Fastiterative methods for least squares estimations

Least squares estimations have been used extensively in many applications, e.g. system identification and signal prediction. When the stochastic process is stationary, the least squares estimators can be found by solving a Toeplitz or near-Toeplitz matrix system depending on the knowledge of the data statistics. In this paper, we employ the preconditioned conjugate gradient method with circulant preconditioners to solve such systems. Our proposed circulant preconditioners are derived from the spectral property of the given stationary process. In the case where the spectral density functions() of the process is known, we prove that ifs() is a positive continuous function, then the spectrum of the preconditioned system will be clustered around 1 and the method converges superlinearly. However, if the statistics of the process is unknown, then we prove that with probability 1, the spectrum of the preconditioned system is still clustered around 1 provided that large data samples are taken. For finite impulse response (FIR) system identification problems, our numerical results show that annth order least squares estimator can usually be obtained inO(n logn) operations whenO(n) data samples are used. Finally, we remark that our algorithm can be modified to suit the applications of recursive least squares computations with the proper use of sliding window method arising in signal processing applications.Research supported in part by HKRGC grant no. 221600070, ONR contract no. N00014-90-J-1695 and DOE grant no. DE-FG03-87ER25037.     

Thermophysics of alkali and related azides II. Heat capacities of potassium,rubidium, cesium,and thallium azides from 5 to 350 K

The heat capacities of potassium, rubidium, cesium, and thallium azides were determined from 5 to 350 K by adiabatic calorimetry. Although the alkali-metal azides studied in this work exhibited no thermal anomalies over the temperature range studied, thallium azide has a bifurcated anomaly with two maxima at (233.0±0.1) K and (242.04±0.02) K. The associated excess entropy was 0.90 cal_th K^?1 mol^?1. The thermal properties of the azides and the corresponding structurally similar hydrogen difluorides are nearly identical. Both have linear symmetrical anions. However, thallium azide shows a solid-solid phase transition not exhibited by thallium hydrogen difluoride. At 298.15 K the values of C_p^o, S^o, and $\text{?{G}{}^{\mathrm{o}}\text{(T)?H}{}^{\mathrm{o}}\text{(0)}}\text{T}$, respectively, are 18.38, 24.86, and 12.676 cal_th K^?1 mol^?1 for potassium azide; 19.09, 28.78, and 15.58 cal_th K^?1 mol^?1 for rubidium azide; 19.89, 32.11, and 18.17 cal_th K^?1 mol^?1 for cesium azide; and 19.26, 32.09, and 18.69 cal_th K^?1 mol^?1 for thallium azide. Heat capacities at constant volume for KN₃ were deduced from infrared and Raman data.     

Determination of rare earth elements in seawater by on-line column preconcentration inductively coupled plasma mass spectrometry

A home made column of commercially available iminodiacetate resin, Muromac A-1 (50–100 mesh) was used to concentrate rare earth elements (REEs) (15 elements: Y, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu) in seawater. An automated low pressure flow analysis method with on-line column preconcentration/inductively coupled plasma mass spectrometry (ICP-MS) is described for the determination of REEs in seawater. Sample solutions (adjusted to pH of 3.0) passed through the column. After washing the column with water, the adsorbed elements were subsequently eluted into the plasma with 0.7 M nitric acid. Calibration curves were accomplished by means of purified artificial seawater with a sample loading time of 120 s. Detection limits (DLs) of the on-line column preconcentration/ICP-MS by eight replicate operations were between 0.040 and 0.251 pg ml⁻¹ for REEs in the artificial seawater. The precision was less than 8.9% for REEs and one sample can be processed in 7 min using a 7 ml of sample. The proposed method was applied to determine REEs in coastal seawater of Hiroshima Bay, Japan.     

新型尾式硫代苯并噻唑基卟啉化合物的合成与表征

通过不对称的单羟基卟啉化合物、溴代烷烃和巯基苯并噻唑合成了一系列新型硫代苯并噻唑基尾式卟啉化合物, 并采用核磁共振氢谱、碳谱、红外光谱、质谱和元素分析对卟啉化合物的结构进行了表征.     

Supercritical fluid extraction-capillary gas chromatography: On-line coupling with a programmed temperature vaporizer

A simple and versatile system is described for the on-line coupling of SFE to capillary GC. The interfacing consists of a programmed temperature vaporizer (PTV) injector. With this injector it is possible to combine solute trapping, elimination of a high flow of extraction fluid, and quantitative transfer of solutes to the seperation column. The problems caused by impurities in the extraction fluid in on-line SFE-GC are discussed. Simple methods are described for the purification of commercially available carbon dioxide. The trapping efficiency of the PTV injector is studied. Applications of the SFE-PTV-GC system are given for the analysis of polymer anti-degradants, polar compounds, and samples with environmental relevance.     

