摘要：
Let
$$\varvec{x}_1,\ldots ,\varvec{x}_n$$
be a random sample of size n from a p-dimensional population distribution, where
$$p=p(n)\rightarrow \infty$$
. Consider a symmetric matrix
$$W=X^\top X$$
with parameters n and p, where
$$X=(\varvec{x}_1,\ldots ,\varvec{x}_n)^\top$$
. In this paper, motivated by model selection theory in high-dimensional statistics, we mainly investigate the asymptotic behavior of the eigenvalues of the principal minors of the random matrix W. For the Gaussian case, under a simple condition that
$$m=o(n/\log p)$$
, we obtain the asymptotic results on maxima and minima of the eigenvalues of all
$$m\times m$$
principal minors of W. We also extend our results to general distributions with some moment conditions. Moreover, we gain the asymptotic results of the extreme eigenvalues of the principal minors in the case of the real Wigner matrix. Finally, similar results for the maxima and minima of the eigenvalues of all the principal minors with a size smaller than or equal to m are also given.
期刊：
Journal of Functional Analysis,2023年284(6):109820 ISSN：0022-1236
通讯作者：
Ting Zhou
作者机构：
[Lu, Zheng-Yi; Liu, Jinsong] Chinese Acad Sci, Acad Math & Syst Sci, HLM, Beijing 100190, Peoples R China.;[Liu, Jinsong] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China.;[Zhou, Ting] Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Ting Zhou] S;School of Mathematics and Statistics, Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan 430079, China
摘要：
Let mu = mu{Rn,Bn} = delta R-1 1 B1 * delta(R2R1)-1B2 * .. . be a Borel probability measure with a compact support, where Rn E M2(Z), BnC Z2 and (Rn, Bn, Ln) forms a Hadamard triple for all n > 1. In this paper, we consider the existence of exponential orthogonal basis in L2(mu). We extend the concept of equi-positive family in [1] to higher dimensions, and provide a new idea to characterize the spectrality of such measures. In details, we study the spectrality and non-spectrality of Moran-Sierpinski type measures specifically under some necessary assumptions. The partial findings of several previous studies are extended by this study, such as Cantor-Moran measures (An-Fu-Lai [1], An-He-He [3]), Moran-Sierpinski type measures (Wang-Dong [47]) and Moran-Cantor-Dust type measures (Chen-Liu-Su-Wang [9]).(c) 2022 Elsevier Inc. All rights reserved.
摘要：
It is beyond dispute that cytotoxic T-lymphocytes (CTLs) exert a vital function in the host's antiviral defense mechanism. With the idea of the above factor and the logistic proliferation of CD4(+) T-cells, we establish a HTLV-I (human T-cell leukemia virus type-I) mathematical model. First, two threshold parameters Script capital R-0 and Script capital R-c (the basic reproduction numbers for viral infection and CTL immune response, respectively) are obtained. Second, sufficient criteria for local and global asymptotic stabilities of the feasible equilibria of the model are deduced, respectively. Third, the sensitivity analyses of Script capital R-0 and Script capital R-c are performed to better understand the effective strategies for HTLV-I infection. Finally, not only numerical simulations are given to illustrate the stability conclusions, but also the biological significance is stated.
期刊：
DESIGNS CODES AND CRYPTOGRAPHY,2023年91(10):3263-3284 ISSN：0925-1022
通讯作者：
Luo, JQ
作者机构：
[Luo, Jinquan; Ma, Wen] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.;[Luo, Jinquan; Ma, Wen] 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.
关键词：
Pomset;Label;Block;MDS codes;Perfect codes
摘要：
In this paper, we introduce codes equipped with pomset block metric. A Singleton type bound for pomset block codes is obtained. Code achieving the Singleton bound, called a maximum distance separable code (for short, MDS (
$${\mathbb {P}},\pi $$
)-code) is also investigated. We extend the concept of I-perfect codes and r-perfect codes to pomset block metric. The relation between I-perfect codes and MDS
$$({\mathbb {P}},\pi )$$
-codes is also considered. When all blocks have the same dimension, we prove the duality theorem for codes and study the weight distribution of MDS pomset block codes when the pomset is a chain.
