Analysis of a right-angle conical reflector resonator by the transfer matrix method

A resonator with a right-angle conical reflector has been proposed to produce high-power CO₂ laser beams. To analyze eigenfields of the right-angle conical reflector resonator, this paper adopts and demonstrates the transfer matrix method. In this paper, the mode-fields and corresponding losses are described as eigenvectors and eigenvalues of a transfer matrix according to the self-reproducing principle of laser field. By solving the transfer matrix for eigenvectors and eigenvalues, we obtain field distributions and losses of the dominant eigenmodes. The calculation results reveal that the right-angle conical reflector resonator could be used for a high-power CO₂ laser to achieve low-order modes. However, the beam quality is reduced due to the residual blind-hole, which is in accord with the experimental result.     

Linear maps preserving the minimum and surjectivity moduli of Hilbert space operators

Let B(H) be the algebra of all bounded linear operators on a complex infinite-dimensional Hilbert space H. For every T∈B(H), let m(T) and q(T) denote the minimum modulus and surjectivity modulus of T respectively. Let ?:B(H)→B(H) be a surjective linear map. In this paper, we prove that the following assertions are equivalent:

(i)

m(T)=m(?(T)) for all T∈B(H),

(ii)

q(T)=q(?(T)) for all T∈B(H),

(iii)

there exist two unitary operators U,V∈B(H) such that ?(T)=UTV for all T∈B(H).

This generalizes the result of Mbekhta [7, Theorem 3.1] to the non-unital case.     

直角棱镜平面反射衰减在激光光束诊断中的应用研究

论述了普通光学元件-直角平面反射镜在激光光束诊断中的应用,提出了利用直角棱镜的直角面反射进行光能衰减,详细论述了采用该方法进行光能衰减的可行性,分析了平面反射衰减法在激光束诊断中对测光束的影响,讨论了激光束发散角在直角面反射中的影响,结合半导体光束诊断进行了应用分析.实验证明,该方法结构简单,误差小,调整方便,利用普通反射棱镜直角面衰减即可满足激光强度的匹配要求,实现了待测激光束的无失真取样,达到了很好的测试效果.     

Zero commutativity of nilpotent elements skewed by ring endomorphisms

The reversible property is an important role in noncommutative ring theory. Recently, the study of the reversible ring property on nilpotent elements is established by Abdul-Jabbar et al., introducing the concept of commutativity of nilpotent elements at zero (simply, a CNZ ring) as a generalization of reversible rings. We here study this property skewed by a ring endomorphism α, and such ring is called a right α-skew CNZ ring which is an extension of CNZ rings as well as a generalization of right α-skew reversible rings, and then investigate the structure of right α-skew CNZ rings and their related properties. Consequently, several known results are obtained as corollaries of our results.     

Polynomial Regression with Censored Data based on Preliminary Nonparametric Estimation

Consider the polynomial regression model , where σ²(X)=Var(Y|X) is unknown, and ε is independent of X and has zero mean. Suppose that Y is subject to random right censoring. A new estimation procedure for the parameters β₀,...,β _p is proposed, which extends the classical least squares procedure to censored data. The proposed method is inspired by the method of Buckley and James (1979, Biometrika, 66, 429–436), but is, unlike the latter method, a noniterative procedure due to nonparametric preliminary estimation of the conditional regression function. The asymptotic normality of the estimators is established. Simulations are carried out for both methods and they show that the proposed estimators have usually smaller variance and smaller mean squared error than the Buckley–James estimators. The two estimation procedures are also applied to a medical and an astronomical data set.     

关于半群环与群环的链条件的等价性

给出了将半群环的链条件转化为群环的链条件的一个定理,并由此将［１］中的结果推广到半群环的情形．     

右Clifford左商半群

本文讨论了右Ｃｌｉｆｆｏｒｄ左商半群．利用所谓的可适对刻划了右Ｃｌｉｆｆｏｒｄ半群中的左次半群,因此扩展了商半群的研究范围．     

有限链上的左(右)零模

为了更好地描述信息的聚合,有限链上的左(右)nullnorm的概念被引入。然后,各种光滑的左(右)nullnorm的结构定理被给出,即给出了一个二元运算是光滑的左(右)nullnorm的充要条件。     

长度偏差右删失数据剩余寿命的分位数回归

本文研究长度偏差数据下剩余寿命分位数模型的估计方法,充分考虑有偏抽样机制对模型估计的影响.如果忽略这种有偏性会导致估计产生严重偏差甚至错误的结果.本文首先针对长度偏差右删失数据的剩余寿命分位数提出了对数形式的线性回归模型,对删失变量与协变量独立和不独立的两种情况利用估计方程给出了模型参数的估计.其次,通过经验过程和弱收敛理论给出了参数估计的相合性和渐近正态性.最后,本文对提出的估计方法进行了数值模拟并用该方法对奥斯卡奖数据进行分析.