期刊:
Results in Mathematics,2023年78(3):1-19 ISSN:1422-6383
通讯作者:
Shuchao Li<&wdkj&>Wanting Sun
作者机构:
[Li, Shuchao; Sun, Wanting] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
通讯机构:
[Shuchao Li; Wanting Sun] F;Faculty of Mathematics and Statistics, Central China Normal University, Wuhan, People’s Republic of China<&wdkj&>Faculty of Mathematics and Statistics, Central China Normal University, Wuhan, People’s Republic of China
关键词:
Adjacency matrix;second largest eigenvalue;outerplanar graph;\(\{K_{2, 3}, K_4\}\)-minor free graph
摘要:
Let
$$\lambda _2$$
be the second largest eigenvalue of the adjacency matrix of a connected graph. In 2021, Liu, Chen and Stanić determined all the connected
$$\{K_{1,3}, K_5 -e\}$$
-free graphs whose second largest eigenvalue
$$\lambda _2\leqslant 1$$
. In this paper, we completely identify all the connected
$$\{K_{2,3},K_4\}$$
-minor free graphs whose second largest eigenvalue does not exceed 1. That is, we characterize all the connected outerplanar graphs satisfying
$$\lambda _2\leqslant 1$$
. Furthermore, all the maximal outerplanar graphs having the same property can be deduced by our result obtained in this paper. Our main tools include analyzing the local structure of the outerplanar graph with respect to its girth.
期刊:
Applied Mathematics and Computation,2023年438:127556 ISSN:0096-3003
通讯作者:
Sun, Wanting(wtsun2018@sina.com)
作者机构:
[Li, Shuchao; Liu, Xin; Sun, Wanting] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.;[Yan, Lixia] Wuhan Business Univ, Sch Informat & Engn, Wuhan 430070, Peoples R China.
通讯机构:
[Wanting Sun] F;Faculty of Mathematics and Statistics, Central China Normal University, Wuhan 430079, PR China
摘要:
The Steiner k-eccentricity of a vertex in a graph G is the maximum Steiner distance over all k-subsets containing the vertex. The average Steiner k-eccentricity of G is the mean value of all vertices' Steiner k-eccentricities in G. Let T-n be the set of all n-vertex trees, T-n,T-Delta be the set of n-vertex trees with maximum degree Delta, T-n,Delta(k) be the set of n-vertex trees with exactly k vertices of a given maximum degree Delta, and let MTnk be the set of n-vertex trees with exactly k vertices of maximum degree. In this paper, we first determine the sharp upper bound on the average Steiner 3-eccentricity of n-vertex trees with a given degree sequence. The corresponding extremal graphs are characterized. Consequently, together with majorization theory, all graphs among T-n,Delta(k) (resp. T-n,T-Delta, MTnk, T-n) having the maximum average Steiner 3-eccentricity are identified. Then we characterize the unique n-vertex tree with a given segment sequence having the minimum average Steiner 3-eccentricity. Finally, we determine all n-vertex trees with a given number of segments having the minimum average Steiner 3-eccentricity. (C) 2022 Elsevier Inc. All rights reserved.
期刊:
Bulletin of the Malaysian Mathematical Sciences Society,2023年46(1):1-9 ISSN:0126-6705
通讯作者:
Meng Fai Lim
作者机构:
[Lim, Meng Fai] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Lim, Meng Fai] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构:
[Meng Fai Lim] 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:
Norm principle;Norm maps;Even K-groups;Finite extensions of number fields
摘要:
We investigate the norm maps of algebraic even K-groups of finite extensions of number fields. Namely, we show that they are surjective in most situations. In the event that they are not surjective, we give a criterion in determining when an element in the even K-group of the base field comes from a norm of an element from the even K-groups of the extension field. This latter criterion is only reliant on the real primes of the base field.
作者机构:
[Fu, Kang; Hu, Jianwei] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Fu, K; Fu, Kang] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei Province, Peoples R China.
通讯机构:
[Fu, K ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei Province, Peoples R China.
