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：
INVERSE PROBLEMS AND IMAGING,2023年17(3):614-628 ISSN：1930-8337
通讯作者：
Yue Zhao
作者机构：
[Zhai, Jian] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China.;[Zhao, Yue] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Yue Zhao] S;School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China
摘要：
This paper is concerned with inverse source problems for the time harmonic elastic wave equations and Maxwell's equations with a single boundary measurement at a fixed frequency. We show the uniqueness and a Lipschitz type stability estimate under the assumption that the source function is piece wise constant on a domain which is made of a union of disjoint convex polyhedral subdomains.
作者机构：
[Long, Junhao; Dai, Yan; Chen, Pu; Lin, Yun; Yang, Juexi] Huazhong Univ Sci & Technol, Union Hosp, Tongji Med Coll, Dept Anesthesiol, Wuhan 430022, Peoples R China.;[Long, Junhao; Dai, Yan; Chen, Pu; Lin, Yun; Yang, Juexi] Huazhong Univ Sci & Technol, Union Hosp, Inst Anesthesia & Crit Care Med, Tongji Med Coll, Wuhan 430022, Peoples R China.;[Long, Junhao; Dai, Yan; Chen, Pu; Lin, Yun; Yang, Juexi] Huazhong Univ Sci & Technol, Key Lab Anesthesiol & Resuscitat, Minist Educ, Wuhan 430022, Peoples R China.;[Gu, Jinglan] Zhejiang Univ, Childrens Hosp, Natl Clin Res Ctr Child Hlth, Dept Nephrol,Sch Med, Hangzhou 310058, Peoples R China.;[Wu, Ming] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Wu, Y ] H;[Wu, M ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;Huazhong Univ Sci & Technol, Union Hosp, Tongji Med Coll, Dept Dermatol, Wuhan 430022, Peoples R China.
关键词：
Mendelian randomization (MR);causality;intestinal flora;inflammatory skin diseases;genome-wide association studies (GWAS)
摘要：
Emerging research underscores the substantial link between gut flora and various inflammatory skin diseases. We hypothesize that there exists a complex gut-skin axis, possibly affecting the progression of conditions such as eczema, acne, psoriasis, and rosacea. However, the precise nature of the causal connection between gut flora and skin diseases remains unestablished. In this study, we started by compiling summary data from genome-wide association studies (GWAS) featuring 211 unique gut microbiota and four types of skin conditions. We scrutinized these data across different taxonomic strata. Subsequently, we leveraged Mendelian randomization (MR) to ascertain if there is a causal link between gut microbiota and these skin conditions. We also performed a bidirectional MR analysis to identify the causality's direction. By utilizing Mendelian randomization, we identified 26 causal connections between the gut microbiome and four recognized inflammatory skin conditions, including 9 positive and 17 negative causal directions. Additional sensitivity analyses of these results revealed no evidence of pleiotropy or heterogeneity. Our MR analysis suggests a causal connection between gut microbiota and skin diseases, potentially providing groundbreaking perspectives for future mechanistic and clinical studies on microbiota-affected skin conditions.
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.
期刊：
Communications in Statistics - Theory and Methods,2023年52(15):5470-5482 ISSN：0361-0926
通讯作者：
Zhao, Hui
作者机构：
[Luo, Lin] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.;[Zhao, Hui] Zhongnan Univ Econ & Law, Sch Stat & Math, Wuhan 430073, Peoples R China.
通讯机构：
[Zhao, Hui] Z;Zhongnan Univ Econ & Law, Sch Stat & Math, Wuhan 430073, Peoples R China.
关键词：
Estimating equation;propensity score;linear transformation model;interval-censored data
摘要：
Interval-censored failure time data often occur in medical follow-up studies among other areas. Regression analysis of linear transformation models with interval-censored data has been investigated by several authors under different contexts, but most of the existing methods assume that the covariates are discrete because these methods rely on the estimation of conditional survival distribution function. Without this assumption, this paper constructs a new generalized estimating equation using the propensity score. The proposed inference procedure does not need to estimate the conditional survival distribution any more and then can be used not only in the discrete but also in the continuous covariate situation. The asymptotic properties of the resulting estimates are given, and an extensive simulation study is performed. Finally, the application to two real datasets is also provided. Key words: Estimating equation; Interval-censored data; Propensity score; Linear transformation model.
