期刊：
Journal of Differential Equations,2025年414:201-241 ISSN：0022-0396
通讯作者：
Chuang Xiang
作者机构：
[Jicai Huang; Min Lu] School of Mathematics and Statistics, Hubei Key Lab–Math. Sci., Central China Normal University, Wuhan, Hubei 430079, PR China;[Chuang Xiang] School of Mathematical Sciences and Key Laboratory of NSLSCS (Ministry of Education), Nanjing Normal University, Nanjing 210023, PR China;[Lan Zou] School of Mathematical Sciences, Capital Normal University, Beijing 100089, PR China
通讯机构：
[Chuang Xiang] S;School of Mathematical Sciences and Key Laboratory of NSLSCS (Ministry of Education), Nanjing Normal University, Nanjing 210023, PR China
期刊：
Applied Mathematics and Computation,2025年484:129018 ISSN：0096-3003
通讯作者：
Zihan Zhou
作者机构：
[Zihan Zhou] Faculty of Mathematics and Statistics, and Hubei Key Lab–Math. Sci., Central China Normal University, Wuhan 430079, China;Key Laboratory of Nonlinear Analysis & Applications (Ministry of Education), Central China Normal University, Wuhan 430079, China;[Shuchao Li] Faculty of Mathematics and Statistics, and Hubei Key Lab–Math. Sci., Central China Normal University, Wuhan 430079, China<&wdkj&>Key Laboratory of Nonlinear Analysis & Applications (Ministry of Education), Central China Normal University, Wuhan 430079, China
通讯机构：
[Zihan Zhou] F;Faculty of Mathematics and Statistics, and Hubei Key Lab–Math. Sci., Central China Normal University, Wuhan 430079, China
摘要：
Characterizing the graph having the maximum or minimum spectral radius in a given class of graphs is a classical problem in spectral extremal graph theory, originally proposed by Brualdi and Solheid. Given a graph G, a vertex subset S is called a maximum generalized 4-independent set of G if the induced subgraph G[S] dose not contain a 4-tree as its subgraph, and the subset S has maximum cardinality. The cardinality of a maximum generalized 4-independent set is called the generalized 4-independence number of G. In this paper, we firstly determine the connected graph (resp. bipartite graph, tree) having the largest spectral radius over all connected graphs (resp. bipartite graphs, trees) with fixed order and generalized 4-independence number, in addition, we establish a lower bound on the generalized 4-independence number of a tree with fixed order. Secondly, we describe the structure of all the n-vertex graphs having the minimum spectral radius with generalized 4-independence number ψ, where ψ⩾⌈3n/4⌉. Finally, we identify all the connected n-vertex graphs with generalized 4-independence number ψ∈{3,⌈3n/4⌉,n−1,n−2} having the minimum spectral radius.
期刊：
Journal of Mathematical Analysis and Applications,2025年541(2):128726 ISSN：0022-247X
通讯作者：
Xiaolong Yang
作者机构：
[Chenchen Liu] School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China;[Xiaolong Yang] School of Mathematics and Statistics, Henan University, Kaifeng 475004, China
通讯机构：
[Xiaolong Yang] S;School of Mathematics and Statistics, Henan University, Kaifeng 475004, China
摘要：
We consider the existence of sign-changing solutions for the following nonlinear Choquard equation {−Δu=(Iα⁎|u|p)|u|p−2u+λu,x∈Ω,u∈H01(Ω), where N≥3,α∈(0,N),λ∈R, p∈(1,N+αN−2] and Ω⊂RN is a smooth bounded domain. Iα:RN→R is the Riesz potential. In critical case p=N+αN−2, if Ω is symmetric about the axis x1, we firstly develop the limit profiles for the symmetric Palais-Smale sequence by the concentration compactness principle. Then we conclude that the problem admits an odd solution with exactly two nodal domains for λ∈(0,λ1),N≥4andα∈(2,N). In contrast, the local Brezis-Nirenberg type problem −Δu=|u|4N−2u+λu,u∈H01(Ω) can not permit such type of odd symmetry solution.
