Occupancy fractional occupation

The logic that leads us to this last result also limits the applicability of the ensuing derivation. Applying the fraction of total lattice sites vacant to the immediate vicinity of the first segment makes the model descriptive of a relatively concentrated solution. This is somewhat novel in itself, since theories of solutions more commonly assume dilute conditions. More to the point, the model is unrealistic for dilute solutions where the site occupancy within the domain of a dissolved polymer coil is greater than that for the solution as a whole. We shall return to a model more appropriate for dilute solutions below. For now we continue with the case of the more concentrated solution, realizing... 

FRACTIONATION,BLOOD - PLASMAFRACTIONATION] (Volll) National Institute for Occupational Safety and Health... 

FIG. 12 Segment density profile as function of the distance from the wall Z for flexible (empty symbols) and semi-rigid (full symbols) living polymer chains at T = 0.4 [28]. The fractional occupancy of lattice sites by polymer segments is shown for the layers in the left half of the box. Dashed lines are guides for the eyes. 

We may generalize this by introducing an occupation number (number of electrons), n, for each MO. For a single determinant wave function this will either be 0, 1 or 2, while it may be a fractional number for a correlated wave function (Section 9.5). 

FIGURE 2.2 Binding and dose-response curves for human calcitonin on human calcitonin receptors type 2. (a) Dose-response curves for microphysiometry responses to human calcitonin in HEK cells (open circles) and binding in membranes from HEK cells (displacement of [,25I]-human calcitonin). Data from [1]. (b) Regression of microphysiometry responses to human calcitonin (ordinates) upon human calcitonin fractional receptor occupancy (abscissae). Dotted line shows a direct correlation between receptor occupancy and cellular response. 

Receptor reserve is a property of the tissue (i.e., the strength of amplification of receptor stimulus inherent to the cells) and it is a property of the agonist (i.e., how much stimulus is imparted to the system by a given agonist receptor occupancy). This latter factor is quantified as the efficacy of the agonist. A high-efficacy agonist need occupy a smaller fraction of the receptor population than a... 

FIGURE 2.11 Receptor-occupancy curves for activation of human calcitonin type 2 receptors by the agonist human calcitonin. Ordinates (response as a fraction of the maximal response to human calcitonin). Abscissae (fractional receptor occupancy by human calcitonin). Curves shown for receptors transfected into three cell types human embryonic kidney cells (HEK), Chinese hamster ovary cells (CHO), and Xenopus laevis melanophores. It can be seen that the different cell types lead to differing amplification factors for the conversion from agonist receptor occupancy to tissue response. 

Different drugs have different inherent capacities to induce response (intrinsic efficacy). Thus, equal cellular responses can be achieved by different fractional receptor occupancies of these drugs. 

FIGURE 3.5 Major components of classical receptor theory. Stimulus is the product of intrinsic efficacy (s), receptor number [R], and fractional occupancy as given by the Langmuir adsorption isotherm. A stimulus-response transduction function f translates this stimulus into tissue response. The curves defining receptor occupancy and response are translocated from each other by the stimulus-response function and intrinsic efficacy. 

This is formally identical to the equation derived by Gaddum and colleagues [3] (see Section 6.8.2) for noncompetitive antagonism. In this case, it is assumed that the only available receptor population in the presence of a fractional receptor occupancy pB by a noncompetitive antagonist is the fraction l-pB. Thus, agonist receptor occupancy is given by... 

Equation 13 has an important implication a clathrate behaves as an ideally dilute solution insofar as the chemical potential of the solvent is independent of the nature of the solutes and is uniquely determined by the total solute concentrations 2K yK1.. . 2x yKn in the different types of cavities. For a clathrate with one type of cavity the reverse is also true for a given value of fjiq (e.g. given concentration of Q in a liquid solution from which the clathrate is being crystallized) the fraction of cavities occupied 2kVk s uniquely determined by Eq. 13. When there are several types of cavities, however, this is no longer so since the individual occupation numbers 2k2/ki . ..,2k yKn, and hence the total solute concentration... 

The occupation numbers yMi, VM2> VP2 follow from Eq. 24" with the appropriate values of the constants CKi- The propane fraction of the gas bound in the hydrate according to Eq. 26" is then equal to... 

In a review of the subject, Ubbelohde [3] points out that there is only a relatively small amount of data available concerning the properties of solids and also of the (product) liquids in the immediate vicinity of the melting point. In an early theory of melting, Lindemann [4] considered that when the amplitude of the vibrational displacements of the atoms of a particular solid increased with temperature to the point of attainment of a particular fraction (possibly 10%) of the lattice spacing, their mutual influences resulted in a loss of stability. The Lennard-Jones—Devonshire [5] theory considers the energy requirement for interchange of lattice constituents between occupation of site and interstitial positions. Subsequent developments of both these models, and, indeed, the numerous contributions in the field, are discussed in Ubbelohde s book [3]. 

The resonating-valence-bond theory of metals discussed in this paper differs from the older theory in making use of all nine stable outer orbitals of the transition metals, for occupancy by unshared electrons and for use in bond formation the number of valency electrons is consequently considered to be much larger for these metals than has been hitherto accepted. The metallic orbital, an extra orbital necessary for unsynchronized resonance of valence bonds, is considered to be the characteristic structural feature of a metal. It has been found possible to develop a system of metallic radii that permits a detailed discussion to be given of the observed interatomic distances of a metal in terms of its electronic structure. Some peculiar metallic structures can be understood by use of the postulate that the most simple fractional bond orders correspond to the most stable modes of resonance of bonds. The existence of Brillouin zones is compatible with the resonating-valence-bond theory, and the new metallic valencies for metals and alloys with filled-zone properties can be correlated with the electron numbers for important Brillouin polyhedra. 

At least for the case of a non-degenerate ground state of a closed shell system, it is possible to delineate the standard Kohn-Sham procedure quite sharply. (The caveat is directed toward issues of degeneracy at the Fermi level, fractional occupation, continuous non-integer electron number, and the like. In many but of course not all works, these aspects of the theory seem to be... 

A dust cloud comprising a distribution of particle sizes soon fractionates, e.g. visible matter settles to the ground in a few minutes. Hence the size distribution of airborne particles may differ significantly from that of the source material. (This is particularly relevant to occupational hygiene measurements involving toxic dust emissions.)... 

The law of mass action has been successfully applied to many drug dose-response relationships since the early work of Clark. The systematic relation between the dose of a drug and the magnitude of its response is based on three assumptions (1) response is proportional to the level of receptor occupancy (occupancy theory), (2) one drug molecule combines with one receptor site, and (3) a negligible fraction of total drug is combined with the receptors. These assumptions must also apply to Beidler s equation. 

Figure 3.2. Partition function and fractional occupation for a two-level system.

The expectancy fi that a cell ( ) is occupied by a segment of a preceding molecule when vacancy of an adjoining cell (f—1) has been established beforehand in the course of seeking out the sets of x contiguous lattice cells available to molecule +1, is not exactly equal to the average expectancy fi of occupation of a cell selected at random. This latter expectancy is, of course, equal to the fraction of all cells in the lattice which are occupied by segments of the i molecules or... 

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