A smoothing method for X-ray spectrum based on best beamforming

X-ray spectrum is widely used in the field of analysis and measurement. Due to the effect of electronic noise and statistical fluctuation of particle, the measurement spectrum is unsmoothed. In order to improve the signal-to-noise ratio of the spectrum, many smoothing methods were applied to process spectrum. The conventional smoothing algorithms regard the spectra as time series. In fact, X-ray spectrum is an angle series, and its essential is spatial spectrum. So the conventional smoothing algorithms are not fit for smoothing X-ray spectrum. In this paper, a new measuring model for X-ray spectrum is built up, and a new smoothing method based on best beam forming is proposed for X-ray spectrum. It regards the measured X-ray spectrum as the classic spectrum estimation result of array signal. The spatial spectrum is re-estimated to smooth the spectrum by best beam forming. The relationship between cross-correlation coefficient and number of array cell is applied to choose parameter q. The experimental results show that the method is effective to smooth X-ray spectrum with high resolution when q is larger than 200.     

Ionization probability of the hydrogen atom suddenly released from confinement

The problem of the stability of a confined atom when it is extracted from the confining cavity has been investigated, modeled by a spherical hard wall potential. The ionization probability when the atom is released from confinement has been obtained. The dependence of the ionization probability on the confinement radius and on the quantum numbers of the initial confined state has been studied. The probability density function of the ionization energy of the ejected electron has been obtained for the different cases considered. The oscillatory structure of this distribution function, with a principal maximum located in the neighborhood of the energy of the initial state and minima very close to zero has been elucidated. The sudden approximation has been applied and the analytic continuation method has been used to calculate the different stationary states.     

Approximate method for calculation of electron transition probability for simple outer-sphere electrochemical reactions

The probability of an elementary act in an outer-sphere electrochemical electron transfer reaction is calculated with arbitrary values of the parameter of reactant-electrode electron interaction for diabatic freeenergy surfaces of the parabolic form. The dependence of effective transmission coefficient on the Landau-Zener parameter is found. Interpolation formulas are obtained that describe this dependence and allow calculating the electron transition probability using the results of quantum chemical calculations of the electronic matrix element as a function of distance.     

Numerical characterization of DNA sequences based on the k-step Markov chain transition probability

A DNA sequence can be regarded as a discrete-time Markov chain. Based on k-step transition probabilities, we construct a series of 4 x 4 k-step transition matrices to characterize the DNA primary sequences. According to the properties of Markov chains, we obtain distributions of A, T, C and G, and analyze the changes among them from yesterday to tomorrow. We can calculate the probabilities of nucleotide triples of DNA primary sequences. Finally, we introduce a correlation of this kind of transition matrices and consider it as an invariant to analyze the similarities/dissimilarities of DNA sequences.     

A new method of fitting approximate vibrational spectra to heat capacities of solids with Tarasov functions

A new, least-squares optimization method with interpolation is devised to fit skeletal vibrational heat capacities to the two parameters θ₁ and θ₃ in the Tarasov function used for heat capacity calculations of linear macromolecules. When heat capacities are available in the proper temperature range, θ₁ and θ₃ can be determined uniquely in a single computer run. Appended to our Advanced THermal Analysis System (ATHAS), this new method offers an improvement in analyzing heat capacity data and facilitates the systematic study of the physical significance of θ₁ and θ₃ values for all polymers and related molecules of the ATHAS data bank.     

Introducing Alternative Algorithms for the Determination of the Distribution of Relaxation Times

Impedance spectroscopy is a powerful characterization method to evaluate the performance of electrochemical systems. However, overlapping signals in the resulting impedance spectra oftentimes cause misinterpretation of the data. The distribution of relaxation times (DRT) method overcomes this problem by transferring the impedance data from the frequency domain into the time domain, which yields DRT spectra with an increased resolution. Unfortunately, the determination of the DRT is an ill-posed problem, and appropriate mathematical regularizations become inevitable to find suitable solutions. The Tikhonov algorithm is a widespread method for computing DRT data, but it leads to unlikely spectra due to necessary boundaries. Therefore, we introduce the application of three alternative algorithms (Gold, Richardson Lucy, Sparse Spike) for the determination of stable DRT solutions and compare their performances. As the promising Sparse Spike deconvolution has a limited scope when using one single regularization parameter, we furthermore replaced the scalar regularization parameter with a vector. The resulting method is able to calculate well-resolved DRT spectra.     

