期刊：
Communications in Statistics - Theory and Methods,2024年 ISSN：0361-0926
通讯作者：
Hu, JW
作者机构：
[Liu, Hang; Hu, Jianwei; Keita, Seydou; Fu, Kang] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.;[Fu, Kang] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan, Peoples R China.;[Hu, Jianwei] Cent China Normal Univ, Key Lab Nonlinear Anal & Applicat, Minist Educ, Wuhan, Peoples R China.
通讯机构：
[Hu, JW ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.
关键词：
Adjacency matrix;network data;singular value;stochastic block model;two-sample test
摘要：
The stochastic block model is widely used for detecting community structures in network data. However, the research interest in much of the literature focuses on the study of one sample of stochastic block models. Detecting the difference between the two community structures is a less studied issue for stochastic block models. In this article, we propose a novel test statistic based on the largest singular value of a residual matrix obtained by subtracting the geometric mean of two estimated block mean effects from the sum of two observed adjacency matrices. We prove that the null distribution of the proposed test statistic converges in distribution to the Tracy-Widom distribution with index 1, and we show the difference between the two samples for stochastic block models can be tested via the proposed method. We show that the proposed test is asymptotically powerful against alternative models. Further, we extend the proposed method to the degree-corrected stochastic block model. Both simulation studies and real-world data examples indicate that the proposed method works well.
期刊：
JOURNAL OF GROUP THEORY,2024年27(1):61-88 ISSN：1433-5883
通讯作者：
Gang Chen
作者机构：
[Chen, Gang; Ren, Qing] School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, P. R. China;[Ponomarenko, Ilia] Steklov Institute of Mathematics at St. Petersburg, St. Petersburg, Russia
通讯机构：
[Gang Chen] S;School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, P. R. China
摘要：
For any finite group 𝐺 and a positive integer 𝑚, we define and study a Schur ring over the direct power G m , which gives an algebraic interpretation of the partition of G m obtained by the 𝑚-dimensional Weisfeiler–Leman algorithm. It is proved that this ring determines the group 𝐺 up to isomorphism if m ≥ 3 , and approaches the Schur ring associated with the group Aut ( G ) acting on G m naturally if 𝑚 increases. It turns out that the problem of finding this limit ring is polynomial-time equivalent to the group isomorphism problem.
期刊：
Discrete Mathematics, Algorithms and Applications,2024年16(01):2250189 ISSN：1793-8309
通讯作者：
Hu, X.
作者机构：
[Xiaolan Hu; Belayneh-Mengistu Legass] School of Mathematics and Statistics and Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, P. O. Box 71010, Wuhan 430079, P. R. China
通讯机构：
[Hu, X.] S;School of Mathematics and Statistics and Hubei Key Laboratory of Mathematical Sciences, P. O. Box 71010, China
摘要：
This paper features a study of statistical inference for linear inverse problems with Gaussian noise and priors in structured Banach spaces. Employing the tools of sectorial operators and Gaussian measures on Banach spaces, we overcome the theoretical difficulty of lacking the bias-variance decomposition in Banach spaces, characterize the posterior distribution of solution though its Radon-Nikodym derivative, and derive the optimal convergence rates of the corresponding square posterior contraction and the mean integrated square error. Our theoretical findings are applied to two scenarios, specifically a Volterra integral equation and an inverse source problem governed by an elliptic partial differential equation. Our investigation demonstrates the superiority of our approach over classical results. Notably, our method achieves same order of convergence rates for solutions with reduced smoothness even in a Hilbert setting.
