Dispersion monotonic

The effect of changing solvent composition (polarity) on molecular weight dispersity is noteworthy. Mw/Mn is quite low (1.69) in the experiment carried out by the use of 100% CH2C12 and it increases monotonically with increasing n-C6H14 content. It is very difficult to interpret these data at this time. 

More specifically, the reduced variable Kj = kjA is defined on [0, ti]. Generally, the error in an FD approximation (or rather its dispersion relation, Eq. (36)) increases with Kj. The Taylor series approach outlined above, which leads to the standard Lagrangian FD approximations, is essentially perfect for very small Kj but quickly deviates from the correct, quadratic dependence, Eq. (37). The generic behavior is that the error increases monotonically with Kj. Instead of requiring that the fit be perfect in the limit of very small Kj, we require that the error be no greater than s from Kj = 0 up to some... 

Figure 4 shows the viscosity of the samples as a function of dispersant dose. Note that the viscosity decreases more or less monotonically with dose throughout and beyond the normal commercial dosage range, but that the reduction in viscosity at doses above 1 % is relatively small. 

Boudart (223) suggested that all reactions might not be equally sensitive to the geometric arrangements in various metal surfaces or to the differences in the electronic structure of sites in different geometric environments (coordination). Boudart divided the reactions into two groups (I) structure insensitive and (II) structure sensitive. The operational criterion of structure sensitivity is the specific activity (the rate per unit surface area) or, the turnover numbers (TONs) (the rate per site) TONs should differ by more than a factor of 5-10 when the dispersion D is varied sufficiently. Bond (224) formulated similar ideas and also suggested several reasons why the variations of TONs with D can monotonically decrease (antipathic), mono-tonically increase (sympathetic), or show a maximum. 

In contradistinction to the spectra obtained in the mica dispersion, Pseudocyanine, when added to the colloidal silver and silver halide systems of Figures IB and 1C, yielded no H-bands but formed well defined J-bands. The latter also exhibited a weak secondary peak located near the absorption maximum of dissolved, unperturbed dye. Although the position and intensity of the J-band varied with the substrate (4, 17, 38, 61), the differential spectra obtained in these silver systems exhibited marked similarities. An increase in the concentration of the substrate produced in both cases a monotonic change in the absorbance of the M-... 

Consider now the frequency dependence of the third cumulant. We will be interested in the case of a good conductor where the charge-relaxation time tq is much shorter than the dwell time td- Unlike the second cumulant of current, the third cumulant P3(wi,w2) in general exhibits a strong dispersion at wy2 1/td [11], For symmetry reasons, this dispersion vanishes for symmetric cavities and cavities with two tunnel or two ballistic contacts. The shape of P3(wi, w2) essentially depends on the parameters of the contacts. In particular, for a cavity with one tunnel and one ballistic contact with equal conductances Gl = Gr = G it exhibits a non-monotonic behavior as one goes from lv1 = uj2 = 0 to high frequencies. A relatively simple analytical expression for this case may be obtained if td 3> tq and one of the frequencies is zero ... 

Both the Factors E, the dripping rate of H2S04, and G, the amount of dispersion agent, exhibit monotonously increasing influences on the mean diameter of particles but both their effects are insignificant. 

What does this kind of exponential frequency mean for the epsilons Happily, the characteristic oscillations of laboratory language transform nicely into the language of exponential frequencies. After transformation, the epsilons behave smoothly, decreasing monotonically versus exponential frequency, without the spikes of absorption and dispersion seen for real oscillations. 

In the framework of the traditional double layer theory, when there is a strong adsorption of a multivalent cation of the electrolyte, the stability ratio of a colloidal dispersion first decreases, passes through a minimum, followed by a maximum, after which it decreases as the concentration of the (multivalent) electrolyte increases. When the adsorption is weak, the stability ratio decreases mono-tonically with increasing electrolyte concentration. For a monovalent electrolyte, the stability ratio calculated in the framework of the classical double layer theory decreases monotonically with increasing electrolyte concentration. Consequently, in the traditional theory, the ion screening becomes dominant at high ionic strength, whereas experiment appears to show that the colloidal dispersion is restabilized. 

It is well known that C0M0O4 is destroyed by the presence of potassium.8 The reduction of Mo(Vl) to Mo (IV) is enhanced by potassium and it is easier to reduce to Mo(IV) during sulphation. The addition of potassium leads to a monotonic decrease in the molybdenum dispersion with the impregnating amount of potassium in the oxidic state catalyst, but it is more complicated after sulphation. Potassium is well spread on the surface in both the oxidic and sulfided states. The catalytic activity for the WGSR was correlated with the potassium content of CoMoK/r-AljC. The electronic effectiveness of potassium on the catalyst is not found. 

Figure 1. Tc ITp as a function of X. Dashed curves show monotonic increase that would result if the CP (linear) dispersion law were not gapped, i.e., if in (5) A was artificially...

In glycerin, the dispersion appears to be stable and behaves as a shear thinning fluid. However, the viscosity does not vary monotonically with silica concentration, instead decreasing initially before increasing at higher concentrations (Fig. 38). The phenomena reflect offsetting effects of adsorption, the reduction in the solution viscosity due to depletion of polymer... 

These theoretical expressions have been tested by experiments on monosized pol3oner lattices [42] and monosized silica [43] suspensions dispersed in water and other liquids. Both the low and the high shear-limiting viscosities are shown in Figure 12.13 to increase monotonically... 

To obtain the best possible fit, a full regression analysis will be necessary, and results of this are not yet available. The outstanding question to be answered is whether the broad absorption is to be regarded as a relaxation process, or whether it is a resonance process, a molecular libration (partial rotation within a potential well) such as is responsible for submillimetre-wavelength absorption bands in many liquids it is possible that both processes contribute. A resonance process would produce an effect in the real permittivity similar to an anomalous dispersion a relaxation process merely produces a monotonic fall in the real permittivity. 

Thus far our discussion has centered upon rotatory dispersion in regions of relative transparency in which measurements are instrumentally feasible and theory reasonably secure. However, the featureless monotonic variation of optical rotation with decreasing wavelength changes radically at optically... 

London s eqn. (15) for the dipole-dipole dispersion energy is not a simple product of properties of the separate atoms. A partial separation was achieved in 1948 by Casimir and Polder who expressed the /r dispersion energy as the product of the polarizability of each molecule at the imaginary frequency iu integrated over u from zero to infinity. The polarizability at imaginary frequencies may be a bizarre property but it is a mathematically well behaved function that decreases monotonically from the static polarizability at m = 0 to zero as u—> oo. 

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