摘要：
In coding theory, it is important to construct codes with optimal parameters. The codes meeting the Griesmer bound are called Griesmer codes. In this paper, we prove nonexistence of some Griesmer codes of dimension four over finite fields of cardinality eight and nine using projective geometry. Moreover, we improve 24 cases on code lengths for given minimal distance and dimension four. Two precise lower bounds of code lengths have also been determined.
期刊：
ELECTRONIC JOURNAL OF COMBINATORICS,2024年31(1) ISSN：1077-8926
通讯作者：
Li, SC
作者机构：
[Lei, Xingyu; 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.
摘要：
For a given graph F, we say that a graph G is F -free if it does not contain F as a subgraph. A graph is color -critical if it contains an edge whose deletion reduces its chromatic number. Let Kr+ (a1, a2,... , ar) be the graph obtained from complete r -partite graph with parts of sizes a1 2, a2, ... , ar, by adding an edge to the first part. In this paper, we focus on the spectral extrema of disjoint colorcritical graphs. For fixed t, a1, ... , ar (r 2) and large enough n, we characterize the unique n -vertex tKr+ (a1, ... , ar)-free graph having the largest spectral radius. Moreover, let F1, ... , Ft be t disjoint color -critical graphs with the same chromatic number. We identify the unique n -vertex Uti=1 Fi-free graph having the largest spectral radius for sufficiently large n. Consequently, we generalize the main results obtained by Ni, Wang and Kang
期刊：
Journal of Mathematical Analysis and Applications,2024年537(1):128270 ISSN：0022-247X
通讯作者：
Huang, JC
作者机构：
[Chen, Shuang; Huang, Jicai] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.;[Chen, Shuang; Huang, Jicai] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Hubei, Peoples R China.
通讯机构：
[Huang, JC ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.;Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Hubei, Peoples R China.
摘要：
In this paper, we study the destabilization of synchronous periodic solutions for patch models. By applying perturbation theory for matrices, we derive asymptotic expressions of the Floquet spectra and provide a destabilization criterion for synchronous periodic solutions arising from closed orbits or degenerate Hopf bifurcations in terms of period functions. Finally, we apply the main results to the well-known two -patch Holling-Tanner model. (c) 2024 Elsevier Inc. All rights reserved.
期刊：
Journal of Mathematical Biology,2024年88(4):1-30 ISSN：0303-6812
通讯作者：
Lu, M
作者机构：
[Lu, Min; Huang, Jicai; Pan, Qin] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Lu, Min; Huang, Jicai; Pan, Qin] Cent China Normal Univ, Key Lab NAA, MOE, Wuhan 430079, Peoples R China.;[Ruan, Shigui] Univ Miami, Dept Math, Coral Gables, FL 33146 USA.
通讯机构：
[Lu, M ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Key Lab NAA, MOE, Wuhan 430079, Peoples R China.
关键词：
Bogdanov–Takens bifurcation;Harvesting;Holling I functional response;Hopf bifurcation;Krill–whale interaction;Predator–prey model
摘要：
In the Antarctic, the whale population had been reduced dramatically due to the unregulated whaling. It was expected that Antarctic krill, the main prey of whales, would grow significantly as a consequence and exploratory krill fishing was practiced in some areas. However, it was found that there has been a substantial decline in abundance of krill since the end of whaling, which is the phenomenon of krill paradox. In this paper, to study the krill–whale interaction we revisit a harvested predator–prey model with Holling I functional response. We find that the model admits at most two positive equilibria. When the two positive equilibria are located in the region
$$\big \{(N,P)|0\le N< 2N_c,\ P\ge 0\big \}$$
, the model exhibits degenerate Bogdanov–Takens bifurcation with codimension up to 3 and Hopf bifurcation with codimension up to 2 by rigorous bifurcation analysis. When the two positive equilibria are located in the region
$$\big \{(N,P)|N>2N_c,\ P\ge 0\big \}$$
, the model has no complex bifurcation phenomenon. When there is one positive equilibrium on each side of
$$N=2N_c$$
, the model undergoes Hopf bifurcation with codimension up to 2. Moreover, numerical simulation reveals that the model not only can exhibit the krill paradox phenomenon but also has three limit cycles, with the outmost one crosses the line
$$N=2N_c$$
under some specific parameter conditions.