期刊：
Bulletin of the Malaysian Mathematical Sciences Society,2023年46(1):1-9 ISSN：0126-6705
通讯作者：
Meng Fai Lim
作者机构：
[Lim, Meng Fai] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Lim, Meng Fai] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Meng Fai Lim] S;School of Mathematics and Statistics and Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, People’s Republic of China
关键词：
Norm principle;Norm maps;Even K-groups;Finite extensions of number fields
摘要：
We investigate the norm maps of algebraic even K-groups of finite extensions of number fields. Namely, we show that they are surjective in most situations. In the event that they are not surjective, we give a criterion in determining when an element in the even K-group of the base field comes from a norm of an element from the even K-groups of the extension field. This latter criterion is only reliant on the real primes of the base field.
作者机构：
[Deng, Yinbin] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[He, Qihan] Guangxi Univ, Coll Math & Informat Sci, Guangxi Ctr Math Res, Nanning 530003, Peoples R China.;[Pan, Yiqing] Beibu Gulf Univ, Coll Sci, Qinzhou 535011, Peoples R China.;[Zhong, Xuexiu] South China Normal Univ, South China Res Ctr Appl Math & Interdisciplinary, Guangzhou 510631, Peoples R China.
通讯机构：
[Qihan He] C;College of Mathematics and Information Science, Guangxi Center for Mathematical Research, Guangxi University, Nanning, 530003, China
摘要：
We consider the existence and nonexistence of the positive solution for the following Br & eacute;zis- Nirenberg problem with logarithmic perturbation: ?-delta u= |u|( 2*-2)u+ lambda u+ mu u u log(2) xE omega, u=0 xE 8 omega, where omega c RN is a bounded open domain, lambda,mu ER,N >_3 and 2 & lowast; := 2 - N is the critical Sobolev exponent for N 2 the embedding H0 omega L omega 1( ) y & lowast;( ). The uncertainty of the sign of s logs2 in (0, +oo) has some interest in itself. 2 We will show the existence of positive ground state solution, which is of mountain pass type provided lambda E R, mu > 0 and N >_ 4. While the case of mu < 0 is thornier. However, for N = 3, 4, lambda E (-oo, lambda 1(omega)), we can also establish the existence of positive solution under some further suitable assumptions. A nonexistence result is also obtained for mu < 0 and - (N-2)mu/2 (N-2)mu /2(-(N-2)mu/2) log lambda lambda(1 )omega 0 ( ) >_ if N >_ 3. Comparing with the results in the study by Br & eacute;zis and Nirenberg (Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math. 36 (1983), 437-477), some new interesting phenomenon occurs when the parameter mu on logarithmic perturbation is not zero.
摘要：
Let $M=(\begin {smallmatrix}\rho ^{-1} & 0 \\0 & \rho ^{-1} \\\end {smallmatrix})$ be an expanding real matrix with $0<\rho <1$, and let ${\mathcal D}_n=\{(\begin {smallmatrix} 0\\ 0 \end {smallmatrix}),(\begin {smallmatrix} \sigma _n\\ 0 \end {smallmatrix}),(\begin {smallmatrix} 0\\ \gamma _n \end {smallmatrix})\}$ be digit sets with $\sigma _n,\gamma _n\in \{-1,1\}$ for each $n\ge 1$. Then the infinite convolution\n$$ \begin{align*}\mu_{M,\{{\mathcal D}_n\}}=\delta_{M^{-1}{\mathcal D}_1}\ast\delta_{M^{-2}{\mathcal D}_2}\ast\cdots\end{align*} $$\nis called a Moran–Sierpinski measure. We give a necessary and sufficient condition for $L^2(\,\mu _{M,\{{\mathcal D}_n\}})$ to admit an infinite orthogonal set of exponential functions. Furthermore, we give the exact cardinality of orthogonal exponential functions in $L^2(\,\mu _{M,\{{\mathcal D}_n\}})$ when $L^2(\,\mu _{M,\{{\mathcal D}_n\}})$ does not admit any infinite orthogonal set of exponential functions based on whether $\rho $ is a trinomial number or not.
期刊：
Applied Mathematics and Computation,2023年438:127556 ISSN：0096-3003
通讯作者：
Sun, Wanting(wtsun2018@sina.com)
作者机构：
[Li, Shuchao; Liu, Xin; Sun, Wanting] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.;[Yan, Lixia] Wuhan Business Univ, Sch Informat & Engn, Wuhan 430070, Peoples R China.
