R robustness

M0Uer SF, Von Frese J, Bro R. Robust methods for multivariate data analysis. J Chemometr... 

For a recent critical evaluation of situations where current DFT approaches experience difficulties, see Davidson E R 1998 How robust is present-day DFT ... 

The long term behavior of any system (3) is described by so-called invariant measures a probability measure /r is invariant, iff fi f B)) = ft(B) for all measurable subsets B C F. The associated invariant sets are defined by the property that B = f B). Throughout the paper we will restrict our attention to so-called SBR-measures (cf [16]), which are robust with respect to stochastic perturbations. Such measures are the only ones of physical interest. In view of the above considerations about modelling in terms of probabilities, the following interpretation will be crucial given an invariant measure n and a measurable set B C F, the value /r(B) may be understood as the probability of finding the system within B. 

The singular value of the sensitivity funetion irfSfja )) and of the eomplementary sensitivity funetion (r(T(ja )) ean be displayed as Bode plots and play an important role in robust multivariable eontrol system design. 

Chiang, R.Y. (1988) Modern Robust Control Theory, PhD Dissertation, USC. 

Chiang, R.Y. and Safonov, M.G. (1992) Robust Control Toolbox for Use with MATLAB. Users Guide, MathWorks. 

Lehtomaki, N.A., Sandell, Jr., N.R. and Athans, M. (1981) Robustness Results in Linear-Quadratic Gaussian Based Multivariable Control Designs, IEEE Trans, on Automat. Contr., AC-26(1), pp. 75-92. 

End view showing male and female rotors and slide valve on an 85-ton intermediate compressor. The robust design of the Series R compressor can ingest amounts of liquid refrigerant that would severely damage reciprocating compressor valves, piston rods, and cylinders. (Used by permission Cat. RLC-DS-2, Aug. 1995. The Trane Company.)... 

Phillips, G. R., and Eyring, E. M., Comparison of Conventional and Robust Regression in Analysis of Chemical Data, Anal. Chem. 55, 1983, 1134-1138. 

Koscielniak, R, Non-linear Robust Regression Procedure for Calibration in Flame Atomic Absorption Spectrometry, Analytica Chimica Acta 278, 1993, 177-187. 

There is little or no capability to evaluate risk. The robustness of the plan to key uncertainties is rarely assessed. Important risks in R D develop-... 

Further development of robust methods tailored for isochron data can be anticipated, with the ultimate goal being a method that yields the same errors as EWLS for well-behaved data (i.e., strictly Gaussian, with accurate estimates of data-point errors), and only modest loss of precision for increasingly dirty data (R. Powell, written commun. 2002). 

Porter PS, Rao ST, Ku J-Y, Poirot RL, Dakins M (1997) Small sample properties of nonparametric bootstrap t confidence intervals. J Air Waste Management Assoc 47 1197-1203 Powell R, Hergt J, Woodhead J (2002) Improving isochron calcttlatiorrs with robust statistics and the bootstrap. Chem Geol 185 191- 204... 

Brase S, Kobberling J, Enders D, Lazny R, Wang M, Brandtner S. Nitrogen-based linker. 3. Triazenes as robust and simple linkers for amines in solid-phase organic synthesis. Tetrahedron Lett 1999 40 2105-2108. 

Penrose R (1955) A generalized inverse for matrices. Proc Cambridge Phil Soc 51 406 Rousseeuw PJ, Leroy AM (1987) Robust regression and outlier detection. Wiley, New York Sachs L (1992) Angewandte Statistik. Springer, Berlin Heidelberg New York Sharaf MA, Illman DL, Kowalski BR (1986) Chemometrics. Wiley, New York... 

Jaitly, N., Monroe, M.E., Petyuk, V.A., Clauss, T.R.W., Adkins, J.N., Smith, R.D. (2006). Robust algorithm for alignment of liquid chromatography-mass spectrometry analyses in an accurate mass and time tag data analysis pipeline. Anal. Chem. 78, 7397-7409. 

Hoegger, D.Freitag, R. (2001). Acrylamide-based monoliths as robust stationary phases for capillary electrochromatography. J. Chromatogr. A 914, 211-222. 

Polshettiwar, V., Baruwati, B. and Varma, R.S. (2009) Nanoparticle-supported and magnetically recoverable nickel catalyst a robust and economic hydrogenation and transfer hydrogenation protocol. Green Chemistry, 11 (1), 127-131. 

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