作者：
Banerjee, Malay;Huang, Jicai;Pan, Qin;Zou, Lan
期刊：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B,2024年 ISSN：1531-3492
通讯作者：
Zou, L
作者机构：
[Banerjee, Malay] IIT Kanpur, Dept Math & Stat, Kanpur 208016, India.;[Huang, Jicai; Pan, Qin] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.;[Zou, Lan; Zou, L] Capital Normal Univ, Sch Math Sci, Beijing 100089, Peoples R China.
通讯机构：
[Zou, L ] C;Capital Normal Univ, Sch Math Sci, Beijing 100089, Peoples R China.
关键词：
Key words and phrases. Generalist predator;stability;limit cycle;Hopf bifurcation;Bogdanov- Takens bifurcation
摘要：
. Consideration of generalist predators leads to relatively complex dynamics due to alternative food sources. Here, we propose and analyze a prey-predator model with a generalist predator. The availability of alternative food sources for the predator and a density-dependent growth rate induces not only bistability and tristability, but also more complicated dynamical behaviors. We have studied the possible number and geometric configurations of positive equilibria in detail. A systematic bifurcation analysis has revealed the existence of the degenerate Bogdanov-Takens bifurcation of codimension four and degenerate Hopf bifurcation of codimension three. We found that degenerate local bifurcations with a higher codimension are responsible for three limit cycles. Derivation of the analytical conditions for three limit cycles for a suitable range of parameters is a crucial finding of this work.
期刊：
BRIEFINGS IN BIOINFORMATICS,2024年25(2) ISSN：1467-5463
通讯作者：
Xiao-Fei Zhang
作者机构：
School of Mathematics and Statistics, Central China Normal University , Wuhan 430079 , China;Key Laboratory of Nonlinear Analysis & Applications (Ministry of Education), Central China Normal University , Wuhan 430079 , China;[Yi-Xuan Xiong; Xiao-Fei Zhang] School of Mathematics and Statistics, 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：
[Xiao-Fei Zhang] S;School of Mathematics and Statistics, Central China Normal University , Wuhan 430079 , China<&wdkj&>Key Laboratory of Nonlinear Analysis & Applications (Ministry of Education), Central China Normal University , Wuhan 430079 , China
摘要：
The proliferation of single-cell RNA-seq data has greatly enhanced our ability to comprehend the intricate nature of diverse tissues. However, accurately annotating cell types in such data, especially when handling multiple reference datasets and identifying novel cell types, remains a significant challenge. To address these issues, we introduce Single Cell annotation based on Distance metric learning and Optimal Transport (scDOT), an innovative cell-type annotation method adept at integrating multiple reference datasets and uncovering previously unseen cell types. scDOT introduces two key innovations. First, by incorporating distance metric learning and optimal transport, it presents a novel optimization framework. This framework effectively learns the predictive power of each reference dataset for new query data and simultaneously establishes a probabilistic mapping between cells in the query data and reference-defined cell types. Secondly, scDOT develops an interpretable scoring system based on the acquired probabilistic mapping, enabling the precise identification of previously unseen cell types within the data. To rigorously assess scDOT’s capabilities, we systematically evaluate its performance using two diverse collections of benchmark datasets encompassing various tissues, sequencing technologies and diverse cell types. Our experimental results consistently affirm the superior performance of scDOT in cell-type annotation and the identification of previously unseen cell types. These advancements provide researchers with a potent tool for precise cell-type annotation, ultimately enriching our understanding of complex biological tissues.
