基于F-P标准具的固体激光可调线宽控制技术

钠导星激光研制需激光线宽在一定范围内可调节。开展了F-P标准具压窄线宽数值模拟,设计一台高光束质量基横模线偏振激光输出全固态1064 nm激光器作为实验装置,结合激光器输出光谱特性进行计算。根据计算结果采用不同规格的单标准具、组合双标准具实现了激光线宽在0.75 ~2.83 GHz范围内的离散调节控制。在标准具未控温情况下,不同线宽时激光中心波长保持1064.58 nm,30 min内波长漂移量小于3 pm。     

Principally Quasi-Baer Skew Power Series Rings

Let α be an endomorphism of R which is not assumed to be surjective and R be α-compatible. It is shown that the skew power series ring R[[x; α]] is right p.q.-Baer if and only if the skew Laurent series ring R[[x, x ^?1; α]] is right p.q.-Baer if and only if R is right p.q.-Baer and every countable subset of right semicentral idempotents has a generalized countable join. Examples to illustrate and delimit the theory are provided.     

Additive Set of Idempotents in Rings

Let R be a ring with identity 1, I(R) be the set of all nonunit idempotents in R, and M(R) be the set of all primitive idempotents and 0 of R. We say that I(R) is additive if for all e, f ∈ I(R) (e ≠ f), e + f ∈ I(R), and M(R) is additive in I(R) if for all e, f ∈ M(R)(e ≠ f), e + f ∈ I(R). In this article, the following points are shown: (1) I(R) is additive if and only if I(R) is multiplicative and the characteristic of R is 2; M(R) is additive in I(R) if and only if M(R) is orthogonal. If 0 ≠ ef ∈ I(R) for some e ∈ M(R) and f ∈ I(R), then ef ∈ M(R), (2) If R has a complete set of primitive idempotents, then R is a finite product of connected rings if and only if I(R) is multiplicative if and only if M(R) is additive in I(R).     

Residually *-Abelian Valuation with Residue Characteristic Not 2

We are given a division ring D with involution (*) and with a *-valuation V such that V(sx ? xs) > V(sx), for all nonzero elements x, s of D with s = s*. Let χ denote the characteristic of the residue class division ring associated with V. We reported in Theorem 3.2.5 Part 4 in [3 Chacron , M. ( 1989 ). c-Valuations and normal c-orderings . Can. J. Math. XLI : 14 – 67 .[Crossref], [Web of Science ®] , [Google Scholar]] that, in the case χ = 0, either D is a standard quaternion division algebra or else D contains no algebraic elements other than the scalars. In this article, we carry out a generalization of the preceding theorem to the case χ ≠ 2. Our results are fairly complete in the finite dimensional case, and generalize theorems of, notably, J. Graeter and A. I. Lichtman, in the infinite dimensional case.     

绕积马氏链的中心极限定理

讨论了具有离散参数的绕积马氏链的中心极限定理,给出了加在过程样本函数上充分条件。得到了绕积马氏链的中心极限定理成立的充分条件.     

Boundedness for a Class of Generalized Commutators on λ-Central Morrey Space

Let 0 ≤α n,Ω be a rough kernel,and let A have derivatives of order m 1 in CBBMOq,μ2 with m ≥ 2.We consider a class of generalized commutators TΩA,α of Cohen-Gosselin type,and obtain the boundedness of TΩA,α from the central Morrey spaces Ep,μ1 to Er,λ for λ = μ1 + μ2 + α/n and 1/r = 1/p + 1/q α/n.     

A Silicon-Based Arrayed Waveguide Grating Operating in Two Communication Channels

Abstract

This article proposes a silicon-based arrayed waveguide grating operating in two wavelength bands simultaneously with central wavelengths of 1,550.12 nm and 1,310.12 nm. If input light to an arrayed waveguide grating consists of wavelengths around 1,550.12 nm, the proposed system will act as a four-channel demultiplexer with channel spacing of 0.8 nm. On the other hand, when input wavelengths are distributed around 1,310.12 nm, the same arrayed waveguide grating will divide the input to seven channels with channel spacing of 0.33 nm.     

Statistical modelling of higher-order correlations in pools of neural activity

Simultaneous recordings from multiple neural units allow us to investigate the activity of very large neural ensembles. To understand how large ensembles of neurons process sensory information, it is necessary to develop suitable statistical models to describe the response variability of the recorded spike trains. Using the information geometry framework, it is possible to estimate higher-order correlations by assigning one interaction parameter to each degree of correlation, leading to a (2^N−1)$(2^N-1)$-dimensional model for a population with N$N$ neurons. However, this model suffers greatly from a combinatorial explosion, and the number of parameters to be estimated from the available sample size constitutes the main intractability reason of this approach. To quantify the extent of higher than pairwise spike correlations in pools of multiunit activity, we use an information-geometric approach within the framework of the extended central limit theorem considering all possible contributions from higher-order spike correlations. The identification of a deformation parameter allows us to provide a statistical characterisation of the amount of higher-order correlations in the case of a very large neural ensemble, significantly reducing the number of parameters, avoiding the sampling problem, and inferring the underlying dynamical properties of the network within pools of multiunit neural activity.