通讯机构：
[Wanting Sun] F;Faculty of Mathematics and Statistics, Central China Normal University, Wuhan 430079, PR China
摘要：
The Steiner k-eccentricity of a vertex in a graph G is the maximum Steiner distance over all k-subsets containing the vertex. The average Steiner k-eccentricity of G is the mean value of all vertices' Steiner k-eccentricities in G. Let T-n be the set of all n-vertex trees, T-n,T-Delta be the set of n-vertex trees with maximum degree Delta, T-n,Delta(k) be the set of n-vertex trees with exactly k vertices of a given maximum degree Delta, and let MTnk be the set of n-vertex trees with exactly k vertices of maximum degree. In this paper, we first determine the sharp upper bound on the average Steiner 3-eccentricity of n-vertex trees with a given degree sequence. The corresponding extremal graphs are characterized. Consequently, together with majorization theory, all graphs among T-n,Delta(k) (resp. T-n,T-Delta, MTnk, T-n) having the maximum average Steiner 3-eccentricity are identified. Then we characterize the unique n-vertex tree with a given segment sequence having the minimum average Steiner 3-eccentricity. Finally, we determine all n-vertex trees with a given number of segments having the minimum average Steiner 3-eccentricity. (C) 2022 Elsevier Inc. All rights reserved.
期刊：
Bulletin of the Malaysian Mathematical Sciences Society,2023年46(1):1-8 ISSN：0126-6705
通讯作者：
Xiaolan Hu
作者机构：
[Legass, Belayneh-Mengistu; Hu, Xiaolan] Cent China Normal Univ, Sch Math & Stat, POB 71010, Wuhan 430079, Peoples R China.;[Legass, Belayneh-Mengistu; Hu, Xiaolan] Cent China Normal Univ, Hubei Key Lab Math Sci, POB 71010, Wuhan 430079, Peoples R China.
通讯机构：
[Xiaolan Hu] S;School of Mathematics and Statistics, and Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, People’s Republic of China
摘要：
An injective k-edge coloring of a graph
$$G=(V(G),E(G))$$
is a k-edge coloring
$$\varphi $$
of G such that
$$\varphi (e_1)\ne \varphi (e_3)$$
for any three consecutive edges
$$e_1,e_2$$
and
$$e_3$$
of a path or a 3-cycle. The injective edge chromatic index of G, denoted by
$$\chi _i'(G)$$
, is the minimum k such that G has an injective k-edge coloring. In this paper, we consider the injective edge coloring of the generalized Petersen graph P(n,k). We show that
$$\chi _i'(P(n,k))\le 4$$
if
$$n\equiv 0(mod~4)$$
and
$$k\equiv 1(mod~2)$$
; and
$$\chi _i'(P(n,k))\le 5$$
if
$$n\equiv 2(mod~4)$$
and
$$k\equiv 1(mod~2)$$
. Moreover,
$$\chi _i'(P(n,3))\le 5$$
,
$$\chi _i'(P(2k+1,k))\le 5$$
and
$$\chi _i'(P(2k+2,k))\le 5$$
.
作者机构：
[Yu, Yuantian; Zhou, Zihan] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.;[Geng, Xianya] Anhui Univ Sci & Technol, Sch Math & Big Data, Huainan, Peoples R China.
通讯机构：
[Xianya Geng] S;School of Mathematics and Big Data, Anhui University of Science & Technology, Huainan, China
摘要：
This article gives some fundamental introduction to spectra of mixed graphs via its kgeneralized Hermitian adjacency matrix. This matrix is indexed by the vertices of the mixed graph, and the entry corresponding to an arc from uto vis equal to the kth root of unity e(-2pi/k) (and its symmetric entry is e(-2pi/k)); the entry corresponding to an undirected edge is equal to 1, and 0 otherwise. For all positive integers k, the non-zero entries of the above matrix are chosen from the gain set {1, e(2pi/k), e(-2pi/k)}, which is not closed under multiplication when k >= 4. In this paper, for all positive integers k, we extract all the mixed graphs whose k-generalized Hermitian adjacency rank (H-k-rank for short) is 3, which partially answers a question proposed by Wissing and van Dam [34]. Furthermore, we study the spectral determination of mixed graphs with H-k-rank 2 and 3, respectively. (C) 2022 Elsevier B.V. All rights reserved.
期刊：
IEEE Transactions on Information Theory,2023年69(2):941-950 ISSN：0018-9448
通讯作者：
Liu, H.