作者机构：
[Liang Cheng; Liang Cheng Liang Cheng Liang Cheng] School of Mathematics and Statistics, Central China Normal University, Wuhan, Hebei, China;[Yongjia Zhang; Yongjia Zhang Yongjia Zhang Yongjia Zhang] School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, China
通讯机构：
[Yongjia Zhang; Yongjia Zhang Yongjia Zhang Yongjia Zhang] S;School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, China
关键词：
noncollapsing;Ricci flow;Type I ancient solution
摘要：
Abstract In this paper, we study complete Type I ancient Ricci flows with positive sectional curvature. Our main results are as follows: in the complete and noncompact case, all such ancient solutions must be noncollapsed on all scales; in the closed case, if the dimension is even, then all such ancient solutions must be noncollapsed on all scales. This furthermore gives a complete classification for three‐dimensional noncompact Type I ancient solutions without assuming the noncollapsing condition.
期刊：
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY,2024年176(2):287-308 ISSN：0305-0041
通讯作者：
Lim, MF
作者机构：
[Lim, MF; Lim, Meng Fai] Cent China Normal Univ, Sch Math & Stat, 152 Luoyu Rd, Wuhan, Hubei, Peoples R China.;[Lim, MF; Lim, Meng Fai] Cent China Normal Univ, Hubei Key Lab Math Sci, 152 Luoyu Rd, Wuhan 430079, Hubei, Peoples R China.
通讯机构：
[Lim, MF ] C;Cent China Normal Univ, Sch Math & Stat, 152 Luoyu Rd, Wuhan, Hubei, Peoples R China.;Cent China Normal Univ, Hubei Key Lab Math Sci, 152 Luoyu Rd, Wuhan 430079, Hubei, Peoples R China.
关键词：
11R23;11G05;11S25
摘要：
This paper is concerned with the study of the fine Selmer group of an abelian variety over a $\mathbb{Z}_{p}$-extension which is not necessarily cyclotomic. It has been conjectured that these fine Selmer groups are always torsion over $\mathbb{Z}_{p}[[ \Gamma ]]$, where $\Gamma$ is the Galois group of the $\mathbb{Z}_{p}$-extension in question. In this paper, we shall provide several strong evidences towards this conjecture. Namely, we show that the conjectural torsionness is consistent with the pseudo-nullity conjecture of Coates–Sujatha. We also show that if the conjecture is known for the cyclotomic $\mathbb{Z}_{p}$-extension, then it holds for almost all $\mathbb{Z}_{p}$-extensions. We then carry out a similar study for the fine Selmer group of an elliptic modular form. When the modular forms are ordinary and come from a Hida family, we relate the torsionness of the fine Selmer groups of the specialization. This latter result allows us to show that the conjectural torsionness in certain cases is consistent with the growth number conjecture of Mazur. Finally, we end with some speculations on the torsionness of fine Selmer groups over an arbitrary p-adic Lie extension.
作者机构：
[Qu, Lianqiang] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.;[Sun, LQ; Sun, Liuquan] Chinese Acad Sci, Inst Appl Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China.;[Sun, Yanqing] Univ North Carolina Charlotte, Dept Math & Stat, 9201 Univ City Blvd, Charlotte, NC 28223 USA.
通讯机构：
[Sun, LQ ] C;Chinese Acad Sci, Inst Appl Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China.
摘要：
Quantile regression has become a widely used tool for analysing competing risk data. However, quantile regression for competing risk data with a continuous mark is still scarce. The mark variable is an extension of cause of failure in a classical competing risk model where cause of failure is replaced by a continuous mark only observed at uncensored failure times. An example of the continuous mark variable is the genetic distance that measures dissimilarity between the infecting virus and the virus contained in the vaccine construct. In this article, we propose a novel mark-specific quantile regression model. The proposed estimation method borrows strength from data in a neighbourhood of a mark and is based on an induced smoothed estimation equation, which is very different from the existing methods for competing risk data with discrete causes. The asymptotic properties of the resulting estimators are established across mark and quantile continuums. In addition, a mark-specific quantile-type vaccine efficacy is proposed and its statistical inference procedures are developed. Simulation studies are conducted to evaluate the finite sample performances of the proposed estimation and hypothesis testing procedures. An application to the first HIV vaccine efficacy trial is provided.
