Construction of a central extension of a Lie group from its class of symplectic cohomology

Bargmann’s group is a central extension of Galilei group motivated by quantum-theoretical considerations. Bargmann’s work suggests that one of the reasons of the failure of naïve attemps to construct actions on quantum wave functions has a cohomologic origin. It is this point, we develop in the context of Lie groups with symplectic actions. Studying the co-adjoint representation of a central extension of a group G$G$, we highlight the link between the extension cocycles and the symplectic cocycles of G$G$. Also, each extension coboundary corresponds to a symplectic coboundary. Finally, we emphasize the condition to be satisfied by the extension cocycle for the class of symplectic cohomology of the extension being null. The method is illustrated by application to Physics.     

A non-analytic proof of the newman—znám result for disjoint covering systems

A direct combinatorial proof is given to a generalization of the fact that the largest modulusN of a disjoint covering system appears at leastp times in the system, wherep is the smallest prime dividingN. The method is based on geometric properties of lattice parallelotopes. This research was supported by grant 85-00368 from the United States-Is rael Binational Science Foundation, Jerusalem, Israel.     

基于核映射多光谱特征融合的高光谱遥感图像分类法

多光谱遥感图像的波段设定在理论和实践上都极具地物针对性,在更有效的数据挖掘方法帮助下可以提取足够的光谱特征以区分地物,本文将光谱匹配技术用于相似性度量,以提高分类准确度.首先选定光谱角制图、光谱相关制图、Mahalanobis距离、光谱相似度和光谱信息差异做为光谱度量;随后选择高斯核函数,在选定核函数之后,得到了核映射下的光谱特征度量来挖掘高光谱遥感数据的光谱特征.最后采用核映射多光谱特征融合法对多光谱遥感图像光谱特征的相似性进行描述,得到基于核映射多光谱特征融合的高光谱遥感图像分类算法.使用MATLAB中的LIBSVM工具箱对AVIRIS高光谱遥感数据进行分类实验,并与已有算法进行对比,结果表明本文提出的算法具有较高的分类准确度和性能.     

Molecular structures of inorganic compounds of low volatility: I. Salts of oxygen acids of the type M2XO4

We report an electron diffraction study of the molecular structure of gaseous cesium and thallium sulphates and cesium molybdate and tungstate. The average structure found for the M₂XO₄ molecules is described by a model (symmetry D_2d) in which the metal atoms bridge two edges of an XO₄ tetrahedron to form two 4-membered mutually perpendicular planar MO₂X rings.The data lead to conclusions on the complex nature of intramolecular motion. This motion may roughly correspond to great displacements of metal atoms on the surface of an imaginary sphere described near the tetrahedral acid residue.     

An electron-diffraction study of the molecular structure of gaseous perbromyl fluoride and calculation of its force field and vibrational amplitudes

The molecular structure of FBrO₃ has been studied by gas-phase electron diffraction. Least-squares refinements of the molecular geometry using fixed spectroscopic amplitudes revealed two geometrical minima. Initially, the amplitudes employed were derived from diagonal force fields obtained by spectroscopic least-squares refinements to fit observed and calculated wave numbers; for each geometry there are two spectroscopic minima. In the lowest geometrical minimum the wave number agreement is poor, however, the introduction of the ∠OBrO/∠FBrO interaction force constant removed the discrepancies; the resulting force field is F(Br-O) = 6.92 ± 0.02 mdyn Å^?1F(Br-F) = 3.22 ± 0.03 mdyn Å^?1, F(∠OBrO) = 1.06 ± 0.02 mdyn Å, F(∠FBrO) = 0.81 ± 0.03 mdyn Å, F(∠OBrO/∠FBrO) = ?0.19 ± 0.02 mdyn Å. In the corresponding geometrical minimum r_g(Br-O) = 1.582 ± 0.001 Å, r_g(Br-F) = 1.708 ± 0.003 Å, r_α(∠OBrO) = 114.9 ± 0.3°, r_α(∠FBrO) = 103.3 ± 0.3°. Perpendicular amplitude correction coefficients, calculated for each force field employed, were used throughout to relate the interatomic distances through the r_α-structure. The geometries of the r_α^o- and r_e-structures are estimated.     

The vibrational analysis of methylarsonic acid,trideuteromethylarsonic acid and their anions

Raman and IR spectra of methylarsonic acid, CH₃AsO₃H₂, trideuteromethylarsonic acid, CD₃AsO₃H₂ and their anions in aqueous solution and the solid state are discussed. Some results of a general valence force field and a Urey-Bradley force field are reported.     

Studies of two interrelated series of triiridatrithia-cyclohexane and trimetallatrithia (or trioxo)-adamantane rhodium and iridium complexes

From a comparativereview on the two title series of compounds, the first part of the paper describes the most salient structural and reactivity properties of these trimetallic complexes, including metal-metal bond formation, conformational changes, enantio, and diastereomorphism. The second part presentsnew results which extend the comparison to a series of trimetallatrioxo adamantane complexes. The single crystal X-ray diffraction of the parent compound [Rh₃{μ ₃−(OCH₂)₃CCH₃}(CO)₆]—a derivative of the commercially available tripod ligand 1,1,1tris (oxomethyl)ethane—is reported together with its crystal packing which is compared to that of its sulfido analog. The paper includes a discussion of the nucleophilic and electrophilic properties of the trimetalla trioxo adamantane rhodium complexes, based on semi-empirical extended Hückel calculations Dedicated to Professor Yves Jeannin on the occasion of his 65 th birthday.     

气相色谱法测定化妆品中的 VE 含量

介绍了一种用气相色谱法准确快速测定品中ＶＥ２含量的新方法。该法以ＶＣ作保护剂,用环已烷提取样品,ＳＥＰ－ＰＡＫ ＡＬＵＭ－Ａ小柱净化。以氯氰菊酯内标物,在１？５％ＯＶ＝－１７色谱柱上进行分离,测定化妆口中ＶＥ含量。内标物与样品的分离度为１．５５。平均回收纺为９４．３％～９８．８％,相对标准偏差为１．７％～３．５％（ｎ＝５）。