期刊：
Complex Analysis and Operator Theory,2023年17(1):1-17 ISSN：1661-8254
通讯作者：
Min-Min Zhang
作者机构：
[Zhang, Min-Min; Wei, Saidi] Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Min-Min Zhang] H;Hubei Key Laboratory of Mathematical Sciences, School of Mathematics and Statistics, Central China Normal University, Wuhan, People’s Republic of China
摘要：
Let
$$\mu _{M,D}$$
be the self-affine measure associated with an expanding integer matrix
$$M=\left( \begin{array}{cc} p &{} 0 \\ 0 &{} q \\ \end{array}\right) $$
and
$$D=\left\{ \,\,\begin{pmatrix} 0\\ 0 \end{pmatrix},\,\,\,\begin{pmatrix} 1\\ 1 \end{pmatrix} \,\,\right\} $$
, where |p| and |q| are distinct odd bigger than 1. Such a measure is the simplest and the most important case in the study of the spectral property of self-affine measures with two-elements digit sets, which is an open problem up to now. In this paper, we first construct two classes of 4-element orthogonal exponentials in the corresponding Hilbert space
$$L^2(\mu _{M,D})$$
. Moreover, we prove that, under certain conditions, the constructed 4-element orthogonal exponentials is maximal.
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.
作者机构：
[Ma, Junru] Hubei Univ, Sch Cyber Sci & Technol, Hubei Key Lab Appl Math, Wuhan 430062, Hubei, Peoples R China.;[Luo, Jinquan] Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Hubei, Peoples R China.
通讯机构：
[Jinquan Luo] S;School of Mathematics and Statistics, Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan 430079, Hubei, China
摘要：
Symbol-pair codes are proposed to guard against pair-errors in symbol-pair read channels. The minimum symbol-pair distance is of significance in determining the error-correcting capability of a symbol-pair code. One of the central themes in symbol-pair coding theory is the constructions of symbol-pair codes with the largest possible minimum symbol-pair distance. Maximum distance separable (MDS) and almost maximum distance separable (AMDS) symbol-pair codes are optimal and sub-optimal regarding the Singleton bound, respectively. In this paper, six new classes of AMDS symbol-pair codes are explicitly constructed through repeated-root cyclic codes. Remarkably, one class of such codes has unbounded lengths and the minimum symbol-pair distance of another class can reach 13.(c) 2023 Elsevier B.V. All rights reserved.
作者机构：
[Cui, Hengjian] Capital Normal Univ, Sch Math Sci, Beijing, Peoples R China.;[Liu, Yanyan] Wuhan Univ, Sch Math & Stat, Wuhan, Hubei, Peoples R China.;[Mao, Guangcai] Cent China Normal Univ, Sch Math & Stat, Wuhan, Hubei, Peoples R China.;[Zhang, Jing] Zhongnan Univ Econ & Law, Sch Stat & Math, Wuhan, Hubei, Peoples R China.;[Zhang, Jing] Zhongnan Univ Econ & Law, Sch Stat & Math, Wuhan 430073, Hubei, Peoples R China.
通讯机构：
[Jing Zhang; Jing Zhang Jing Zhang Jing Zhang] S;School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, Hubei, China
关键词：
conditional distance correlation;model-free screening;sure screening property;ultrahigh-dimensional survival data
摘要：
How to select the active variables that have significant impact on the event of interest is a very important and meaningful problem in the statistical analysis of ultrahigh-dimensional data. In many applications, researchers often know that a certain set of covariates are active variables from some previous investigations and experiences. With the knowledge of the important prior knowledge of active variables, we propose a model-free conditional screening procedure for ultrahigh dimensional survival data based on conditional distance correlation. The proposed procedure can effectively detect the hidden active variables that are jointly important but are weakly correlated with the response. Moreover, it performs well when covariates are strongly correlated with each other. We establish the sure screening property and the ranking consistency of the proposed method and conduct extensive simulation studies, which suggests that the proposed procedure works well for practical situations. Then, we illustrate the new approach through a real dataset from the diffuse large-B-cell lymphoma study S1.
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：
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.
