Average defined

Threshold limit value—time weighted average. Defined as the maximum time weighted average concentration to which a worker may be exposed repeatedly and without adverse effects for a normal 8 h/d, 40 h/wk period. 

The average defining the potential of mean force, (8.49), can be written as an average over a skewed distribution of initial momenta as described by (8.55). We can anticipate that skewed trajectories are associated with lower work, as the momenta can be biased so that important degrees of freedom tend to move in the same direction as the pulling potential. Specifically, the instantaneous contribution to the work of... 

If the averages defined by (36) are independent of the time, the ensemble is in statistical equilibrium and dg/dt = 0. As a sufficient condition for equilibrium it is, according to (37) therefore necessary that [g, H] = 0. In general therefore, an ensemble is in statistical equilibrium if the density operator commutes with the Hamiltonian. 

For the purpose of this calculation it was necessary to know the diffusion coefficient for ligand and whole molecules of hemocyanin (Table I) and the value of the diffusion coefficient for half molecules of hemocyanin. If the level of calcium ion is reduced in pH 9.6 glycine buffer to the point where no whole molecules remain, the half molecules always are contaminated with one-twelfth size (5S) subunits, so that it is impossible to measure directly the diffusion coefficient of half molecules. For a self-associating system, the Gouy method leads to an average diffusion coefficient which is the Z-average, defined by... 

The quantity of physical interest in applications normally proves to be not the instantaneous value of the function / itself, but rather its time average, defined as... 

For this particle, an infinite number of statistical diameters radiating from the center of gravity of the particle exist. The average imrolled diameter of the projected contour is the integrated average defined by [2]... 

For tiie equations listed in Table 6.27, it is assumed that the relative volatility is constant, but short cut methods are frequently used when the relative volatility varies. In this case, an average relative volatility is used. King [30] shows that the most appropriate average is the geometric average, defined by Equations 6.27.19. The equations listed in Table 6.27 are restricted to solutions fliat contain similar confounds, such as alaphatic or aromatic hydrocarbons. 

From a practical point of view, the thermal averages defined 1 Eq. (7.6) are not very meaningful as they depend on the specific realization of the matrix. Therefore one needs to supplement the thermal average by a disorder average over matrix configurations, 3delding the double average... 

For multicomponent systems, calculations with the Fenske equation are straightforward if fractional recoveries of the two keys, A and B, are specified. If the relative volatility is not constant, the average defined in equation (6-60) can be approximated by... 

The result of the measurement is reported as the arithmetic average defined by... 

Note that in the terminology of the theory of statistics, a function, such as (x), that is defined over fi, is called a random variable the brackets <> denote a statistical average defined with the Boltzmann PD. We now define a total absolute entropy S that depends on both the coordinates and the momenta (see Eqs. [IJ and [2], ... 

Once this data table has been completed, it is possible to compute the molecular weight averages or moments of the distribution. The most common averages defined in terms of the molecular weight at each time slice and either the number of molecules n, or the area of each time slice are... 

The average in (3.2.34) is taken with the distribution of the two states L and H of the empty polymer, given in Eq. (3.2.2). Here we introduce the subscript (0, 0) to stress the condition that both sites are empty to distinguish this average from the conditional average defined below. 

In this figure we have introduced the fact that in a particular sample the measured molar mass is an average. Here we have used a number average defined as... 

The foregoing equal-time average defining the ET2 function amounts to saying that the diagonal elements of the density matrix are taken into account in this formulation (Eq. 71). In the limit P -> oo there would be theoretical accuracy, as for the rest of PI estimates for properties. Note that the k = 0 component of 5 is related to the number fluctuations and, therefore, to the isothermal compressibility... 

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