关键词:
community detection;multilayer network;profile-pseudo likelihood;stochastic block model;strong consistency
摘要:
The multilayer stochastic block model is one of the fundamental models in multilayer networks and is often used to represent multiple types of relations between different individuals. In this paper, we extend the profile-pseudo likelihood method for the single-layer stochastic block model to the case of the multilayer stochastic block model. Specifically, by assuming all network layers have identical community membership labels, we investigate the multilayer stochastic block model with a common community structure. In this paper, we develop a profile-pseudo likelihood algorithm to fit a multilayer stochastic block model and estimate the community label. Meantime, we prove that the algorithm has convergence guarantee and that the estimated community label is strongly consistent. Further, for estimating the number of communities K $$ K $$ , we extend the corrected Bayesian information criterion to multilayer stochastic block models. We also extend this algorithm to fit the multilayer degree-corrected stochastic block model. Both simulation studies and real-world data examples indicate that the proposed method works well.
摘要:
Let $M=(\begin {smallmatrix}\rho ^{-1} & 0 \\0 & \rho ^{-1} \\\end {smallmatrix})$ be an expanding real matrix with $0<\rho <1$, and let ${\mathcal D}_n=\{(\begin {smallmatrix} 0\\ 0 \end {smallmatrix}),(\begin {smallmatrix} \sigma _n\\ 0 \end {smallmatrix}),(\begin {smallmatrix} 0\\ \gamma _n \end {smallmatrix})\}$ be digit sets with $\sigma _n,\gamma _n\in \{-1,1\}$ for each $n\ge 1$. Then the infinite convolution\n$$ \begin{align*}\mu_{M,\{{\mathcal D}_n\}}=\delta_{M^{-1}{\mathcal D}_1}\ast\delta_{M^{-2}{\mathcal D}_2}\ast\cdots\end{align*} $$\nis called a Moran–Sierpinski measure. We give a necessary and sufficient condition for $L^2(\,\mu _{M,\{{\mathcal D}_n\}})$ to admit an infinite orthogonal set of exponential functions. Furthermore, we give the exact cardinality of orthogonal exponential functions in $L^2(\,\mu _{M,\{{\mathcal D}_n\}})$ when $L^2(\,\mu _{M,\{{\mathcal D}_n\}})$ does not admit any infinite orthogonal set of exponential functions based on whether $\rho $ is a trinomial number or not.
作者机构:
[Xiaoli Hu] School of Artificial Intelligence, Jianghan University, Wuhan, Hubei 430056, People's Republic of China;Department of Mathematics, North Carolina State University, Raleigh, NC 27695, United States of American;School of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei 430079, People's Republic of China;[Naihuan Jing] Department of Mathematics, North Carolina State University, Raleigh, NC 27695, United States of American<&wdkj&>School of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei 430079, People's Republic of China
通讯机构:
[Xiaoli Hu] S;[Naihuan Jing] D;Department of Mathematics, North Carolina State University, Raleigh, NC 27695, United States of American<&wdkj&>School of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei 430079, People's Republic of China<&wdkj&>School of Artificial Intelligence, Jianghan University, Wuhan, Hubei 430056, People's Republic of China
摘要:
Skew information is a pivotal concept in quantum information, quantum measurement, and quantum metrology. Further studies have lead to the uncertainty relations grounded in metric-adjusted skew information. In this work, we present an in-depth investigation using the methodologies of sampling coordinates of observables and convex functions to refine the uncertainty relations in both the product form of two observables and summation form of multiple observables.
期刊:
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY,2023年151(02):763-770 ISSN:0002-9939
作者机构:
[Qiu, W. E. I. F. E. N. G.] CIity Univ HONG KONG, Dept Math, 83 Tat Chee Ave, Hong Kong, Peoples R China.;[Tang, L. A. N.] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
摘要:
This paper is devoted to establishing global W^{2, p} estimate for strong solutions to the Dirichlet problem of uniformly elliptic equations in the non-divergence form where the domain is a Lipschitz polyhedra.
