柔性变焦镜的理论计算和设计

设计了由压电陶瓷施压的柔性变焦镜的结构。根据弹性力学建立了相应的数学模型,采用有限元法计算了镜面受力的挠变形值。当柔性变焦镜最大挠度为9μm时,镜面的曲率半径从610mm变至590mm,此时采用环形筋条结构的反射镜镜面和理想球面的面形偏差PV值仅为1μm,面形相对偏差为0.3%。     

Aggregating Knockoffs for False Discovery Rate Control with an Application to Gut Microbiome Data

Recent discoveries suggest that our gut microbiome plays an important role in our health and wellbeing. However, the gut microbiome data are intricate; for example, the microbial diversity in the gut makes the data high-dimensional. While there are dedicated high-dimensional methods, such as the lasso estimator, they always come with the risk of false discoveries. Knockoffs are a recent approach to control the number of false discoveries. In this paper, we show that knockoffs can be aggregated to increase power while retaining sharp control over the false discoveries. We support our method both in theory and simulations, and we show that it can lead to new discoveries on microbiome data from the American Gut Project. In particular, our results indicate that several phyla that have been overlooked so far are associated with obesity.     

关于质点弹簧系统在重力作用下的静平衡与振动

质点弹簧系统在重力作用下的静平衡状态由此系统的有效质量决定;其本征振动频率wn则由弹簧与质点的质量之比ml/m2 决定;Wn的平均值w与w2由此系统的初始条件决定,不同的初始条件导致不同的平均值.例如,若u(y,O)=uαf(y)=uaf(y)=u0y,则可得w2=k/(m2+1/3m1).并给出一个计算θ1:w1/w0的近似公式.     

大长宽比、变发散角光束二维变焦整形研究

为实现激光束形状的二维整形,同时灵活适应入射光束发散角、尺寸等参数的变化,提高光束质量,提出了一种适用于大长宽比、变发散角的激光束二维变焦整形方法。该方法利用光线变换矩阵方法分析光路,采用柱透镜、球透镜对光束进行二维变焦整形,通过镜片位置和间距的动态调节,实现对光束在x,y两个维度上的尺寸、发散角共四个参数各自独立的调整,实时校正激光束的低阶像差,使出射光束始终保持为预定状态。试验研究表明,该方法具有光路结构简单、综合像差小、调节范围大等优点,能够显著改善高功率激光器的光束质量,尤其适用于具有大长宽比增益区的板条激光器和化学激光器的输出光束整形。     

1H and 13C NMR assignments for two anthraquinones and two xanthones from the mangrove fungus (ZSUH-36)

We report the unambiguous assignments of the (1)H and (13)C NMR spectra of one new natural product, namely, 6,8-di-O-methyl versiconol (1) together with one known anthraquinone aversin (2) and two xanthones 5-methoxysterigmatocystin (3) and sterigmatocystin (4). These compounds were all isolated from the mangrove endophytic fungus ZSUH-36 from the South China Sea. 1D and 2D NMR experiments including COSY, HMQC and HMBC were used to elucidate the structures. Variations in the (1)H NMR spectrum of 6,8-di-O-methyl versiconol (1) were also observed in the temperature range 25-75 degrees C. In addition, the plausible biogenetic path from 1 to 2 is discussed.     

State reduction theories,their classical analogs and some comments

Recently several theories have been proposed to account for the state reduction due to measurement. The resulting evolution is given by a new density matrix equation which suppresses linear superpositions of states with large spatial separations. We raise some pertinent questions regarding these theories. We also show that the evolution for the density matrix obtained in these theories has a classical analog.     

用双光电门研究变加速运动

本文介绍了在气垫导轨上运用双光电门研究变加速运动的方法。     

双层交叉叠合式共振亚波长光栅

提出了一种防伪光栅结构-双层交叉叠合式共振亚波长光栅,其特点是可以展宽共振亚波长光栅的共振波长宽度,使得当将其应用于防伪时能得到更佳的光变效果。分析了半峰全宽展宽的原理,指出共振宽度值的大小依赖于耦合到光栅波导层内一级衍射光的能量。优化设计了此种光栅的结构参量。用矢量衍射理论对该结构的共振特性和制作工艺误差进行了研究。研究表明：这种防伪光栅的共振光谱峰值并不随着入射角的改变而降低,共振半峰全宽最大值约为同等条件下基本共振光栅结构的7倍,该结构的共振性能对光栅制作误差不是很敏感,是一种应用价值较高的防伪光栅结构。     

A uniform asymptotic expansion of the single variable Bell polynomials

In this paper, we investigate the uniform asymptotic behavior of the single variable Bell polynomials on the negative real axis, to which all zeros belong. It is found that there exists an ascending sequence {Z_k}₁^∞(−e,0) such that the polynomials are represented by a finite sum of infinite asymptotic series, each in terms of the Airy function and its derivative, and the number of series under this sum is 1 in the interval (−∞,Z₁) and k+1 in [Z_k,Z_k+1), k1. Furthermore, it is shown that an asymptotic expansion, also in terms of Airy function and its derivative, completed with error bounds, holds uniformly in (−∞,−δ] for positive δ.