Barrett Moment

Another tjrpe of expectation value, which has also some importance for the characterization of nuclear charge density distributions, is the Barrett moment [24],... 

For the definition of the complete and incomplete gamma functions, F(a) and P a,x), see [28, Chap. 6]. Thus Rpa is the radius of a homogeneous charge density distribution yielding the same value for the Barrett moment as the charge density distribution under discussion. For Barrett equivalent radii parameters see, e.g., [35,46,47]. 

The expectation value (In (r)) is not defined (divergence to —oo), but the moment function M k) can be defined for A = 0, so that M k) =0 for all integer k>0. The Barrett moment for this charge density distribution simply yields zero,... 

The function Si (a ) is the sine integral [28, (5.2.1)]. The Barrett moment can be evaluated from incomplete gamma functions with complex arguments [60, (1.5.51.3)],... 

The quadrature method of moments (QMOM) is a presumed PDF approach that determines the unknown parameters by forcing the lower-order moments of the presumed PDF to agree with the moment transport equations (McGraw 1997 Barrett and Webb 1998 Marchisio et al. 2003a Marchisio et al. 2003b). As with the multi-environment presumed PDF method discussed in Section 5.10, the form of the presumed PDF is... 

Barrett, J. C. Jheeta, J. S. 1996 Improving the accuracy of the moments method for solving the aerosol dynamic equation. Journal of Aerosol Science 27,1135-1142. 

The most widely used comparisons of optical isotope shifts have been with results from muonic atom X-rays and electron scattering. These have been reviewed recently by Shera. The analysis of several muonic X-ray transitions allows the extraction of various radial moment parameters, as well as of the Barrett radius defined earlier. The experiments are limited to stable isotopes, as targets of the order of 0.1 g or more are required for such muonic X-ray studies. Absolute calibrations of optical measurements for these stable isotopes can thus be made, which in turn allow more precise extraction of nuclear data for the radioisotopes. This has been done recently for barium.The muonic experiments have also allowed the de-... 

The possible molecular mechanisms underlying the involvement of iNOS in Barrett s metaplasia-dysplasia-carcinoma sequence is that iNOS switches to an antiapoptotic phenotype because of increased Bcl-xl expression and decreased Bax expression (Van der Woude et al. 2002) however, at the moment no clear correlation can be established between iNOS expression and activation of pro-apoptotic and antiapoptotic genes. 

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