Filter Diagonalization with Finite Fourier Transform Eigenfunctions

Below, we briefly report on the progress in the development of the Filter Diagonalization technique when filtering is carried out with the aid of Finite Fourier Transform (FFT) eigenfunctions. During recent years interest in these functions, also known as ‘prolates’, or ‘slepians’, has increased among scientists doing research in the field of signal processing. The main explanation to this follows from the set of very special extremal and orthogonality properties exibited by the FFT eigenfunctions. Recent results of Walter and Shen on sampling with prolate spheroidal functions will necessary produce a new wave of interest. In the presented, Filter diagonalization machinery, we show that the sampling formula of Walter and Shen simplifies essentially the computation of matrix elements as certain 2D–integrals involving FFT eigenfunctions.     

中药配方颗粒红外光谱法的快速鉴别

采用红外光谱法对中药配方颗粒及其辅料进行了鉴别研究。结果表明：不同生产厂商的配方颗粒中所添加的辅料类型及用量有较大差别；不同种的配方颗粒在辅料含量较低的情况下有较明显的指纹性，而辅料含量较高时，采用差谱技术可以提高谱图的指纹性，达到中药配方颗粒--鉴别的目的。该法简便、快速、可靠，是中药配方颗粒宏观质控的一个强有力的手段。     

Møller-Plesset (MP2) perturbation theory for large molecules

Summary A novel formulation of MP2 theory is presented which starts from the Laplace transform MP2 ansatz, and subsequently moves from a molecular orbital (MO) representation to an atomic orbital (AO) representation. Consequently, the new formulation is denoted AO-MP2. As in traditional MP2 approaches electron repulsion integrals still need to be transformed. Strict bounds on the individual MP2 energy contribution of each intermediate four-index quantity allow to screen off numerically insignificant integrals with a single threshold parameter. Implicit in our formulation is a bound to two-particle density matrix elements. For small molecules the computational cost for AO-MP2 calculations is about a factor of 100 higher than for traditional MO-based approaches, but due to screening the computational effort in larger systems will only grow with the fourth power of the size of the system (or less) as is demonstrated both in theory and in application. MP2 calculations on (non-metallic) crystalline systems seem to be a feasible extension of the Laplace transform approach. In large molecules the AO-MP2 ansatz allows massively parallel MP2 calculations without input/output of four-index quantities provided that each processor has in-core memory for a limited number of two-index quantities. Energy gradient formulas for the AO-MP2 approach are derived.Dedicated to Prof. W. Kutzelnigg whose books on theoretical chemistry aroused my interest in this field     

激光拉曼光谱在高分子中的应用

论述了激光拉曼光谱对高分子结构、结晶形态和表征,反应动力学过程和取向的研究,还介绍了纵向声学模、共振、高温高压、光波导和付里叶拉曼光谱在高分子研究中的最新进展。     

Progress on phthalocyanine-conjugated Ag and Au nanoparticles: Synthesis,characterization, and photo-physicochemical properties

Phthalocyanine (Pc) complexes are an important class of dyes with numerous (e.g., biological, photophysical, and analytical) applications. Among the methods used to improve the properties of these complexes, one should mention the introduction of different substituents, variation of the central metal ion, ligand exchange, and conjugation to nanomaterials (e.g., carbon-based nanomaterials and metal nanoparticles (NPs)). This work briefly reviews Pc complex conjugation to Ag and Au NPs, highlights the different NP shapes, and discusses the diversity of conjugation approaches. Moreover, the use of UV–Vis spectroscopy, powder X-ray diffraction, X-ray photoelectron spectroscopy, transmission electron microscopy, atomic force microscopy, dynamic light scattering and Fourier transform infrared spectroscopy to characterize Pc-NP hybrids is summarized. The effect of conjugation on Pc photo-physicochemical properties (fluorescence, singlet oxygen generation, triplet state formation, and optical limiting behavior) is discussed, and future perspectives for the synthesis and applications of new hybrids are provided.     

Evaluation of molecular structure in Langmuir monolayers of zinc stearate and zinc 12-hydroxystearate by IR external reflection spectroscopy

 In situ polarized Fourier transform IR external reflection spectra of Langmuir monolayers of zinc stearate and zinc 12-hydroxystearate on a water surface were recorded for various surface areas, and their molecular structures were estimated. In the zinc stearate monolayer, the wavenumbers and the absorbances of the antisymmetric and symmetric methylene stretching bands did not change during monolayer compression, which means that orientational and conformational changes of the hydrocarbon chain did not occur. However, wavenumber changes of the antisymmetric and symmetric carboxylate stretching bands were observed during surface compression. The change in the binding nature of the zinc cation to the carboxylate group was speculated. Moreover, it was elucidated that the structure of the hydrocarbon chain in the zinc 12-hydroxystearate monolayer was different from that in the zinc stearate monolayer. Received: 21 March 2001 Accepted: 6 July 2001     

Carbon dioxide supercritical fluid chromatography-Fourier transform infrared spectrometry

Summary The coupling of carbon dioxide supercritical fluid chromatography with Fourier transform infrared spectrometry (SFC-FTIR) is a powerful tool for the separation and on-line identification of non-volatile compounds. The IR transparency of carbon dioxide in the Fermi resonance bands region versus its density has been studied. Functional groups with stretching vibrations outside the transparent window of carbon dioxide are examined. SFC-FTIR separations allow Gram-Schmidt reconstruction chromatograms or IR window chemigrams with high quality spectra to be obtained. This SFC-FTIR lightpipe (flow cell, beam condensing optics, narrow band detector) has allowed detection limits of 250ng for benzonitrile and 70ng for methyl benzoate to be reached. The feasibility of very rapid SFC-FTIR separations is shown along with the subsequent peak spectra.     

Fourier transform IR spectrum and photoreactivity of the C3O2:HCl complex isolated in solid argon

IR spectroscopy was coupled with the matrix isolation technique to study the molecular complex formed between C₃O₂ and HCl and its photodissociation. The vibrational frequencies of the complex were compared with those of HCl and C₃O₂ monomers. For C₃O₂, a bent structure was characterized in the solid environment.

The vibrational frequencies were calculated in the 4000–400 cm⁻¹ range using an ab initio method at the MP2/6-31G** level for the most stable complex; these frequencies describe the hydrogen interaction with the central carbon atom of C₃O₂ (T complex). The measured shifts between the vibrational mode frequencies of the complex and monomers were in good agreement with the calculated values.

Broad-band UV irradiation ( > 230 nm) of the T complex leads preferentially to ketene chloride and carbon monoxide. Ketene chloride formation can be explained by the reaction between HCl and the carbene C₂O, which results from photo-dissociation at the C=CO bond of C₃O₂.     

The transient blended queue

This study aims to determine the transient behavior of the blended queue. Priority customers arrive over time and benefit from a threshold reservation policy, while non-priority ones can be contacted at any time. We show how to compute the Laplace transforms of the transient probabilities. Using the uniformization technique, we prove some monotonicty properties of the expected number of customers in the queue, explaining why the optimal transient reservation threshold should be lower than the stationary one.     

N叉树上的离散时间量子随机行走

通过离散时间量子随机行走的框架,我们研究了在N叉树上的离散时间量子随机行走,该框架不需要硬币空间,仅仅只需要选择一个除了酉性再无其它限制的演化算子,并且包含了使用再生结构的轨道枚举和z变换.作为结果,我们在封闭形式中计算了在根处的振幅的生成函数.