期刊：
Journal of Differential Equations,2024年389:38-89 ISSN：0022-0396
通讯作者：
Zi, RZ
作者机构：
[Huang, Jinrui] Wuyi Univ, Sch Math & Computat Sci, Jiangmen 529020, Peoples R China.;[Liu, Qiao] Cent South Univ, Sch Math & Stat, HNP, LAMA, Changsha 410083, Hunan, Peoples R China.;[Zi, Ruizhao; Zi, RZ] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Zi, Ruizhao; Zi, RZ] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Zi, RZ ] 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：
Oldroyd-B model;Cauchy problem;Decay rates
摘要：
In this paper, we consider the Oldroyd-B model with stress tensor diffusion in R-d with d > 2. We first establish the global well-posedness of solutions to this model for small initial data (u(0), tau(0)) is an element of (Bp-1 (d /p-1) boolean AND B-p ,1(d /p+1) ) (d)x (B( p, 1 )d/p)(d xd ) with 1 <= p < infinity. Furthermore, under some additional L-2 type conditions on (u(0), tau(0)), but without any more smallness restrictions, we get the L-2 decay rates of all derivatives of (u, tau). It is shown that the velocity u decays as fast as the solution to the corresponding homogeneous linear heat equation, and the symmetry tau decays as fast as Du. In particular, when d = 3 the velocity u admits the decay rate faster than (1 + t)(-3/4) in L-2 (c) 2024 Elsevier Inc. All rights reserved.
期刊：
Cryptography and Communications,2024年16(1):21-48 ISSN：1936-2447
通讯作者：
Xiaoqiang Wang
作者机构：
[Wang, Xiaoqiang; Zheng, Dabin] Hubei Univ, Fac Math & Stat, Hubei Key Lab Appl Math, Wuhan 430062, Peoples R China.;[Ding, Cunsheng] Hong Kong Univ Sci & Technol, Dept Comp Sci & Engn, Kowloon, Clear Water Bay, Hong Kong, Peoples R China.;[Liu, Hongwei] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Xiaoqiang Wang] H;Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan, China
作者机构：
[Bao, Kangbo] Lanzhou Univ Finance & Econ, Sch Informat Engn & Artificial Intelligence, Lanzhou 730020, Peoples R China.;[Zhang, Xinan; Bao, Kangbo; Zhang, XA] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Liang, Guizhen] Xinxiang Univ, Sch Math & Informat Sci, Xinxiang 453003, Henan, Peoples R China.;[Tian, Tianhai] Monash Univ, Sch Math Sci, Melbourne, Vic 3800, Australia.
通讯机构：
[Zhang, XA ] C;[Tian, TH ] M;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;Monash Univ, Sch Math Sci, Melbourne, Vic 3800, Australia.
摘要：
Drug resistance is one of the most intractable issues in targeted therapy for cancer diseases. It has also been demonstrated to be related to cancer heterogeneity, which promotes the emergence of treatment-refractory cancer cell populations. Focusing on how cancer cells develop resistance during the encounter with targeted drugs and the immune system, we propose a mathematical model for studying the dynamics of drug resistance in a conjoint heterogeneous tumor-immune setting. We analyze the local geometric properties of the equilibria of the model. Numerical simulations show that the selectively targeted removal of sensitive cancer cells may cause the initially heterogeneous population to become a more resistant population. Moreover, the decline of immune recruitment is a stronger determinant of cancer escape from immune surveillance or targeted therapy than the decay in immune predation strength. Sensitivity analysis of model parameters provides insight into the roles of the immune system combined with targeted therapy in determining treatment outcomes.
摘要：
A graph is said to be k -factor -critical if deleting any of its k vertices results in a graph with a perfect matching. In this paper, we establish three sufficient conditions for a graph with given minimum degree to be k -factor -critical. These three sufficient conditions include the following: the size condition, Q -index condition and distance spectral radius condition. (c) 2024 Elsevier B.V. All rights reserved.
摘要：
Schur rings over the infinite dihedral group Z (sic) Z(2) are studied according to properties of Schur rings over infinite groups and the classification of Schur rings over infinite cyclic groups. Schur rings over Z (sic) Z(2) are classified under the assumption that Z is an A-subgroup. Those Schur rings are proved to be traditional.
作者机构：
[Xia, Sijia; Zhang, Xiongjun] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Qiu, Duo] Wuhan Inst Technol, Sch Math & Phys, Wuhan 430205, Peoples R China.;[Zhang, Xiongjun] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Qiu, D ] W;Wuhan Inst Technol, Sch Math & Phys, Wuhan 430205, Peoples R China.
