Range-function

Long range functionalization of alcohols via nitrites leading to y-hydroxy oximes... 

The dipole moment induced in a molecule, or in a group of molecules, is a finite range function of the intermolecular separations, R, which falls off faster than R-3 for R —> oo. Van Kranendonk has argued that, therefore, it is possible to expand the above equation in a series of cluster functions [400, 402]. If ft( 1 n) designates the dipole moment induced in the cluster of molecules 1 n when these are present alone in the given volume V, cluster functions 1/(1 n) can be defined according to... 

Collision-induced absorption takes place by /c-body complexes of atoms, with k = 2,3,... Each of the resulting spectral components may perhaps be expected to show a characteristic variation ( Qk) with gas density q. It is, therefore, of interest to consider virial expansions of spectral moments of binary mixtures of monatomic gases, i.e., an expansion of the observed absorption in terms of powers of gas density [314], Van Kranendonk and associates [401, 403, 314] have argued that the virial expansion of the spectral moments is possible, because the induced dipole moments are short-ranged functions of the intermolecular separations, R, which decrease faster than R 3. We label the two components of a monatomic mixture a and b, and the atoms of species a and b are labeled 1, 2, N and 1, 2, N, respectively. A set of fc-body, irreducible dipole functions U 2, Us,..., Uk, is introduced (as in Eqs. 4.46), according to... 

There is much more to this functional complexity than we have been able to discuss in this review. For instance, we have not touched on the complex intranuclear network mediated by the nuclear lamins, which is critically important for human health as reflected in the numerous disease phenotypes that are emerging due to mutation in lamins and their associated protein partners. We have also not discussed the association of IFs with molecules involved in bacterial and viral pathogenesis, such as the Ebstein-Barr virus latent infection membrane protein (LMP) (Liebowitz et al., 1987) or viral kinases such as the herpes simplex virus US3 kinase (Murata et at, 2002) that may be important in remodeling IFs during infection. It is clear, however, from the many critical cellular functions we have discussed in this review, that the IF structural and signaling scaffold is involved in wide-ranging functions that are important for fundamental... 

Thus the inclusion of long-range functions seems to be of crucial importance, as well as Cl, in describing the n state. Table 5 gives the excitation energies for various states of CjHi from this work. 

Ion-water polarization energies calculated from classical electrostatics represent a large percent of the total pair interaction energy. If this contribution is added to Coulombic and short-range functions, the total energy differs substantially from the ab initio curve. We conclude that the effective ionic charges used in the Coulombic term implicitly include the effect of ion-water polarization. 

In this way it is possible to deal with short range functions and the long range behavior of the ion-dipole potential can be treated explicitly. 

This detailed article reports on the latest advances in the field of haemo-compatible and antimicrobial coatings. Section headings include two routes to haemocompatibility, features and mechanisms, wide-ranging functions of heparin, beneficial effects of sulphonated groups, hydrophilic PEO chains, findings, advances in antimicrobial coatings, summary, and acknowledgements. 20 refs. 

Thus, if we know the dielectric constant of the fluid, then Eq. (3.3.15) could be used to improve the results obtained from the SSOZ-MSA approximation, for example. This has been done for dipolar hard dumbbell fluid by Lee and Rasaiah using Monte Carlo simulation results for the dielectric constant (Morriss ), and by Rossky, Pettitt and Stell. However, this approach does not seem to have any value as a predictive tool. Moreover, in the case of some interaction site models, notably hard linear triatomics, the site-site direct correlation function is not a short-range function but in fact increases with increasing r. This notwithstanding, the Cummings-Stell analysis remains an important contribution to our understanding of the SSOZ equation. 

Note that there is no coupling-constant average here. For large values of u, g r, r + u) -> 1, so that h(u) is typically a long-ranged function of u. We may separate out a reasonably short-ranged contribution, in the spirit of the LSD approximation. We write... 

Let us consider the implications of assuming that the value of 9g5(r)/9/ at r = d+ is representative of its value in the small-/" range over which the short-range function makes its greatest contribution to the integral... 

---