Martens number

The methods of determining Martens number and Vicat and heat... 

S.W. Martens and K.W. Thurston, Society of Automotive Engineers Paper Number 680125, 1968. 

One reason for the inclusion of a large number of variables is tliat typical analytical chemistry data do not obey some of the assumptions of the statistical methods used in variable selection (Martens and Naes, 1989). The results from these algorithms can therefore only be used as a guide and should not be... 

When the number of noisy (noninformative) variables is too large, PLS models may also supply rather poor predictive performance. In order to overcome such a matter, a number of techniques for the elimination of noisy variables or the selection of useful predictors have been deployed, such as iterative stepwise elimination (ISE), iterative predictor weighting (IPW), uninformative variable elimination (UVE), and Martens uncertainty test (MUT) (Forina et ah, 2007). 

Flash Point by Pensky-Martens Closed Cup Tester Saponification Number of Petroleum Products Pour Point of Petroleum Products... 

Jansen MW, Brandenburg H, Wildschut HI, Martens AC, Hagenaars AM, Wladimiroff JW, Veld PA, The effect of chorionic villus sampling on the number of fetal cells isolated from maternal blood and on maternal serum alpha-fetoprotein levels, Prenat. Diagn., 17 953-959, 1997. 

The idea to investigate structures of resonances in frequency space was, to the authors knowledge, devised by Martens et al. [19] and then sophisticatedly implemented by Laskar and co-workers [13,20,21]. Instead of using FFT as their methods, we concentrate on a simple toy model and adapt rotation numbers as basic frequencies. By this way, we can easily compute basic frequency so that we can investigate global features of resonances and those dependence on parameters. 

The increasing reactivity of the chlorinated ethanes with increasing number of chlorines may be rationalized by the decreasing C-Cl bond dissociation energy with increasing chlorination (Goldfinger and Martens, 1961), and by the availability of an increasing number of chlorines to stabilize the radical. 

There is some debate in the literature about which principal components should be taken in T. In Equation (3.30) the first R, associated with the R largest singular values of X are selected, but alternatives exist. It may, e.g, be advantageous to use the components that correlate maximally with y [Mason Gunst 1985], but common practice is to use the ones as in Equation (3.30). Especially for data where most of the variation is known to be unrelated to the dependent variable, it may be better to select components. Note that there is a pay-off too few components do not fit X and do not predict Y well, whereas too many components overfit Y and X, leading to unstable new predicted Y values. Validation methods can be used to estimate the optimal number of components [Martens Naes 1989],... 

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