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：
Complex Analysis and Operator Theory,2023年17(1):1-17 ISSN：1661-8254
通讯作者：
Min-Min Zhang
作者机构：
[Zhang, Min-Min; Wei, Saidi] Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Min-Min Zhang] H;Hubei Key Laboratory of Mathematical Sciences, School of Mathematics and Statistics, Central China Normal University, Wuhan, People’s Republic of China
摘要：
Let
$$\mu _{M,D}$$
be the self-affine measure associated with an expanding integer matrix
$$M=\left( \begin{array}{cc} p &{} 0 \\ 0 &{} q \\ \end{array}\right) $$
and
$$D=\left\{ \,\,\begin{pmatrix} 0\\ 0 \end{pmatrix},\,\,\,\begin{pmatrix} 1\\ 1 \end{pmatrix} \,\,\right\} $$
, where |p| and |q| are distinct odd bigger than 1. Such a measure is the simplest and the most important case in the study of the spectral property of self-affine measures with two-elements digit sets, which is an open problem up to now. In this paper, we first construct two classes of 4-element orthogonal exponentials in the corresponding Hilbert space
$$L^2(\mu _{M,D})$$
. Moreover, we prove that, under certain conditions, the constructed 4-element orthogonal exponentials is maximal.
期刊：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS,2023年43(1):482-506 ISSN：1078-0947
通讯作者：
Angela Pistoia
作者机构：
[Chen, Haixia] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.;[Pistoia, Angela] Sapienza Univ Roma, Dipartimento Sci Base & Applicate Ingn, Rome, Italy.;[Vaira, Giusi] Univ Bari Aldo Moro, Dipartimento Matemat, Bari, Italy.
通讯机构：
[Angela Pistoia] D;Dipartimento di Scienze di Base e Applicate per l'Ingegneria, Sapienza Università di Roma, Italy
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.
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.
作者机构：
[Yuan, Ganghua] Northeast Normal Univ, Sch Math & Stat, KLAS, Changchun 130024, Jilin, Peoples R China.;[Zhao, Yue; Zhao, Y] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Zhao, Y ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
期刊：
Journal of Functional Analysis,2023年284(6):109816 ISSN：0022-1236
通讯作者：
Xiaohua Yao
作者机构：
[Li, Ping] Yangtze Univ, Sch Informat & Math, Jingzhou 434000, Peoples R China.;[Soffer, Avy] Rutgers State Univ, Math Dept, New Brunswick, NJ 08903 USA.;[Yao, Xiaohua] Cent China Normal Univ, Dept Math, Wuhan 430079, Peoples R China.;[Yao, Xiaohua] Cent China Normal Univ, Hubei Prov Key Lab Math Phys, Wuhan 430079, Peoples R China.
通讯机构：
[Xiaohua Yao] D;Department of Mathematics and Hubei Province Key Laboratory of Mathematical Physics, Central China Normal University, Wuhan, 430079, China
关键词：
Decay estimates;Fourth-order Schr?dinger operators;Asymptotic expansion of resolvent;Dimension two
摘要：
In this paper we study the decay estimates of the fourth order Schrodinger operator H = Delta 2 + V(x) on R2 with a bounded decaying potential V(x). We first deduce the asymptotic expansions of resolvent of H near zero threshold in the presence of resonances or eigenvalue, and then use them to establish the L1 - L infinity decay estimates of e-itH generated by the fourth order Schrodinger operator H. Our methods used in the decay estimates depend on Littlewood-Paley decomposition and oscillatory integral theory. Moreover, we also classify these zero resonances as the distributional solutions of H phi = 0 in suitable weighted spaces. Due to the degeneracy of Delta 2 at zero threshold, we remark that the asymptotic expansions of resolvent RV (lambda 4) and the classifications of resonances are much more involved than Schrodinger operator -Delta + V in dimension two.(c) 2022 Elsevier Inc. All rights reserved.
期刊：
Journal of Mathematical Physics,2023年64(1):011506 ISSN：0022-2488
作者机构：
[An, Xiaoming] Guizhou Univ Finance & Econ, Sch Math & Stat, Guiyang 550025, Peoples R China.;[Yang, Xian] Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
摘要：
In this paper, we show a connection between fractional Schrodinger equations with power-law nonlinearity and fractional Schrodinger equations with logarithm-law nonlinearity. We prove that ground state solutions of power-law fractional equations, as p & RARR; 2(+), converge to a ground state solution of logarithm-law fractional equations. In particular, we provide a new proof to the existence of a ground state of logarithm-law fractional Schrodinger equations.