作者机构：
[Chen, Bocong] South China Univ Technol, Sch Math, Guangzhou 510641, Peoples R China.;[Liu, Hongwei] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Liu, H.] C;Central China Normal University, China
关键词：
Codes;Measurement;Upper bound;Symbols;Shape;Hamming distances;Decoding;Symbol-pair read channel;symbol-pair code;coding theory;codes for storage media
期刊：
IEEE JOURNAL OF BIOMEDICAL AND HEALTH INFORMATICS,2023年27(6):3061-3071 ISSN：2168-2194
通讯作者：
Zhao, Weizhong;Shen, XJ
作者机构：
[Shen, Xianjun; Wang, Haodong; Wang, Yue; Zhao, Weizhong; Zhao, WZ; Shen, XJ; Jiang, Xingpeng; Li, Dandan] Cent China Normal Univ, Sch Comp, Hubei Prov Key Lab Artificial Intelligence & Smart, Wuhan 430079, Peoples R China.;[Sun, Han] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Shen, Xianjun; Wang, Haodong; Wang, Yue; Zhao, Weizhong; Zhao, WZ; Shen, XJ; Jiang, Xingpeng; Li, Dandan] Cent China Normal Univ, Natl Language Resources Monitoring & Res Ctr Netwo, Wuhan 430079, Peoples R China.
通讯机构：
[Zhao, WZ; Shen, XJ ] C;Cent China Normal Univ, Sch Comp, Hubei Prov Key Lab Artificial Intelligence & Smart, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Natl Language Resources Monitoring & Res Ctr Netwo, Wuhan 430079, Peoples R China.
关键词：
graph representation learning;heterogeneous information network;multi-head attention mechanism;Phage-host interactions prediction
摘要：
In the treatment of bacterial infectious diseases, overuse of antibiotics may lead to not only bacterial resistance to antibiotics but also dysbiosis of beneficial bacteria which are essential for maintaining normal human life activities. Instead, phage therapy, which invades and lyses specific pathogenic bacteria without affecting beneficial bacteria, becomes more and more popular to treat bacterial infectious diseases. For the effective phage therapy, it requires to accurately predict potential phage-host interactions from heterogeneous information network consisting of bacteria and phages. Although many models have been proposed for predicting phage-host interactions, most methods fail to consider fully the sparsity and unconnectedness of phage-host heterogeneous information network, deriving the undesirable performance on phage-host interactions prediction. To address the challenge, we propose an effective model called GERMAN-PHI for predicting Phage-Host Interactions via Graph Embedding Representation learning with Multi-head Attention mechaNism. In GERMAN-PHI, the multi-head attention mechanism is utilized to learn representations of phages and hosts from multiple perspectives of phage-host associations, addressing the sparsity and unconnectedness in phage-host heterogeneous information network. More specifically, a module of GAT with talking-heads is employed to learn representations of phages and bacteria, on which neural induction matrix completion is conducted to reconstruct the phage-host association matrix. Results of comprehensive experiments demonstrate that GERMAN-PHI performs better than the state-of-the-art methods on phage-host interactions prediction. In addition, results of case study for two high-risk human pathogens show that GERMAN-PHI can predict validated phages with high accuracy, and some potential or new associated phages are provided as well.
期刊：
JOURNAL OF GEOMETRIC ANALYSIS,2023年33(3):1-22 ISSN：1050-6926
通讯作者：
Xuexiu Zhong
作者机构：
[Deng, Yinbin; Shuai, Wei] Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Zhong, Xuexiu] South China Normal Univ, South China Res Ctr Appl Math & Interdisciplinary, Guangzhou 510631, Peoples R China.
通讯机构：
[Xuexiu Zhong] ;South China Research Center for Applied Mathematics and Interdisciplinary Studies, South China Normal University, Guangzhou, People’s Republic of China
摘要：
We consider the following singularly perturbed Kirchhoff-type equations
$$\begin{aligned} -\varepsilon ^2 M\left( \varepsilon ^{2-N}\int _{{\mathbb {R}}^N}|\nabla u|^2 \textrm{d}x\right) \Delta u +V(x)u=|u|^{p-2}u~\hbox {in}~{\mathbb {R}}^N, u\in H^1({\mathbb {R}}^N),N\ge 1, \end{aligned}$$
where
$$M\in C([0,\infty ))$$
and
$$V\in C({\mathbb {R}}^N)$$
are given functions. Under very mild assumptions on M, we prove the existence of single-peak or multi-peak solution
$$u_\varepsilon $$
for above problem, concentrating around topologically stable critical points of V, by a direct corresponding argument. This gives an affirmative answer to an open problem raised by Figueiredo et al. (Arch Ration Mech Anal 213(3):931–979, 2014)