摘要：
In a graph G, let rho(Delta)(G) denote the minimum size of a set of edges and triangles that cover all edges of G, and let alpha(1)(G) be the maximum size of an edge set that contains at most one edge from each triangle. Motivated by a question of Erdos, Gallai, and Tuza, we study the relationship between rho(Delta)(G) and alpha(1)(G) and establish a sharp upper bound on rho(Delta)(G). We also prove Nordhaus-Gaddum-type inequalities for the considered invariants. (c) 2024 The Author(s).
期刊：
Journal of Algebra,2025年661:123-159 ISSN：0021-8693
通讯作者：
Yuanyang Zhou
作者机构：
[Fuming Jiang; Yuanyang Zhou] School of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, PR China
通讯机构：
[Yuanyang Zhou] S;School of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, PR China
摘要：
We define inertial blocks of finite groups over arbitrary fields and prove that a block covered by an inertial block over a bigger field of characteristic p is still inertial if p is odd or if the inertial block has abelian defect groups. Combined with some known facts, this result implies that Broué's conjecture over arbitrary fields holds for many blocks, for example, blocks for p-solvable groups with abelian defect groups. Consequently, we partially prove Puig's finiteness conjecture for inertial blocks over fields with odd characteristic or with abelian defect groups.
期刊：
Journal of Mathematical Analysis and Applications,2025年543(2, Part 2):128937 ISSN：0022-247X
通讯作者：
Wei-Jie Wang
作者机构：
Hubei Key Laboratory of Mathematical Sciences, College of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei 430079, China;Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), College of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, China;[Wei-Jie Wang] Hubei Key Laboratory of Mathematical Sciences, College of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei 430079, China<&wdkj&>Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), College of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, China
通讯机构：
[Wei-Jie Wang] H;Hubei Key Laboratory of Mathematical Sciences, College of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei 430079, China<&wdkj&>Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), College of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, China
期刊：
Journal of Functional Analysis,2025年288(1):110671 ISSN：0022-1236
通讯作者：
Xiaohua Yao
作者机构：
[Miao Chen] Department of Mathematics, Central China Normal University, Wuhan, 430079, China;[Ping Li] School of Informations and Mathematics, Yangtze University, Jingzhou 434000, China;[Avy Soffer] Mathematics Department, Rutgers University, New Brunswick, NJ, 08903, USA;[Xiaohua Yao] Department of Mathematics and Key Laboratory of Nonlinear Analysis and Applications (Ministry of Education), Central China Normal University, Wuhan, 430079, China
通讯机构：
[Xiaohua Yao] D;Department of Mathematics and Key Laboratory of Nonlinear Analysis and Applications (Ministry of Education), Central China Normal University, Wuhan, 430079, China
期刊：
Journal of Mathematical Analysis and Applications,2025年543(1):128833 ISSN：0022-247X
通讯作者：
Shuai Li
作者机构：
School of Mathematics and Physics, Wuhan Institute of Technology, Wuhan 430205, People's Republic of China;[Shuai Li] College of Informatics, Huazhong Agricultural University, Wuhan 430070, People's Republic of China;[Peiye Zhong] School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, People's Republic of China;[Yongshuai Gao] School of Mathematics and Physics, Wuhan Institute of Technology, Wuhan 430205, People's Republic of China<&wdkj&>School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, People's Republic of China
通讯机构：
[Shuai Li] C;College of Informatics, Huazhong Agricultural University, Wuhan 430070, People's Republic of China
作者机构：
[Zhou, Zihan; Li, Shuchao] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.;[Zhou, Zihan; Li, Shuchao] Cent China Normal Univ, Key Lab Nonlinear Anal & Applicat, Minist Educ, Wuhan 430079, Peoples R China.;[Sun, Wanting] Shandong Univ, Data Sci Inst, Jinan 250100, Peoples R China.;[Wei, Wei] Shanghai Univ Engn Sci, Ctr Intelligent Comp & Appl Stat, Sch Math Phys & Stat, Shanghai 201620, Peoples R China.;[Zhang, Minjie; Zhang, MJ] Hubei Univ Arts & Sci, Sch Math & Stat, Xiangyang 441053, Peoples R China.
