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.
作者机构:
[Fan, Aihua] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Fan, Aihua] Univ Picardie, LAMFA, UMR 7352, CNRS, F-80039 Amiens, France.;[Meyer, Yves] Univ Paris Saclay, CNRS, ENS Cachan, CMLA, F-91190 Paris, France.
通讯机构:
[Aihua Fan] S;School of Mathematics and Statistics, Central China Normal University, Wuhan, China<&wdkj&>LAMFA, CNRS UMR 7352, University of Picardie, Amiens, France
摘要:
The random trigonometric series
$$\sum\nolimits_{n = 1}^\infty {{\rho _n}\cos \left( {nt + {\omega _n}} \right)} $$
on the circle
$$\mathbb{T}$$
are studied under the conditions ∑∣ρn∣2 = ∞ and ρn → 0, where {ωn} are independent and uniformly distributed random variables on
$$\mathbb{T}$$
. They are almost surely not Fourier-Stieltjes series but determine pseudo-functions. This leads us to develop the theory of trigonometric multiplicative chaos, which produces a class of random measures. The kernel and the image of chaotic operators are fully studied and the dimensions of chaotic measures are exactly computed. The behavior of the partial sums of the above series is proved to be multifractal. Our theory holds on the torus
$${\mathbb{T}^d}$$
of dimension d ⩾ 1.
作者机构:
[Songliang CHEN] School of Mathematics and Big Data,Guizhou Education University,Guizhou 550018,P.R.China;[Yun FAN] School of Mathematics and Statistics,Central China Normal University,Hubei 430079,P.R.China
关键词:
norm;Dedekind group;Hamiltonian group;$\pi $-group;structure of finite group;Sylow subgroup
摘要:
Let G be a finite group and N(G) be its norm. Then N(G) is a characteristic subgroup of G which normalizes every subgroup of G. In this paper, we will study the structure of G under one of the following conditions: 1) norm quotient group G/N(G) is cyclic; 2) all Sylow subgroups of G/N(G) are cyclic and in particular if the order of G/N(G) is a square-free number.
作者机构:
[Chen, Hua] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China.;[Luo, Peng] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Tian, Shuying] Wuhan Univ Technol, Sch Sci, Dept Math, Wuhan 430070, Peoples R China.
通讯机构:
[Hua Chen; Peng Luo] S;[Shuying Tian] D;School of Mathematics and Statistics, Wuhan University, Wuhan, China<&wdkj&>School of Mathematics and Statistics, Central China Normal University, Wuhan, China<&wdkj&>Department of Mathematics, School of Science, Wuhan University of Technology, Wuhan, China
摘要:
In this paper, the authors study the asymptotically linear elliptic equation on manifold with conical singularities
$$ - {\Delta _{\mathbb{B}}}u + \lambda u = a\left( z \right)f\left( u \right),\,\,\,\,\,\,u \ge 0\,\,{\rm{in}}\,\,_ + ^N,$$
where N = n + 1 ≥ 3, λ > 0, z = (t, x1, ⋯, xn), and
$${\Delta _{\mathbb{B}}} = {\left( {t{\partial _t}} \right)^2} + \partial _{{x_1}}^2 + \cdots + \partial _{{x_n}}^2$$
. Combining properties of cone-degenerate operator, the Pohozaev manifold and qualitative properties of the ground state solution for the limit equation, we obtain a positive solution under some suitable conditions on a and f.
摘要:
Let G be a finite group, H be a proper subgroup of G, and S be a unitary subring of C. The kernel of the restriction map S[Irr(G)] → S[Irr(H)] as a ring homomorphism is studied. As a corollary, the main result in [Isaacs, I. M. and Navarro, G., Injective restriction of characters, Arch. Math., 108, 2017, 437–439] is reproved.