期刊:
Mathematical Methods in the Applied Sciences,2023年46(4):3429-3444 ISSN:0170-4214
通讯作者:
Shuang Li<&wdkj&>Shuang Li Shuang Li Shuang Li
作者机构:
[Li, Shuang] Henan Normal Univ, Coll Math & Informat Sci, Xinxiang 453007, Henan, Peoples R China.;[Li, Yong] Yangtze Univ, Sch Informat & Math, Jingzhou, Peoples R China.;[Zhang, Xinan] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.
通讯机构:
[Shuang Li; Shuang Li Shuang Li Shuang Li] C;College of Mathematics and Information Science, Henan Normal University, Xinxiang, China
关键词:
Lévy noise;persistence in the mean;predator–prey;stochastic perturbation
摘要:
An eco-epidemiological system with Levy noise and white noise is proposed. In this prey-predator system, assume that the predator population is infected by disease and divided into two classes: susceptible predator and infected predator. The existence of global positive solution is derived. Threshold conditions of extinction and persistence in the mean for prey and predator population are given by Ito's formula and comparison theorem for stochastic model. The long-time behavior of this random system is also discussed by constructing suitable Lyapunov function, which shows the relationship between the solution of stochastic system and the equilibria of corresponding deterministic system. Finally, these results are verified by numerical simulation. Our results illustrate whether Levy noise and white noise are both unfavorable to the population size of species.
期刊:
International Journal of Energy Research,2023年2023 ISSN:0363-907X
作者机构:
[Cheng, Fei] Zhejiang Huayun Informat Technol Co Ltd, Hangzhou, Peoples R China.;[Wei, Cong] Zhejiang Univ Finance & Econ, Sch Econ, Hangzhou, Peoples R China.;[Wei, Cong] Springfield Coll, Springfield, MA USA.;[Tang, Tian; Kong, Jiayang] Cent China Normal Univ, Sch Econ & Business Adm, Wuhan, Peoples R China.;[Tang, Tian; Kong, Jiayang] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.
摘要:
In recent years, the Chinese Central Government has put great emphasis on the marine economy, since it has been a new driving force of the national economic development. Yet, the relationship between marine economic development and energy efficiency remains unknown. In this paper, we investigate whether marine economic development affected energy efficiency. We focused on the Zhoushan Archipelago, the first National New Area for marine economic development in China. We applied panel data approach to construct the counterfactual of Zhoushan Archipelago. We compared Zhoushan and its counterfactual, the synthetic Zhoushan, and viewed the difference between them, after the Zhoushan Archipelago New Area, as the impact of marine economic development on energy efficiency. We found that compared with its counterfactual, the real Zhoushan had a more substantial improvement in energy efficiency after the National New Area construction. We estimated that the construction of the National New Area for Marine Economy increased energy efficiency by about 10 percentage points. We also applied the bootstrapping technique to illustrate the significance of the estimated results. The results suggest that the Zhoushan Archipelago New Area construction had a statistically significant impact on energy efficiency. In addition, we conducted two tests, including leave-one-out tests and permutation tests, to check the robustness of estimated results, which also serve as an illustration of significance of the estimated results from an alternative empirical perspective. The results from these two tests are similar to each other, both indicating that the Zhoushan Archipelago New Area construction had a statistically significant positive impact on energy efficiency. Overall, our results suggest that marine economic development had a sizable improvement in energy efficiency.
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.
作者机构:
[Sun, Wanting] Shandong Univ, Data Sci Inst, Jinan 250100, Peoples R China.;[Li, Shuchao; Li, SC] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Li, Shuchao; Li, SC] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.;[Wei, Wei] Shanghai Univ Engn Sci, Sch Math Phys & Stat, Shanghai 201620, Peoples R China.
