Comparison of the solutions from a novel variational method with numerical results for the study of beam propagation in a Kerr medium with nonlinear absorption

We present results from a novel variational method for the study of beam propagation in a Kerr medium with nonlinear absorption. This new method combines the variational method and a nonlinear absorption equation and gives a concise expression for the combination. The results obtained with this method show good quantitative agreement with numerical solutions obtained with the finite-difference method. It is shown that the variational method takes much less time than a numerical simulation with the finite-difference method for analysis of beam propagation in a thick medium with nonlinear absorption and nonlinear refraction. The new method makes detailed analysis of beam propagation in a Kerr medium with nonlinear absorption very simple and fast.     

(2+1)-Dimensional Fermion Determinant in a Constant Background Field at Finite Temperature and Density

We evaluate exactly both the nonrelativistic and relativistic fermion determinant in 2+1 dimensions in a constant background field at finite temperature. The effect of finite chemical potential is also considered. In both cases, the systems are decoupled into an infinite number of 1+1 fermions by Fourier transformation in the -variable. The total effective actions demonstrate nonextensiveness in the -dimension.     

钨酸锌晶体的受激拉曼散射和光致发光研究

采用皮秒532nm 激光激发，研究了ZnWO₄晶体的受激拉曼散射和本征荧光发射.在SRS光谱中观察到一级(558.7nm)和二级(588.6nm)斯托克斯光，线宽分别为130和77cm^－1, 一级斯托克斯光的抽运阈值为6.8mJ.在532nm激光抽运下ZnWO₄晶体的荧光光谱呈现出由能量为2.30，2.45和2.83eV的3个高斯分量组成的独特结构.光致发光表明晶体具有从400nm到650nm的宽带本征发光，其峰值波长为472.0nm，相应于钨氧之间的辐射跃迁. 关键词： 晶体 钨酸锌 受激拉曼散射 闪烁体     

Combined neural network and reduced FRF techniques for slight damage detection using measured response data

Summary  This paper deals with structural damage detection using measured frequency response functions (FRF) as input data to artificial neural networks (ANN). A major obstacle, the impracticality of using full-size FRF data with ANNs, was circumvented by applying a data-reduction technique based on principal component analysis (PCA). The compressed FRFs, represented by their projection onto the most significant principal components, were used as the ANN input variables instead of the raw FRF data. The output is a prediction of the actual state of the specimen, i.e. healthy or damaged. A further advantage of this particular approach is its ability to deal with relatively high measurement noise, which is a common occurrence when dealing with industrial structures. The methodology was applied to detect three different states of a space antenna: reference, slight mass damage and slight stiffness damage. About 600 FRF measurements, each with 1024 spectral points, were included in the analysis. Six 2-hidden layer networks, each with an individually-optimised architecture for a specific FRF reduction level, were used for damage detection. The results showed that it was possible to distinguish between the three states of the antenna with good accuracy, subject to using an adequate number of principal components together with a suitable neural network configuration. It was also found that the quality of the raw FRF data remained a major consideration, though the method was able to filter out some of the measurement noise. The convergence and detection properties of the networks were improved significantly by removing those FRFs associated with measurement errors. Received 9 March 2000; accepted for publication 12 December 2000     

Synthesis and Crystal Structure of Mercury(II) Metal Crown Ether with N‐Heterocyclic Carbene Linkage

The mercury(II) metal crown ether ( 2a ) was obtained in high yield by reaction of the carbene precursor 1,2‐bis[N‐(1‐naphthylmethylene)imidazoliumethoxy]benzene dihexafluorophosphate ( 1 ) and Hg(OAc)₂. Addition of NaI to the acetone solution of 2a resulted in precipitation of pale yellow solid 2b . The structures of 2a and 2b were determined by single‐crystal X‐ray diffractometry. Both molecules display a helical conformation with a torsional cycle. The mercury atom in complex 2a is tricoordinated by two intramolecular carbene carbon atoms and an acetate oxygen atom. The mercury atom in complex 2b is tetracoordinated by two intramolecular carbene carbon atoms and two cis‐iodine atoms.