How electrons guard the space: shape optimization with probability distribution criteria

Efficient formulas for computing the probabilities of finding exactly electrons in an arbitrarily chosen volume ³ for Hartree–Fock wavefunctions are presented. These formulas allow the use of shape optimization techniques, such as level set methods, for optimizing with respect to various criteria involving such probabilities. The criterion defined as the difference between the Hartree–Fock and the independent-particle model probabilities of finding electrons in stresses the quantum effects due to the Pauli principle. We have implemented a 2D level set method for optimizing this criterion in order to study spatial separation of electron pairs in linear molecules. The method is described and the illustrative example of the BH molecule is reported.Contribution to the Jacopo Tomasi Honorary Issue     

不同制备工艺聚硅氯化铝的红外光谱和晶貌研究

聚硅金属盐 (主要是铝盐和铁盐 )是一类新型高效无机高分子混凝剂 ,不同的制备工艺会获得分子相对质量不同 ,分子结构有差异 ,因而混凝效果与稳定性能明显不同的产品。由于基础研究过于薄弱 ,严重影响了其实行大规模工业生产[1] 。聚硅氯化铝 (ＰＡＳＣ)属于聚硅金属盐 ,它的制备大多采用将聚硅酸与铝盐混合 ,在陈化中令其自然聚合 (或适当加热 )的方法[2～ 4 ] 。作者在该方法的基础上增加碱化聚合手段 ,继而引入代号为Ａ的聚合助剂 ,使制得的ＰＡＳＣ具有更好的混凝效果[5] 。为此 ,对不同制备工艺的ＰＡＳＣ进行红外光谱和晶形貌象研究 ,…     

A simple method for non-parametric estimation of the probability distribution function of diatomic molecules by electron diffraction

Treating the Debye intensity relationship as a linear Fredholm integral equation of the first kind, a method is developed for a non-parametric estimation of the probability distribution function P/r) for diatomic molecules from electron-diffraction data. Since the problem is an ill-posed one, Tikhonov's regularization procedure was used for the solution. The method was applied to iodine for which the non-parametric P/r) function is obtained. Based on this function the electron-diffraction parameters r_g, r_a and l_a are estimated by the linear least-squares method without a priori assumptions about the form of the vibrational potential. Approximating the potential by the Dunham expansion, the parameters r_e, ω_e, K₃ and K₄ are also estimated. The results are compared with those obtained from conventional analytical representation of an intensity function. Comparison is also made with spectroscopic data for iodine.     

一种基于光谱分析的二元不完全重叠色谱峰的分离解析方法

基于二极管阵列检测器获得的色谱-光谱数据,建立了一种二元不完全重叠液相色谱峰的解析方法: 色谱数据经过去噪、归一化处理后,计算各时间点的光谱差异并进行系统聚类分析,提取特征光谱后,利用非负最小二乘法对色谱-光谱矩阵进行解析,得到基于特征光谱的流出曲线,进而得到分离后的色谱峰。将解析结果和纯标样的色谱峰进行比较,解析后的光谱图和纯标样的光谱图无显著差异,保留时间相差小于0.01 min。实验结果表明,该方法在二元不完全重叠液相色谱峰的解析方面能取得良好的效果。     

Angular distribution of the photoelectron spectrum for benzene

The angular distribution of photoelectrons ejected from benzene using 21.22 eV radiation has been measured and the results applied to the analysis of the ionization bands.     

数理统计在地球化学样品分析质量控制中的应用

使用Excel2013和Minitab两种常用软件对地球化学样品中CaO含量分布情况进行了研究,运用描述性统计、正态分布、背景值与异常方法对实验室分析的广西某地地球化学样品的分析数据进行了质量评价,结果表明:综合运用计算机软件和数理统计方法,能快速找到分析数据的详细信息和数据特征,判别地球化学样品实验室分析数据的准确性,找出元素的背景值和异常值并剔除异常值,比较发现,样品中CaO含量分析数据对数转换后比原始数据的分布更趋于正态分布,相比于X射线荧光光谱方法,用电感耦合等离子体发射光谱法测定的结果更符合正态分布。方法对地球化学调查样品的分析数据质量评价作了有益的尝试,揭示了数理统计方法是地球化学样品分析质量控制的有效手段。     

Scattered wave packet formalism for the energy-resolved reaction probability

The scattered wave packet formalism developed for a quantum subsystem interacting with reservoirs through open boundaries is utilized to calculate the energy-resolved transmission probability. The total wave function is split into incident and scattered components. Markovian outgoing wave boundary conditions are imposed on the scattered or total wave function by the polynomial method. The wave packet correlation function approach is employed to compute the energy-resolved transmission probability for a one-dimensional potential barrier and a one-dimensional model chemical reaction exhibiting a quantum resonance. Accurate results demonstrate that this formalism can significantly reduce the number of grid points required in a dynamical calculation for the reaction probability.     

