期刊：
Journal of Pure and Applied Algebra,2023年227(7):107322 ISSN：0022-4049
通讯作者：
Chengkang Xu
作者机构：
[Guo, Hongyan] Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Xu, Chengkang] Shangrao Normal Univ, Shangrao, Jiangxi, Peoples R China.
通讯机构：
[Chengkang Xu] S;Shangrao Normal University, Shangrao, Jiangxi, China
摘要：
This paper studies restricted modules of gap-p Virasoro algebra g(p) and their intrinsic connection to twisted modules of certain vertex algebras. We first establish an equivalence between the category of restricted g(p)-modules of level (l) under bar and the category of twisted modules of vertex algebra V-Np((l) under bar, 0), where N-p is a new Lie algebra, (l) under bar :=(l(0), 0, center dot center dot center dot, 0) is an element of C[p/2]+1, l(0) is an element of C is the action of the Virasoro center. Then we focus on the construction and classification of simple restricted g(p)-modules of level (l) under bar. More explicitly, we give a uniform construction of simple restricted g(p)-modules as induced modules. We present several equivalent characterizations of simple restricted g(p)-modules, as locally nilpotent (equivalently, locally finite) modules with respect to certain positive part of g(p). Moreover, simple restricted g(p)-modules of level (l) under bar are classified. They are either highest weight modules or simple induced modules. At the end, we exhibit several concrete examples of simple restricted g(p)-modules of level (l) under bar (including Whittaker modules). (c) 2023 Elsevier B.V. All rights reserved.
摘要：
In this article, we investigate the asymptotic behavior of solutions for a non-autonomous regularized magnetohydrodynamics equations on 3D bounded domains. More precisely, the upper bounds on the number of determining modes and determining nodes for the system are established. The results show that the asymptotic behavior of the weak solution can be determined completely by its first finite number of Fourier modes and the large time behavior of the strong solution can be determined by its values on a finite number of points.
关键词：
The linearized Moser-Trudinger problem;The first eigenvalue;The first eigenfunction;Asymptotic behavior
摘要：
We revisit the following Moser-Trudinger problem {−Δu=λueu2in Ω,u>0in Ω,u=0on ∂Ω,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \textstyle\begin{cases} -\Delta u=\lambda ue^{u^{2}} &\text{in } \Omega , \\ u>0&\text{in } \Omega , \\ u=0 &\text{on } \partial \Omega , \end{cases} $$\end{document} where Ω⊂R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Omega \subset \mathbb{R}^{2}$\end{document} is a smooth bounded domain and λ>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\lambda >0$\end{document} is sufficiently small. Qualitative analysis of peaked solutions for Moser-Trudinger type equation in R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb{R}^{2}$\end{document} has been widely studied in recent decades. In this paper, we continue to consider the qualitative properties of the eigenvalues and eigenfunctions for the corresponding linearized Moser-Trudinger problem by using a variety of local Pohozaev identities combined with some elliptic theory in dimension two. Here we give some fine estimates for the first eigenvalue and eigenfunction of the linearized Moser-Trudinger problem. Since this problem is a critical exponent for dimension two and will lose compactness, we have to obtain some new and technical estimates.
期刊：
Journal of Mathematical Biology,2023年86(6):1-45 ISSN：0303-6812
通讯作者：
Huang, JC;Wang, H
作者机构：
[Zhang, Yuyue; Huang, Jicai] Cent China Normal Univ, Sch Math & Stat, Minist Educ, Wuhan 430079, Hubei, Peoples R China.;[Zhang, Yuyue; Huang, Jicai] Cent China Normal Univ, Key Lab Nonlinear Anal & Applicat, Minist Educ, Wuhan 430079, Hubei, Peoples R China.;[Wang, Hao] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada.;[Wang, Hao] Univ Alberta, Interdisciplinary Lab Math Ecol & Epidemiol, Edmonton, AB T6G 2G1, Canada.
通讯机构：
[Wang, H ] U;[Huang, JC ] C;Cent China Normal Univ, Sch Math & Stat, Minist Educ, Wuhan 430079, Hubei, Peoples R China.;Cent China Normal Univ, Key Lab Nonlinear Anal & Applicat, Minist Educ, Wuhan 430079, Hubei, Peoples R China.;Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada.
