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}.
摘要：
In this paper, we consider the following logarithmic Schrödinger equation $ \begin{equation*} -\varepsilon^2\Delta u + V(x)u = u\log u^2\ \ \text{in}\ {\mathbb R}^N, \end{equation*} $ where $ \varepsilon>0 $, $ N\ge 1 $, $ V(x)\in C({\mathbb R}^N, {\mathbb R}) $ is a continuous potential which can be unbounded below. By variational methods and penalized idea, we show that the problem has a family of solutions $ u_{\varepsilon} $ concentrating at any finite given local minima of $ V $. Our results generalize the single peak case in [36] to the multi-peak case but the penalization in this paper is different.
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：
Selima, Ehab S.;Abu-Nab, Ahmed K.;Morad, Adel M.
期刊：
Mathematical Methods in the Applied Sciences,2023年 ISSN：0170-4214
通讯作者：
Morad, AM
作者机构：
[Abu-Nab, Ahmed K.; Morad, Adel M.; Selima, Ehab S.] Menoufia Univ, Fac Sci, Dept Math & Comp Sci, Shibin Al Kawm, Egypt.;[Selima, Ehab S.] Cent China Normal Univ, Fac Math & Stat, Wuhan, Peoples R China.;[Abu-Nab, Ahmed K.; Selima, Ehab S.] Acad Sci Res & Technol ASRT, Cairo, Egypt.;[Abu-Nab, Ahmed K.] Moscow Inst Phys & Technol, Phystech Sch Appl Math & Informat, Dolgoprudnyi, Russia.;[Morad, Adel M.] Univ Sadat City, Fac Comp & Artificial Intelligence, Sadat City, Egypt.
通讯机构：
[Morad, AM ] M;Menoufia Univ, Fac Sci, Dept Math & Comp Sci, Shibin Al Kawm 32511, Egypt.
摘要：
The ( 2 + 1 ) $$ \left(2+1\right) $$ -dimensional coupled cubic–quintic complex Ginzburg–Landau equations ( ( 2 + 1 ) $$ \left(2+1\right) $$ -DCC-QCGLEs) can simulate a variety of binary fluid thermal convection characteristics, containing complex parameters. The analysis of pattern formation in chaotic and nonlinear dynamical systems can benefit greatly from the use of this thermal convection model. The primary goal of this study is to find analytical solutions for some recent advances that have been made for Rayleigh–Bénard convection by applying the ( 2 + 1 ) $$ \left(2+1\right) $$ -DCC-QCGLEs model for slowly varying spatio-temporal amplitudes of the wave motion. In addition, novel traveling solitary wave solutions for the model equation are derived using a very useful method to investigate how complex physical coefficients affect the profiles of propagating waves. Furthermore, we introduce the WTC-Kruskal algorithm of the Painlevé methodology to examine the integrability of the ( 2 + 1 ) $$ \left(2+1\right) $$ -DCC-QCGLEs and the truncated Painlevé expansion is used to extract the Bäcklund transform, from which new solitary solutions can be acquired. The results also demonstrated a good agreement with previous works and were more significant and accurate in two and three dimensions of the proposed model. Finally, the computational results indicate that the effects of the physical parameters of the considered equations can be demonstrated by utilizing 2D and 3D graphics for different values of these parameters.
期刊：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS,2023年44(1):182-204 ISSN：1078-0947
通讯作者：
Guo, YJ
作者机构：
[Li, Yan; Guo, Yujin; Liang, Wenning] Cent China Normal Univ, Sch Math & Stat, Key Lab Nonlinear Anal & Applicat, Minist Educ, Wuhan 430079, Peoples R China.
通讯机构：
[Guo, YJ ] C;Cent China Normal Univ, Sch Math & Stat, Key Lab Nonlinear Anal & Applicat, Minist Educ, Wuhan 430079, Peoples R China.