期刊：
Journal of Functional Analysis,2024年286(2):110206 ISSN：0022-1236
通讯作者：
Xie, HF
作者机构：
[Luo, Peng] Cent China Normal Univ, Sch Math & Stat, Key Lab Nonlinear Anal & Applicat, Minist Educ, Wuhan 430079, Peoples R China.;[Tang, Zhongwei] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China.;[Xie, Huafei] Nanyang Normal Univ, Sch Math & Stat, Nanyang 473061, Peoples R China.
通讯机构：
[Xie, HF ] N;Nanyang Normal Univ, Sch Math & Stat, Nanyang 473061, Peoples R China.
摘要：
In this paper we study the following eigenvalue problem {-Delta v = lambda C(alpha)(p(alpha) - epsilon)vertical bar x vertical bar(alpha)u(epsilon)(p alpha-epsilon-1)v in Omega, u=0 on partial derivative Omega, where Omega subset of R-N is a smooth bounded domain containing the origin, C(alpha) = (N + alpha)(N - 2), N >= 3, p(alpha) = N+2+2 alpha/N-2, alpha > 0, epsilon > 0 is a small parameter and u(epsilon) is a single peaked solution of Henon equation {-Delta u = C(alpha)vertical bar x vertical bar(alpha)u(p alpha-epsilon) in Omega, u > 0 in Omega, u=0 on partial derivative Omega, which established by Gladiali and Grossi (2012) [21]. By using various local Pohozaev identities and blow-up analysis, we prove some asymptotic behavior of the eigen values lambda(epsilon,i) and corresponding eigen functions v(epsilon,i), i = 2, ... , Sigma(1 <= k <= 2+alpha/2) (N + 2k - 2) (N + k - 3)!/(N - 2)!k! + 2 when alpha is not an even integer. As a consequence, if 0 < alpha < 2, we have that the Morse index of the single peaked solutions is N + 1, which gives an affirmative answer to a conjecture raised by Gladiali and Grossi. (c) 2023 Elsevier Inc. All rights reserved.
期刊：
PSYCHOLOGY AND PSYCHOTHERAPY-THEORY RESEARCH AND PRACTICE,2024年115(1):66-89 ISSN：1476-0835
通讯作者：
Zhang, Y
作者机构：
[Li, Hao; Zhang, Ying; Chen, Gaowei] Univ Hong Kong, Fac Educ, Hong Kong, Peoples R China.;[Li, Bo; Li, Na] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.;[Zhou, Xin] Sichuan Univ, Middle Sch, Chengdu, Peoples R China.;[Zhang, Ying; Zhang, Y] Univ Hong Kong, Fac Educ, Pokfulam, Hong Kong, Peoples R China.
通讯机构：
[Zhang, Y ] U;Univ Hong Kong, Fac Educ, Pokfulam, Hong Kong, Peoples R China.
摘要：
Bullying victimization can undermine adolescents' well-being. However, few studies have comprehensively investigated the contributions of various victimization forms to well-being and compared which forms were more harmful than others. Evidence on whether resilience and social support moderate such associations is also limited. Using a sample of 12,058 Chinese adolescents in the Programme for International Student Assessment (PISA) 2018, this cross-sectional study aimed to (1) investigate the associations of physical, verbal and relational victimization with well-being; (2) compare the strengths of these associations; and (3) examine the moderating roles of resilience and teacher and parent support in these associations. Results showed that three victimization forms were associated with poorer well-being. Relational and physical victimization were more harmful to most studied well-being outcomes than verbal victimization. Furthermore, resilience weakened the negative effects of physical victimization on negative affect and life satisfaction but aggravated the negative effects of verbal victimization on both outcomes and the negative effect of relational victimization on school belonging. Teacher support intensified the negative effects of physical victimization on school belonging. Parent support was not effective in regulating the victimization-well-being association. The findings underscored the detrimental effects of bullying victimization on adolescents' well-being and the potentially harmful sides of resilience and social support. Implications for bullying prevention were discussed.