摘要：
In this paper, we study the problem of a batch of linearly correlated image alignment, where the observed images are deformed by some unknown domain transformations, and corrupted by additive Gaussian noise and sparse noise simultaneously. By stacking these images as the frontal slices of a third-order tensor, we propose to utilize the tensor factorization method via transformed tensor-tensor product to explore the low-rankness of the underlying tensor, which is factorized into the product of two smaller tensors via transformed tensor-tensor product under any unitary transformation. The main advantage of transformed tensor-tensor product is that its computational complexity is lower compared with the existing literature based on transformed tensor nuclear norm. Moreover, the tensor
$$\ell _p$$
$$(0<p<1)$$
norm is employed to characterize the sparsity of sparse noise and the tensor Frobenius norm is adopted to model additive Gaussian noise. A generalized Gauss-Newton algorithm is designed to solve the resulting model by linearizing the domain transformations, and a proximal Gauss-Seidel algorithm is developed to solve the corresponding subproblem. Furthermore, the convergence of the proximal Gauss-Seidel algorithm is established according to Kurdyka-Łojasiewicz property, whose convergence rate is also analyzed. Extensive numerical examples on real-world image datasets are carried out to demonstrate the superior performance of the proposed method as compared to several state-of-the-art methods in both accuracy and computational time.
期刊：
Bulletin of the London Mathematical Society,2024年56(4) ISSN：0024-6093
通讯作者：
Yang, X
作者机构：
[Deng, Yinbin; Yang, X; Yang, Xian] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Deng, Yinbin; Yang, X; Yang, Xian] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Yang, X ] 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.
摘要：
Abstract In the paper, we study the higher regularity and decay estimates for positive solutions of the following fractional Choquard equations: 0.1 (−Δ)su+λu=(Iα∗|u|p)|u|p−2uinRN,lim|x|→∞u(x)=0,u∈Hs(RN),$$\begin{equation} {\left\lbrace \begin{aligned} &(-\Delta)^s u+\lambda u=(I_\alpha *|u|^p)|u|^{p-2}u\quad \mathrm{in}\ \mathbb {R}^N,\\ &\lim _{|x|\rightarrow \infty }u(x)=0,\quad u\in H^s(\mathbb {R}^N), \end{aligned}\right.} \end{equation}$$where Iα=1|x|N−α$I_\alpha =\frac{1}{|x|^{N-\alpha }}$, λ>0$\lambda >0$ is a constant, N⩾2$N\geqslant 2$, s∈(0,1)$s\in (0,1)$, α∈(0,N)$\alpha \in (0,N)$, p∈(N+αN,N+αN−2s)$p\in (\frac{N+\alpha }{N},\frac{N+\alpha }{N-2s})$. Let Q$Q$ be a positive solution of (0.1). We obtain an optimal decay estimate for Q$Q$ and reveal the relation between p$p$ and the decay rate of Q$Q$ for all p∈(N+αN,N+αN−2s)$p\in (\frac{N+\alpha }{N},\frac{N+\alpha }{N-2s})$ permitting p<2$p<2$. We skillfully use the properties of Bessel kernel to deduce our main result by iteration. Moreover, by the decay estimates, the stronger regular estimates for Q$Q$ are obtained.
期刊：
EURASIP JOURNAL ON ADVANCES IN SIGNAL PROCESSING,2024年2024(1):1-23 ISSN：1687-6180
通讯作者：
Cheng, HH
作者机构：
[Cheng, Huanhuan; Liu, Bing; Cheng, HH] Huainan Normal Univ, Sch Econ & Management, Huainan 232038, Peoples R China.;[Liu, Bing] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Cheng, HH ] H;Huainan Normal Univ, Sch Econ & Management, Huainan 232038, Peoples R China.