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：
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：
[Ye, Jianguo] Kashi Univ, Res Ctr Modern Math & Its Applicat, Sch Math & Stat, Kashi 844000, Peoples R China.;[Yan, Guozheng] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Guozheng Yan] S;School of Mathematics and Statistics, Central China Normal University, Wuhan, China
摘要：
We consider the interior inverse scattering problem for recovering the shape of a penetrable partially coated cavity with external obstacles from the knowledge of measured scattered waves due to point sources. In the first part, we obtain the well-posedness of the direct scattering problem by the variational method. In the second part, we establish the mathematical basis of the linear sampling method to recover both the shape of the cavity, and the shape of the external obstacle, however the exterior transmission eigenvalue problem also plays a key role in the discussion of this paper.
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.
作者机构：
[Qin, Hong; Xiao, Yao] Zhongnan Univ Econ & Law, Sch Stat & Math, Wuhan, Peoples R China.;[Qin, Hong; Wang, Shiqi; Ning, Jianhui] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.
通讯机构：
[Jianhui Ning] S;School of Mathematics and Statistics, Central China Normal University, Wuhan, People's Republic of China
关键词：
Weighted uniform designs;sequential designs;weighted discrepancy;Gaussian process model
摘要：
Uniform designs seek to distribute design points uniformly in the experimental domain. Some discrepancies have been developed to measure the uniformity by treating all factors equally. It is reason-able when there exists no prior information about the system or when the potential model is completely unclear. However, in the sit-uation of sequential designs, experimental information, such as the importance of each factor, would be obtained from previous stage experiments. With this fact, the weighted L-2-discrepancy is more suit-able than the original discrepancy for choosing follow-up designs. In this paper, the sequentially weighted uniform design is proposed, which is obtained by minimizing the weighted L-2-discrepancy. The weights, indicating the relative importance of each factor, are esti-mated through a Bayesian hierarchical Gaussian process method based on serial experimental data. Results from several classic com-puter simulator examples, as well as a real application in circuit design, demonstrate that the performance of our new method sur-passes that of its counterparts.
期刊：
Machine Learning with Applications,2023年13:100479 ISSN：2666-8270
通讯作者：
Michael K. Ng
作者机构：
[Xiongjun Zhang] School of Mathematics and Statistics and Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan 430079, China;[Jin Wu] School of Biological Sciences, The University of Hong Kong, Pokfulam, Hong Kong;[Michael K. Ng] Department of Mathematics, The University of Hong Kong, Pokfulam, Hong Kong
通讯机构：
[Michael K. Ng] D;Department of Mathematics, The University of Hong Kong, Pokfulam, Hong Kong
摘要：
In this paper, we study the problem of multilinear multitask learning (MLMTL), in which all tasks are stacked into a third-order tensor for consideration. In contrast to conventional multitask learning, MLMTL can explore inherent correlations among multiple tasks in a better manner by utilizing multilinear low rank structure. Existing approaches about MLMTL are mainly based on the sum of singular values for approximating low rank matrices obtained by matricizing the third-order tensor. However, these methods are suboptimal in the Tucker rank approximation. In order to elucidate intrinsic correlations among multiple tasks, we present a new approach by the use of transformed tensor nuclear norm (TTNN) constraint in the objective function. The main advantage of the proposed approach is that it can acquire a low transformed multi-rank structure in a transformed tensor by applying suitable unitary transformations which is helpful to determine principal components in grouping multiple tasks for describing their intrinsic correlations more precisely. Furthermore, we establish an excess risk bound of the minimizer of the proposed TTNN approach. Experimental results including synthetic problems and real-world images, show that the mean-square errors of the proposed method is lower than those of the existing methods for different number of tasks and training samples in MLMTL.