关键词：
The planar Schrodinger-Poisson system;constraint minimizers;loga-rithmic potentials;asymptotic expansions;refined spike profiles
摘要：
This paper is concerned with constraint minimizers of the planar Schrodinger-Poisson system with a logarithmic convolution potential and a logarithmic external potential V (x) = ln(1+|x|(2)). It is known that minimizers exist if and only if the particle mass p > 0 satisfies p < p* for some threshold p* is an element of(0, infinity). As a continuation of [22], this paper is devoted to analyzing the refined spike profiles of constraint minimizers as p NE arrow p*.
期刊：
CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE,2023年:- ISSN：0319-5724
通讯作者：
Liu, YY
作者机构：
[Jin, Shaojia; Liu, Yanyan] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China.;[Jin, Shaojia] Wuhan Text Univ, Sch Math & Phys Sci, Wuhan 430200, Peoples R China.;[Mao, Guangcai] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Mao, Guangcai] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Sun, Jianguo] Univ Missouri, Dept Stat, Columbia, MO USA.
通讯机构：
[Liu, YY ] W;Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China.
摘要：
Abstract This article discusses nonparametric estimation of a survival function in the presence of measurement errors on the observation of the failure time of interest. One situation where such issues arise would be clinical studies of chronic diseases where the observation on the time to the failure event of interest such as the onset of the disease relies on patient recall or chart review of electronic medical records. It is easy to see that both situations can be subject to measurement errors. To resolve this problem, we propose a simulation extrapolation approach to correct the bias induced by the measurement error. To overcome potential computational difficulties, we use spline regression to approximate the unspecified extrapolated coefficient function of time, and establish the asymptotic properties of our proposed estimator. The proposed method is applied to nonparametric estimation based on interval‐censored data. Extensive numerical experiments involving both simulated and actual study datasets demonstrate the feasibility of this proposed estimation procedure. Résumé Cet article traite de l'estimation non paramétrique d'une fonction de survie en présence d'erreurs de mesure lors de l'observation du temps de défaillance d'intérêt. Une situation où de telles problématiques se posent fréquemment est celle des études cliniques sur les maladies chroniques, où l'observation du temps écoulé jusqu'à l'événement de défaillance d'intérêt, tel que l'apparition de la maladie, repose sur la mémoire du patient ou sur l'examen des dossiers médicaux électroniques. Il est évident que ces deux contextes sont sujets à des erreurs de mesure. Pour résoudre ce défi, les auteurs de cet article proposent une approche d'extrapolation par simulation visant à corriger le biais induit par l'erreur de mesure. Afin de surmonter d'éventuelles complexités computationnelles, ils utilisent la régression spline pour approximer la fonction de coefficient extrapolée non spécifiée en fonction du temps, tout en établissant les propriétés asymptotiques de l'estimateur proposé. Cette méthode est ensuite appliquée à l'estimation non paramétrique basée sur des données censurées par intervalles. Des expérimentations numériques approfondies, incluant à la fois des jeux de données simulés et des données d'études réelles, mettent en évidence la faisabilité de cette procédure d'estimation proposée.
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
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.
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.
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：
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)
作者机构：
[Liu, Ning; Jiang, Anguo] South China Univ Technol, Sch Math, Guangzhou 510640, Guangdong, Peoples R China.;[Jing, Naihuan] North Carolina State Univ, Dept Math, Raleigh, NC 27695 USA.;[Jing, Naihuan] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
通讯机构：
[Naihuan Jing] D;Department of Mathematics, North Carolina State University, Raleigh, USA<&wdkj&>School of Mathematics and Statistics, Central China Normal University, Wuhan, China
摘要：
We study the Q-Kostka polynomials
$$L_{\lambda \mu }(t)$$
by the vertex operator realization of the Q-Hall–Littlewood functions
$$G_{\lambda }(x;t)$$
and derive new formulae for
$$L_{\lambda \mu }(t)$$
. In particular, we have established stability property for the Q-Kostka polynomials. We also introduce spin Green polynomials
$$Y^{\lambda }_{\mu }(t)$$
as both an analogue of the Green polynomials and deformation of the spin irreducible characters of
$$\mathfrak S_n$$
. Iterative formulas of the spin Green polynomials are given and some favorable properties parallel to the Green polynomials are obtained. Tables of
$$Y^{\lambda }_{\mu }(t)$$
are included for
$$n\le 7.$$
