Trace of matrix

We have proposed a method for approximating a high order RDM in terms of the lower order ones [15] and we can use this approximation to replace the former ones, appearing on the r.h.s. of eq. (3) by the lower order ones forming a matrix M [9,10]. In this case, the trace of matrix M must be equal to S times No, which provides a new value for . Then, by dividing M by this new value of 5, a new l-RDM is found. The iterative procedure may then start again. 

Target transform, factor analysis, 91 Trace, of matrix, 73 Training set, 124 Transfer functions, 150... 

Centrifuge supernatant and filter the resulting supernatant through a 0 2-pm Millipore syringe filter unit to remove all traces of matrix and proceed to affintiy purification. 

It is well known that the trace of a square matrix (i.e., the sum of its diagonal elements) is unchanged by a similarity transfonnation. If we define the traces... 

The quantity is called the trace of the matrix which is then the character of the... 

The X-ray determination of REE in geological samples is normally complicated by the relatively low concentrations of the REE, their complex X-ray spectra, the high concentration of matrix elements and the lack of reference standards with certified values for REE. A rapid and sensitive ion exchange and X-ray fluorescence procedure for the determination of trace quantities of rare earths is described. The REE in two U.S.G.S. standards, two inhouse synthetic mixtures and three new Japanese standards have been determined and corrections for inter-rare earth element interferences are made. 

In the Atoms In Molecules approach (Section 9.3), the Laplacian (trace of the second derivative matrix with respect to the coordinates) of the electron density measures the local increase or decrease of electrons. Specifically, if is negative, it marks an area where the electron density is locally concentrated, and therefore susceptible to attack by an electrophile. Similarly, if is positive, it marks an area where the electron density is locally depleted, and therefore susceptible to attack by a... 

In investigations of the failure of fiber compositions (PETP — short glass fibers) [251] it was found that the main process responsible for composite failure under load is the rupture at the matrix-fiber interface. The author of [251] observed formation of microvoids in loaded samples, both at the interphases and in the bulk. The microvoids, or cavities) grow in size and become interconnected by microcracks, and this results in fiber separation from the binder. However, when the matrix-fiber bond is strong enough, the cavities appear mostly in the bulk of matrix, the failure of the specimen does not over-power cohesion and traces of polymer remain on the fibers. 

The samples have two important characteristics that facilitate these very difficult determinations First, the matrix (all of the sample but the element being determined) is essentially organic matter containing only traces of heavy metals. Second, the samples are of less than critical thickness (6.4). As a consequence, absorption and enhancement effects (7.3) are absent and the scattered background is relatively weak (7.4). 

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