作者机构:
[Shan, Ming-yu; Jin, Shao-jia; Liu, Yan-yan] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China.;[Mao, Guang-cai] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构:
[Mao, GC ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
关键词:
auxiliary covariate;Kernel smoothing;logistic regression;mean residual life;mixture cure model
摘要:
As biological studies become more expensive to conduct, it is a frequently encountered question that how to take advantage of the available auxiliary covariate information when the exposure variable is not measured. In this paper, we propose an induced cure rate mean residual life time regression model to accommodate the survival data with cure fraction and auxiliary covariate, in which the exposure variable is only assessed in a validation set, but a corresponding continuous auxiliary covariate is ascertained for all subjects in the study cohort. Simulation studies elucidate the practical performance of the proposed method under finite samples. As an illustration, we apply the proposed method to a heart disease data from the Study of Left Ventricular Dysfunction.
作者机构:
[Duan, Renjun] Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China.;[Liu, Shuangqian] Cent China Normal Univ, Sch Math, Wuhan 430079, Peoples R China.;[Liu, Shuangqian] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Yang, Tong; Zhang, Zhu] Hong Kong Polytech Univ, Dept Appl Math, Hong Kong, Peoples R China.
通讯机构:
[Renjun Duan; Tong Yang; Zhu Zhang] D;[Shuangqian Liu] S;Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong, China<&wdkj&>School of Mathematics and Statistics and Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, China<&wdkj&>Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China<&wdkj&>Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China
作者机构:
[Chen, Gang; Ponomarenko, Ilia] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Ponomarenko, Ilia] Steklov Inst Math St Petersburg, St Petersburg, Russia.;[Ponomarenko, Ilia] Sobolev Inst Math, Novosibirsk, Russia.
通讯机构:
[Gang Chen] S;School of Mathematics and Statistics, Central China Normal University, Wuhan, China
摘要:
A Cartesian decomposition of a coherent configuration
$${\cal X}$$
is defined as a special set of its parabolics that form a Cartesian decomposition of the underlying set. It turns out that every tensor decomposition of
$${\cal X}$$
comes from a certain Cartesian decomposition. It is proved that if the coherent configuration
$${\cal X}$$
is thick, then there is a unique maximal Cartesian decomposition of
$${\cal X}$$
, i.e., there is exactly one internal tensor decomposition of
$${\cal X}$$
into indecomposable components. In particular, this implies an analog of the Krull-Schmidt theorem for the thick coherent configurations. A polynomial-time algorithm for finding the maximal Cartesian decomposition of a thick coherent configuration is constructed.
作者机构:
[Qin, Hong; Zou, Na] Zhongnan Univ Econ & Law, Sch Math & Stat, Wuhan 430073, Peoples R China.;[Qin, Hong] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
通讯机构:
[Hong Qin] S;School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, China<&wdkj&>Faculty of Mathematics and Statistics, Central China Normal University, Wuhan, China
作者机构:
[Huang, Ji-cai; Dong, Yue-ping; Xu, Qiang-hui; Dong, YP] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Huang, Ji-cai; Dong, Yue-ping; Xu, Qiang-hui; Dong, YP] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Takeuchi, Yasuhiro] Aoyama Gakuin Univ, Coll Sci & Engn, Sagamihara, Kanagawa 2525258, Japan.
通讯机构:
[Dong, YP ] 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:
HIV infection and persistence;T cell homeostatic proliferation;delayed model;dynamics analysis;Hopf bifurcation
作者机构:
[Huang, Xiaoyun; Huo, Ban; He, Tingting; Jiang, Xingpeng; Sun, Han; Fu, Lingling] Cent China Normal Univ, Hubei Prov Key Lab Artificial Intelligence & Smar, Wuhan 430079, Peoples R China.;[Huang, Xiaoyun; Huo, Ban; He, Tingting; Jiang, Xingpeng; Sun, Han; Fu, Lingling] Cent China Normal Univ, Sch Comp, Wuhan 430079, Peoples R China.;[Sun, Han; Fu, Lingling] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Huang, Xiaoyun] Cent China Normal Univ, Collaborat & Innovat Ctr Educ Technol, Wuhan 430079, Peoples R China.;[He, Tingting; Jiang, Xingpeng] Cent China Normal Univ, Natl Language Resources Monitoring & Res Ctr Netw, Wuhan 430079, Peoples R China.