关键词：
Degenerate Bogdanov–Takens bifurcation;Generalist predator;Nilpotent cusp of codimension 4;Nilpotent focus of codimension 3;Predator–prey model;Specialist predator
摘要：
In this paper, we revisit a predator-prey model with specialist and generalist predators proposed by Hanski et al. (J Anim Ecol 60:353-367, 1991) , where the density of generalist predators is assumed to be a constant. It is shown that the model admits a nilpotent cusp of codimension 4 or a nilpotent focus of codimension 3 for different parameter values. As the parameters vary, the model can undergo cusp type (or focus type) degenerate Bogdanov-Takens bifurcations of codimension 4 (or 3). Our results indicate that generalist predation can induce more complex dynamical behaviors and bifurcation phenomena, such as three small-amplitude limit cycles enclosing one equilibrium, one or two large-amplitude limit cycles enclosing one or three equilibria, three limit cycles appearing in a Hopf bifurcation of codimension 3 and dying in a homoclinic bifurcation of codimension 3. In addition, we show that generalist predation stabilizes the limit cycle driven by specialist predators to a stable equilibrium, which clearly explains the famous Fennoscandia phenomenon.
期刊：
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY,2023年108(2):187-199 ISSN：0004-9727
通讯作者：
MINJIE ZHANG
作者机构：
[Miao, Shujing; 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：
[MINJIE ZHANG] S;School of Mathematics and Statistics, Hubei University of Arts and Science, Xiangyang 441053, PR China
摘要：
We first establish a lower bound on the size and spectral radius of a graph G to guarantee that G contains a fractional perfect matching. Then, we determine an upper bound on the distance spectral radius of a graph G to ensure that G has a fractional perfect matching. Furthermore, we construct some extremal graphs to show all the bounds are best possible.
期刊：
Mathematical Methods in the Applied Sciences,2023年46(5):5099-5118 ISSN：0170-4214
通讯作者：
Hangzhou Hu<&wdkj&>Hangzhou Hu Hangzhou Hu Hangzhou Hu
作者机构：
[Hu, Hangzhou; Zhao, Dun] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Gansu, Peoples R China.;[Li, Yuan] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
通讯机构：
[Hangzhou Hu; Hangzhou Hu Hangzhou Hu Hangzhou Hu] S;School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000 Gansu, China
关键词：
asymptotic behavior;ground states;NLS equations;periodic magnetic field;variational methods for second-order elliptic equations;XFEL Schrodinger equation
摘要：
We consider the following X‐ray free electron lasers Schrödinger equation (i∇−A)2u+V(x)u−μ|x|u=1|x|∗|u|2u−K(x)|u|q−2u,x∈ℝ3,$$ {\left(i\nabla -A\right)}&#x0005E;2u&#x0002B;V(x)u-\frac{\mu }{\mid x\mid }u&#x0003D;\left(\frac{1}{\mid x\mid}\ast {\left&#x0007C;u\right&#x0007C;}&#x0005E;2\right)u-K(x){\left&#x0007C;u\right&#x0007C;}&#x0005E;{q-2}u,x\in {\mathbb{R}}&#x0005E;3, $$ where A∈Lloc2(ℝ3,ℝ3)$$ A\in {L}_{loc}&#x0005E;2\left({\mathbb{R}}&#x0005E;3,{\mathbb{R}}&#x0005E;3\right) $$ denotes the magnetic potential such that the magnetic field B=curlA$$ B&#x0003D;\operatorname{curl}\kern0.4em A $$ is ℤ3$$ {\mathbb{Z}}&#x0005E;3 $$‐periodic, μ∈ℝ,K∈L∞ℝ3$$ \mu \in \mathbb{R},K\in {L}&#x0005E;{\infty}\left({\mathbb{R}}&#x0005E;3\right) $$ is ℤ3$$ {\mathbb{Z}}&#x0005E;3 $$ periodic and non‐negative, q∈(2,4)$$ q\in \left(2,4\right) $$. Using the variational method, based on a profile decomposition of the Cerami sequence in HA1ℝ3$$ {H}_A&#x0005E;1\left({\mathbb{R}}&#x0005E;3\right) $$, we obtain the existence of the ground state solution for suitable μ≥0$$ \mu \ge 0 $$. When μ<0$$ \mu &lt;0 $$ is small, we also obtain the non‐existence. Furthermore, we give a description of the asymptotic behavior of the ground states as μ→0+$$ \mu \to {0}&#x0005E;{&#x0002B;} $$.
