Significant difference

If the vapor mixture contains only ideal gases, the integrals in Equations (3) and (6) are zero, z is unity for all compositions, and ()i equals 1 for each component i. At low pressures, typically less than 1 bar, it is frequently a good assumption to set ( ) = 1, but even at moderately low pressures, say in the vicinity of 1 to 10 bars, (f) is often significantly different from unity, especially if i is a polar component. 

There is a significant difference between the results shown in Figure 2 and calculated results given in Brit. Chem. Eng. Proc. Tech. 16 1036 (1971). We believe the latter to be in error. 

If there is a significant difference between the effect of pressure on... 

Flence it can be seen that from the density of a fluid, the pressure gradient may be caloulated. Furthermore, the densities of water, oil and gas are so significantly different, that they will show quite different gradients on a pressure-depth plot. 

The refractograp of figure 4 shows highly oriented micro cracks of a polystyrene sample. The orientation of the cracks is perpendicular to the mechanical strain direction. The X-ray refracted intensitiy can be interpreted as crack density, i.e. the inner surfaces within a unit volume. Changing the tilt angle (of polystyrene and polystyrene blend samples) with respect to the primary beam leads to significantly different distributions of crack orientation (Fig. 5). 

All standard states, both for pure substances and for components in mixtures and solutions, are defined for a pressure of exactly 1 atmosphere. However the temperature must be specified. (There is some movement towards metricating this to a pressure of 1 bar = 100 kPa = 0.986 924 atm. This would make a significant difference only for gases at J= 298 K, this would decrease a p by 32.6 J moT )... 

The collision k, kj and reaction (k ) efficiencies may significantly differ between different excited... 

There are significant differences between tliese two types of reactions as far as how they are treated experimentally and theoretically. Photodissociation typically involves excitation to an excited electronic state, whereas bimolecular reactions often occur on the ground-state potential energy surface for a reaction. In addition, the initial conditions are very different. In bimolecular collisions one has no control over the reactant orbital angular momentum (impact parameter), whereas m photodissociation one can start with cold molecules with total angular momentum 0. Nonetheless, many theoretical constructs and experimental methods can be applied to both types of reactions, and from the point of view of this chapter their similarities are more important than their differences. 

The amplitude and therefore the intensity, of the scattered radiation is detennined by extending the Fourier transfomi of equation (B 1.8.11 over the entire crystal and Bragg s law expresses die fact that this transfomi has values significantly different from zero only at the nodes of the reciprocal lattice. The amplitude varies, however, from node to node, depending on the transfomi of the contents of the unit cell. This leads to an expression for the structure amplitude, denoted by F(hld), of the fomi... 

Atmospheric corrosion results from a metal s ambient-temperature reaction, with the earth s atmosphere as the corrosive environment. Atmospheric corrosion is electrochemical in nature, but differs from corrosion in aqueous solutions in that the electrochemical reactions occur under very thin layers of electrolyte on the metal surface. This influences the amount of oxygen present on the metal surface, since diffusion of oxygen from the atmosphere/electrolyte solution interface to the solution/metal interface is rapid. Atmospheric corrosion rates of metals are strongly influenced by moisture, temperature and presence of contaminants (e.g., NaCl, SO2,. ..). Hence, significantly different resistances to atmospheric corrosion are observed depending on the geographical location, whether mral, urban or marine. 

However, one significant difference between the AFM experiment and its simulations cannot be avoided at present Whereas the AFM experiment... 

Note that this latter method differs from the midpoint method, where one would use r(q +i/2) = (qn+i + qn)/2 instead of (7c) for r +i/2 in (7b). For highly oscillatory systems with k e, this can be a significant difference, because r is discretized directly in (7). An example in 4 below shows that the midpoint method can become unstable while (7) and (6) remain. stable. 

To obtain the unconditional stability of the midpoint method in local coordinates, one would have to consider the decoupling transformation from cartesian to local coordinates for the discrete variables etc. But this transformation, which for the continuous variables is not constant, necessarily is in error which depends on k, not e. The stability properties of the discrete dynamical systems obtained by the midpoint discretization in the different sets of coordinatc.s may therefore be significantly different when it 3> e [3]. 

To simplify we restrict our study to the case of a system with just two particles of significantly different masses, m and M, having coordinates x G IR" and q IR. Thus, the time-dependent Schrbdinger equation becomes... 

Three-body and higher terms are sometimes incorporated into solid-state potentials. The Axilrod-Teller term is the most obvious way to achieve this. For systems such as the alkali halides this makes a small contribution to the total energy. Other approaches involve the use of terms equivalent to the harmonic angle-bending terms in valence force fields these have the advantage of simplicity but, as we have already discussed, are only really appropriate for small deviations from the equilibrium bond angle. Nevertheless, it can make a significant difference to the quality of the results in some cases. 

Quinaldine (or 2-methylquinoline) can be prepared by the Doebner.Miller Synthesis, which in some respects is closely similar to the Skraup Synthesis (p. 297) but has some significant differences. 

The fact that good correlations are observed with d" rather than with a, is indicative of a strong infiuence of the substituent through a direct resonance interaction with a positive charge in the reacting system. The p-values are positive, which is expected for substituted dienophiles in a normal electron demand Diels-Alder reaction. Furthermore, the p-values do not exceed unity and are not significantly different from literature values reported for the uncatalysed reaction. It is tempting to... 

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