Analyzing electrochemical noise with Chebyshev’s discrete polynomials

The principles underlying a novel method intended for analyzing experimental data obtained when studying fluctuation processes are considered. The method in question is Chebyshev’s spectroscopy. The application of this method allows one to determine statistic characteristics of steady-state electrochemical noise against the background of severe deterministic interference without invoking the procedure of the fitting of the initial data. The potentialities of this novel method, which is intended for treating noise experiment, are demonstrated by examining model examples and analyzing the electrochemical noise generated by a lithium electrode placed in an aprotic organic electrolyte.     

Approximation of titration curves and other sigmoidal functions by proportionally spaced cubic B-splines

Proportionally spaced cubicB-splines are an appropriate function system for the approximation of titration curves and other sigmoidal functions. They give a smooth weighted leastsquares fit without instability problems. The degree of smoothing depends only on the number of spline function which can be chosen by the user. The equivalence points of titration curves can be estimated with high accuracy from the zeros of the second derivative.The method gives good approximation curves even in the case of empty data regions, i. e. there are no artefacts in subranges where no data points exist. The routine has been tested successfully with large series of simulated and experimental data.     

Determination of Low Contents of Fenpiverine Bromide by Extraction Spectrophotometry

An ion-pair extraction spectrophotometry method was developed for the determination of fenpiverine bromide in tablets. To determine this substance it was necessary to find experimental conditions that would allow eliminating the influence of other components of the tablets. Attention was paid to the fact that a suitable pH of water phase was necessary to achieve high selectivity.Received December 11, 2002; accepted April 24, 2003 Published online July 28, 2003     

Error estimation in peak‐shape analysis of XPS core‐level spectra using UNIFIT 2003: how significant are the results of peak fits?

An error analysis for numerically evaluating random uncertainties in x‐ray photoelectron spectroscopy has been implemented in version 2003 of the spectra treatment and analysis software UNIFIT in order to improve the understanding of the statistical basis and the reliability of the model parameters for photoelectron spectra. The theoretical basis as well as two approaches to obtain error limits of the fit parameters have been considered. Several test spectra have been analysed and discussed. A representative example has been chosen to demonstrate the relevance of the error estimation for practical surface analysis. Suggestions for the minimization of errors in the peak‐fitting procedures are presented. Copyright © 2004 John Wiley & Sons, Ltd.     

Flexible matching of test ligands to a 3D pharmacophore using a molecular superposition force field: Comparison of predicted and experimental conformations of inhibitors of three enzymes

Summary A computer procedure TFIT, which uses a molecular superposition force field to flexibly match test compounds to a 3D pharmacophore, was evaluated to find out whether it could reliably predict the bioactive conformations of flexible ligands. The program superposition force field optimizes the overlap of those atoms of the test ligand and template that are of similar chemical type, by applying an attractive force between atoms of the test ligand and template which are close together and of similar type (hydrogen bonding, charge, hydrophobicity). A procedure involving Monte Carlo torsion perturbations, followed by torsional energy minimization, is used to find conformations of the test ligand which cominimize the internal energy of the ligand and the superposition energy of ligand and template. The procedure was tested by applying it to a series of flexible ligands for which the bioactive conformation was known experimentally. The 15 molecules tested were inhibitors of thermolysin, HIV-1 protease or endothiapepsin for which X-ray structures of the bioactive conformation were available. For each enzyme, one of the molecules served as a template and the others, after being conformationally randomized, were fitted. The fitted conformation was then compared to the known binding geometry. The matching procedure was successful in predicting the bioactive conformations of many of the structures tested. Significant deviation from experimental results was found only for parts of molecules where it was readily apparent that the template did not contain sufficient information to accurately determine the bioactive conformation.     

腔长失调对光腔衰荡法测量精度的影响

 只考虑腔长失调因素下建立了反射率模拟测量的理论模型。根据高斯光束传输规律分析了腔长失调对衰荡腔模式耦合的影响，推导了腔长失调与谐振腔输出脉冲信号、衰荡信号与反射率之间的关系，模拟了腔长失调在±10mm范围内的光脉冲衰荡现象。结果表明：对于光敏面直径为0.2mm的高速探测器，为了保证10^-6的测量精度，腔长的失调量应控制在±1mm之间。在光路调节中采用具有对数变换功能的示波器和动态范围较大的探测器，可以提高测量精度。     

高空核电磁脉冲模拟波形的双指数函数拟合法

 许多标准和公开出版物中都用双指数函数描述高空核电磁脉冲典型波形。通过数值方法，研究了双指数函数一项重要的性质。根据该性质，详细讨论了高空核电磁脉冲模拟波形数值拟合中，双指数函数特征参数与脉冲峰值、前沿、后沿以及半宽等物理参数的关系，从而提出一种简单有效的脉冲参数计算方法。通过IEC标准中规定的高空核电磁脉冲参数的估计与一个实测高空核电磁脉冲模拟波形的数值拟合，验证了该方法的有效性和可靠性。该方法能够适应多种峰值、前沿和半宽的高宽核电磁脉冲模拟波形的数值拟合。     

测量圆盘转动惯量产生误差的曲线研究

结合三线摆实验的基本过程,进行实验数据的采集。利用投影法来测量圆盘的转角大小,借助于matlab的cftool工具箱,对数据进行曲线拟合,对测出来的二组数据拟合,得到转角与百分差曲线图。通过误差的大小比较,得出圆盘转动惯量测量值与理论值的百分差随转角变化最接近于三次曲线。     

A fitting algorithm for real coefficient polynomial rooting

A new algorithm for computing all roots of polynomials with real coefficients is introduced. The principle behind the new algorithm is a fitting of the convolution of two subsequences onto a given polynomial coefficient sequence. This concept is used in the initial stage of the algorithm for a recursive slicing of a given polynomial into degree-2 subpolynomials from which initial root estimates are computed in closed form. This concept is further used in a post-fitting stage where the initial root estimates are refined to high numerical accuracy. A reduction of absolute root errors by a factor of 100 compared to the famous Companion matrix eigenvalue method based on the unsymmetric QR algorithm is not uncommon. Detailed computer experiments validate our claims.     

A high‐precision instrument for mapping of rotational errors in rotary stages

A rotational stage is a key component of every X‐ray instrument capable of providing tomographic or diffraction measurements. To perform accurate three‐dimensional reconstructions, runout errors due to imperfect rotation (e.g. circle of confusion) must be quantified and corrected. A dedicated instrument capable of full characterization and circle of confusion mapping in rotary stages down to the sub‐10 nm level has been developed. A high‐stability design, with an array of five capacitive sensors, allows simultaneous measurements of wobble, radial and axial displacements. The developed instrument has been used for characterization of two mechanical stages which are part of an X‐ray microscope.