作者机构：
[Liu, Zhongyuan] Henan Univ, Sch Math & Stat, Kaifeng 475004, Peoples R China.;[Luo, Peng] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Luo, Peng] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Peng Luo] S;School of Mathematics and Statistics and Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, China
摘要：
In this paper, we study the following critical elliptic problem with a variable exponent:
$$\left\{ {\matrix{{ - \Delta u = {u^{p + \epsilon a\left( x \right)}}} \hfill & {{\rm{in}}\,\,\Omega ,} \hfill \cr {u > 0} \hfill & {{\rm{in}}\,\,\Omega ,} \hfill \cr {u = 0} \hfill & {{\rm{on}}\,\partial \Omega ,} \hfill \cr } } \right.$$
where
$$a\left( x \right) \in {C^2}\left( {\overline \Omega } \right),\,p = {{N + 2} \over {N - 2}},\,\,\epsilon > 0$$
, and Ω is a smooth bounded domain in ℝN (N ≽ 4). We show that for ∊ small enough, there exists a family of bubble solutions concentrating at the negative stable critical point of the function a(x). This is a new perturbation to the critical elliptic equation in contrast to the usual subcritical or supercritical perturbation, and gives the first existence result for the critical elliptic problem with a variable exponent.
期刊：
Journal of Algebra,2023年636:42-74 ISSN：0021-8693
通讯作者：
Wang, Q
作者机构：
[Guo, Hongyan] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Guo, Hongyan] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Li, Haisheng] Rutgers State Univ, Dept Math Sci, Camden, NJ 08102 USA.;[Wang, Qing; Tan, Shaobin] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China.
通讯机构：
[Wang, Q ] X;Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China.
摘要：
In this paper, we study a family of infinite-dimensional Lie algebras X ⠂S, where X stands for the type: A, B, C, D, and S is an abelian group, which generalize the A, B, C, D series of trigonometric Lie algebras. Among the main results, we identify X ⠂S with what are called the covariant algebras of the affine Lie algebra L ⠃S with respect to some automorphism groups, where LS is an explicitly defined associative algebra X ⠂S- viewed as a Lie algebra. We then show that restricted modules of level $ naturally correspond to equivariant quasi modules for affine vertex algebras related to LS. Furthermore, for any finite cyclic group S, we completely determine the structures of these four families of Lie algebras, showing that they are essentially affine Kac-Moody Lie algebras of certain types.& COPY; 2023 Elsevier Inc. All rights reserved.
作者机构：
[Li, Shuchao; Sun, Wanting] Cent China Normal Univ, Fac Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, 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：
Second largest eigenvalue;Spectral radius;Spectral Turán type problem;{C3,C5}-free graph
摘要：
In this paper we consider the extremal problem on adjacency spectral radius of {C-3, C-5}-free graphs. Assume that G is a graph with m edges having no isolated vertices, and let lambda be the spectral radius of its adjacency matrix. Firstly, by using the method of characterizing {C-3, C-5}-free non-bipartite graphs whose second largest eigenvalue is less than 4 root 5, we show that, if G is a {C-3, C-5}-free non-bipartite graph of size m, then [GRAPHICS] . Equality holds if and only if G congruent to C-7, where d(u) is the degree of vertex u and f denotes the number of 4-cycles in G. Secondly, we show that, if G is a {C-3, C-5}-free non-bipartite graph of odd size m, then lambda <= theta(m) with equality if and only if G congruent to RK2, m-3/2, where theta(m) is the largest root of chi(4) - chi(3) - (m - 3)chi(2) + (m - 4)chi + m - 5 = 0 and RK2, m-3/2 is obtained by replacing an edge of the complete bipartite graph K-2,K- m-3/2 with P5. (c) 2023 Elsevier B.V. All rights reserved.
