Intensity functions

The intensity function A(t) = E(t)/[1 — E(t)] occurs in the maximum mixing concept and is of value, for instance, in detecting maldistributions of catalyst and channeling in a packed vessel. 

Functional Group Absorption (cm ) Intensity Functional Group Absorption cm 1) Intensity... 

The intensive function Gm for a pure substance is known as the chemical potential. We will see that it is the potential that drives the flow of mass during a chemical process or a phase change. 

The scattering of electrons by an atom pair separated by a rigid distance, r, averaged over all possible orientations in space, gives rise to a molecular scattering intensity function which can be represented in the following way1 ... 

Molecular ensembles usually exist in some distribution over several vibrational states. Denoting the population of the vth state by pv, the total molecular intensity function can then be calculated by summing over the states ... 

For polyatomic molecules the situation is somewhat more complex but essentially the same. The effect of intramolecular motion upon the scattering of fast electrons by molecular gases was first described by Debye3 for the particular case of a molecular ensemble at thermal equilibrium. The corresponding average molecular intensity function can be expressed in the following way ... 

In the future, it is likely that many labor-intensive functional immunological assays performed in vivo or ex vivo will be replaced by high throughput multiparameter cytometric-based assays. The challenges faced both today and in the future have been recently described.56 For example, translational aspects of the nonclinical data to the clinical setting are difficult because despite much similarity, there are still species differences in some of the very basic aspects of the immune system. Additionally, reagents... 

If this were a true Gamma distribution the limiting value of the intensity function would be A(co) = n = 12.9, instead of the approximately 18 found here. That last number, however, may not be valid because data at the high end are uncertain. 

The intensity function of tracer flow in a reactor has these values,... 

The intensity function A(tr) was evaluated numerically is curve fitted, as shown on the graph, by... 

It is well known that under the weak-phase-object approximation (WPOA) [19], the image intensity function is linear to the convolution of the projected potential distribution function cpt (x, y) and the inverse Fourier transform (FT) of the contrast transfer function (CTF) r(u) of the electron microscope ... 

Here /i g(u) is the Fourier components of the image intensity function. u is the lattice vector in reciprocal space. F (u) is the Fourier spectmm of the projected potential y>,(x, y). In crystallography, F (u) is the structure factor of the crystal. 

The internal energy per unit mass e is an intensive (state) function. Enthalpy h, a compound thermodynamic function defined by Equation 1.8, is also an intensive function. 

The intensity functions for the diffuse reflector and the sample are, respectively,... 

Fig. 8. Curve decomposition of the SANS intensity function of NIPA gd (G083) at 29 °C. The solid squares, dashed line, and dotted line indicate the observed data points, the Lotentzian and Gaussian components, respectively...

According to the Borue and Erukhimovich theory for polyelectrolyte solutions [84], the scattered intensity function for ionic gels may be given by the... 

Fig. 12. Observed (symbols) and calculated (solid Ones) scattered intensity functions for the NIPA/AAc gels having = 0.107...

The time evolution of a system may also be characterized according to the degree of perturbation from its equilibrium state. Linear theories hold if local equilibrium prevails, that is, each volume element of the non-equilibrium system can still be unambiguously defined by the usual set of (local) thermodynamic state variables. Often, a crystal is in (partial) equilibrium with respect to externally predetermined P and 7j but not with external component chemical potentials pik. Although P, T, and nk are all intensive functions of state, AP relaxes with sound velocity, A7 by heat conduction, and A/ik by matter transport. In solids, matter transport is normally much slower than the other modes of relaxation. 

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