关键词：
Time series classification;Decomposition-ensemble;Empirical mode decomposition;Quantitative portfolio investment
摘要：
This paper proposes a classification method for financial time series that addresses the significant issue of noise. The proposed method combines improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) and wavelet threshold de-noising. The method begins by employing ICEEMDAN to decompose the time series into modal components and residuals. Using the noise component verification approach introduced in this paper, these components are categorized into noisy and de-noised elements. The noisy components are then de-noised using the Wavelet Threshold technique, which separates the non-noise and noise elements. The final de-noised output is produced by merging the non-noise elements with the de-noised components, and the 1-NN (nearest neighbor) algorithm is applied for time series classification. Highlighting its practical value in finance, this paper introduces a two-step stock classification prediction method that combines time series classification with a BP (Backpropagation) neural network. The method first classifies stocks into portfolios with high internal similarity using time series classification. It then employs a BP neural network to predict the classification of stock price movements within these portfolios. Backtesting confirms that this approach can enhance the accuracy of predicting stock price fluctuations.
关键词：
oriented split graphs;planar digraphs;Seymour's second neighbourhood conjecture;Sullivan's second neighbourhood conjecture
摘要：
Abstract For a vertex x $x$ of a digraph, d + ( x ) ${d}^{+}(x)$ (d − ( x ) ${d}^{-}(x)$, respectively) is the number of vertices at distance 1 from (to, respectively) x $x$ and d + + ( x ) ${d}^{++}(x)$ is the number of vertices at distance 2 from x $x$. In 1995, Seymour conjectured that for any oriented graph D $D$ there exists a vertex x $x$ such that d + ( x ) ≤ d + + ( x ) ${d}^{+}(x)\le {d}^{++}(x)$. In 2006, Sullivan conjectured that there exists a vertex x $x$ in D $D$ such that d − ( x ) ≤ d + + ( x ) ${d}^{-}(x)\le {d}^{++}(x)$. We give a sufficient condition in terms of the number of transitive triangles for an oriented graph to satisfy Sullivan's conjecture. In particular, this implies that Sullivan's conjecture holds for all orientations of planar graphs and triangle‐free graphs. An oriented graph D $D$ is an oriented split graph if the vertices of D $D$ can be partitioned into vertex sets X $X$ and Y $Y$ such that X $X$ is an independent set and Y $Y$ induces a tournament. We also show that the two conjectures hold for some families of oriented split graphs, in particular, when Y $Y$ induces a regular or an almost regular tournament.
作者机构：
[Lu, Jian; Lu, J; Liu, Huiqing] Hubei Univ, Fac Math & Stat, Hubei Key Lab Appl Math, Wuhan 430062, Peoples R China.;[Hu, Xiaolan] Cent China Normal Univ, Sch Math & Stat, POB 71010, Wuhan 430079, Peoples R China.;[Hu, Xiaolan] Cent China Normal Univ, Hubei Key Lab Math Sci, POB 71010, Wuhan 430079, Peoples R China.
通讯机构：
[Lu, J ] H;Hubei Univ, Fac Math & Stat, Hubei Key Lab Appl Math, Wuhan 430062, Peoples R China.
关键词：
Strong edge-coloring;Strong chromatic index;Maximum average degree
摘要：
A strong edge-coloring of a graph G is a proper edge-coloring such that any two edges with distance at most 2 receive different colors. The strong chromatic index of G, denoted by chi(s)'(G), is the least possible number of colors in a strong edge-coloring of G. Erdos and Nesetril conjectured that every graph G with maximum degree Delta(G) has chi(s)'(G <= 5/4 Delta(G)(2) - 1/2 increment (G) + 1/4 if increment (G) is odd and chi(s)'(G <= 5/4 Delta(G)(2) if Delta(G) is even. In this paper, we prove that if G is a graph with increment (G) <= 5 and maximum average degree less than 22/5, then chi(s)'(G <= 29. Our result implies that Erdos' conjecture holds for the case Delta(G) = 5, if G has no subgraph with average degree at least 22/5 .(c) 2023 Published by Elsevier B.V.