摘要：
Let G be a graph. For two positive integers d and h, a (d, h)-decomposition of G is a pair (G, H) such that H is a subgraph of G of maximum degree at most h and D is an acyclic orientation of G-E(H)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G-E(H)$$\end{document} of maximum out-degree at most d. A graph G is (d, h)-decomposable if G has a (d, h)-decomposition. In this paper, we prove that every planar graph without intersecting 3-cycles and adjacent 4-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$4^-$$\end{document}-cycles is (2, 1)-decomposable. As a corollary, we obtain that every planar graph without intersecting 3-cycles and adjacent 4-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$4^-$$\end{document}-cycles has a matching M such that G-M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G-M$$\end{document} is 2-degenerate and hence G-M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G-M$$\end{document} is DP-3-colorable and Alon-Tarsi number of G-M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G-M$$\end{document} is at most 3.
期刊：
Calculus of Variations and Partial Differential Equations,2023年62(3):1-35 ISSN：0944-2669
通讯作者：
Peng Luo
作者机构：
[Luo, Peng; Zhou, Yang; Peng, Shuangjie] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Luo, Peng; Peng, Shuangjie] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Peng Luo] S;School of Mathematics and Statistics and Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, China
关键词：
35A01;35B25;35J20;35J60
摘要：
We revisit the well known prescribed scalar curvature problem
$$\begin{aligned} {\left\{ \begin{array}{ll} -\Delta u=\big (1+\varepsilon K(x)\big )u^{2^*-1}, u(x)>0,~~ &{}{x\in \mathbb {R}^N},\\ u\in \mathcal {D}^{1,2}(\mathbb {R}^N),\\ \end{array}\right. } \end{aligned}$$
where
$$2^*=\frac{2N}{N-2}$$
,
$$N\ge 5$$
,
$$\varepsilon >0$$
and
$$K(x)\in C^1(\mathbb {R}^N)\cap L^{\infty }(\mathbb {R}^N)$$
. It is known that there are a number of results related to the existence of solutions concentrating at the isolated critical points of K(x). However, if K(x) has non-isolated critical points with different degenerate rates along different directions, whether there exist solutions concentrating at these points is still an open problem. We give a certain positive answer to this problem via applying a blow-up argument based on local Pohozaev identities and modified finite dimensional reduction method when the dimension of critical point set of K(x) ranges from 1 to
$$N-1$$
, which generalizes some results in Cao et al. (Calc Var Partial Differ Equ 15:403–419, 2002) and Li (J Differ Equ 120:319–410, 1995; Commun Pure Appl Math 49:541–597, 1996).
摘要：
Cancer is a complex disease caused primarily by genetic variants. Reconstructing gene networks within tumors is essential for understanding the functional regulatory mechanisms of carcinogenesis. Advances in high-throughput sequencing technologies have provided tremendous opportunities for inferring gene networks via computational approaches. However, due to the heterogeneity of the same cancer type and the similarities between different cancer types, it remains a challenge to systematically investigate the commonalities and specificities between gene networks of different cancer types, which is a crucial step towards precision cancer diagnosis and treatment. In this study, we propose a new sparse regularized multi-layer decomposition graphical model to jointly estimate the gene networks of multiple cancer types. Our model can handle various types of gene expression data and decomposes each cancer-type-specific network into three components, i.e., globally shared, partially shared and cancer-type-unique components. By identifying the globally and partially shared gene network components, our model can explore the heterogeneous similarities between different cancer types, and our identified cancer-type-unique components can help to reveal the regulatory mechanisms unique to each cancer type. Extensive experiments on synthetic data illustrate the effectiveness of our model in joint estimation of multiple gene networks. We also apply our model to two real data sets to infer the gene networks of multiple cancer subtypes or cell lines. By analyzing our estimated globally shared, partially shared, and cancer-type-unique components, we identified a number of important genes associated with common and specific regulatory mechanisms across different cancer types.(c) 2023 The Author(s). Published by Elsevier B.V. on behalf of Research Network of Computational and Structural Biotechnology. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
作者机构：
[Qi, Yingfan; Cao, Rongjun; Chen, Minghua; Shi, Jiankang] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Peoples R China.;[Yin, Xiaobo] Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Chen, MH ] L;Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Peoples R China.
