Theoretical study of homogeneous perturbations. II. Least-squares fitting method to obtain "deperturbed" crossing Morse curves. Application to the perturbed 1Σu+ states of N2

1969 ◽  
Vol 47 (5) ◽  
pp. 541-545 ◽  
Author(s):  
H. Lefebvre-Brion
Keyword(s):  
Least Squares ◽  
Theoretical Study ◽  
Interaction Matrix ◽  
Least Squares Fitting ◽  
Fitting Method ◽  
Vibrational Levels ◽  
Set Up

A method to obtain a "deperturbation" of perturbed vibrational levels is developed. The vibrational functions associated with two (or three) crossing Morse curves are used to set up an interaction matrix. The eigenvalues of this matrix are compared with the observed levels and the "deperturbed" Morse curves are obtained by a least-squares fitting. This method applied to the 1Σu+ states of N2 confirms the interpretation given by Dressler (following paper).

Application of Legendre Polynomial in Predicting Total Energy Consumption

2015 ◽  
Vol 713-715 ◽  
pp. 1627-1630
Author(s):  
Hong Qin Zhang ◽  
Lai Bin Gao
Keyword(s):  
Energy Consumption ◽  
Total Energy ◽  
Least Squares ◽  
Legendre Polynomial ◽  
Statistical Data ◽  
Least Squares Method ◽  
Total Energy Consumption ◽  
Least Squares Fitting ◽  
Fitting Method

Based on statistical data of National Statistical Bureau of China, and given the least-squares fitting of Legendre polynomial, the data of total energy consumption from 1978 to 2012 is analyzed by least squares method and Legendre polynomial least squares method respectively. The results showed that Legendre polynomial least squares fitting method is excellent and the data of total energy consumption from 2013 to 2016 is predicted by this method.

scholarly journals MULTIPLICITIES IN ULTRARELATIVISTIC PROTON–(ANTI)PROTON COLLISIONS AND NEGATIVE BINOMIAL DISTRIBUTION FITS

2011 ◽  
Vol 26 (19) ◽  
pp. 3171-3184 ◽  
Author(s):  
DARIUSZ PROROK
Keyword(s):  
Charged Particle ◽  
Least Squares ◽  
Likelihood Ratio ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Likelihood Ratio Tests ◽  
Proton Collisions ◽  
Least Squares Fitting ◽  
Fitting Method

Likelihood ratio tests are performed for the hypothesis that charged-particle multiplicities measured in proton–(anti)proton collisions at [Formula: see text] and 2.36 TeV are distributed according to the negative binomial form. Results indicate that the hypothesis should be rejected in the all cases of ALICE-LHC measurements in the limited pseudorapidity windows, whereas should be accepted in the corresponding cases of UA5 data. Possible explanations of that and of the disagreement with the least-squares fitting method are given.

scholarly journals Predicting Environmental Performance of Construction Projects by Using Least-Squares Fitting Method and Robust Method

2007 ◽  
Vol 2 (1) ◽  
pp. 143-155 ◽  
Author(s):  
Vivian W. Y Tam ◽  
Khoa N Le
Keyword(s):  
Least Squares ◽  
Environmental Performance ◽  
Construction Projects ◽  
Environmental Management System ◽  
Least Squares Fitting ◽  
Robust Fitting ◽  
Fitting Method ◽  
Environmental Performance Assessment ◽  
Early Indication ◽  
Environmental Performance Indicators

Recently, an Environmental Management System (EMS) has been used to promote effective environmental protection. Environmental Performance Assessment (EPA) is a critical tool of the EMS in checking, reviewing, monitoring and evaluating environmental performance of organizations. To implement EPA, the relations between Environmental Operational Indicators (EOIs) used in EPA and Environmental Performance Indicators (EPIs) are required, which, however, are lacking in the construction industry. This paper attempts to develop a series of EOIs and EPIs of individual construction projects for EPA and to measure their relations by using least-squares fitting and robust fitting methods. The results show that the defined EOIs correlate strongly with EPIs. Therefore, EPA can be used to identify areas for continuous improvement, and also can provide an early indication of the environmental performance for an organization.

scholarly journals Molecular Constants of the 2\(^1\Pi\) State of \(\text{NaLi}\) Molecule

2013 ◽  
Vol 23 (2) ◽  
pp. 135
Author(s):  
Nguyen Tien Dung ◽  
Le Canh Trung ◽  
Dinh Xuan Khoa ◽  
Nguyen Huy Bang
Keyword(s):  
Least Squares ◽  
Spectral Lines ◽  
Experimental Uncertainty ◽  
Linear Least Squares ◽  
Molecular Constants ◽  
Least Squares Fitting ◽  
Fitting Method

We report our determination of molecular constants for the 21Π state of NaLi from set of 732 spectral lines. Using the linear least-squares fitting method, an optimum set of molecular constants, which corresponds to dimensionless root mean of squares of deviation σ = 0.62 within 0.1 cm-1 experimental uncertainty, have been derived.

Further results relating to the electronic spectrum of 175Lu16O

1986 ◽  
Vol 64 (3) ◽  
pp. 246-251 ◽  
Author(s):  
A. Bernard ◽  
C. Effantin
Keyword(s):  
Least Squares ◽  
Electronic Spectrum ◽  
Ground State ◽  
Rotational Analysis ◽  
Least Squares Fitting ◽  
Fitting Procedure ◽  
Vibrational Levels ◽  
Unique Band ◽  
Π State ◽  
New System

Further results are presented concerning the three known systems of the molecule LuO; i.e., A2Π, B2Π, C2Σ+ → X2Σ+. The observed wavenumbers in each of the 12 analyzed bands are reduced using an iterative, least squares fitting procedure. Rotational constants are given for vibrational levels ν = 0 and 1 in the C state and up to ν = 7 in the X and B states. The 1–1 band of the A → X system is partly analyzed. These new calculations confirm level B to be the 3/2 component of a 2Π state; but they give no such confirmation for the identification of the A level, whose 2Π nature is well established, as the 1/2 component of the same state.Moreover, a unique band at 5120 Å that cannot be classified into any of the three known systems is described and attributed to a new system of LuO. A partial rotational analysis is made showing that the band corresponds to a transition involving the level ν = 0 in the ground state. The nature of the upper state is discussed.

Mueller Matrix Ellipsometer Based on Nonlinear Least Squares Fitting Method

2013 ◽  
Vol 40 (4) ◽  
pp. 0408004
Author(s):  
侯俊峰 Hou Junfeng ◽  
王东光 Wang Dongguang ◽  
邓元勇 Deng Yuanyong ◽  
孙英姿 Sun Yingzi ◽  
张志勇 Zhang Zhiyong
Keyword(s):  
Least Squares ◽  
Nonlinear Least Squares ◽  
Mueller Matrix ◽  
Least Squares Fitting ◽  
Fitting Method
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