期刊：
Calculus of Variations and Partial Differential Equations,2024年63(3):1-34 ISSN：0944-2669
通讯作者：
Ruan, LZ
作者机构：
[Lin, Mengyuan; Chen, Yufeng; Ruan, Lizhi; Gao, Junpei; Ding, Wenjuan] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Lin, Mengyuan; Chen, Yufeng; Ruan, Lizhi; Gao, Junpei; Ding, Wenjuan] Cent China Normal Univ, Key Lab NAA, MOE, Wuhan 430079, Peoples R China.
通讯机构：
[Ruan, LZ ] 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：
35B35;35B40;35B45;35M33;35Q35
摘要：
This paper is concerned with the initial-boundary value problem on the isentropic Euler-Poisson equations arising in plasma physics in the half space for the spatial dimension n=1,2,3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=1, 2, 3$$\end{document}. By assuming that the velocity of the positive ion satisfies the Bohm criterion at the far field, we establish the global unique existence and the large time asymptotic stability of boundary layer (i.e., stationary solution) in some weighted Sobolev spaces by weighted energy method. Moreover, the time-decay rates are also obtained.
作者机构：
[Guo, Yuxia] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China.;[Yan, Shusen] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Yuxia Guo] D;Department of Mathematical Science, Tsinghua University, Beijing, People’s Republic of China
关键词：
Primary 35J60;Secondary 35B33
摘要：
We study an elliptic problem involving critical growth in a strip, satisfying the periodic boundary condition. As a consequence, we prove that the prescribed scalar curvature problem in
$${\mathbb {R}}^N$$
has solutions which are periodic in some variables, if the scalar curvature K(y) is periodic.
期刊：
Communications in Algebra,2024年 ISSN：0092-7872
通讯作者：
Gao, ZC
作者机构：
[Miao, Long; Zhou, Wenxia] Hohai Univ, Sch Math, Nanjing, Peoples R China.;[Gao, Zhichao] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Gao, Baijun] Yili Normal Univ, Coll Math & Stat, Yining, Xinjiang, Peoples R China.;[Liu, Wei] Yangzhou Univ, Sch Math Sci, Yangzhou, Peoples R China.
通讯机构：
[Gao, ZC ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
关键词：
phi-simple subgroups;Frattini subgroups;maximal subgroups;second maximal subgroups;the core of subgroups
摘要：
In this paper, we will investigate the structure of groups with the property of the core relation between some second maximal subgroups and corresponding maximal subgroups, and obtained some new results about finite groups.ARTICLE HISTORY Received 7 September 2023 Revised 13 December 2023 Communicated by Mandi Schaeffer Fry
期刊：
Journal of Mathematical Physics,2024年65(3):031506 ISSN：0022-2488
通讯作者：
Zhang, YP
作者机构：
[Zhang, Yiping; Zhang, YP] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Zhang, Yiping; Zhang, YP] Cent China Normal Univ, Key Lab Nonlinear Anal & Applicat, Minist Educ, Wuhan 430079, Peoples R China.
通讯机构：
[Zhang, YP ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Key Lab Nonlinear Anal & Applicat, Minist Educ, Wuhan 430079, Peoples R China.
摘要：
In this paper, we consider the convergence rates for the 2D stationary and non-stationary Navier-Stokes Equations over highly oscillating periodic bumpy John domains with C-2 regularity in some neighborhood of the boundary point (0,0). For the stationary case, using the variational equation satisfied by the solution and the correctors for the bumpy John domains obtained by Higaki and Zhuge [Arch. Ration. Mech. Anal. 247(4), 66 (2023)] after correcting the values on the inflow/outflow boundaries ({0} boolean OR {1}) x (0, 1), we can obtain an O(epsilon(3/2)) approximation in L-2 for the velocity and an O(epsilon(3/2)) convergence rates in L-2 approximated by the so called Navier's wall laws, which generalized the results obtained by J & auml;ger and Mikelic [J. Differ. Equations 170(1), 96-122 (2001)]. Moreover, for the non-stationary case, using the energy method, we can obtain an O(epsilon(3/2) + exp(-Ct)) convergence rate for the velocity in L-x(2).