关键词：
Asymptotically compatible scheme;Nonlocal model;Shifted-symmetric collocation;Stability and convergence analysis
摘要：
The piecewise quadratic polynomial collocation is used to approximate the nonlocal model, which generally leads to a nonsymmetric indefinite system (Chen et al. (2021) [5]). In this case, the discrete maximum principle is not satisfied, which might be trickier for the stability analysis of the high-order numerical schemes (D'Elia et al. (2020) [10]; Leng et al. (2021) [26]). Here, we present a modified (shifted-symmetric) piecewise quadratic polynomial collocation for solving the linear nonlocal diffusion model, which leads to a symmetric positive definite system and satisfies the discrete maximum principle. Using Faulhaber's formula and Riemann zeta function, the perturbation error for symmetric positive definite system and nonsymmetric indefinite system are given. Then rigorous convergence analysis for the nonlocal models are provided under the general horizon parameter delta = O (h beta), with beta >= 0. More concretely, the global error is O (hmin{2,1+beta}) if delta is not set as a grid point, while it recovers O (hmax{2,4-2 beta}) when delta is set as a grid point. We also prove that the shifted-symmetric scheme is asymptotically compatible, which has the global error O (hmin{2,2 beta}) as delta, h -> 0. The numerical experiments (including two-dimensional case) are performed to verify the convergence.(c) 2022 IMACS. Published by Elsevier B.V. All rights reserved.
期刊：
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS,2023年22(1):304-317 ISSN：1534-0392
通讯作者：
Wu, S
作者机构：
[Wu, Shuang; Wu, S; Gao, Yongshuai; Guo, Yujin] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Guo, Yujin] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Wu, S ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
期刊：
Complex Analysis and Operator Theory,2023年17(8):1-18 ISSN：1661-8254
通讯作者：
Chen, ML
作者机构：
[Zheng, Jia] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.;[Zheng, Jia] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Hubei, Peoples R China.;[Chen, Ming-Liang] Gannan Normal Univ, Sch Math & Comp Sci, Ganzhou 341000, Jiangxi, Peoples R China.
通讯机构：
[Chen, ML ] G;Gannan Normal Univ, Sch Math & Comp Sci, Ganzhou 341000, Jiangxi, Peoples R China.
关键词：
Iterated function system;Self-affine measure;Orthogonality;Spectrality
摘要：
Ever since Jorgensen and Pedersen (J Anal Math 75:185-228, 1998) discovered the first singular spectral measure, the spectral and non-spectral problems of fractal measures have received a lot of attention in recent years. In this work, we study the planar self-affine measure
$$\mu _{M,D}$$
generated by an expanding matrix
$$M\in M_2(\mathbb {Z})$$
and a collinear digit set
$$D=\{0,d_1,d_2,d_3\}\varvec{v}$$
, where
$$\varvec{v}\in \mathbb {Z}^2\backslash \{\varvec{0}\}$$
and
$$d_1,d_2,d_3$$
are different non-zero integers. For the case that
$$\{\varvec{v},M\varvec{v}\}$$
is linearly dependent, the sufficient and necessary condition for
$$\mu _{M,D}$$
to be a spectral measure is given. Moreover, we estimate the number of orthogonal exponential functions in
$$L^2(\mu _{M,D})$$
and give the exact maximal cardinality when
$$\mu _{M,D}$$
is a non-spectral measure. At the same time, partial results are also obtained for the case that
$$\{\varvec{v},M\varvec{v}\}$$
is linearly independent.
作者机构：
[Yu, Yuantian; Li, Shuchao] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.;[Zhang, Huihui; Zhang, HH] Luoyang Normal Univ, Dept Math, Luoyang 471934, Peoples R China.
通讯机构：
[Zhang, HH ] L;Luoyang Normal Univ, Dept Math, Luoyang 471934, Peoples R China.
