A formula for the number of Latin squares

We establish an explicit formula for the number of Latin squares of order n:

, where B_n is the set of n×n(0,1) matrices, σ₀(A is the number of zero elements of the matrix A and per A is the permanent of the matrix A.     

Yb原子高激发态的斯塔克光谱

采用ππ偏振激光，通过两步激发和光电离方法，在０－１５４Ｖ／ｃｍ电场范围内，测定了Ｙｂ原子ｎ－１８附近ｍ＝０的斯塔克光谱，首次把包含斯塔克效应的能量矩阵对角化方法推广到Ｙｂ原子，所获得的理论斯塔克图与实验结果基本符合，观察到低场中斯塔克簇随电场增加呈现线性结构以及＾１Ｐ１态与斯塔克簇在抗交叉过程中振子强度发生转移的现象，讨论了结构与量子亏损的关系。     

Studies on self-pumped phase conjugation in Cu-doped (K0.5Na0.5)0.2(Sr0.61Ba0.39)0.9Nb2O6 crystals

The use of Cu-doped (K_0.5Na_0.5)_0.2(Sr_0.61Ba_0.39)_0.9Nb₂O₆ as self-pumped phase conjugators using internal reflection is reported. Reflectivities as high as 63% at 5145.5 nm and 60% at 632.8 nm were realized. It was found that the photorefractive response changes significantly at different doping concentration. The responses of the crystals to the laser wavelength, incident angle and dopant concentration are studied.     

快度中心区强子物质输运系数和粘滞流体演化

用Chapman-Enskog方法计算了相对论性重离子碰撞快度中心区产生的π介子物质的输运系数,并建立了相应的粘滞流体力学方程,进而讨论了粘滞对π介子物质演化过程的影响.结果表明,粘滞将减缓快度中心区π介子物质的冷却速度.     

激光二极管侧面抽运Nd:YAG锁模激光器的研究

利用谐振腔的稳定条件对激光二极管侧面抽运的Nd：YAG锁模直腔的稳区特性和谐振腔内的光斑分布进行了分析。根据对腔参量的分析，选取合适的腔参量设计了一个简单的侧面抽运直腔，该谐振腔腔形简单，没有像散，振荡光模式好，有利于激光器的锁模运转。实验中采用国内自行研制的半导体可饱和吸收镜，实现了激光二极管侧面抽运半导体可饱和吸收镜锁模Nd：YAG激光器的连续锁模运转，平均输出功率为2W，锁模脉冲宽度为10ps，重复频率为100MHz。结合实验结果进一步讨论了半导体可饱和吸收镜的一些参量如饱和恢复时间、调制深度等对实现稳定连续锁模的影响。     

Effect of carbon content on the microstructure and the cracking susceptibility of Fe-based laser-clad layer

The laser cladding of Fe-based alloys on a medium carbon steel substrate was performed using a CO₂ laser and Ar shielding gas that was blown into a molten pool. The microstructure and cracking susceptibility of the laser-clad layers were studied in terms of carbon additions. Results show that the small change of the carbon content in the alloy powders can obviously change the microstructure and properties of the layers. When the carbon content is in the range of 0.3–0.4 wt.%, the decrease of the carbon content in alloy powders will increase the hardness and toughness of the layers simultaneously under the same process parameters. As a result, crack-free coatings with high hardness can be obtained. As the carbon content increases from 0.2 wt.% to 0.4 wt.%, the segregation ratio of chromium increases, while the segregation ratios of nickel, manganese, and silicon first decrease and then increase. At the same time, a new designing principle concerning the composition and microstructure has been put forward, and the principal mechanisms of strengthening and toughening of the layers are fine-grain strengthening and low carbon martensitic phase transformation strengthening.     

A note on an SOR-like method for augmented systems

Golub et al. (2001, BIT, 41, 71–85) gave a generalizedsuccessive over-relaxation method for the augmented systems.In this paper, the connection between the SOR-like method andthe preconditioned conjugate gradient (PCG) method for the augmentedsystems is investigated. It is shown that the PCG method isat least as accurate (fast) as the SOR-like method. Numericalexamples demonstrate that the PCG method is much faster thanthe SOR-like method.     

Nonlinear Filtering for Diffusions in Random Environments

Suppose that the signal X to be estimated is a diffusion process in a random medium W and the signal is correlated with the observation noise. We study the historical filtering problem concerned with estimating the signal path up until the current time based upon the back observations. Using Dirichlet form theory, we introduce a filtering model for general rough signal X ^W and establish a multiple Wiener integrals representation for the unnormalized pathspace filtering process. Then, we construct a precise nonlinear filtering model for the process X itself and give the corresponding Wiener chaos decomposition.     

Vancomycin Analogues Containing Monosaccharides Exhibit Improved Antibiotic Activity: A Combined One‐Pot Enzymatic Glycosylation and Chemical Diversification Strategy

Many natural products contain carbohydrate moieties that contribute to their biological activity. Manipulation of the carbohydrate domain of natural products through multiple glycosylations to identify new derivatives with novel biological activities has been a difficult and impractical process. We report a practical one‐pot enzymatic approach with regeneration of cosubstrates to synthesize analogues of vancomycin that contain an N‐alkyl glucosamine, which exhibited marked improvement in antibiotic activity against a vancomycin‐resistant strain of Enterococcus.     

New Synthetic Method for Industrial Manufacture of Glutaric Dialdehyde

A new synthetic method for the manufacture of glutaric dialdehyde is investigated. Glutaric dialdehyde was prepared by the addition-hydrolysis reaction of benzimidazolium salt with saturated dihalide as the di-Grignard reagent. The yield of glutaric dialdehyde by this method can reach 73%. Both infrared spectra and melting point of the compound were consistent with those reported earlier. Translated from Journal of Northwest University (Natural Science Edition), 2005, 35(2) (in Chinese)