机构：
[Shuchao Li] H;Hubei Key Laboratory of Mathematical Science, and Faculty of Mathematics and Statistics, Central China Normal University, Wuhan 430079, PR China
关键词：
Maximal A(alpha)-index problem;A(alpha)-matrix;Maximal graph;Threshold graph;Neighborhood equivalence class
摘要：
For any real number alpha is an element of[0, 1], by the A(alpha)-matrix of a graph G we mean the matrix A(alpha) (G) = alpha D(G) + (1 - alpha)A(G), where A(G) and D(G) denote respectively the adjacency matrix and the diagonal matrix of vertex degrees of G. The largest eigenvalue of A(alpha)(G) is called the A(alpha)-index of G. Chang and Tam (2011) have proved that for every pair of integers n, k with -1 <= k <= n - 3, H-n,H-k, the graph obtained from the star K-1,K-n-1 by joining a vertex of degree 1 to k + 1 other vertices of degree 1, is the unique connected graph that maximizes the Q-index (i.e., the signless Laplacian spectral radius or, equivalently, the A(1/2)-index) over all connected graphs with n vertices and n + k edges. In this paper it is proved that for every pair of integers n, k with -1 <= k <= n - 3, when 1/2 < alpha < 1 or alpha = 1/2 and k not equal 2, the graph H-n,H-k is the unique connected graph that maximizes the A(alpha)-index over all connected graphs with n vertices and n + k edges. This work extends (and also provides an alternative proof for) the above-mentioned result of Chang and Tam. A complete overview of the history of the maximal index problems is also given. (c) 2023 Elsevier Inc. All rights reserved.
期刊：
Linear Algebra and its Applications,2023年668:11-27 ISSN：0024-3795
通讯作者：
Yu, YT
作者机构：
[Yu, YT; Yu, Yuantian; Li, Shuchao] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Yu, YT ] C;Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
关键词：
Extremal graph;A & alpha;-index;Even cycle
摘要：
Given a graph G, for a real number alpha is an element of[0, 1], Nikiforov (2017) proposed the A alpha-matrix of Gas A alpha(G) = alpha D(G) + (1 - alpha)A(G), where A(G) and D(G) are the adjacency matrix and the degree diagonal matrix of G, respectively. The largest eigenvalue of A alpha(G) is called the A alpha-index of G. For n > k, let S-n,S-k be the join of a clique on kvertices with an independent set of n - k vertices. Then S-n,k(+) denotes the graph obtained from S-n,S-k by adding an edge to connect two vertices of degree k. Very recently, Cioab.a, Desai and Tait resolved the Nikiforov's conjecture: For fixed k >= 2, and sufficiently large n, the {C-2k+1, C-2k+2}-free graph of order nwith maximum adjacency spectral radius is S-n,S-k and the C2k+2-free graph of order nwith maximum adjacency spectral radius is S-n,k(+). In this paper, we confirm the A alpha-spectral version of this conjecture: For fixed k >= 2, 0 < alpha < 1and n >= 324k(6)(k+1)2|alpha(6)(1-alpha)(2), the {C2k+1, C2k+2}-free graph of order nwith maximum Aa-index is Sn,kand the C2k+2-free graph of order nwith maximum Aa-index is S+ n,k. (c) 2023 Elsevier Inc. All rights reserved.
摘要：
Given a graph G with S subset of VG, we call S a maximum dissociation set if the induced subgraph G[S] contains no path of order 3, and subject to this condition, the subset S has the maximum cardinality. The dissociation number of G is the cardinality of a maximum dissociation set. Inspired by the results of [26, 27] on the maximal number of maximum dissociation sets, in this contribution we investigate the maximal number of maximum dissociation sets in forests with fixed order and dissociation number. Firstly, a lower bound on the dissociation number of a forest with fixed order is established, and all extremal graphs are determined. Secondly, all trees (resp. forests) having the largest and the second largest number of maximum dissociation sets among trees (resp. forests) with given order and dissociation number are completely characterized. Finally, we show that the results in [26, 27] can be deduced by our results.
期刊：
Journal of Mathematical Biology,2023年86(4):1-35 ISSN：0303-6812
通讯作者：
Jicai Huang<&wdkj&>Hao Wang
作者机构：
[Lu, Min; Huang, Jicai] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.;[Lu, Min; Huang, Jicai] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Hubei, Peoples R China.;[Gao, Daozhou] Cleveland State Univ, Dept Math, Cleveland, OH 44115 USA.;[Gao, Daozhou] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China.;[Wang, Hao] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada.
