Homogeneity and Canonical Connections of Isoparametric Manifolds

On every isoparametric submanifold M a connection with parallel second fundamental form is constructed geometrically such that M is an orbit of an s-representation if and only if the connection is a canonical one. If the rank of M is greater than one this connection is in case of homogeneity the canonical connection of the reductive decomposition given by the orbit of s-representation. This revised version was published online in June 2006 with corrections to the Cover Date.     

Implementation and efficiency of an automatic peak-purity-control procedure in HPLC-UV-VIS-coupling based on principal component analysis

Summary Based on a thorough knowledge of the actual system precision significance testing of the primary eigen values, resulting from principal component analysis of the two-dimensional data array of HPLC with photodiode-array detection, is a powerful means to uncover unresolved chromatographic peaks. The implementation of this chemometric technique for assuring peak homogeneity and results showing the efficiency for two-component peaks in regard to spectral characteristics, chromatographic resolution and absorbance ratio of the investigated compounds are presented.     

Spectroscopy and Structure of Sol-Gel Systems

Sol-gel derived glasses may differ from conventional melt-quenched glasses owing to the peculiar microstructures existing at the gel state, such that, even after gel densification, some differences may remain in their composition and molecular structure.This paper discusses structural characteristics of thin film oxide gels and glasses, with a special emphasis on SiO2-TiO2 based systems, which are of particular interest for sol-gel integrated optics applications. Short range structure aspects are discussed based on infrared, X-ray photoemission and X-ray photoabsorption spectroscopies. The chemical homogeneity of sol-gel materials is evaluated, based on X-ray photoemission and nuclear magnetic resonance spectroscopies, dealing in particular with the issue of homo- vs. heterocondensation. Finally, some microstructural features of sol-gel derived films are analyzed, namely the relationship between infrared absorption and porosity and the structure of nanocrystalline sol-gel films, based on grazing incidence X-ray diffraction and micro-Raman spectroscopy. The types of structural information obtainable by each different technique are compared in detail.     

Radial sample load distribution under overload conditions: Analytical scale columns

The homogeneity of the sample load across the radial cross section of analytical scale columns was determined when operating under overload conditions. The study was performed using active flow technology columns operating in parallel segmentation mode. The outlet segmentation ratio was varied to enable different volume fractions of mobile phase, and thus sample, to elute from the peripheral and central flow regions of the column. The amount of solute exiting the peripheral and radial central exit ports was determined as a function of the flow segmentation ratio. The experimental data using an analytical scale column with dimensions, 100?×?4.6?mm, indicated that the sample load distribution was essentially uniform as a function of the column radial cross section.     

Solid Particle Distribution in Centrifugal Impeller Contactors

The recently developed centrifugal impeller is examined to investigate the solid–liquid mixing in a mechanically agitated contactor. Using the sample withdrawal method, the effects of impeller geometrical parameters, impeller rotational speed (200–700 rpm), solid particle size (500–1100 µm), and solid loading (2–10 vol%) on the degree of homogeneity are studied. The axial and the radial solid concentration profiles and the minimum impeller speed for the complete homogenization are also determined. In comparison with a widely used propeller impeller, considerably higher homogeneity values in lower impeller speeds are obtained (90% homogeneity against 16% homogeneity at 200 rpm at the same conditions). Having also lower power consumption makes this a superior impeller in solid–liquid mixing processes especially in shear-sensitive systems.      

Determination of PEGylation homogeneity of polyethylene glycol-modified canine uricase

Polyethylene glycol-modified canine uricase (PEG-UHC) was prepared by modifying the ε-amino group of lysine residues on the canine uricase (UHC) protein to near-saturation with 5 kDa monomethoxyl-polyethylene glycol succinimide (mPEG-SPA-5k). In order to accurately determine the PEGylation uniformity of PEG-UHC, CZE, 3–8% gradient gel SDS-PAGE, and imaging CIEF (iCIEF) analyses were compared. CZE could not effectively separate PEG-UHC proteins with different degrees of modification, 3–8% gradient gel SDS-PAGE could separate PEG-UHC into seven gel bands; however, most of the gel bands were smeared or blurred, and the separation of PEG-UHC samples by iCIEF was significantly better than that by 3–8% gradient gel SDS-PAGE. Under denatured conditions, iCIEF separated 12 pI peaks, and could also accurately quantify the relative monomer PEG-UHC content. More than 85% of the total monomeric PEG-UHC was conjugated with 7–12 PEG molecules; of this 85%, approximately 40% was conjugated with 9–10 PEG molecules. These results demonstrated that iCIEF exhibits good potential for determining the PEGylation homogeneity of PEGylated protein drugs.     

Electron microscope study of alkoxide-derived compositions within the PbZrO3-PbTiO3 phase diagram

Pb(Zr_0.50Ti_0.50)O₃ solid solution was prepared using lead acetate and transition metal n-propoxides in n-propanol or n-butoxides in n-butanol. The complex solutions were hydrolysed with an excess of H₂O. The resultant powders were calcined up to 700°C for 30 minutes in a flowing oxygen atmosphere. Scanning electron microscope analysis showed different morphologies of the resultant powders. The n-propoxide derived powder consisted of gel fragments, while the n-butoxide derived one had agglomerated submicrometre particles. EDS analysis of the powders revealed no chemical heterogeneities in the examined samples upon calcining up to 600°C, notwithstanding the type of precursor used. Both samples, calcined at 700°C, exhibited a slight deficiency of lead in the pyrochlore type phase as compared to the perovskite phase.     

大尺寸磷酸二氢钾晶体的折射率均一性研究

采用德国Trioptics公司生产的新一代全自动高精度折射率测量仪,测量了磷酸二氢钾(KDP)晶体不同部位的样品位于近紫外到近红外波段(0.253—1.530μm)内12个不同波长处的折射率,测量精度达到10-6量级.结果表明,大尺寸KDP晶体不同部位样品的折射率存在不均一性,靠近晶体恢复区的样品折射率小于晶体锥头区的样品折射率,偏差在10-5—10-4量级.研究发现,这种折射率不均一性与晶体不同部位的结晶质量存在差异有关.另外,将测量数据与其他文献中的数据进行对比.结果显示,所测试的样品数、波段宽度、测量点数量以及数据的精度均超过其他文献,结合测试条件分析了不同文献数据存在差异的原因.最后,使用最小二乘法拟合得到了KDP晶体较为可靠的Sellmeier方程.     

Independence of Likelihood Ratio Criteria for Homogeneity of Several Populations

Let _i be an i-tb population with a probability density function f(· | _i ) with one dimensional unknown parameter _i = 1, 2, ... , k. Let n _i sample be drawn from each _i . The likelihood ratio criteria _j|(j–1) for testing hypothesis that the first j parameters are equal against alternative hypothesis that the first (j – 1) parameters are equal and the j-th parameter is different with the previous ones are defined, j = 2, 3, ... , k. The paper shows the asymptotic independence of _j|(j–1)'s up to the order 1/n under a hypothesis of equality of k parameters, where n is a number of total samples.