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：
Journal of Mathematical Physics,2023年64(1):011506 ISSN：0022-2488
通讯作者：
Xiaoming An<&wdkj&>Xian Yang
作者机构：
[An, Xiaoming] Guizhou Univ Finance & Econ, Sch Math & Stat, Guiyang 550025, Peoples R China.;[Yang, Xian] Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Xiaoming An; Xian Yang] S;School of Mathematics and Statistics, Hubei Key Laboratory of Mathematical Sciences, Central China Normal University , Wuhan 430079, People’s Republic of China<&wdkj&>School of Mathematics and Statistics, Guizhou University of Finance and Economics , Guiyang 550025, People’s Republic of China
摘要：
In this paper, we show a connection between fractional Schrödinger equations with power-law nonlinearity and fractional Schrödinger equations with logarithm-law nonlinearity. We prove that ground state solutions of power-law fractional equations, as p → 2+, converge to a ground state solution of logarithm-law fractional equations. In particular, we provide a new proof to the existence of a ground state of logarithm-law fractional Schrödinger equations.
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：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS,2023年43(1):482-506 ISSN：1078-0947
通讯作者：
Angela Pistoia
作者机构：
[Chen, Haixia] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.;[Pistoia, Angela] Sapienza Univ Roma, Dipartimento Sci Base & Applicate Ingn, Rome, Italy.;[Vaira, Giusi] Univ Bari Aldo Moro, Dipartimento Matemat, Bari, Italy.
通讯机构：
[Angela Pistoia] D;Dipartimento di Scienze di Base e Applicate per l'Ingegneria, Sapienza Università di Roma, Italy
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.
期刊：
Journal of Algebra,2023年635:463-485 ISSN：0021-8693
通讯作者：
Guo, HY
作者机构：
[Li, Huaimin; Guo, Hongyan] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Li, Huaimin; Guo, Hongyan] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Guo, HY ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
摘要：
In this paper, a family of infinite dimensional Lie algebras G & SIM; is introduced and investigated, called the extended Heisenberg-Virasoro algebra, denoted by G & SIM;. These Lie algebras are related to the N = 2 superconformal algebra and the Bershadsky-Polyakov algebra. We study restricted modules and associated vertex algebras of the Lie algebra G & SIM;. More precisely, we construct its associated vertex (operator) algebras VL & SIM;(e123, 0), and show that the category of vertex algebra VL & SIM;(�123, 0)-modules is equivalent to the category of restricted & SIM; of level & POUND;123. Then we give uniform constructions of simple restricted G & SIM;-modules. Also, we present several equivalent characterizations of simple restricted modules over G & SIM;.& COPY; 2023 Elsevier Inc. All rights reserved. G-modules
期刊：
Journal of Functional Analysis,2023年284(6):109816 ISSN：0022-1236
通讯作者：
Xiaohua Yao
作者机构：
[Li, Ping] Yangtze Univ, Sch Informat & Math, Jingzhou 434000, Peoples R China.;[Soffer, Avy] Rutgers State Univ, Math Dept, New Brunswick, NJ 08903 USA.;[Yao, Xiaohua] Cent China Normal Univ, Dept Math, Wuhan 430079, Peoples R China.;[Yao, Xiaohua] Cent China Normal Univ, Hubei Prov Key Lab Math Phys, Wuhan 430079, Peoples R China.
通讯机构：
[Xiaohua Yao] D;Department of Mathematics and Hubei Province Key Laboratory of Mathematical Physics, Central China Normal University, Wuhan, 430079, China
关键词：
Decay estimates;Fourth-order Schr?dinger operators;Asymptotic expansion of resolvent;Dimension two
摘要：
In this paper we study the decay estimates of the fourth order Schrodinger operator H = Delta 2 + V(x) on R2 with a bounded decaying potential V(x). We first deduce the asymptotic expansions of resolvent of H near zero threshold in the presence of resonances or eigenvalue, and then use them to establish the L1 - L infinity decay estimates of e-itH generated by the fourth order Schrodinger operator H. Our methods used in the decay estimates depend on Littlewood-Paley decomposition and oscillatory integral theory. Moreover, we also classify these zero resonances as the distributional solutions of H phi = 0 in suitable weighted spaces. Due to the degeneracy of Delta 2 at zero threshold, we remark that the asymptotic expansions of resolvent RV (lambda 4) and the classifications of resonances are much more involved than Schrodinger operator -Delta + V in dimension two.(c) 2022 Elsevier Inc. All rights reserved.
