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Nonlinear Preserver Problems on B（H）

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Acta Mathematica Sinica,English Series 2011年第1期27卷 193-202页

作者： jian Lian cui Department of Mathematical Science University of Tsinghua Beijing 100084 P. R. China

Let H be a complex Hilbert space of dimension greater than 2, and B（H） denote the Banach algebra of all bounded linear operators on H. For A, B C B（H）, define the binary relation A ≤ B by A＊A = A＊B and AA＊ = AB＊. Then （B（H）, ＂〈.＂） is a partially ordered set and the relation ＂≤＂ is called the star order on B（H）. Denote by Bs（H） the set of all self-adjoint operators in B（H）. In this paper, we first characterize nonlinear continuous bijective maps on Bs（H） which preserve the star order in both directions. We characterize also additive maps （or linear maps） on B（H）（or nest algebras） which are multiplicative at some invertible operator.

关键词： Star order fundamental operator algebras nest algebras preserver problems

Efficient Estimation of a Varying-coefficient Partially Linear Binary Regression Model

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Acta Mathematica Sinica,English Series 2010年第11期26卷 2179-2190页

作者： TaoHU Heng jian cui School of Mathematical Sciences Capital Normal University Beijing 100048 P. R. China School of Mathematical Sciences Beijing Normal University Beijing 100875 P. R. China

This article considers a semiparametric varying-coefficient partially linear binary regression model. The semiparametric varying-coefficient partially linear regression binary model which is a generalization of binary regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable. A Sieve maximum likelihood estimation method is proposed and the asymptotic properties of the proposed estimators are discussed. One of our main objects is to estimate nonparametric component and the unknowen parameters simultaneously. It is easier to compute, and the required computation burden is much less than that of the existing two-stage estimation method. Under some mild conditions, the estimators are shown to be strongly consistent. The convergence rate of the estimator for the unknown smooth function is obtained, and the estimator for the unknown parameter is shown to be asymptotically efficient and normally distributed. Simulation studies are carried out to investigate the performance of the proposed method.

关键词： Partially linear model varying-coefficient binary regression asymptotically efficient estimator sieve MLE

A Generalization of Strongly Nil Clean Rings

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Algebra Colloquium 2018年第4期25卷 585-594页

作者： jian cui Xiaobin Yin Department of Mathematics Anhui Normal UniversityWuhuAnhui 241002China

Generalizing the notion of strongly nil clean rings,we introduce strongly quasinil clean *** fundamental properties and equivalent characterizations of this class of rings are *** means of g-Drazin inverses,Cline's fo... 详细信息

关键词： strongly quasi-nil clean ring strongly nil clean ring strongly clean ring g-Drazin inverse

On π-Regular Rings with Involution

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Algebra Colloquium 2018年第3期25卷 509-518页

作者： jian cui Xiaobin Yin Department of Mathematics Anhui Normal University Wuhu Anhui 241000 China

A ring R is π-regular if for every a in R, there is a positive integer n such that a^n R is generated by an idempotent. In this paper, we introduce the notion of π-＊-regular rings, which is the ＊-version of π-regular rings. We prove various properties of π-＊-regular rings, and establish many equivalent characterizations of abelian π-＊-regular rings.

关键词： r-regular ring π-*-regular ring abelian ring generalized p.p. *-ring

Robust Error Density Estimation in Ultrahigh Dimensional Sparse Linear Model

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Acta Mathematica Sinica,English Series 2022年第6期38卷 963-984页

作者： Feng ZOU Heng jian cui School of Mathematical Sciences Capital Normal UniversityBeijing 100048P.R.China

This paper focuses on error density estimation in ultrahigh dimensional sparse linear model,where the error term may have a heavy-tailed ***,an improved two-stage refitted crossvalidation method combined with some robust variable screening procedures such as RRCS and variable selection methods such as LAD-SCAD is used to obtain the submodel,and then the residual-based kernel density method is applied to estimate the error density through LAD *** given conditions,the large sample properties of the estimator are also ***,we explicitly give the relationship between the sparsity and the convergence rate of the kernel density *** simulation results show that the proposed error density estimator has a good performance.A real data example is presented to illustrate our methods.

