Author Keywords: Chemometrics; Modelling; Fitting; Polynomial analytical function; Linear regression; Experimental design 相似文献
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1.
An algorithm for searching the best polynomial analytical function for describing different experimental systems is presented. It is based
1. (1)on the generation of all possible analytical functions of a given order, with a given number of terms and with a given number of independent variables, and
2. (2)on the calculation of the parameters of all selected functions using the linear regression method.
To show the ability of the program two different examples are given:
1. (1) searching the best univariate polynomial model, and
2. (2) modelling of the stability of a two-component mixture as a function of three factors.
2.
Computational schemes are presented with which to evaluate the electrostatic Coulomb energy in relativistic molecular electronic
structure calculations using a basis of four-component Dirac spinor amplitudes. We demonstrate that algorithms may be constructed
and implemented which differ only in minor details from those in common use in nonrelativistic quantum chemistry, and that
the four-component formalism is neither as complicated nor as expensive as has been suggested recently in the literature.
Spherically symmetrical atomic basis sets are presented which indicate that accurate representations of the Coulomb energy
may be obtained using modest expansions of the electronic density in a scalar auxiliary basis set of spherical harmonic Gaussian-type
functions.
Received: 15 April 2002 / Accepted: 15 May 2002 / Published online: 29 July 2002 相似文献
3.
4.
Dynamic information is generally extracted from deuterium quadrupole echo spectra by matching a spectrum calculated for a particular motional model to the experimental spectrum. In this work, a set of computer programs has been written to facilitate fitting of calculated spectra to experimental spectra that represent from one to five motional models. The fitting program requires pre-calculated libraries of spectra for the models of interest, and accomplishes the fitting either by a systematic method or by simulated annealing. The systematic method is convenient for fitting with one or two motional models, but the simulated annealing method is faster for two or more models, if the libraries are made up of hundreds of spectra. The parameter Q, with the standard deviation of the spectral points estimated as the standard deviation of the baseline noise, provides a stringent measure of goodness of fit. Acceptable fits of experimental data as judged by this criterion have not been found, even in the case of ring flip motion in phenylalanine-d(5) in which the fit may be judged acceptable by eye. An example of fitting with isotropic and methyl rotation motional models of alanine-d(3), which have distinct spectral patterns, shows that it is possible to obtain reasonably accurate estimates of the relative amounts of deuterium representing the different models, even from poorly fitted spectra. 相似文献
5.
Summary Two programs, OVID and SUPER, for exploring the similarity of molecules with respect to their action at a receptor are described. OVID accepts two molecules as input and optimizes the three-dimensional overlap of specified atoms in one molecule with specified atoms in the second molecule. The result is expressed as a percent of the theoretical maximum. OVID gives a quantitative measure of the extent of a guessed correspondence between two molecules based on volume overlap of selected atoms. The Achilles' heel of OVID is that the correspondence between the two molecules has to be guessed. We realized that it would be better to systematically examine all possible correspondences of two structures to minimize the chance of overlooking a superior correspondence. We created SUPER to satisfy this need. SUPER accepts two molecules as input and finds the top twenty correspondences of their surfaces and charge distributions, giving a quantitative measure of the extent of each correspondence. An instructive example of the application of OVID and SUPER to the design of leukotriene D4 receptor antagonists is described. SUPER appears to be a practical brainstorming tool for the medicinal chemist trying to understand how molecules whose structures may not resemble one another in an obvious way can bind to the same site. 相似文献
6.
假设G是一个有限群,H是G的一个子群.称H在G是s-置换的,若对G的任意的Sylow-子群Gp,有HG_p=G_pH:称H在G是弱s-可补的,若存在G的子群T使得G=HT且H∩T≤H_(sG),其中H_(sG)是所有包含在H中的G的s-置换子群生成的子群.本文给出了下列定理:设F是一个包含超可解群系u的饱和群系,有限群G有一个正规子群H使得G/H∈F.若F~*(H)的每个Sylow子群的所有极大子群在G中是弱s-可补的,其中F~*(H)是H的广义Fitting子群,则G∈F.它是J.Algebra,2007,315:192-209一文中的Skiba公开问题在极大子群情形下的肯定回答. 相似文献
7.
Matthieu Le Floc''h 《K-Theory》2002,27(3):281-292
Let F be an Abelian number field and S the set of primes of F that are either ramified or over p, with p an odd prime. In this paper we compute the (first) Fitting ideal of K
2i–2
ét
(O
F
S
() for i 2, where O
F
S
is the ring of S-integers of F and is a character of Gal(F/) of order prime to p different from the ith power of the Teichmüller character. This Fitting ideal proves to be principal and generated by a Stickelberger element. 相似文献
8.
9.
Jean-Louis Féménias 《Journal of Molecular Spectroscopy》2005,232(1):80-101
Applications of the χ2 test, the F test, the Durbin-Watson d test, and the f (or Sign) test, to examples of correlated data treatment, show important drawbacks with the d test and (apparently) with the f test. An analytical approach based on residual analysis suggests an improvement in their use that leads to better results at lowest order; it also points out a distinction between goodness-of-fit tests, as the f test, and goodness-of-modeling tests, as the χ2 and F tests. The residual analysis method is applied to the same examples; it looks faster, simpler, and often more accurate than the classical ones. 相似文献
10.
用等离子体粒子能谱拟合温度的新方法 总被引:1,自引:1,他引:0
秦运文 《核聚变与等离子体物理》2001,21(1):49-52
用最小二乘法拟合等离子体粒子能谱实验数据时,通常使拟合函数与实验能谱数据之间的误差平方和极小化。如果将能谱实验数据的对数拟合成直线以求得粒子温度,则最好对温度误差的平方和极小化。给出了这种拟合方法的计算公式,并对两种不同方法得到的结果进行了比较。 相似文献