摘要：
Given a graph G and 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), written as lambda(alpha)(G), is called the A alpha-index of G. A set of cycles in a graph G is called independent if no two cycles in it have a common vertex in G. For n > 2k - 1, let S-n,S- 2k-1 be the join of a clique on 2k - 1vertices with an independent set of n - (2k - 1) vertices. The famous Erdos-Posa theorem shows that for k >= 2 and n >= 24k, every n-vertex graph G with at least (2k - 1)(n - k) edges contains kindependent cycles, unless G congruent to S-n,S- 2k-1. In this paper, we consider an A(alpha)-spectral version of this theorem. We show that for fixed k >= 1, 0 < alpha < 1and n >= 104k(3)/alpha(a)(1- alpha), if an n-vertex graph Gsatisfies lambda(alpha)(G) >= lambda(alpha)(S-n,S- 2k-1), then it contains kindependent cycles, unless G congruent to Sn, 2k-1. This extends the result of Zhai and Liu (2022), in which they obtained the adjacency spectral version of the Erd.os-Posa theorem. (c) 2023 Elsevier B.V. All rights reserved.
期刊：
Mathematical Methods in the Applied Sciences,2023年46(2):2275-2287 ISSN：0170-4214
通讯作者：
Zhiyuan Li<&wdkj&>Zhiyuan Li Zhiyuan Li Zhiyuan Li
作者机构：
[Jiang, Daijun] Cent China Normal Univ, Hubei Key Lab Math Sci, Sch Math & Stat, Wuhan, Peoples R China.;[Li, Zhiyuan] Ningbo Univ, Sch Math & Stat, 818 Fenghua Rd, Ningbo 315211, Zhejiang, Peoples R China.;[Pauron, Matthieu] ENS Rennes, Bruz, France.;[Yamamoto, Masahiro] Univ Tokyo, Grad Sch Math Sci, Tokyo, Japan.;[Yamamoto, Masahiro] Acad Romanian Scientists, Bucharest, Romania.
通讯机构：
[Zhiyuan Li; Zhiyuan Li Zhiyuan Li Zhiyuan Li] S;School of Mathematics and Statistics, Ningbo University, 818 Fenghua Road, Zhejiang, Ningbo, China
摘要：
In this article, we discuss a solution to time-fractional diffusion equation partial differential t alpha(u-u0)+Au=0$$ {\partial}_t<^>{\alpha}\left(u-{u}_0\right)+ Au=0 $$ with the homogeneous Dirichlet boundary condition, where an elliptic operator -A$$ -A $$ is not necessarily symmetric. We prove that the solution u$$ u $$ is identically zero if its normal derivative with respect to the operator A$$ A $$ vanishes on an arbitrarily chosen subboundary of the spatial domain over a time interval. The proof is based on the Laplace transform and the spectral decomposition for a nonsymmetric elliptic operator. As a direct application, we prove the uniqueness result for an inverse problem on determining the spatial component in the source term by Neumann boundary data on subdoundary.
期刊：
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY,2023年376(05):3063-3085 ISSN：0002-9947
作者机构：
[Yau, Shing-Tung] Harvard Univ, Dept Math, Cambridge, MA 02138 USA.;[Zhao, Quanting] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Zhao, Quanting] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Zheng, Fangyang] Chongqing Normal Univ, Sch Math Sci, Chongqing 401331, Peoples R China.
摘要：
In this paper, we study a special type of compact Hermitian manifolds that are Strominger Ka.hler-like, or SKL for short. This condition means that the Strominger connection (also known as Bismut connection) is Ka.hler-like, in the sense that its curvature tensor obeys all the symmetries of the curvature of a Ka.hler manifold. Previously, we have shown that any SKL manifold (Mn, g) is always pluriclosed, and when the manifold is compact and g is not Ka.hler, it cannot admit any balanced or strongly Gauduchon (in the sense of Popovici) metric. Also, when n = 2, the SKL condition is equivalent to the Vaisman condition. In this paper, we give a classification for compact non-Ka.hler SKL manifolds in dimension 3 and those with degenerate torsion in higher dimensions. We also present some properties about SKL manifolds in general dimensions, for instance, given any compact non-Ka.hler SKL manifold, its Ka.hler form represents a non-trivial Aeppli cohomology class, the metric can never be locally conformal Ka.hler when n >= 3, and the manifold does not admit any Hermitian symplectic metric.