Shannon information entropy of fractional occupation probability as an electron correlation measure in atoms and molecules

A new method to determine electron correlation energy is presented for atoms and molecules. This method is based on Shannon information entropy that is obtained by fractional occupation probabilities of natural atomic orbitals. It is indicated that the Shannon entropy increases as the number of electrons increases and thus can be considered as a possible measure for the electron correlation in atomic and molecular systems. For neutral atoms and singly charged positive ions we proposed an expression for correlation energy with explicit dependence on the Shannon entropy and atomic number. The obtained correlation energies have been used to compute the first ionization potentials of the ground state of the main group elements from hydrogen through krypton. The calculated ionization potentials are in reasonably good agreement with their corresponding experimental values.We also developed the additivity scheme to find a connection between Shannon entropy and molecular correlation energy. The estimated molecular correlation energies show an excellent agreement with those obtained by elaborate G3 method with R² = 0.990.     

Multiple Markov transition matrix method: Obtaining the stationary probability distribution from multiple simulations

We herein propose the multiple Markov transition matrix method (MMMM), an algorithm by which to estimate the stationary probability distribution from independent multiple molecular dynamics simulations with different Hamiltonians. Applications to the potential of mean force calculation in combination with the umbrella sampling method are presented. First, the performance of the MMMM is examined in the case of butane. Compared with the weighted histogram analysis method (WHAM), the MMMM has an advantage with respect to the reasonable evaluation of the stationary probability distribution even from nonequilibrium trajectories. This method is then applied to Met‐enkephalin nonequilibrium simulation. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2009     

Determination of the orientation distribution function of anisotropic paramagnetic species from the angular dependence of the ESR spectra

A method for determination of the orientation distribution function of anisotropic paramagnetic species from the angular dependence of the ESR spectra based on simulation of the spectra was developed. The orientation distribution function is represented as a sum of orthonormal functions. The weight coefficients are determined by minimizing the deviations of the theoretical spectra from experimental ones. The method was numerically tested. The method is relatively insensitive to the presence of noise and foreign ESR signals not related to the sample orientation in the magnetic field.__________Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 12, pp. 2595–2601, December, 2004.     

Derivative spectrum chromatographic method for the determination of trimethoprim in honey samples using an on-line solid-phase extraction technique

A simple, selective and rapid analytical method for determination of trimethoprim (TMP) in honey samples was developed and validated. This method is based on a SPE technique followed by HPLC with photodiode array detection. After dilution and filtration, aliquots of 500 μL honey samples were directly injected to an on-line SPE HPLC system. TMP was extracted on an RP SPE column, and separated on a hydrophilic interaction chromatography column during HPLC analysis. At the first detection step, the noise level of the photodiode array data was reduced with two-dimensional equalizer filtering, and then the smoothed data were subjected to derivative spectrum chromatography. On the second-derivative chromatogram at 254 nm, the limit of detection and the limit of quantification of TMP in a honey sample were 5 and 10 ng/g, respectively. The proposed method showed high accuracy (60-103%) with adequate sensitivity for TMP monitoring in honey samples.     

吸热型碳氢燃料正癸烷热裂解机理、热沉及产物分布的理论研究

采用密度泛函理论(DFT)的B3LYP方法在6-311G(d,p)基组水平上对正癸烷裂解过程中涉及的反应物、产物及过渡态进行了几何构型优化和振动频率计算,运用B3LYP/aug-cc-pVTZ方法计算单点能并构建势能剖面图。利用TheRate程序包及Eckart校正模型计算了各反应速率常数k。采用统计热力学原理求得不同温度下的热容C_p,m^θ及熵S_{298 K}^θ,并通过设计等键反应获得了各物种的标准生成焓△_fH_{298 K}^θ。用Chemkin II程序模拟预测了产物分布,理论计算了热沉值,并讨论了温度、压力对产物分布和热沉的影响。结果表明,C-C键断裂过程是反应的初始步骤,且抽氢反应较β键断裂反应更易进行。裂解起始温度为500 ℃,反应主要发生在600~700 ℃,其主要产物为氢气、甲烷、乙烯、乙烷、丙烯和1,3-丁二烯,且产物分布随温度不同而变化。模拟计算获得正癸烷在温度600 ℃、压力2.5 MPa条件下的总热沉值为2.334 MJ/kg,对应的热裂解转化率为25.9%,该热沉值可以满足速率为5~6马赫数的飞行器的冷却要求。     

A theoretical determination of the electronic spectrum of Methylenecyclopropene

The vertical electronic spectrum of methylenecyclopropene, the prototype of the nonalternant hydrocarbons known as fulvenes, has been studied using multiconfigurational second-order perturbation theory. The calculations comprise three valence states and the 3s, 3p, and 3d members of the Rydberg series converging to the first ionization limit. Vertical excitation energies to three valence states are found at 4.13, 6.12, and 6.82 eV. The second of them corresponds to an excitation from the highest occupied orbital to a ^* orbital, while the other two are ^* excitations. The third transition gives rise to the most intense feature in the electronic spectrum. The results are rationalized within the scheme of two interacting double bonds. Comparisons are made between this and the previous theoretical calculations of the electronic spectra of related systems and also between the available experimental data of methylenecyclopropene in solution.