通讯机构：
[Zhang, MJ ] H;Hubei Univ Arts & Sci, Sch Math & Stat, Xiangyang 441053, Peoples R China.
关键词：
Signed mixed graph;Eisenstein matrix;Spectral radius
摘要：
A mixed graph M-G is obtained from a simple graph G by orienting an edge subset of G. A signed mixed graph is a mixed graph with arcs and edges signed + or -. The unit Eisenstein matrix (epsilon-matrix for short) of a signed mixed graph was recently introduced by Wissing and van Dam [32]. This novel matrix is indexed by the vertices of the signed mixed graph, and the entry corresponding to a positive arc from u to v is equal to omega = 1+i root 3/2 (and its symmetric entry is (omega) over bar = 1-i root 3/2); the entry corresponding to a negative arc is equal to -omega (and its symmetric entry is -(omega) over bar); the entry corresponding to a positive edge is equal to 1; the entry corresponding to a negative edge is equal to -1; and 0 otherwise. In this paper, we study the spectral properties of this epsilon-matrix. We characterize all the signed mixed graphs whose eigenvalues are contained in (-alpha, alpha) for alpha is an element of {root 2, root 3, root 2} .(c) 2023 Elsevier B.V. All rights reserved.
期刊：
DESIGNS CODES AND CRYPTOGRAPHY,2024年:1-24 ISSN：0925-1022
通讯作者：
Yu, ZH
作者机构：
[Yu, Zihao; Liu, Hongwei; Yu, ZH] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Yu, ZH ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
关键词：
Linear code;Subfield code;Simplicial complex;Griesmer code
摘要：
In this article we mainly study linear codes over
$${\mathbb {F}}_{2^n}$$
and their binary subfield codes. We construct linear codes over
$${\mathbb {F}}_{2^n}$$
whose defining sets are the certain subsets of
$${\mathbb {F}}_{2^n}^m$$
obtained from mathematical objects called simplicial complexes. We will consider simplicial complexes with one maximal element. The relation of the weights of codewords in two special codes obtained from simplicial complexes is illustrated by using LFSR sequences. And then we determine the parameters of these codes with the help of Boolean functions. As a result, we obtain five infinite families of distance optimal codes and give sufficient conditions for these codes to be minimal.
期刊：
Journal of Inverse and Ill-posed Problems,2024年0:- ISSN：0928-0219
通讯作者：
Xiang, JL
作者机构：
[Xiang, Jianli; Xiang, JL] China Three Gorges Univ, Coll Sci, Three Gorges Math Res Ctr, Yichang 443002, Peoples R China.;[Yan, Guozheng] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Yan, Guozheng] Hubei Key Lab Math Phys, Wuhan, Peoples R China.
通讯机构：
[Xiang, JL ] C;China Three Gorges Univ, Coll Sci, Three Gorges Math Res Ctr, Yichang 443002, Peoples R China.
摘要：
Consider time-harmonic electromagnetic wave scattering by an infinitely long, cylindrical, orthotropic dielectric partially coated with a very thin layer of a highly conductive material, which can be modeled by a transmission problem with mixed boundary conditions. Having established the well-posedness of the direct and interior transmission problem by the variational method under certain conditions, we make use of the classical linear sampling method to reconstruct the shape of the obstacle. Then, based on a modification of the general data-to-pattern operator G, we propose a novel and simple method to justify the modified linear sampling method.
摘要：
We study a new family of metrics, weighted poset block metric, which generalizes the weighted coordinates poset metric introduced by Panek and Pinheiro (IEEE Trans Inf Theory 66(11):6823–6834, 2020) and the metric for linear error-block codes introduced by Feng et al. (Finite Fields Appl 12(4):638–652, 2006). This metric covers various metrics such as Hamming metric, Lee metric, poset metric, pomset metric, poset block metric, pomset block metric and so on. We give a complete description of the groups of linear isometries of these metric spaces in terms of a semi-direct product. Moreover, we obtain a Singleton type bound for codes equipped with weighted poset block metric and define MDS codes. When the poset is a chain, we study the relationship between MDS codes and perfect codes.