通讯机构:
[Li, SC ] C;Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
关键词:
F-free graphs;Spectral radius;Turán-type extremal problem
摘要:
Let F denote a set of graphs. A graph G is said to be F-free if it does not contain any element of F as a subgraph. The Turan number is the maximum possible number of edges in an F-free graph with n vertices. It is well known that classical Turan type extremal problem aims to study the Turan number of fixed graphs. In 2010, Nikiforov [17] proposed analogously a spectral Turan type problem which asks to determine the maximum spectral radius of an F-free graph with n vertices. It attracts much attention and many such problems remained elusive open even after serious attempts, and so they are considered as one of the most intriguing problems in spectral extremal graph theory. It is interesting to consider another spectral Turan type problem which asks to determine the maximum spectral radius of an F-free graph with m edges. Denote by Q(m, F) the set of F-free graphs with m edges having no isolated vertices. Each of the graphs among Q(m, F) having the largest spectral radius is called a maximal graph. Let 9p,q,r be a theta graph formed by connecting two distinct vertices with three independent paths of length p, q and r, respectively (length refers to the number of edges). In this paper, we firstly determine the unique maximal graph among Q(m, 91,2,3) and Q(m, 91,2,4), respectively. Then we determine all the maximal graphs among Q(m, C5) (resp. Q(m, C6)) excluding the book graph. These results extend some earlier results.& COPY; 2023 Elsevier B.V. All rights reserved.
作者机构:
[Qin, Hong; Zou, Na; Qin, H] Zhongnan Univ Econ & Law, Sch Stat & Math, Wuhan, Peoples R China.;[Qin, Hong; Qin, H] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.;[Chatterjee, Kashinath] Visva Bharati Univ, Dept Stat, Santini Ketan, W Bengal, India.;[Chatterjee, Kashinath] Augusta Univ, Med Coll Georgia, Dept Biostatist & Data Sci, Populat Hlth Sci, Augusta, GA USA.
通讯机构:
[Qin, H ] Z;Zhongnan Univ Econ & Law, Sch Stat & Math, Wuhan, Peoples R China.;Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.
关键词:
Average Lee discrepancy;average Lee-moment;uniformity;lower bound;62K15;62K10;62K99
摘要:
In this paper, we proposed the average Lee discrepancy to measure the uniformity of designs and studied its connection with the standard optimality measures used in the context of design of experiments. Lower bounds to such measure are provided as a benchmark to obtain uniform designs. We also defined the minimum average Lee-moment aberration criterion used to compare and screen the optimal design, and some lower bounds to such criterion are also provided.
期刊:
Cryptography and Communications,2023年:1-28 ISSN:1936-2447
通讯作者:
Xiaoqiang Wang
作者机构:
[Wang, Xiaoqiang; Zheng, Dabin] Hubei Univ, Fac Math & Stat, Hubei Key Lab Appl Math, Wuhan 430062, Peoples R China.;[Ding, Cunsheng] Hong Kong Univ Sci & Technol, Dept Comp Sci & Engn, Kowloon, Clear Water Bay, Hong Kong, Peoples R China.;[Liu, Hongwei] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构:
[Xiaoqiang Wang] H;Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan, China
摘要:
Given a graph $G$ with $S \subseteq V_G$, 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 Physics,2023年64(5):051508 ISSN:0022-2488
通讯作者:
Wang, LS
作者机构:
[Tang, Zhongwei] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China.;[Wang, Lushun] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Peoples R China.;[Xie, Huafei] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构:
[Wang, LS ] Z;Zhejiang Normal Univ, Dept Math, Jinhua 321004, Peoples R China.
摘要:
This paper is devoted to a class of singularly perturbed nonlinear Schrodinger systems defined on a smooth bounded domain in R-N(N = 2,3). We use the Lyapunov-Schmidt reduction method to construct synchronized vector solutions with multiple spikes both on the boundary and in the interior of the domain. For each vector solution that has been constructed, we point out that the interior spikes locate near sphere packing points in the domain, and the boundary spikes locate near the critical points of the mean curvature function related to the boundary of the domain.
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:
The second Zagreb index;Lanzhou index;Forgotten index;Independence number;Bounds
期刊:
Linear Algebra and its Applications,2023年662:110-135 ISSN:0024-3795
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.
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.