作者机构：
[Deng, Qingquan] Cent China Normal Univ, Sch Math & Stat, Key Lab Nonlinear Anal & Applicat, Minist Educ, Wuhan 430079, Peoples R China.;[Fan, Dashan] Univ Wisconsin Milwaukee, Dept Math Sci, Milwaukee, WI 53201 USA.;[Zhao, Ruizhi] Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Deng, QQ ] C;Cent China Normal Univ, Sch Math & Stat, Key Lab Nonlinear Anal & Applicat, Minist Educ, Wuhan 430079, Peoples R China.
摘要：
In this paper we study the Hp–Hq estimates of the solutions for a class of dispersive equations
$$\left\{ {\matrix{{i{\partial _t}u(t,x) = - P(|\nabla |)u(t,x),} \hfill & {(t,x) \in \mathbb{R} \times {\mathbb{R}^n},} \hfill \cr {u(0,x) = {u_0}(x),} \hfill & {x \in {\mathbb{R}^n},} \hfill \cr } } \right.$$
where P: ℝ+ → ℝ is smooth away from the origin and enjoy different scalings. As applications, we obtain the decay estimates for the solutions of higher order homogeneous and inhomogeneous Schrödinger equations.
期刊：
Communications in Statistics - Theory and Methods,2024年 ISSN：0361-0926
通讯作者：
Jing, L
作者机构：
[Ouyang, Yang] Natl Inst Cultural Dev, Wuhan, Peoples R China.;[Jing, Luo; Zhimeng, Xu; Jing, L] South Cent Minzu Univ, Dept Math & Stat, Wuhan 430074, Peoples R China.;[Jing, Luo; Jing, L] Cent China Normal Univ, Sch Math & Stat, Minist Educ, Wuhan 430079, Peoples R China.;[Jing, Luo; Jing, L] Cent China Normal Univ, Key Lab Nonlinear Anal & Applicat, Minist Educ, Wuhan 430079, Peoples R China.;[Qiuping, Wang] Zhaoqing Univ, Sch Math & Stat, Zhaoqing, Peoples R China.
通讯机构：
[Jing, L ] S;South Cent Minzu Univ, Dept Math & Stat, Wuhan 430074, Peoples R China.;Cent China Normal Univ, Sch Math & Stat, Minist Educ, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Key Lab Nonlinear Anal & Applicat, Minist Educ, Wuhan 430079, Peoples R China.
摘要：
The Bradley-Terry model is a common model for analyzing paired comparison data. Under differential private mechanism, there is a lack of asymptotic properties for the parameter estimator of parameters in this model. In this article, we show that the moment estimators of the parameters based on the differential private degree sequence with Laplace noise is uniformly consistent and asymptotically normal. Simulations are provided to illustrate asymptotic results.