Electron and light microscopical investigation of defect structures in mesophases of pharmaceutical substances

 Transmission electron microscopy of freeze fractured and replicated samples (TEM) and polarizing light microscopy (PLM) are used to investigate the defect structures of the thermotropic and lyotropic mesophases of the non-steroidal antiinflammatory drug fenoprofen sodium and of the thermotropic mesophase of the nonionic surfactant sucrose oleate (O1570). All mesophases have a layered, smectic structure. The thermotropic liquid crystal of feno-profen sodium is an interdigitated smectic A phase (smectic Ad) having the highest viscosity of the investigated samples. The thermotropic mesophase of the sugar ester is also of the type smectic A, likely to be of subtype smectic A2 (bilayered smectic structure). The lyotropic mesophase is of lamellar liquid crystalline nature and has a much lower viscosity than the thermotropic mesophases. In the PLM the lyotropic fenoprofen mesophase has a strong tendency to form a pseudoisotropic texture, indicating a strong tendency to form undisturbed layered structures. Other textures exhibited in the PLM are fan-shaped texture and maltese-cross texture. Confocal domains, cylinders, pits and peaks as well as screw dislocations are found in great number in the TEM. However, no greater regions of undisturbed lamellar arrangement in the lyotropic mesophase could be detected. The only texture of the thermotropic fenoprofen mesophase visible in the PLM is the fan-shaped texture, indicating confocal domains as predominant structural elements. However, no confocal domains (tori or Dupin cyclides) are found in the TEM. In the PLM the sugar–ester mesophase exhibited a fan-shaped texture, maltese crosses and oily streaks as dominant textures. In the TEM only a few +π and −π disclinations and imperfect confocal domains could be detected. The discrepancies in the appearance of defect structures and textures between the mesophases as well as the discrepancies in the findings in the PLM and in the TEM investigations are caused by the different sample preparation and the different viscosities of the mesophases. Received: 28 May 1997 Accepted: 2 September 1997     

Computer interactive identification system for polycyclic aromatic hydrocarbons in reversed-phase microcolumn liquid chromatography

Summary A computer interactive identification system is proposed which is based on the relationship between retention and molecular properties such as the size and shape of polycyclic aromatic hydrocarbons (PAHs). This system offers an automatic analytical process for liquid chromatography, providing a reliable identification of the separated components. The identification can be further enhanced by the use of multiple detectors such as a multichannel UV detector. The system can be used for optimization procedures, resulting in a highly automatic complex analytical system.     

铝(Ⅲ)-桑色素-十二烷基硫酸钠体系在滤纸基质的荧光反应研究及其分析应用

本文探讨了在滤纸基质上表面活性剂SLS对铝-桑色素荧光反应的增敏作用及最佳实验条件。铝含量在0～6.0ng范围的工作曲线呈良好的线性关系(r=0.9998),方法的检测限为0.001ng。含铝4.0ng的溶液11次测定结果的相对标准偏差为4.3％。方法用于含铝水样的测定获得满意结果,回收率为96.0～100.5％。     

傅里叶变换红外光谱和傅里叶变换拉曼光谱法无损鉴别药材的真伪

利用傅里叶变换红外（FT-IR）和近红外傅里叶变换拉曼（NIR FT-aman）光谱法对大黄（西宁大黄）与伪品大黄（华北大黄、山大黄、水根大黄）进行了无损快速的鉴别。结果表明：尽管正品大黄与伪品大黄差别较小，有大部分的化学成分有很大的相同之处，但在红外、拉曼谱图中各自的特征峰较突出，根据谱峰的强度和位置可容易地将它们区别开来。红外和拉曼光谱法相互印证，相互补充，具有快速、准确、操作简单、重复性好、不需对样品进行分离提取，可直接鉴别等特点。     

皱叶香茶菜化学成分的研究

从采自西藏的皱叶香茶菜中分离鉴定了3对B-闭联对映贝壳杉烯型二萜化合物:二萜化合物皱叶香茶菜素(Ⅰ)和二氢皱叶香茶菜素(Ⅱ);isodocarpin(Ⅲ)和dihydroisodocarpin(Ⅳ)及Carpalasionin(Ⅴ)和dihydrocarpalasionin(Ⅵ)。(Ⅰ)、(Ⅲ)和(Ⅴ)分别与对应的二氢化合物(Ⅱ)、(Ⅳ)和(Ⅵ)以混合物的形式被分离和鉴定。化合物(Ⅱ)为新化合物,(Ⅰ)、(Ⅳ)和(Ⅵ)首次在自然界发现,(Ⅲ)和(Ⅴ)为已知化合物。