通讯机构：
[Jicai Huang] S;[Hao Wang] D;School of Mathematics and Statistics and Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, People’s Republic of China<&wdkj&>Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Canada
摘要：
In this paper, we propose a two-patch SIRS model with a nonlinear incidence rate:
$$\beta _i(1+\nu _iI_i)I_i S_i$$
and nonconstant dispersal rates, where the dispersal rates of susceptible and recovered individuals depend on the relative disease prevalence in two patches. In an isolated environment, the model admits Bogdanov–Takens bifurcation of codimension 3 (cusp case) and Hopf bifurcation of codimension up to 2 as the parameters vary, and exhibits rich dynamics such as multiple coexistent steady states and periodic orbits, homoclinic orbits and multitype bistability. The long-term dynamics can be classified in terms of the infection rates
$$\beta _i$$
(due to single contact) and
$$\nu _i$$
(due to double exposures). In a connected environment, we establish a threshold
$$R_0=1$$
between disease extinction and uniform persistence under certain conditions. We numerically explore the effect of population dispersal on disease spread when
$$\nu _i=0$$
and patch 1 has a lower infection rate, our results indicate: (i)
$$R_0$$
can be nonmonotonic in dispersal rates and
$$R_0\le \max \limits \{R_{01},R_{02}\}$$
(
$$R_{0i}$$
is the basic reproduction number of patch i) may fail; (ii) the constant dispersal of susceptible individuals (or infective individuals) between two patches (or from patch 2 to patch 1) will increase (or reduce) the overall disease prevalence; (iii) the relative prevalence-based dispersal may reduce the overall disease prevalence. When
$$\nu _i>0$$
and the disease outbreaks periodically in each isolated patch, we find that: (a) small unidirectional and constant dispersal can lead to complex periodic patterns like relaxation oscillations or mixed-mode oscillations, whereas large ones can make the disease go extinct in one patch and persist in the form of a positive steady state or a periodic solution in the other patch; (b) relative prevalence-based and unidirectional dispersal can make periodic outbreak earlier.
期刊：
SIAM JOURNAL ON MATHEMATICAL ANALYSIS,2023年55(2):773-804 ISSN：0036-1410
通讯作者：
Guo, YJ
作者机构：
[Peng, Shuangjie; Guo, Yujin; Luo, Yong] Cent China Normal Univ, Sch Math & Stat, POB 71010, Wuhan 430079, Peoples R China.;[Peng, Shuangjie; Guo, Yujin; Luo, Yong] Cent China Normal Univ, Hubei Key Lab Math Sci, POB 71010, Wuhan 430079, Peoples R China.
通讯机构：
[Guo, YJ ] C;Cent China Normal Univ, Sch Math & Stat, POB 71010, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Hubei Key Lab Math Sci, POB 71010, Wuhan 430079, Peoples R China.
关键词：
Bose–Einstein condensates;rotational velocity;ground states;free of vortices;35J20;35J60;35Q40;46N50
摘要：
We study ground states of two-dimensional Bose–Einstein condensates with repulsive ( \(a\gt 0\) ) or attractive ( \(a\lt 0\) ) interactions in a trap \(V (x)\) rotating at velocity \(\Omega\) . It is known that there exist critical parameters \(a^{\ast }\gt 0\) and \(\Omega^{\ast }:=\Omega^{\ast }(V(x))\gt 0\) such that if \(\Omega \gt \Omega^{\ast }\) , then there is no ground state for any \(a\in \mathbb{R}\) ; if \(0\le \Omega \lt \Omega^{\ast }\) , then ground states exist if and only if \(a\in (-a^{\ast },+\infty )\) . As a completion of the existing results, in this paper, we focus on the critical case where \(0\lt \Omega =\Omega^{\ast }\lt +\infty\) to classify the existence and nonexistence of ground states for any \(a\in \mathbb{R}\) . Moreover, for a suitable class of radially symmetric traps \(V(x)\) , employing the inductive symmetry method, we prove that up to a constant phase, ground states must be real valued, unique, and free of vortices as \(\Omega \searrow 0\) , no matter whether the interactions of the condensates are repulsive or not.
期刊：
Applied Mathematics and Computation,2023年445:127842 ISSN：0096-3003
通讯作者：
Zhang, Shunzhe(shunzhezhang@hubu.edu.cn)
作者机构：
[Chen, Guantao] Georgia State Univ, Dept Math & Stat, Atlanta, GA 30303 USA.;[Chen, Yuan] Wuhan Text Univ, Res Ctr Nonlinear Sci, Sch Math & Phys Sci, Wuhan 430073, Peoples R China.;[Hu, Zhiquan] Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Zhang, Shunzhe] Hubei Univ, Fac Math & Stat, Hubei Key Lab Appl Math, Wuhan 430062, Peoples R China.