期刊：
Advances in Mathematics,2023年434:109320 ISSN：0001-8708
通讯作者：
Lim, MF
作者机构：
[Lei, Antonio] Univ Ottawa, Dept Math & Stat, 150 Louis Pasteur Pvt, Ottawa, ON K1N 6N5, Canada.;[Lim, MF; Lim, Meng Fai] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Lim, MF; Lim, Meng Fai] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Mueller, Katharina] Univ Laval, Dept Math & Stat, Pavill Alexandre Vachon,1045 Ave Med, Quebec City, PQ G1V 0A6, Canada.
通讯机构：
[Lim, MF ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
关键词：
Anticyclotomic Iwasawa theory;Elliptic curves;Supersingular primes;Tate-Shafarevich groups
摘要：
Let p >= 5 be a prime number and E/Q an elliptic curve with good supersingular reduction at p. Under the generalized Heegner hypothesis, we investigate the p-primary subgroups of the Tate-Shafarevich groups of E over number fields contained inside the anticyclotomic Z(p)-extension of an imaginary quadratic field where p splits. (c) 2023 Elsevier Inc. All rights reserved.
期刊：
Advances in Mathematics,2023年431:109257 ISSN：0001-8708
通讯作者：
Lai, CK
作者机构：
[An, Lixiang] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[An, Lixiang] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Lai, Chun-Kit] San Francisco State Univ, Dept Math, 1600 Holloway Ave, San Francisco, CA 94132 USA.
通讯机构：
[Lai, CK ] S;San Francisco State Univ, Dept Math, 1600 Holloway Ave, San Francisco, CA 94132 USA.
关键词：
Pro duct-form;Hadamard triples;Self-similar measures;Spectral measures
摘要：
In a previous work by Laba and Wang, it was proved that whenever there is a Hadamard triple (N, D, L), then the associated one-dimensional self-similar measure mu N,D generated by maps N-1(x + d) with d is an element of D, is a spectral measure. In this paper, we introduce pro duct-form digit sets for finitely many Hadamard triples (N, Ak, Lk) by putting each triple into different scales of N. Our main result is to prove that the associated self-similar measure mu N,D is a spectral measure. This result allows us to show that pro duct-form self-similar tiles are spectral sets as long as the tiles in the group ZN obey the Coven-Meyerowitz (T 1), (T 2) tiling condition. Moreover, we show that all self-similar tiles with N = p alpha q are spectral sets, answering a question by Fu, He and Lau in 2015. Finally, our results allow us to offer new singular spectral measures not generated by a single Hadamard triple. Such new examples allow us to classify all spectral self-similar measures generated by four equi-contraction maps, which will appear in a forthcoming paper. (c) 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC license (http:// creativecommons .org /licenses /by -nc /4 .0/).
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.
作者机构：
[Yaping WU] School of Artificial Intelligence,Jianghan University,Hubei 430056,P.R.China;[Huiqing LIU] School of Mathematics and Statistics,Hubei University,Hubei 430062,P.R.China;[Qiong FAN] School of Mathematics and Statistics,Central China Normal University,Hubei 430079,P.R.China
摘要：
Given a simple graph G, the oriented graph Gσ is obtained from G by orienting each edge and G is called the underlying graph of Gσ. The skew-symmetric adjacency matrix S(Gσ)of Gσ, where the(u, v)-entry is 1 if there is an arc from u to v, and -1 if there is an arc from v to u(and 0 otherwise), has eigenvalues of 0 or pure imaginary. The k-th-skew spectral moment of Gσis the sum of power k of all eigenvalues of S(Gσ), where k is a non-negative integer. The skew spectral moments can be used to produce graph catalogues. In this paper, we researched the skew spectral moments of some oriented trees and oriented unicyclic graphs and produced their catalogues in lexicographical order. We determined the last 2■ oriented trees with underlying graph of diameter d and the last 2■ + 1 oriented unicyclic graphs with underlying graph of girth g, respectively.
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.