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635:463-485 ISSN：0021-8693
通讯作者：
Guo, HY
作者机构：
[Li, Huaimin; Guo, Hongyan] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Li, Huaimin; Guo, Hongyan] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Guo, HY ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
摘要：
In this paper, a family of infinite dimensional Lie algebras G & SIM; is introduced and investigated, called the extended Heisenberg-Virasoro algebra, denoted by G & SIM;. These Lie algebras are related to the N = 2 superconformal algebra and the Bershadsky-Polyakov algebra. We study restricted modules and associated vertex algebras of the Lie algebra G & SIM;. More precisely, we construct its associated vertex (operator) algebras VL & SIM;(e123, 0), and show that the category of vertex algebra VL & SIM;(�123, 0)-modules is equivalent to the category of restricted & SIM; of level & POUND;123. Then we give uniform constructions of simple restricted G & SIM;-modules. Also, we present several equivalent characterizations of simple restricted modules over G & SIM;.& COPY; 2023 Elsevier Inc. All rights reserved. G-modules
期刊：
BMC PUBLIC HEALTH,2023年23(1):1-10 ISSN：1471-2458
通讯作者：
Wang, N.;Xu, T.
作者机构：
[Li, Lin] Natl Res Inst Family Planning, Clin Med Ctr, Beijing, Peoples R China.;[Xu, Tao; Chen, Feilong] Chinese Acad Med Sci, Inst Basic Med Sci, Dept Epidemiol & Biostat, Beijing, Peoples R China.;[Xu, Tao; Chen, Feilong] Peking Union Med Coll, Sch Basic Med, Beijing, Peoples R China.;[Wang, Ning; Gao, Yiyuan; Li, Xiaoyan] Natl Res Inst Family Planning, Ctr Hlth Qual, Beijing, Peoples R China.;[Diao, Xiyezi; Zhu, Silin] Cent China Normal Univ, Dept Stat, Wuhan, Hubei, Peoples R China.
通讯机构：
[Ning Wang] C;[Tao Xu] D;Center for Health Quality, National Research Institute for Family Planning, Beijing, China<&wdkj&>Department of Epidemiology and Biostatistics Institute of Basic Medical Sciences, Chinese Academy of Medical Sciences & School of Basic Medicine, Peking Union Medical College, Beijing, China
关键词：
The elderly;Calf circumference;Incontinence;Sarcopenia;Risk factor
作者机构：
[Ma, Junru] Hubei Univ, Sch Cyber Sci & Technol, 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 430079, Hubei, China
摘要：
Symbol-pair codes are proposed to guard against pair-errors in symbol-pair read channels. The minimum symbol-pair distance is of significance in determining the error-correcting capability of a symbol-pair code. One of the central themes in symbol-pair coding theory is the constructions of symbol-pair codes with the largest possible minimum symbol-pair distance. Maximum distance separable (MDS) and almost maximum distance separable (AMDS) symbol-pair codes are optimal and sub-optimal regarding the Singleton bound, respectively. In this paper, six new classes of AMDS symbol-pair codes are explicitly constructed through repeated-root cyclic codes. Remarkably, one class of such codes has unbounded lengths and the minimum symbol-pair distance of another class can reach 13.(c) 2023 Elsevier B.V. All rights reserved.
作者：
Gong, Di;Yang, Harrison Hao;Wu, Di;Dai, Jinjun
期刊：
Education and Information Technologies,2023年28(2):1715-1733 ISSN：1360-2357
通讯作者：
Harrison Hao Yang
作者机构：
[Gong, Di; Yang, Harrison Hao; Wu, Di] Cent China Normal Univ, Fac Artificial Intelligence Educ, Wuhan, Peoples R China.;[Yang, Harrison Hao] SUNY Coll Oswego, Sch Educ, Oswego, NY 13126 USA.;[Dai, Jinjun] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.
通讯机构：
[Harrison Hao Yang] F;Faculty of Artificial Intelligence in Education, Central China Normal University, Wuhan, China<&wdkj&>School of Education, State University of New York at Oswego, Oswego, USA
作者：
Prasangika, K. D.;Tang, Wan;Yao, Zeng;Zuo, Guoxin
期刊：
Communications in Statistics - Theory and Methods,2023年52(5):1385-1399 ISSN：0361-0926
通讯作者：
Zuo, Guoxin(zuogx@mail.ccnu.edu.cn)
作者机构：
[Prasangika, K. D.] Univ Ruhuna, Dept Math, Matara, Sri Lanka.;[Tang, Wan] Tulane Univ, Dept Biostat & Data Sci, New Orleans, LA 70118 USA.;[Yao, Zeng; Zuo, Guoxin] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.
通讯机构：
[Guoxin Zuo] S;School of Mathematics and Statistics, Central China Normal University, Wuhan, P.R. China
关键词：
Non parametric regression;local linear regression;double smoothing local linear regression;time series;asymptotic properties
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.
