Taylor senes

In these last equations, P, a and r are now the expectation values (solutions) of the quantities defined above, and 0p is the covariance matrix of the parameters. is the number of observables and m the number of parameters. Because the functional dependence of the observables (rotational constants, principal moments of inertia or planar moments) on the structural parameters is strongly non-linear in most cases, an iterative process is essential. Typically, one begins with an assumed structure and expands the moment of inertia functions in terms of the parameters of this structure in a Taylor senes up to the linear term. 

Note carefully that the arguments of both [[h ]] and Cl are identical to those of the distribution function Pj. Since we will generally assume that varies slowly with the position of the center of mass (i.e., with the first independent vanable), the integrand may be expanded m a Taylor senes about r. This gives ... 

This completes the discussion of the various contnbutions to the stress tensor. Table 1 gives a summary of the expressions for the flux expressions that are obtained by taking the first term in the Taylor-senes expansions of the fluxes, and Table 2 summarizes the complete expressions (except for the inter-molecular contributions). 

We begin with ( ), the kinetic contnbution to the stress tensor at first order, given by the first term in the Taylor senes in the second line of Eq. 7.8. In this equation we replace f — v by f — u and then add a compensating term. This gives ... 

In Table 1 we have summarized the contributions to the flux expressions as given by the first term in the Taylor-senes expansion of each of the fluxes this tabulation emphasizes some of the similarities among the various fluxes. In Table 2 we pve more general expressions, from which higher-order terms in the Taylor senes can be generated. These expressions are needed pnmanly for the study of the cross-effects. 

Fluormated Carbohydrates Chemical and Biochemical Aspects Taylor, N F, Ed, ACS Symposium Senes 374, Amencan Chemical Society Washington, DC, 1988... 

Santi, D V, Pogolotti, A L Jr, Newman, E M, Wataya, T In Biomedia nal Aspects of Fluorine Chemistry, Filler, R, Kobayashi, Y, Eds, Kodan-shaLtd Tokyo, and Elsevier Biomedical Amsterdam, 1982, pp 123-142 Withers, S G, Street, I P,Percival, M D a Fluonnated Carbohydrates Chemical and Biological Aspects, Taylor, N F, Ed, ACS Symposium Senes 374, Amencan Chemical Society Washmgton, DC, 1988, pp 59 77... 

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