Choice of the initial approximation in the decomposition of complex spectral profiles into components

1982 ◽  
Vol 37 (3) ◽  
pp. 1072-1075
Author(s):  
D. K. Buslov
Keyword(s):  
Initial Approximation ◽  
Spectral Profiles

scholarly journals Optical Transitions and Charge-Exchange in Highly Charged Quasi-Molecules

2010 ◽  
Vol 2010 ◽  
pp. 1-12 ◽  
Author(s):  
A. Devdariani ◽  
E. Dalimier ◽  
P. Sauvan
Keyword(s):  
Dense Plasma ◽  
Dipole Moments ◽  
Initial Approximation ◽  
Optical Transitions ◽  
Neutral Species ◽  
Nonrelativistic Case ◽  
Dense Plasmas ◽  
Nonadiabatic Transitions ◽  
Spectral Profiles ◽  
Bound Electron

The interaction between quasimolecular states produces not only nonadiabatic transitions but also some exotic features in the wings of the spectral profiles emitted by the ions in collision. Although this concept has been fruitfully used for neutral species, some new highlighted experimental data on quasimolecular optical transitions in hot dense plasma have renewed the interest to the concept in the recent years. The present review deals with highly charged quasimolecules and it is dedicated specifically to quasimolecules formed by two bare nuclei and one bound electron. The reason for this choice is that, for such quasimolecules, the energy terms and the dipole moments of the optical transitions can be obtained straightforwardly in nonrelativistic case without any approximation that are typical for neutrals. Although the results obtained in the frame of the approach developed here are directly applicable to the case of single collisions or to low-density plasmas, they form a reasonable initial approximation for the problem of optical profiles in hot dense plasmas and can be regarded as a safe framework for qualitative discussions of profiles in those environments.

HOMOTOPY ANALYSIS METHOD TO SOLVE BOUSSINESQ EQUATIONS

2015 ◽  
Vol 10 (3) ◽  
pp. 2825-2833
Author(s):  
Achala Nargund ◽  
R Madhusudhan ◽  
S B Sathyanarayana
Keyword(s):  
Homotopy Analysis Method ◽  
Degrees Of Freedom ◽  
Initial Approximation ◽  
Boussinesq Equations ◽  
Convergent Series ◽  
Boussinesq System ◽  
Analysis Method ◽  
Analytical Technique ◽  
Homotopy Analysis ◽  
Region Of Convergence

In this paper, Homotopy analysis method is applied to the nonlinear coupleddifferential equations of classical Boussinesq system. We have applied Homotopy analysis method (HAM) for the application problems in [1, 2, 3, 4]. We have also plotted Domb-Sykes plot for the region of convergence. We have applied Pade for the HAM series to identify the singularity and reflect it in the graph. The HAM is a analytical technique which is used to solve non-linear problems to generate a convergent series. HAM gives complete freedom to choose the initial approximation of the solution, it is the auxiliary parameter h which gives us a convenient way to guarantee the convergence of homotopy series solution. It seems that moreartificial degrees of freedom implies larger possibility to gain better approximations by HAM.

scholarly journals Polyhedral approximations of the semidefinite cone and their application

2021 ◽  
Author(s):  
Yuzhu Wang ◽  
Akihiro Tanaka ◽  
Akiko Yoshise
Keyword(s):  
Initial Approximation ◽  
Semidefinite Relaxation ◽  
Stable Set ◽  
Cutting Plane Methods ◽  
Diagonally Dominant Matrices ◽  
Maximum Stable Set ◽  
Simple Expansion ◽  
Diagonally Dominant ◽  
Polyhedral Approximations ◽  
Semidefinite Cone

AbstractWe develop techniques to construct a series of sparse polyhedral approximations of the semidefinite cone. Motivated by the semidefinite (SD) bases proposed by Tanaka and Yoshise (Ann Oper Res 265:155–182, 2018), we propose a simple expansion of SD bases so as to keep the sparsity of the matrices composing it. We prove that the polyhedral approximation using our expanded SD bases contains the set of all diagonally dominant matrices and is contained in the set of all scaled diagonally dominant matrices. We also prove that the set of all scaled diagonally dominant matrices can be expressed using an infinite number of expanded SD bases. We use our approximations as the initial approximation in cutting plane methods for solving a semidefinite relaxation of the maximum stable set problem. It is found that the proposed methods with expanded SD bases are significantly more efficient than methods using other existing approximations or solving semidefinite relaxation problems directly.

scholarly journals LandTrendr smoothed spectral profiles enhance woody encroachment monitoring

2021 ◽  
Vol 262 ◽  
pp. 112521
Author(s):  
P.J. Gelabert ◽  
M. Rodrigues ◽  
J. de la Riva ◽  
A. Ameztegui ◽  
M.T. Sebastià ◽  
...  
Keyword(s):  
Woody Encroachment ◽  
Spectral Profiles

scholarly journals Analysis of Rayleigh-Brillouin spectral profiles and Brillouin shifts in nitrogen gas and air

2014 ◽  
Vol 22 (2) ◽  
pp. 2092 ◽  
Author(s):  
Yong Ma ◽  
Hao Li ◽  
ZiYu Gu ◽  
Wim Ubachs ◽  
Yin Yu ◽  
...  
Keyword(s):  
Nitrogen Gas ◽  
Spectral Profiles

Searching for an Explanation for Diphthong Perception: Dynamic Tones and Dynamic Spectral Profiles

Phonetica ◽  
2000 ◽  
Vol 57 (1) ◽  
pp. 17-39
Author(s):  
M.E.H. Schouten ◽  
W.J.M. Peeters
Keyword(s):  
Spectral Profiles

scholarly journals Use of data mining and spectral profiles to differentiate condition after harvest of coffee plants

2012 ◽  
Vol 32 (1) ◽  
pp. 184-196 ◽  
Author(s):  
Rubens A. C. Lamparelli ◽  
Jerry A. Johann ◽  
Éder R. dos Santos ◽  
Julio C. D. M. Esquerdo ◽  
Jansle V. Rocha
Keyword(s):  
Data Mining ◽  
Expectation Maximization ◽  
Spectral Behavior ◽  
Use Of Data ◽  
Spectral Profiles ◽  
Coffee Plants ◽  
Using Data ◽  
Hyperion Image ◽  
Noise Fraction ◽  
Behavior Profiles

This study aimed at identifying different conditions of coffee plants after harvesting period, using data mining and spectral behavior profiles from Hyperion/EO1 sensor. The Hyperion image, with spatial resolution of 30 m, was acquired in August 28th, 2008, at the end of the coffee harvest season in the studied area. For pre-processing imaging, atmospheric and signal/noise effect corrections were carried out using Flaash and MNF (Minimum Noise Fraction Transform) algorithms, respectively. Spectral behavior profiles (38) of different coffee varieties were generated from 150 Hyperion bands. The spectral behavior profiles were analyzed by Expectation-Maximization (EM) algorithm considering 2; 3; 4 and 5 clusters. T-test with 5% of significance was used to verify the similarity among the wavelength cluster means. The results demonstrated that it is possible to separate five different clusters, which were comprised by different coffee crop conditions making possible to improve future intervention actions.

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