通讯机构:
[Jiang, Xingpeng] C;Cent China Normal Univ, Hubei Prov Key Lab Artificial Intelligence & Smar, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Sch Comp, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Natl Language Resources Monitoring & Res Ctr Netw, Wuhan 430079, Peoples R China.
摘要:
The dysbiosis of microbiome may have negative effects on a host phenotype. The microbes related to the host phenotype are regarded as microbial association signals. Recently, statistical methods based on microbiome-phenotype association tests have been extensively developed to detect these association signals. However, the currently available methods do not perform well to detect microbial association signals when dealing with diverse sparsity levels (i.e., sparse, low sparse, non-sparse). Actually, the real association patterns related to different host phenotypes are not unique. Here, we propose a powerful and adaptive microbiome-based association test to detect microbial association signals with diverse sparsity levels, designated as MiATDS. In particular, we define probability degree to measure the associations between microbes and the host phenotype and introduce the adaptive weighted sum of powered score tests by considering both probability degree and phylogenetic information. We design numerous simulation experiments for the task of detecting association signals with diverse sparsity levels to prove the performance of the method. We find that type I error rates can be well-controlled and MiATDS shows superior efficiency on the power. By applying to real data analysis, MiATDS displays reliable practicability too. Copyright (C) 2021, Institute of Genetics and Developmental Biology, Chinese Academy of Sciences, and Genetics Society of China. Published by Elsevier Limited and Science Press. All rights reserved.
摘要:
Clustered interval-censored failure time data often occur in a wide variety of research and application fields such as cancer and AIDS studies. For such data, the failure times of interest are interval-censored and may be correlated for subjects coming from the same cluster. This paper presents a robust semiparametric transformation mixed effect models to analyze such data and use a U-statistic based on rank correlation to estimate the unknown parameters. The large sample properties of the estimator are also established. In addition, the authors illustrate the performance of the proposed estimate with extensive simulations and two real data examples.
作者机构:
[He, Yiming; Zi, Ruizhao] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Zi, Ruizhao] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构:
[Ruizhao Zi] S;School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, China
摘要:
Some sufficient conditions of the energy conservation for weak solutions of incompressible viscoelastic flows are given in this paper. First, for a periodic domain in ℝ3, and the coefficient of viscosity μ = 0, energy conservation is proved for u and F in certain Besov spaces. Furthermore, in the whole space ℝ3, it is shown that the conditions on the velocity u and the deformation tensor F can be relaxed, that is,
$$u \in B_{3,c(\mathbb{N})}^{{1 \over 3}}$$
, and
$$F \in B_{3,\infty }^{{1 \over 3}}$$
. Finally, when μ > 0, in a periodic domain in ℝd again, a result independent of the spacial dimension is established. More precisely, it is shown that the energy is conserved for u ∈ Lr (0, T; Ls (Ω)) for any
$${1 \over r} + {1 \over s} \leqslant {1 \over 2}$$
, with s ⩾ 4, and F ∈ Lm(0, T; Ln(Ω)) for any
$${1 \over m} + {1 \over n} \leqslant {1 \over 2}$$
, with n ⩾ 4.
作者机构:
[Lim, Meng Fai; Ahmed, Suman] 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:
[Lim, Meng Fai] 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:
Algebraic functional equation;mixed signed Selmer groups
摘要:
Let p be an odd prime number, and let E be an elliptic curve defined over a number field which has good reduction at every prime above p. Under suitable assumptions, we prove that the η-eigenspace and the
$$\overline \eta $$
-eigenspace of mixed signed Selmer group of the elliptic curve are pseudo-isomorphic. As a corollary, we show that the η-eigenspace is trivial if and only if the
$$\overline \eta $$
-eigenspace is trivial. Our results can be thought as a reflection principle which relates an Iwasawa module in a given eigenspace with another Iwasawa module in a “reflected” eigenspace.