摘要：
Let mu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document} be a Borel probability measure with compact support on R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}$$\end{document}, we say mu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document} is a spectral measure if there exists a countable set Lambda subset of R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Lambda \subset {\mathbb {R}}$$\end{document} such that the collection of exponential functions E(Lambda):={e-2 pi i <lambda,x >:lambda is an element of Lambda}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E(\Lambda ):=\{e<^>{-2\pi i\langle \lambda , x\rangle }: \lambda \in \Lambda \}$$\end{document} forms an orthonormal basis for the Hilbert space L2(mu)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L<^>2(\mu )$$\end{document}. In this case, Lambda\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Lambda $$\end{document} is called a spectrum of mu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document}. In this paper, we first characterize the spectral structure of self-similar spectral measures mu t,D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu _{t,D}$$\end{document} on R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}$$\end{document}, where D is a strict product-form digit set with respect to an integer b and t is an integer which has a proper factor b. And then we settle the spectral eigenvalue (or scaling spectrum) problem for the spectral measure mu t,D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu _{t,D}$$\end{document}.
作者机构：
[Huang, Jing] Guangzhou Univ, Sch Math & Informat Sci, Guangzhou, Peoples R China.;[Geng, Xianya] Anhui Univ Sci & Technol, Sch Math & Big Data, Huainan, Peoples R China.;[Zhou, Zihan] Cent China Normal Univ, Fac Math & Stat, Wuhan, Peoples R China.;[Zhou, Zihan] Cent China Normal Univ, Key Lab Nonlinear Anal & Applicat, Minist Educ, Wuhan, Peoples R China.
通讯机构：
[Zhou, ZH ] C;Cent China Normal Univ, Fac Math & Stat, Wuhan, Peoples R China.;Cent China Normal Univ, Key Lab Nonlinear Anal & Applicat, Minist Educ, Wuhan, Peoples R China.
摘要：
Identifying the graph with maximum or minimum spectral radius among a given class of graphs is a central problem in extremal spectral graph theory, known as the Brualdi- Solheid problem. For a graph G = (V-G, E-G), a subset S subset of V-G is called a maximum dissociation set if the induced subgraph G[S] does not contain P-3 as its subgraph, and the subset has maximum cardinality. The dissociation number of G is the number of vertices in a maximum dissociation set of G. In this paper, we first characterize all the connected graphs (resp. bipartite graphs, trees) having maximum spectral radius among connected graphs (resp. bipartite graphs, trees) with given order and dissociation number. Secondly, we show that the connected n-vertex graph with dissociation number phi having minimum spectral radius is a tree, where phi >= [2/3n] . Finally, we determine the graphs having minimum spectral radius with fixed order n and dissociation number phi is an element of {2, [2n/3], n - 1, n - 2}.(c) 2023 Elsevier B.V. All rights reserved.
摘要：
A graph G has a
$${\mathcal {P}}_{\geqslant k}$$
-factor if G has a spanning subgraph H such that every component of H is a path of order at least k. A graph G is
$${\mathcal {P}}_{\geqslant k}$$
-factor deleted if
$$G-e$$
has a
$${\mathcal {P}}_{\geqslant k}$$
-factor for each edge e of G. In this paper, we give two necessary and sufficient conditions defining a
$${\mathcal {P}}_{\geqslant 2}$$
-factor deleted graph and a
$${\mathcal {P}}_{\geqslant 3}$$
-factor deleted graph, respectively. Based on the result of
$${\mathcal {P}}_{\geqslant 2}$$
-factor deleted graphs, we establish respectively a lower bound on the size and a lower bound on the spectral radius to ensure whether or not a graph is
$${\mathcal {P}}_{\geqslant 2}$$
-factor deleted. Furthermore, by constructing extremal graphs, we show that all the above bounds are best possible.
