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.
摘要：
For high-dimensional models with a focus on classification performance, the ℓ1-penalized logistic regression is becoming important and popular. However, the Lasso estimates could be problematic when penalties of different coefficients are all the same and not related to the data. We propose two types of weighted Lasso estimates, depending upon covariates determined by the McDiarmid inequality. Given sample size n and a dimension of covariates p, the finite sample behavior of our proposed method with a diverging number of predictors is illustrated by non-asymptotic oracle inequalities such as the ℓ1-estimation error and the squared prediction error of the unknown parameters. We compare the performance of our method with that of former weighted estimates on simulated data, then apply it to do real data analysis.
作者机构：
[Jin, Jing; Jiang, Qin] Huanggang Normal Univ, Sch Math & Stat, Huanggang 438000, Peoples R China.;[Rehman, Noor] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Jin, Jing] H;Huanggang Normal Univ, Sch Math & Stat, Huanggang 438000, Peoples R China.
摘要：
In 2018, Duan [1] studied the case of zero heat conductivity for a one-dimensional compressible micropolar fluid model. Due to the absence of heat conductivity, it is quite difficult to close the energy estimates. He considered the far-field states of the initial data to be constants; that is,
$$\mathop {\lim }\limits_{x \to \pm \infty } ({v_0},{u_0},{\omega _0},{\theta _0})(x) = (1,0,0,1)$$
. He proved that the solution tends asymptotically to those constants. In this article, under the same hypothesis that the heat conductivity is zero, we consider the far-field states of the initial data to be different constants — that is,
$$\mathop {\lim }\limits_{x \to \pm \infty } ({v_0},{u_0},{\omega _0},{\theta _0})(x) = ({v_ \pm },{u_ \pm },0,{\theta _ \pm })$$
-and we prove that if both the initial perturbation and the strength of the rarefaction waves are assumed to be suitably small, the Cauchy problem admits a unique global solution that tends time — asymptotically toward the combination of two rarefaction waves from different families.
作者机构：
[Li, Gongbao] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Li, Gongbao] C;Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
摘要：
In this paper, we study the existence and multiplicity of solutions with a prescribed L-2-norm for a class of nonlinear fractional Choquard equations in Double-struck capital R-N: (-Delta)su-lambda u=(kappa a*|u|p-2u)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${( - \Delta )<^>s}u - \lambda u = ({\kappa _a}*|u{|<^>{p - {2_u}}})$$\end{document} where N > 3, s is an element of (0, 1), alpha is an element of (0, N), p is an element of(max{1+a+2sN,2}N+aN-2s)and kappa a(x)=|x|a-N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p \in (max\{ 1 + \frac{{a + 2s}}{N},2\} \frac{{N + a}}{{N - 2s}})and{\kappa _a}(x) = |x{|<^>{a - N}}$$\end{document} considered, the functional I is unbounded from below on S(c). By using the constrained minimization method on a suitable submanifold of S(c), we prove that for any c > 0, I has a critical point on S(c) with the least energy among all critical points of I restricted on S(c). After that, we describe a limiting behavior of the constrained critical point as c vanishes and tends to infinity. Moreover, by using a minimax procedure, we prove that for any c > 0, there are infinitely many radial critical points of I restricted on S(c).
作者机构：
[Yang, Qing] South Cent Univ Nationalities, Sch Math & Stat, Wuhan 430074, Peoples R China.;[Zhu, Jiayan] Hubei Univ Chinese Med, Sch Informat Engn, Wuhan 430065, Peoples R China.;[Li, Zhengbang] Cent China Normal Univ, Sch Math, Wuhan 430079, Peoples R China.;[Li, Zhengbang] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Zhu, Jiayan] H;Hubei Univ Chinese Med, Sch Informat Engn, Wuhan 430065, Peoples R China.
关键词：
Maximum test;quadratic form statistics;score test;asymptotic statistical property
摘要：
This article proposes the maximum test for a sequence of quadratic form statistics about score test in logistic regression model which can be applied to genetic and medicine fields. Theoretical properties about the maximum test are derived. Extensive simulation studies are conducted to testify powers robustness of the maximum test compared to other two existed test. We also apply the maximum test to a real dataset about multiple gene variables association analysis.
摘要：
This paper proposes a double penalized quantile regression for linear mixed effects model, which can select fixed and random effects simultaneously. Instead of using two tuning parameters, the proposed iterative algorithm enables only one optimal tuning parameter in each step and is more efficient. The authors establish asymptotic normality for the proposed estimators of quantile regression coefficients. Simulation studies show that the new method is robust to a variety of error distributions at different quantiles. It outperforms the traditional regression models under a wide array of simulated data models and is flexible enough to accommodate changes in fixed and random effects. For the high dimensional data scenarios, the new method still can correctly select important variables and exclude noise variables with high probability. A case study based on a hierarchical education data illustrates a practical utility of the proposed approach.
