作者机构：
[Peng, Pai; Li, Le; Chen, Qiyuan] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Yang, Haitong] Cent China Normal Univ, Sch Comp Sci, Wuhan 430079, Peoples R China.;[Li, Le] Hubei Key Lab Math Sci, Wuhan 430072, Peoples R China.
通讯机构：
[Li, L.] C;Central China Normal University, China
作者机构：
[Deng, Yinbin; Xu, Liangshun; Guo, Yujin] Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Yinbin Deng] S;School of Mathematics and Statistics, Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, China
关键词：
Bose-Einstein condensates;Gross-Pitaevskii functional;nonlinear elliptic system
摘要：
This paper is concerned with ground states of two-component trapped Bose-Einstein condensates passing an obstacle in Double-struck capital R-2, where the intraspecies interactions are attractive and the interspecies interactions are repulsive. We address the classification on the existence and non-existence of ground states. The limiting profiles of ground states are also studied by the energy analysis and the elliptic partial differential equation theory.
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.
作者机构：
[Li, Hui-Sheng; Tu, Jia-Juan; Yan, Hong] Ctr Intelligent Multidimens Data Anal, Hong Kong Sci Pk, Hong Kong 999077, Peoples R China.;[Li, Hui-Sheng; Zhang, Xiao-Fei] Cent China Normal Univ, Sch Math & Stat, Dept Stat, Wuhan 430079, Peoples R China.;[Li, Hui-Sheng; Zhang, Xiao-Fei] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Yan, Hong] City Univ Hong Kong, Dept Elect Engn, Hong Kong 999077, Peoples R China.
通讯机构：
[Zhang, XF ] C;Cent China Normal Univ, Sch Math & Stat, Dept Stat, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
摘要：
Motivation: Spatially resolved gene expression profiles are the key to exploring the cell type spatial distributions and understanding the architecture of tissues. Many spatially resolved transcriptomics (SRT) techniques do not provide single-cell resolutions, but they measure gene expression profiles on captured locations (spots) instead, which are mixtures of potentially heterogeneous cell types. Currently, several cell-type deconvolution methods have been proposed to deconvolute SRT data. Due to the different model strategies of these methods, their deconvolution results also vary. Results: Leveraging the strengths of multiple deconvolution methods, we introduce a new weighted ensemble learning deconvolution method, EnDecon, to predict cell-type compositions on SRT data in this work. EnDecon integrates multiple base deconvolution results using a weighted optimization model to generate a more accurate result. Simulation studies demonstrate that EnDecon outperforms the competing methods and the learned weights assigned to base deconvolution methods have high positive correlations with the performances of these base methods. Applied to real datasets from different spatial techniques, EnDecon identifies multiple cell types on spots, localizes these cell types to specific spatial regions and distinguishes distinct spatial colocalization and enrichment patterns, providing valuable insights into spatial heterogeneity and regionalization of tissues. Availability and implementation : The source code is available at https://github.com/Zhangxf-ccnu/EnDecon. Contact: zhangxf@ccnu.edu.cn Supplementary information: Supplementary data are available at Bioinformatics online.
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.
作者机构：
[Fu, Kang; Hu, Jianwei] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Fu, K; Fu, Kang] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei Province, Peoples R China.
通讯机构：
[Fu, K ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei Province, Peoples R China.
关键词：
community detection;multilayer network;profile-pseudo likelihood;stochastic block model;strong consistency
摘要：
The multilayer stochastic block model is one of the fundamental models in multilayer networks and is often used to represent multiple types of relations between different individuals. In this paper, we extend the profile-pseudo likelihood method for the single-layer stochastic block model to the case of the multilayer stochastic block model. Specifically, by assuming all network layers have identical community membership labels, we investigate the multilayer stochastic block model with a common community structure. In this paper, we develop a profile-pseudo likelihood algorithm to fit a multilayer stochastic block model and estimate the community label. Meantime, we prove that the algorithm has convergence guarantee and that the estimated community label is strongly consistent. Further, for estimating the number of communities K $$ K $$ , we extend the corrected Bayesian information criterion to multilayer stochastic block models. We also extend this algorithm to fit the multilayer degree-corrected stochastic block model. Both simulation studies and real-world data examples indicate that the proposed method works well.
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：
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.
作者机构：
[Xiang, Jianli] China Three Gorges Univ, Coll Sci, Three Gorges Math Res Ctr, Yichang 443002, 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
关键词：
conductive boundary condition;uniqueness;phaseless far field data;inverse scattering
摘要：
In this paper, we establish the unique determination result for inverse acoustic scattering of a penetrable obstacle with a general conductive boundary condition by using phaseless far field data at a fixed frequency. It is well-known that the modulus of the far field pattern is invariant under translations of the scattering obstacle if only one plane wave is used as the incident field, so it is impossible to reconstruct the location of the underlying scatterers. Based on some new research results on the impenetrable obstacle and inhomogeneous isotropic medium, we consider different types of superpositions of incident waves to break the translation invariance property.