关键词：
cell signaling pathway;epidermal growth factor;inference;mathematical model;mitogen-activated protein kinase;single cell
摘要：
The mitogen-activated protein kinase (MAPK) pathway is an important intracellular signaling cascade that plays a key role in various cellular processes. Understanding the regulatory mechanisms of this pathway is essential for developing effective interventions and targeted therapies for related diseases. Recent advances in single-cell proteomic technologies have provided unprecedented opportunities to investigate the heterogeneity and noise within complex, multi-signaling networks across diverse cells and cell types. Mathematical modeling has become a powerful interdisciplinary tool that bridges mathematics and experimental biology, providing valuable insights into these intricate cellular processes. In addition, statistical methods have been developed to infer pathway topologies and estimate unknown parameters within dynamic models. This review presents a comprehensive analysis of how mathematical modeling of the MAPK pathway deepens our understanding of its regulatory mechanisms, enhances the prediction of system behavior, and informs experimental research, with a particular focus on recent advances in modeling and inference using single-cell proteomic data.
摘要：
The sampling importance resampling method is widely utilized in various fields, such as numerical integration and statistical simulation. In this paper, two modified methods are presented by incorporating two variance reduction techniques commonly used in Monte Carlo simulation, namely antithetic sampling and Latin hypercube sampling, into the process of sampling importance resampling method, respectively. Theoretical evidence is provided to demonstrate that the proposed methods significantly reduce estimation errors compared to the original approach. Furthermore, the effectiveness and advantages of the proposed methods are validated through both numerical studies and real data analysis.
关键词：
Compressible Navier-Stokes-Allen-Cahn system;Strong/classical solutions;Density-dependent viscosity;Large initial data
摘要：
This paper is concerned with a one-dimensional isentropic compressible Navier-Stokes-Allen-Cahn system with density-dependent viscosity, which models the motion of a mixture of two viscous compressible fluids. The case when the pressure $ p(\rho) = \rho^\gamma $, the viscosity $ \nu(\rho, \chi) = \rho^\alpha $, the interface thickness $ \delta(\rho) = \rho^\beta $ and the relaxation time function $ a(\rho, \chi, \chi_y) = \rho^\lambda $ is considered, where $ \rho $ and $ \chi $ are the density and the phase variable, respectively, and $ \gamma, \alpha, \beta, \lambda\in\mathbb{R} $ are parameters. Under some suitable assumptions on the parameters $ \gamma , \alpha, \beta, \lambda $ and the initial data, we prove the global existence and large-time behavior of nonvacuum strong and classical solutions to its Cauchy problem with large initial data. This appears to be the first global existence result on the Cauchy problem of the compressible Navier-Stokes-Allen-Cahn system with density-dependent viscosity and large data.
期刊：
Journal of Mathematical Analysis and Applications,2024年530(1):127636 ISSN：0022-247X
通讯作者：
Duan, R
作者机构：
[Duan, Ran; Chang, Shengchuang] Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Duan, R ] C;Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
关键词：
Navier-Stokes-quantum equations;Rayleigh-Taylor instability;Hadamard sense
摘要：
Consider the linear and nonlinear Rayleigh-Taylor instability of the three-dimensional incompressible viscous Navier-Stokes-Quantum equations. For linearized problem, we determine the critical number.cprecisely. Then, we construct a linear growth solution by a modified variational method for k <.k(c). In addition, we show that.cis infinite for a special steady state <(rho)over bar>, which implies that quantum potential inhibit the instability instead of cutting it off. Based on this unstable linear solution and the priori estimates of the smooth solution to the perturbed problem, we establish the nonlinear instability of the density and the velocities in the sense of Hadamard. Compared with the related study on Navier-Stokes-Korteweg equations (Zhang (2022) [41]), we do not ask the capillarity coefficient to be small. (c) 2023 Elsevier Inc. All rights reserved.