期刊：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B,2024年29(2):812-832 ISSN：1531-3492
通讯作者：
Zhijun Liu
作者机构：
[Liu, Zhijun; Wang, Lianwen] School of Mathematics and Statistics, Hubei Minzu University, Enshi, Hubei 445000, China;[Chen, Siyu; Zhang, Xingan] School of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei 430079, China
通讯机构：
[Zhijun Liu] S;School of Mathematics and Statistics, Hubei Minzu University, Enshi, Hubei 445000, China
摘要：
This paper is devoted to proposing a mathematical model in order to explore the dynamics of HTLV-Ⅰ (human T-cell leukemia virus type-Ⅰ) infection, in which the closely related target cell-virus-immune system interaction and the time-delay cytotoxic T lymphocyte (CTL) immune response are taken into consideration. Firstly, we give the relevant lemma for the existence of feasible equilibrium points of the model, and then further certify the global asymptotic stabilities of the infection-free equilibrium (IFFE) $ E_1 $ and the immune-free equilibrium (IMFE) $ E_2 $. Furthermore, we research the existence of Hopf bifurcation (HB) occurring at the immune equilibrium (IE) $ E^* $ due to the influence of the delay bifurcation parameter. Also, the numerical simulations confirm this fact. In addition, we obtain the explicit expressions which determine the direction and stability of HB. Finally, a succinct discussion shows that the delay in CTL response can destabilize $ E^* $ and generate HB, but not affect stabilities of $ E_1 $ and $ E_2 $.
作者机构：
[Liu, Botao; Tu, Zhengge; Liu, BT] Cent China Normal Univ, Sch Econ & Business Adm, Wuhan 430079, Peoples R China.;[Liu, Botao; Tu, Zhengge; Liu, BT] Cent China Normal Univ, Res Ctr Low Carbon Econ & Environm Policies, Wuhan 430079, Peoples R China.;[Kong, Jiayang] Qinghai Univ Sci & Technol, Coll Comp & Informat Sci, Xining 810016, Peoples R China.;[Kong, Jiayang] Qinghai Univ, Dept Comp Technol & Applicat, Xining 810016, Peoples R China.;[Sun, Liping] Shandong Normal Univ, Audit Off, Jinan 250014, Peoples R China.
通讯机构：
[Liu, BT ] C;Cent China Normal Univ, Sch Econ & Business Adm, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Res Ctr Low Carbon Econ & Environm Policies, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
关键词：
digital economy;entropy method;internet development;regional development imbalance;rural-urban income gap
摘要：
Currently, the Chinese government is considering two major strategies, namely, developing the digital economy and achieving common prosperity, to address regional development imbalances. Using panel data from 276 Chinese cities spanning from 2011 to 2019, the article first employs the entropy method to measure China’s digital economy development, digital fusion application, and Internet accessibility. Subsequently, the paper evaluates the influence of the digital economy on regional development imbalances, focusing on the rural-urban income gap. The results show a significant reduction in the rural-urban income gap due to digital economy development. Notably, digital fusion applications have a greater impact on reducing the rural-urban income gap than Internet accessibility. In addition, a heterogeneity analysis reveals that the influence of the digital economy on the rural-urban income gap is only reflected in the eastern and western regions, with a more substantial effect observed in the western region. This study, to some extent, helps Chinese government officials distinguish the diverse impacts of different dimensions and regional variations in digital economies on the rural-urban income gap. Such insights can guide the government in strategically advancing digital economy development to accelerate the mitigation of regional disparities and achieve sustainable economic development.
期刊：
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS,2024年 ISSN：0308-2105
通讯作者：
Chen, T
作者机构：
[Chen, Ting; Zi, Ruizhao; Chen, T] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Zi, Ruizhao] Cent China Normal Univ, Key Lab Nonlinear Anal & Applicat, Minist Educ, Wuhan 430079, Peoples R China.
通讯机构：
[Chen, T ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
关键词：
MHD equations;Couette flow;stability
摘要：
In this work, we study the Sobolev stability of shear flows near Couette in the 2D incompressible magnetohydrodynamics (MHD) equations with background magneticfield (alpha,0)(T)on TxR. More precisely, for sufficiently large alpha, we show that when the initial datum of the shear flow satisfies & Vert;U(y)-y & Vert;HN+6 << 1, with N>1, and the initial perturbationsu in and b(in) satisfy & Vert;(u(in),b(in))& Vert;HN+1=<<nu 5/(6)+ delta for any fixed delta>0, then the solution of the 2D MHD equations remains nu-((1)/(3)+ (delta)/(2))is an element of-close to(e(nu t partial derivative yy)U(y),0)(T)for allt>0.