摘要：
Let E = K(n, m, D) be a Bedford-McMullen carpet with expanding factors n, m and digit set D. We call a = (aj)m-1 j=0 the distribution sequence of D where aj = #{i; (i, j) & ISIN; D}. Under a certain vertical separation condition, Li et al. (2013) [7] showed that if two totally disconnected Bedford-McMullent carpets share the same distribution sequence, then they are Lipschitz equivalent. In this paper, we define a metric & rho; on D & INFIN; and call (D & INFIN;, & rho;) a half-symbolic space. We show that if E is totally disconnected and satisfies the vertical separation condition, then E is Lipschitz equivalent to (D & INFIN;, & rho;). Thanks to this result, we extend the result of Li et al. by showing that two Bedford-McMullen carpets K(n, m, D) and K(n, m, D ⠃) are Lipschitz equivalent if a, the distribution sequence of D, is a permutation of a ⠃, the distribution sequence of D ⠃, and that a and a ⠃ satisfy a certain color matchable condition. & COPY; 2023 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
$$\chi _i'(P(2k+2,k))\le 5$$
.
期刊：
SIAM JOURNAL ON DISCRETE MATHEMATICS,2023年37(4):2486-2507 ISSN：0895-4801
通讯作者：
Peng, X
作者机构：
[Hu, Xiaolan] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Hu, Xiaolan] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Peng, X; Peng, Xing] Anhui Univ, Ctr Pure Math, Sch Math Sci, Hefei 230601, Peoples R China.
通讯机构：
[Peng, X ] A;Anhui Univ, Ctr Pure Math, Sch Math Sci, Hefei 230601, Peoples R China.
摘要：
For a simple graph G, let \chif (G) be the fractional chromatic number of G. In this paper, we aim to establish upper bounds on \chif (G) for those graphs G with restrictions on the clique number. Namely, we prove that for \Delta \geq 4, if G has maximum degree at most \Delta and is K =-free, then \chif (G) \leq \Delta -81 unless G = C82 or G = C5 \boxtimes K2. This improves the result in [A. King, L. Lu, and X. Peng, SIAM J. Discrete Math., 26 (2012), pp. 452--471] for \Delta \geq 4 and the result in [K. Edwards and A. D. King, SIAM J. Discrete Math., 27 (2013), pp. 1184--1208] for \Delta \in {6, 7, 8}.
作者机构：
[Meknani, Bassem; Zhang, Jun] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.;[Meknani, Bassem] Univ Freres Mentouri Constantine, Dept Math, Constantine, Algeria.;[Abdelhamid, Talaat] Menoufiya Univ, Fac Elect Engn, Phys & Math Engn Dept, Menoufia, Egypt.;[Abdelhamid, Talaat] Chinese Acad Sci, Shenzhen Inst Adv Technol, Shenzhen, Peoples R China.
通讯机构：
[Bassem Meknani] S;School of Mathematics and Statistics, Central China Normal University, Wuhan, People's Republic of China<&wdkj&>Département de Mathematiques, Université frères Mentouri Constantine, Constantine, Algeria
关键词：
Almost periodic solutions;pseudo-almost periodic solutions;integral solutions;evolution equations;nonlocal initial conditions;34C27;34K14;35B15;37L05;47J35
期刊：
Journal of Differential Equations,2023年343:263-284 ISSN：0022-0396
通讯作者：
Shuai, W
作者机构：
[Shuai, W; Shuai, Wei] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Shuai, W; Shuai, Wei] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Shuai, W ] 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：
Logarithmic nonlinearity;Multiplicity of solutions;Variational methods
摘要：
We are interested in the following elliptic equation {-Delta u = a(x)u log vertical bar u vertical bar, x is an element of Omega, (0.1) u = 0, on partial derivative Omega, where Omega is a bounded domain of R-N (N >= 2) with smooth boundary partial derivative Omega, and a(x) is an element of C(Omega). The existence and multiplicity of solutions are obtained by using variational methods. Quite surprisingly, the existence of solutions is deeply influenced by the sign of a(x). More precisely, (i) if a(x) > 0, equation (0.1) possesses a sequence of solutions whose energy and H-0(1)(Omega)-norms diverge to positive infinity; (ii) if a(x) < 0, equation (0.1) possesses a sequence of solutions whose energy and H-0(1)(Omega)-norms converge to zero; (iii) if a(x) is sign-changing, equation (0.1) possesses two sequences of solutions: one sequence of solutions is with energy and H-0(1)(Omega)-norms diverging to positive infinity, while the other one is with energy and H-0(1)(Omega)-norms converging to zero. (c) 2022 Elsevier Inc. All rights reserved.
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)
摘要：
We obtain optimal lower bounds for the eigenvalues of the Dirac–Witten operator on locally reducible spacelike submanifolds in terms of intrinsic and extrinsic quantities. The limiting cases are also studied.