关键词： Ultrahigh dimensional sparse linear model robust density estimation refitted crossvalidation method asymptotic properties

Reliability analysis of reinforced concrete columns under combined seismic and blast loads

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Science China(Technological Sciences) 2023年第2期66卷 363-377页

作者： SHI YanChao SUN XiaoZhe cui jian Key Laboratory of Coast Civil Structure Safety of Ministry of Education Tianjin UniversityTianjin 300354China School of Civil Engineering Tianjin UniversityTianjin 300354China

It is possible for certain building structures to encounter both the seismic load and blast load during their service *** the development of the economy and the increase of security demand,the need for design of building structures against multi-hazard is becoming more and more ***,the damage analysis of building structures under the combined action of multiple hazards has become a very urgent requirement for disaster prevention and *** this paper,the refined finite element model of reinforced concrete(RC)columns is established by using the explicit dynamic analysis software *** with the Monte Carlo method,the damage law of RC columns under the combined action of random single earthquake or explosion disaster and multi-hazard is studied,and the damage groups are distinguished according to the damage *** on the support vector machine(SVM)algorithm,the dividing line between different damage degree groups is determined,and a rapid method for determining the damage degree of RC columns under the combined seismic and blast loads is ***,suggestions for the design of RC column against multi-disaster are put forward.

关键词： reliability analysis reinforced concrete(RC)column damage probability seismic load blast load Monte-Carlo method

Hypothesis Test for the Parameters of Linear Part in the Partial Linear EV Model

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Acta Mathematicae Applicatae Sinica 2015年第4期31卷 1153-1166页

作者： Juan ZHANG Heng-jian cui Capital University of Economics and Business Capital Normal University

Hypothesis testing for the parametric component in the partial linear errors-in-variables （EV） regression models is discussed in this paper. Based on the corrected profile least square estimator, five test statistics are proposed and the asymptotic null distributions of them are deduced. Simulations have been done to show the performance of these test statistics under null and alternative hypothesis.

关键词： partial linear model measurement error bandwidth selection hypothesis testing

Approximately Linear Mappings in Banach Modules over a C~*-algebra

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Acta Mathematica Sinica,English Series 2007年第11期23卷 1919-1936页

作者： Choonkil PARK jian Lian cui Department of Mathematics Hanyang University Seoul 133 791 Republic of Korea Department of Mathematical Sciences Tsinghua University Beijing 100084 P. R. China

Let X and Y be vector spaces. The authors show that a mapping f ： X →Y satisfies the functional equation 2d f（∑^2d j=1（-1）^j＋1xj/2d）=∑^2dj=1（-1）^j＋1f（xj） with f（0） = 0 if and only if the mapping f ： X→ Y is Cauchy additive, and prove the stability of the functional equation （≠） in Banach modules over a unital C^＊-algebra, and in Poisson Banach modules over a unital Poisson C＊-algebra. Let A and B be unital C^＊-algebras, Poisson C^＊-algebras or Poisson JC^＊- algebras. As an application, the authors show that every almost homomorphism h ： A →B of A into is a homomorphism when h（（2d-1）^nuy） =- h（（2d-1）^nu）h（y） or h（（2d-1）^nuoy） = h（（2d-1）^nu）oh（y） for all unitaries u ∈A, all y ∈ A, n = 0, 1, 2,.... Moreover, the authors prove the stability of homomorphisms in C^＊-algebras, Poisson C^＊-algebras or Poisson JC^＊-algebras.

关键词： C^*-algebra homomorphism stability Poisson C^*-algebra homomorphism Poisson Banach module over Poisson C^*-algebra Poisson JC^*-algebra homomorphism

Variance Variation Criterion and Consistency in Estimating the Number of Significant Signals of High-dimensional PCA

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Acta Mathematicae Applicatae Sinica 2022年第3期38卷 513-531页

作者： Guan-peng WANG Heng-jian cui School of Mathematical Sciences Capital Normal UniversityBeijing 100048China

In this paper,we propose a criterion based on the variance variation of the sample eigenvalues to correctly estimate the number of significant components in high-dimensional principal component analysis(PCA),and it corresponds to the number of significant eigenvalues of the covariance matrix for p-dimensional *** the random matrix theory,we derive that the consistent properties of the proposed criterion for the situations that the significant eigenvalues tend to infinity,as well as that the bounded significant population *** simulation shows that the probability of estimator is correct by our variance variation criterion converges to 1 is faster than that by criterion of Passemier and Yao[Estimation of the number of spikes,possibly equal,in the high-dimensional *** Anal.,(2014)](PYC),AIC and BIC under the finite fourth moment condition as the dominant population eigenvalues tend to ***,in the case of the maximum eigenvalue bounded,once the gap condition is satisfied,the rate of convergence to 1 is faster than that of PYC and AIC,especially the effect is better than AIC when the sample size is *** is worth noting that the variance variation criterion significantly improves the accuracy of model selection compared with PYC and AIC when the random variable is a heavy-tailed distribution or finite fourth moment not exists.

关键词： consistency variance variation criterion significant eigenvalues high dimension spiked model