Quasiperiodic spectra and orthogonality for iterated function system measures

We extend classical basis constructions from Fourier analysis to attractors for affine iterated function systems (IFSs). This is of interest since these attractors have fractal features, e.g., measures with fractal scaling dimension. Moreover, the spectrum is then typically quasi-periodic, but non-periodic, i.e., the spectrum is a “small perturbation” of a lattice. Due to earlier research on IFSs, there are known results on certain classes of spectral duality-pairs, also called spectral pairs or spectral measures. It is known that some duality pairs are associated with complex Hadamard matrices. However, not all IFSs X admit spectral duality. When X is given, we identify geometric conditions on X for the existence of a Fourier spectrum, serving as the second part in a spectral pair. We show how these spectral pairs compose, and we characterize the decompositions in terms of atoms. The decompositions refer to tensor product factorizations for associated complex Hadamard matrices. Research supported in part by a grant from the National Science Foundation DMS-0704191.     

Miniaturized matrix solid phase dispersion procedure and solid phase microextraction for the analysis of organochlorinated pesticides and polybrominated diphenylethers in biota samples by gas chromatography electron capture detection

This work has developed a miniaturized method based on matrix solid phase dispersion (MSPD) using C18 as dispersant and acetonitrile–water as eluting solvent for the analysis of legislated organochlorinated pesticides (OCPs) and polybrominated diphenylethers (PBDEs) in biota samples by GC with electron capture (GC-ECD). The method has compared Florisil^®-acidic Silica and C18 as dispersant for samples as well as different solvents. Recovery studies showed that the combination of C18–Florisil^® was better when using low amount of samples (0.1 g) and with low volumes of acetonitrile–water (2.6 mL). The use of SPME for extracting the analytes from the solvent mixture before the injection resulted in detection limits between 0.3 and 7.0 μg kg⁻¹ (expressed as wet mass). The miniaturized procedure was easier, faster, less time consuming than the conventional procedure and reduces the amounts of sample, dispersant and solvent volume by approximately 10 times. The proposed procedure was applied to analyse several biota samples from different parts of the Comunidad Valenciana.     

Determination of melamine in rat plasma,liver, kidney,spleen, bladder and brain by liquid chromatography–tandem mass spectrometry

In this study, we describe a method for the analysis of melamine in rat plasma, liver, kidney, spleen, bladder, and brain using trichloroacetic acid precipitation with mixed-mode cation-exchange solid-phase extraction and hydrophilic interaction chromatography coupled to tandem mass spectrometry detection. Method validation was investigated completely, including linearity, precision, accuracy, matrix effect, extraction recovery, and carryover for the determination of melamine. The method exhibited a good linear range covering 20–500 ng/mL, and the overall precision ranged from 1.6 to 16.3%, with the accuracy varying from −7.9 to 15.1%. The mean matrix effects of melamine in rat plasma, liver, kidney, spleen, bladder, and brain ranged from 66.2 ± 6.7 to 95.5 ± 13.2%, and the mean recoveries for melamine varied from 79.8 ± 8.2 to 113.0 ± 9.6%. Rat kidney showed the highest level among the organs (192.5% of the plasma melamine level), and the average concentration of melamine in the brain was only 7.5% of the plasma melamine concentration. This work has pointed out that even with the application of two popular preparation procedures (acid precipitation and solid-phase extraction) of melamine, the matrix effect in analyzing biological samples still exists in certain kinds of matrices.     

Comparison of microconcentric and membrane-desolvation sample introduction systems for determination of low rare earth element concentrations in surface and subsurface waters using sector field inductively coupled plasma mass spectrometry

Analytical performances of a microconcentric nebulizer (MCN) and a membrane-desolvation sample introduction system (Aridus) were compared for determination of low concentrations of rare earth elements (REEs) in surface and subsurface waters using a double focusing sector field inductively coupled plasma mass spectrometer. Conventional figures of merit were employed, such as sensitivities, limits of detection (LOD), REE–O⁺ formation, matrix induced interferences, long term signal variations, and recovery from spiked sea water samples and a pristine water CRM.     

Two-Step Modulus-Based Synchronous Multisplitting Iteration Methods for Linear Complementarity Problems

To reduce the communication among processors and improve the computing time for solving linear complementarity problems, we present a two-step modulus-based synchronous multisplitting iteration method and the corresponding symmetric modulus-based multisplitting relaxation methods. The convergence theorems are established when the system matrix is an $H_+$-matrix, which improve the existing convergence theory. Numerical results show that the symmetric modulus-based multisplitting relaxation methods are effective in actual implementation.     

