Annihilation method

In this section we focus on methods for the quantitation of a compound in the presence of an unknown interference without the requirement that this interference should be identified first or its spectrum should be estimated. Hyphenated methods are the main application domain. The methods we discuss are generalized rank annihilation method (GRAM) and residual bilinearization (RBL). 

E. Sanchez, L.S. Ramos and B.R. Kowalski, Generalized rank annihilation method. I. Application to liquid chromatography-diode array ultraviolet detection data. J. Chromatog., 385... 

Chemometric methods can greatly increase the number of analyzable peaks in MDLC in particular, the generalized rank annihilation method (GRAM) can quantify overlapping peaks by deconvoluting the combined signal to those of each dimension. Standards with precise retention time are required, and there must be some resolution in both dimensions [60,61]. 

Windig, W. and Antalek, B., Direct exponential curve resolution algorithm (Decra) — a novel application of the generalized rank annihilation method for a single spectral mixture data set with exponentially decaying contribution profiles, Chemom. Intell. Lab. Syst., 1997, 37, 241-254. 

Three-way calibrations methods, such as the generalized rank annihilation method (GRAM) and parallel factor analysis (PARAFAC), are becoming increasingly prevalent tools to solve analytical challenges. The main advantage of three-way calibration is estimation of analyte concentrations in the presence of unknown, uncalibrated... 

Rank annihilation methods employ eigenvalue-eigenvector analyses for direct determination of analyte concentration with or without intrinsic profile determination. With the exception of rank annihilation factor analysis, these methods obtain a direct, noniterative solution by solving various reconstructions of the generalized eigenvalue-eigenvector problem. 

An alternative method to solving Equation 12.3 is to reduce both Rj and R2 to square, nonsingular, nonidentity matrices by projecting each matrix independently onto the space formed jointly by the two matrices. This permits calculation of A and F, via the QZ algorithm [23] and, by extension, relative concentration estimates, Z, and estimates of the true underlying factors in the X- and Y-ways. This is known as the generalized rank annihilation method (GRAM) [24, 25],... 

Li, S. and Gemperline, P.J., Generalized rank annihilation method using similarity transformations, Anal. Chem., 64, 599-607, 1992. 

Generalized Rank Annihilation Method as per Wilson, Sanchez, and Kowalski. %INPUT... 

The values of Df and dh for studied compositions HDPE+Z in table 1 are cited. The value dh can be compared with corresponding experimental data obtained by positrons annihilation method. For HDPE at 7=323 K experimental value is (4 6,8 A [14], This value dh corresponds well enough with corresponding calculated values dh cited in table 1. 

The data and methods discussed in the previous sections show the power of positron and positronium annihilation methods for the characterization of porous materials and low-k dielectrics in particular. The obvious question is, whether this power can be harnessed for an online diagnostic tool in a semiconductor production line. Such a tool should be reliable, compatible with existing processes, rapid, and not more complex than any other system. 

Opportunity for a large-area test of the oriental fruit fly male annihilation method on an entire isolated infestation presented itself... 

Despite all simplifications the model of particle in the rectangular potential well, extended to include the population of excited le els. describes quite well the dependence of ortho-positronium lifetime on the pore radius. In this model the o-Ps lifetime is ruled entirely by geometrical factors, however, maybe the chemical composition of the medium should be taken into account. The lifetime vs. average radius dependence is particularly steep below 5 nm. and in this range the positron annihilation method can be useful for determination of average pore radii. The specific surface determines the distribution of o-Ps between small voids in the bulk and pores. 

The positron annihilation method like the small angle scattering techniques is suitable in characterization of closed pores which are inaccessible for adsorbate molecules in classic experiments, like adsorption, mercury intrusion or thermoporometry. 

The basic theory behind the generalized rank annihilation method is that the rank reduction can be re-expressed and automated. A scalar y (relative concentration of the analyte in the unknown sample) is sought such that the matrix pencil... 

A practical numerical issue in the use of the generalized rank annihilation method is that, at certain times, complex-valued solutions may arise. Means have been provided, though, for eliminating this problem by simple similarity transformations [Faber 1997, Li et al. 1992],... 

Given an array X of size I x J x K, two slices in, say, the third mode are needed in order to be able to use the generalized rank annihilation method. These may be formed as weighted averages of all the slices. A sensible way to define two such samples is to determine two slices that preserve the total variation in X maximally in a least squares sense. Additionally these two slices must be within an I -dimensional subspace (R is the number of components in the PARAFAC model) in the first and second mode in order to maximize directly the appropriateness of the span of the data matrices. Thus, two slices Gi and G2 of size R x R are sought such that these are representative of the variation in X. This may be accomplished in a least squares sense by fitting a Tucker3 model with dimensionality R x R x 2,... 

The basic principle of the generalized rank annihilation method has been (re-)invented several times, e.g., in signal processing under the name ESPRIT [Roy Kailath 1989] and... 

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