通讯机构：
[Shunzhe Zhang] H;Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan 430062, PR China
作者：
Du, Yuqing;Qu, Lianqiang;Yan, Ting;Zhang, Yuan
期刊：
Scandinavian Journal of Statistics,2023年50(4):1687-1715 ISSN：0303-6898
通讯作者：
Qu, LQ
作者机构：
[Yan, Ting; Qu, Lianqiang; Du, Yuqing] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.;[Zhang, Yuan] Ohio State Univ, Dept Stat, Columbus, OH USA.
通讯机构：
[Qu, LQ ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
摘要：
Abstract We extend the well‐known β$$ \beta $$‐model for directed graphs to dynamic network setting, where we observe snapshots of adjacency matrices at different time points. We propose a kernel‐smoothed likelihood approach for estimating 2n$$ 2n $$ time‐varying parameters in a network with n$$ n $$ nodes, from N$$ N $$ snapshots. We establish consistency and asymptotic normality properties of our kernel‐smoothed estimators as either n$$ n $$ or N$$ N $$ diverges. Our results contrast their counterparts in single‐network analyses, where n→∞$$ n\to \infty $$ is invariantly required in asymptotic studies. We conduct comprehensive simulation studies that confirm our theory's prediction and illustrate the performance of our method from various angles. We apply our method to an email dataset and obtain meaningful results.
摘要：
Consider the nonlinear stability of the Couette flow in the Boussinesq equations with vertical dissipation on T×R. We prove that if the initial perturbations uin and θin to the Couette flow vs=(y,0)⊤ and θs=1, respectively, satisfy ‖uin‖HN+1+ν−12‖θin‖HN+ν−13‖|∂x|13θ‖HN≪ν13, N>7, then the resulting solution remains close to the Couette flow in L2 at the same order for all time.
Considérons la stabilité nonlinéaire du flux de Couette dans l'équation de Boussinesq avec dissipation verticale sur T×R. On montre que si les perturbations initiales uin et θin des flux de Couette vs=(y,0)⊤ et θs=1 satisfont ‖uin‖HN+1+ν−12‖θin‖HN+ν−13‖|∂x|13θ‖HN≪ν13, N>7, la solution obtenue reste alors proche du flux de Couette dans L2 avec le même ordre tout le temps.
作者机构：
[An, L. -X.] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[An, L. -X.] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Lai, C. -K.] San Francisco State Univ, Dept Math, 1600 Holloway Ave, San Francisco, CA 94132 USA.
通讯机构：
[C.-K. Lai] D;Department of Mathematics, San Francisco State University, San Francisco, USA
摘要：
Given an expansive matrix R is an element of M-d(DOUBLE-STRUCK CAPITAL Z) and a finite set of digit B taken from DOUBLE-STRUCK CAPITAL Z(d)/R(DOUBLE-STRUCK CAPITAL Z(d)). It was shown previously that if we can find an L such that (R, B, L) forms a Hadamard triple, then the associated fractal self-affine measure generated by (R, B) admits an exponential orthonormal basis of certain frequency set ?, and hence it is termed as a spectral measure. In this paper, we show that if #B < |det(R)|, not only it is spectral, we can also construct arbitrarily sparse spectrum ? in the sense that its Beurling dimension is zero.
作者机构：
[Deng, Yinbin; Yang, Xiaolong; Shuai, Wei] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Deng, Yinbin; Shuai, Wei] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Shuai, W] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Shuai, W] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Shuai, W ] ;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：
Schrödinger-Poisson system;ground state solution;sign-changing solution;critical growth
摘要：
In this paper, we study the following Schrödinger-Poisson system with critical growth: {−Δu+V(x)u+ϕ(x)u=f(u)+∣u∣4u,x∈ℝ3,−Δϕ=u2,x∈ℝ3.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left\{ {\matrix{{ - \Delta u + V(x)u + \phi (x)u = f(u) + |u{|^4}u,} \hfill & {x \in {\mathbb{R}^3},} \hfill \cr { - \Delta \phi = {u^2},} \hfill & {x \in {\mathbb{R}^3}.} \hfill \cr } } \right.$$\end{document} We establish the existence of a positive ground state solution and a least energy sign-changing solution, providing that the nonlinearity f is super-cubic, subcritical and that the potential V(x) has a potential well.