基于元素对研究激光剥蚀-电感耦合等离子体质谱分析硫化物矿物的基体效应

基体效应是影响LA-ICP-MS分析结果准确性的主要因素之一,但目前却没有一种量化基体效应研究的方法。提出了一种以分析元素与内标元素的强度比(I_i/I_is)为纵坐标、浓度比(c_i/c_is)为横坐标绘制I_i/I_is-c_i/c_is图,以元素对I_i/I_is-c_i/c_is图的线性相关系数ｒ量化基体效应的思路。以Fe为内标,考察了13个常用玻璃标准物质与2个硫化物标准及多个硫化物矿物中6个元素对的基体效应,结果显示Cu/Fe和Zn/Fe的线性相关系数r都小于0.99,而痕量元素对Mn/Fe,Co/Fe,Ga/Fe,Pb/Fe的线性相关系数r都大于0.999;以S为内标,考察了2个硫化物标准与多个硫化物矿物中三个主量元素对Fe/S,Cu/S和Zn/S的基体效应,结果显示其线性相关系数r都小于0.999。无论是以Fe为内标结合玻璃标准为外标,还是以S为内标结合硫化物标准为外标分析硫化物矿物,主量元素大多数分析结果的误差大于10%;而以Fe为内标时,绝大多数玻璃标准获得的痕量元素分析结果与MASS-1较为一致,误差小于15%。研究表明,玻璃标准及硫化物矿物标准均与硫化物矿物存在一定的基体效应差异,而采用元素对I_i/I_is-c_i/c_is图的线性相关系数r量化基体效应具有一定的合理性与实用性。研究也表明了以Fe为内标,采用非基体匹配的玻璃标准可用于定量分析硫化物矿物中的痕量元素,尤其是具有较高痕量元素含量的NIST610。     

白云鄂博矿中铈铁钙EDXRF分析的基体效应研究

由于用Energy-Dispersive X-Ray Fluorescence(EDXRF)测量白云鄂博矿中铈元素含量的基体效应主要来自铁和钙,而这两个元素含量的变化非常大,使得通常用的标样方法不适用。以白云鄂博矿元素平均含量为基础制备一组测试样品,采用最小二乘法线性多元拟合来确定铁、钙对铈含量和X射线荧光光谱信号之间的线性关系系数的影响。这样确定的系数反映了铈在测量时发出的荧光强度被铁增强和被钙吸收的基体效应,且适用于大幅度变化的场合。当系数被用来通过EDXRF测量白云鄂博矿中铈的含量时相对误差小于10％。     

Multiplication rule of similarity transformations in the coherent state representation and its mapping onto quantum optical generalized ABCD law

We find that classical similarity transformations in the coherent state representation projects onto the similarity transformation operators (STO), these operators constitute a loyal representation of symplectic group. Remarkably, the multiplication rule of the STOs naturally leads to the quantum optical generalized ABCD law, which is the quantum mechanical correspondence of the classical optical ABCD law. Throughout the whole derivation, the technique of integration within an ordered product (IWOP) of operators is employed.     

基体溶液改进-原子荧光法测定食品中的汞

探讨改进基体溶液双道原子荧光光谱法测定食品样品中的汞。样品消解后用6mol/L盐酸、硫脲+抗坏血酸(50g/L)作为基体溶液进行仪器测定。本方法检出限0.051μg/g,最低检出质量浓度0.10μg/L,相对标准偏差为7.45%、6.76%,回收率为88.6%—113.2%。方法具稳定性好、灵敏度高、检出限低等优点。     

智能型金纳米棒荧光探针的制备及其肿瘤细胞成像研究

开发能特异和灵敏检测基质金属蛋白酶-2(MMP-2)的智能型荧光分子探针,对于癌症的早期精准诊断与治疗至关重要。本文基于MMP-2特异性识别的多肽底物,利用一价铜离子催化的"点击"化学反应将荧光素(FITC)和多肽底物GPLGVRGY相偶联,与SH-PEG-COOH修饰的金纳米棒在EDC和Sulfo-NHS的作用下通过酰胺化反应,制备得到一种新的MMP-2特异性响应的荧光共振能量转移(FRET)金纳米棒探针GNR@FITC。体外重组酶检测实验、MTT实验及细胞共聚焦显微成像结果表明,该探针对MMP-2过表达小鼠乳腺癌细胞4T1表现出较好的特异性和检测灵敏度,具有进一步开发应用于乳腺癌早期诊断的极大潜力。