作者机构：
[Li, Gongbao] Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Li, Gongbao] C;Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
作者机构：
[Wang, Chunhua; Zhou, Jing] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Wang, Chunhua; Zhou, Jing] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Zhou, Jing] South Cent Univ Nationalities, Sch Math & Stat, Wuhan 430000, Peoples R China.
通讯机构：
[Zhou, Jing] C;[Zhou, Jing] S;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.;South Cent Univ Nationalities, Sch Math & Stat, Wuhan 430000, Peoples R China.
摘要：
In this paper, we consider the following coupled Schrödinger system with χ(2) nonlinearities $\left\{ \begin{array}{l} - \Delta {u_1} + {V_1}\left( x \right){u_1} = \alpha {u_1}{u_2},\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x \in {^N}, \\ - \Delta {u_2} + {V_2}\left( x \right){u_2} = \frac{\alpha }{2}u_1^2 + \beta u_2^2,\,\,\,\,\,\,\,\,\,\,\,\,\,x \in {^N}, \\ \end{array} \right.$ which arises from second-harmonic generation in quadratic media. Here V1(x) and V2(x) are radially positive functions, 2 ≤ N < 6, α > 0 and α > β. Assume that the potential functions V1(x) and V2(x) satisfy some algebraic decay at infinity. Applying the finite dimensional reduction method, we construct an unbounded sequence of non-radial vector solutions of synchronized type.
作者：
Chen, You Li;Liu, Yan Yan*;Mao, Guang Cai;Wu, Yuan Shan;Yan, Fei
期刊：
数学学报：英文版,2020年36(9):1014-1024 ISSN：1439-8516
通讯作者：
Liu, Yan Yan
作者机构：
[Chen, You Li] Wuhan Univ, Law Sch, Wuhan 430072, Peoples R China.;[Liu, Yan Yan; Yan, Fei] 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.;[Wu, Yuan Shan] Zhongnan Univ Econ & Law, Sch Stat & Math, Wuhan 430073, Peoples R China.
通讯机构：
[Liu, Yan Yan] W;Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China.
摘要：
Among recent measures for risk management, value at risk (VaR) has been criticized because it is not coherent and expected shortfall (ES) has been criticized because it is not robust to outliers. Recently, [Math. Oper. Res., 38, 393–417 (2013)] proposed a risk measure called median shortfall (MS) which is distributional robust and easy to implement. In this paper, we propose a more generalized risk measure called quantile shortfall (QS) which includes MS as a special case. QS measures the conditional quantile loss of the tail risk and inherits the merits of MS. We construct an estimator of the QS and establish the asymptotic normality behavior of the estimator. Our simulation shows that the newly proposed measures compare favorably in robustness with other widely used measures such as ES and VaR.
作者机构：
[Fan, Ai Hua] Univ Picardie, LAMFA, UMR CNRS 7352, 33 Rue St Leu, F-80039 Amiens, France.;[Fan, Shi Lei] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Fan, Shi Lei] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Fan, Ai Hua] U;Univ Picardie, LAMFA, UMR CNRS 7352, 33 Rue St Leu, F-80039 Amiens, France.
作者机构：
[Guedjiba, Djalal Eddine; Deng, Qingquan] Cent China Normal Univ, Sch Math & Stat, Hubei Prov Key Lab Math Phys, Wuhan 430079, Peoples R China.;[Guedjiba, Djalal Eddine] Univ Batna 2, Dept Math, 53 Route Constantine, Fesdis 05078, Batna, Algeria.
通讯机构：
[Deng, Qingquan] C;Cent China Normal Univ, Sch Math & Stat, Hubei Prov Key Lab Math Phys, Wuhan 430079, Peoples R China.
关键词：
Produce Hardy space;Ap weights;Davies-Ga_ney estimates
摘要：
Assuming that the operators L1, L2 are self-adjoint and
$${{\rm{e}}^{ - t{L_i}}}$$
(i = 1, 2) satisfy the generalized Davies-Gaffney estimates, we shall prove that the weighted Hardy space
$$H_{{L_1},{L_2},\omega }^1({\mathbb{R}^{{n_1}}} \times {\mathbb{R}^{{n_2}}})$$
associated to operators L1, L2 on product domain, which is defined in terms of area function, has an atomic decomposition for some weight ω.