摘要：
Subspace codes have important applications in random network coding. It is a classical problem to construct subspace codes where both their size and their minimum distance are as large as possible. In particular, cyclic constant dimension subspace codes have additional properties which can be used to make encoding and decoding more efficient. In this paper, we construct large cyclic constant dimension subspace codes with minimum distances 2k-2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2k-2$$\end{document} and 2k. These codes are contained in Gq(n,k)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathscr {G}_q(n, k)$$\end{document}, where Gq(n,k)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathscr {G}_q(n, k)$$\end{document} denotes the set of all k-dimensional subspaces of the finite filed Fqn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {F}_{q<^>n}$$\end{document} of qn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q<^>n$$\end{document} elements (q a prime power). Consequently, some results in [7, 15], and [23] are extended.
期刊：
ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS,2024年:1-23 ISSN：0167-8094
通讯作者：
Luo, JQ
作者机构：
[Ma, Wen] Nanjing Forestry Univ, Sch Sci, Nanjing 210037, Jiangsu, Peoples R China.;[Luo, Jinquan] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.;[Luo, Jinquan] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan, Peoples R China.
通讯机构：
[Luo, JQ ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.;Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan, Peoples R China.
摘要：
Weighted poset block metric is a generalization of two types of metrics: one is weighted poset metric introduced by Panek and Pinheiro
(2010) and the other is metric for linear error-block codes introduced by Feng and Hickernell
(2006). This type of metrics includes many classical metrics such as Hamming metric, Lee metric, poset metric, pomset metric, poset block metric, pomset block metric and so on. In this work, we focus on constructing new codes under weighted poset block metric from given ones. Some basic properties such as minimum distance and covering radius are studied.
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.;[Pianzola, Arturo; Kuttler, Jochen] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada.;[Pianzola, Arturo] Ctr Altos Estudios Ciencias Exactas CAECE, Av Mayo 866, Buenos Aires, Argentina.
通讯机构：
[Pianzola, A ] U;Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada.
关键词：
11E72;14L30;14E20;17B67;17B01
摘要：
Let
$${\mathfrak {g}}$$
be a finite-dimensional perfect Lie algebra over a field k of characteristic 0. In infinite-dimensional Lie theory we encounter Lie algebras of the form
$${\mathfrak {g}}\otimes _k R$$
, where R is a k-ring (usually a Laurent polynomial ring in finitely many variables over k), and étale twisted forms
$${\mathcal {L}}$$
of
$${\mathfrak {g}}\otimes _k R$$
. Thus
$${\mathcal {L}}$$
is an R-Lie algebra that becomes isomorphic to the S-Lie algebra
$${\mathfrak {g}}\otimes _k S$$
after some étale cover base ring extension S/R. The interesting infinite-dimensional Lie algebras are “built” out of
$${\mathcal {L}}$$
by adding a centre
$${\mathcal {Z}}$$
and a Lie algebra of derivations
$${\mathcal {D}}$$
(the affine Kac-Moody Lie algebras are the simplest examples).
$${\mathcal {D}}$$
, which determines
$${\mathcal {Z}}$$
, is a Lie subalgebra of
$${\text {Der}}_{k}(\mathcal {L})$$
of
$${\mathcal {L}}$$
. The understanding of this last Lie algebra is crucial. While the R-Lie algebra
$${\mathcal {L}}$$
can be given by étale descent, the same cannot be openly said about
$${\text {Der}}_{k}({\mathcal {L}})$$
since it is not an R-Lie algebra. In the present paper we give such a descent presentation within the more general framework of relative R/k-sheaves of Lie algebras that we believe is of independent interest.
