Wold decomposition in Banach spaces

We propose a natural analog of the Wold decomposition in the case of a linear noninvertible isometry V in a Banach space X. We obtain a criterion for the existence of such a decomposition. In a reflective space, this criterion is reduced to the existence of the linear projection P: X → VX with unit norm. Separately, we discuss the problem of the Wold decomposition for the isometry V _φ induced by an epimorphism φ of a compact set H in the space of continuous functions C(H). We present a detailed study of the mapping z → z ^m of the circle |z| = 1 with an integer m ≥ 2.     

A New Expectation Identity and Its Application in the Calculations of Predictive Powers Assuming Normality

For calculating the predictive powers, we suggest an elegant expectation identity to directly calculate the expectations. We calculate the predictive powers of the hypotheses with a nonzero threshold for five different categories, which are non-sequential trials with classical power and Bayesian power, and sequential trials with hybrid predictions, Bayesian predictions, and classical predictions. Moreover, the calculations of the various predictive powers are illustrated through three examples. Finally, when calculating the average success probability in \ncite{9}, it is tricky to find the predictive distribution for the predictive power, whereas, it is straightforward to utilize the expectation identity for the calculation.     

Exchange rings in which all regular elements are one-sided unit-regular

Let R be an exchange ring in which all regular elements are one-sided unit-regular. Then every regular element in R is the sum of an idempotent and a one-sided unit. Furthermore, we extend this result to exchange rings satisfying related comparability.     

波前功率谱密度函数评价方法探讨

 波前功率谱密度PSD（Power Spectral Density）能定量给出波前畸变的空间频率分布、限定波纹度和粗糙度指标，全面反映ICF驱动器对高功率激光光学元件加工质量的特殊要求。给出了波前功率谱密度PSD的定义及计算方法，并使用大口径相移干涉仪作为波前检测仪器，对光学磷酸盐钕玻璃透射波前进行了测试实验，获得波前一维PSD分布，证实功率谱密度为高功率激光光学元件波前参数的一种有效表征方式。同时，还对PSD与均方根RMS之间的关系进行了初步的讨论。     

A note on testing two-dimensional normal mean

Summary For the problem of testing a composite hypothesis with one-sided alternatives of the mean vector of a two-dimensional normal distribution, a characterization of similar tests is presented and an unbiased test dominating the likelihood ratio test is proposed. A sufficient condition for admissibility is given, which implies the result given by Cohen et al. (1983,Studies in Econometrics, Time Series and Multivariate Statistics, Academic Press): the admissibility of the likelihood ratio test.     

Rank-one operators in reflexive one-sided<Emphasis Type="Italic">A</Emphasis>-submodules

In this paper, we first characterize reflexive one-sided A-submodulesU of a unital operator algebraA inB(H) completely. Furthermore we investigate the invariant subspace lattice LatR and the reflexive hull RefR, whereR is the submodule generated by rank-one operators inU; in particular, ifL is a subspace lattice, we obtain when the rank-one algebraR of AlgL is big enough to determined AlgL in the following senses: AlgL = Alg LatR and AlgL = RefR.     

位置探测器PSD应用于三维坐标测量的理论研究

提出了一种应用位置探测器 PSD进行三维坐标测量的新技术 ,介绍了由三套 PSD对空间发光点交汇成像而构成的三坐标测量系统。阐述了该系统的测量原理及测量精度分析。该系统具有结构简单、应用方便、自动化程度高、测量精度高、适用范围广等重要特点 ,可有效地应用于机械制造、机器人及汽车检测、航空及医学等测量领域     

枕型二维位敏探测器的结构和性能研究

本文从二维位敏探测器(PSD)的结构和性能的比较出发,对枕型结构PSD的性能作了理论上的推导和分析,由此得到的结论和现有的实验结果相符.     

指示光源衍射所引起的位置敏感探测器附加定位误差探讨

介绍位置敏感探测器工作原理,分析了其自动取光斑重心的定位机理。概括了位置敏感探测器的各种工作方式,指出了在许多位置敏感探测器的应用场合,光源衍射不可避免,并从理论上分析了因衍射而造成的对位置第三探测器定位的影响,为估算由此造成的定位误差提供了理论依据,同时对工程应用也有一定的参考价值。     

High-order sum-of-squares structured tensors:theory and applications

Tensor decomposition is an important research area with numerous applications in data mining and computational neuroscience.An important class of tensor decomposition is sum-of-squares(SOS)tensor decomposition.SOS tensor decomposition has a close connection with SOS polynomials,and SOS polynomials are very important in polynomial theory and polynomial optimization.In this paper,we give a detailed survey on recent advances of high-order SOS tensors and their applications.It first shows that several classes of symmetric structured tensors available in the literature have SOS decomposition in the even order symmetric case.Then,the SOS-rank for tensors with SOS decomposition and the SOS-width for SOS tensor cones are established.Further,a sharper explicit upper bound of the SOS-rank for tensors with bounded exponent is provided,and the exact SOS-width for the cone consists of all such tensors with SOS decomposition is identified.Some potential research directions in the future are also listed in this paper.