作者机构：
[Hu, Xiao Lan] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Hu, Xiao Lan] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Li, Jia Ao] Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China.;[Li, Jia Ao] Nankai Univ, LPMC, Tianjin 300071, Peoples R China.
通讯机构：
[Jia Ao Li] S;School of Mathematical Sciences and LPMC, Nankai University, Tianjin, P. R. China
作者机构：
[Hua, Hongbo] Huaiyin Inst Technol, Fac Math & Phys, Huaian 223003, Jiangsu, Peoples R China.;[Hu, Xiaolan] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Hongbo Hua] F;Faculty of Mathematics and Physics, Huaiyin Institute of Technology, Huai’an, Jiangsu 223003, PR China
关键词：
Bounds;Forgotten index;Independence number;Lanzhou index;The second Zagreb index
作者机构：
[Yu, Yuantian; Zhou, Zihan; Li, Shuchao; Li, SC] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Li, SC ] C;Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
关键词：
Hermitian adjacency matrix of the second kind;Mixed graph;Smallest eigenvalue
摘要：
Mixed graphs unify simple graphs and oriented graphs naturally. The Hermitian adjacency matrix of a mixed graph for the second kind (N-matrix for short) was recently introduced by Mohar [13]. This matrix is indexed by the vertices of the mixed graph, and the entry & RADIC; corresponding to an arc from u to v is equal to the principal sixth root of unity & omega; = 1+i 3 & RADIC; 2 (and its symmetric entry is & omega; = 1-i2); the entry corresponding to an undirected edge 3 is equal to 1, and 0 otherwise. In this paper, we completely characterize the connected mixed graphs whose N-matrices have the smallest eigenvalue greater than -32. It may be considered as the continuance of the work of J.H. Smith [18] who considered the classical problem of characterizing the graphs whose eigenvalues lie in a given interval. & COPY; 2023 Elsevier B.V. All rights reserved.
作者机构：
[Liu, Nannan; 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：
[Shuchao Li] F;Faculty of Mathematics and Statistics, Central China Normal University, Wuhan 430079, PR China
关键词：
Diameter;Matching number;Normality;Tree
摘要：
Given a connected graph G, the eccentricity epsilon G(v) of a vertex v in G is the maximum distance from v to any other vertex, in which the vertex v satisfying epsilon G(v) = max{epsilon G(u) : u E VG} is called a peripheral vertex. The normality of a vertex v is the minimum distance from v to all peripheral vertices in G. The sum of normalities of G is denoted by Norm(G). The difference between the eccentricity and normality at a vertex v is denoted by lambda G(v). Let Lambda(G) = n-ary sumation vEV(G)lambda G(v). Very recently, Chen, Wang and Zhang (Chen et al., 2020) started a new research on the two novel parameters Norm(middot) and Lambda(middot) of trees. As a continuance of it, we obtain some relationship between Norm(T) (resp. Lambda(T)) with the matching number and the order of the tree T. We characterize all the n-vertex trees with given matching number having the largest (resp. smallest) sum of normalities. As well we establish sharp upper and lower bounds on Lambda(middot) of an n-vertex tree T with given matching number. Some further research problems are proposed.(c) 2022 Elsevier B.V. All rights reserved.
摘要：
We study the coexistence of limit cycles in a predator-prey model of Leslie type with generalized Holling type III functional response. When the prey reproduces much faster than the predator, we prove for this model that: (i) the existence of the configuration of one large stable limit cycle enclosing two small unstable limit cycles, (ii) the cyclicity of singular double-head canard cycles is three and reached, and (iii) the coexistence of two stable limit cycles surrounding three equilibria. The last result gives a positive answer to Coleman's problem on the coexistence of two ecologically stable limit cycles in predator-prey models.& COPY; 2023 Elsevier Inc. All rights reserved.
摘要：
In this paper, we study constraint minimizers u of the planar Schrodinger-Poisson system with a logarithmic convolution potential ln |x| * u2 and a logarithmic external potential V (x) = ln(1 + |x|2), which can be described by the L2-critical constraint minimization problem with a subcritical perturbation. We prove that there is a threshold p* e (0, co) such that constraint minimizers exist if and only if 0 < p < p*. In particular, the local uniqueness of positive constraint minimizers as p J' p* is analyzed by overcoming the sign-changing property of the logarithmic convolution potential and the non-invariance under translations of the logarithmic external potential. & COPY; 2023 Elsevier Inc. All rights reserved.
