Solution validation

Moreover, the arguments we have used to prove the existence of the solutions validate the estimate... 

Previously derived results for the charge-density profile and polarization profile in this model solution, valid only for small fields, were used. Although these did not consider the penetration of the electrons into the solution, the change in the field is small. A Harrison-type pseudopotential84 was used to represent the effect of core electrons of the solution species on the metal electrons. 

Figure 3.18 shows how this varies as the (-potential is varied at an electrolyte concentration of 10-2M potassium chloride. Once the potential exceeds 50 mV the calculation error becomes large and Equation (3.59) should really be restricted to tea > 100. However, Figure 3.18 shows how small the effect normally is. A numerical solution valid for any potential and all Ka values was published by Watterson and White.29... 

Combining equations (8.5) and (8.6) we see that the general solution valid in the neighbourhood of the origin is... 

Relaxing the restriction of low Reynolds number, Rimmer (1968,1969) used a matched asymptotic expansion technique to develop a solution in terms of Pe and the Schmidt number Sc (or Prandtl number Pr for heat transfer), where Sc = v/D.j and Pr = v/a in which v is the kinematic viscosity of the flowing fluid. His solution, valid for Pe < 1 and Sc = 0(1), is... 

The Solution Validation. Obvious conditions that the resultant solution must satisfy are a) must be non-negative b) the operation Gia should provide a noise-free measured function and c) the areas under the measured and the corrected chromatograms must be equal. It should be emphasized that condition b) is a necessary but not sufficient for good results. Apart from the mentioned checks, a validation procedure based on the analysis of the innovations will now be presented. 

This is called the inner solution, and is valid in a time interval of order e Eq. (241) is the outer solution, valid everywhere else it will be denoted by capitals U and V (see Fig. 17). The challenge is to see if we can splice it onto the inner solution. We have Uo at our disposal to do this. 

In cesium chloride the main contribution to V2 comes from cesium ion states acting as intermediaries in a form that can be obtained from perturbation theory. We need not be further concerned here with the origin of Fj. (We shall discuss the ionic crystal matrix elements in Chapter 14.) For a particular value of J in Eq. (2-2), there are only seven values of i that contribute to the sum / = j numbered as 0, and the six nearest-neighbor chlorine s states. The solution (valid for any j) is... 

Validation experts mnst take care not to assume that there is only one way to validate. Rather they should be flexible in their approach, so that when the inevitable problems arise they do not instinctively resist exploring new solutions. Validation experts do not have to be leaders, provided they have management support and can articulate their views to management in order that they can receive appropriate direction. 

Validate spreadsheets if going to alternative solutions validate these, too. 

Compounds to Supersaturate in Solution—Validation Study. J Pharm Sci 2006 95 1298-1307. 

In the case when the ionic conductivity prevails (a c>v ). the solution valid for... 

It is evident, on further examination, that the solution (11-57) cannot be uniformly valid within the thermal boundary layer because it cannot be made to satisfy the matching condition (11 7b) for any choice of the coefficient a(x). Hence (11-56) and the solution (11-57) are only valid in the part of the thermal layer that lies closest to the body surface, and, to obtain a(x), we must seek a second solution, valid in the outer part of the thermal boundary layer, with a(x) determined from matching. 

The structure of MQDT involves a compact target state within a radius ro and an asymptotic solution, valid at large r, which is joined to the wavefunction of the inner region in order to determine amplitudes and phases. Thus, MQDT is simply a special form of scattering theory, specially adapted to handle bound Rydberg states of atoms and adjacent structure in the base of the ionisation continuum. 

To enable us to compare the long-pipe approximation with the exact solution valid for a horizontal pipe, we substitute equation (A2.29) into (A2.13) with the additional condition that zi = Zs. i-e. ... 

Under conditions where the conversion of B to A in solution is pseudo-lst-order, approximate solutions, valid for either extremely large or small k, were obtained by Klatt and Blaedel [103]. A more complete treatment, valid for all values of k, was given by Matsuda and co-workers [104]. The analysis showed that the catalytic reaction caused the diffusion-limited current in the presence of the catalytic cycle, 7cat, to be increased over the current that would be observed in the absence of the cycle (k = 0), Jd, by an amount depending on the parameter... 

Now, we have the single-valued general solution valid in the whole asymptotic region. For instance, we can obtain the following connection formula for the physical solution on the real axis ... 

The diffusional flow rate to a cylindrical collector, whose axis is normal to the flow direction, has also been determined by a procedure similar to that outlined for the spherical collector. Although no steady, uniformly valid, inertia free, Stokes solution exists for an unbounded medium, a solution valid near the... 

R.H.M. Hatley, C. van den Berg and F. Franks, The unfrozen water content of maximally freeze concentrated carbohydrate solutions - validity of the methods used for its determination, CryoLetters, 1991, 12, 113-126. 

No initial condition is specified as in the previous example since asymptotic solution valid after exponential growth has started. A trial solution is therefore we seek the... 

Taylor (Tib, T2) has, however, obtained first-order perturbation solutions valid for two limiting cases. 

Similar agreement exists for the quasi-steady approach of a sphere towards a rigid plane wall. If F is the force on the sphere of radius a, and h is the distance from the sphere center to the wall, the exact solution, valid for all ajh, is (B14, M6)... 

A solution valid for the sediment and the water column (if z is defined positive as the distance to the interface), where A222 signifies the Rn activity at the interface (Figure 8). In the sediment, this corresponds to an integrated depletion of ... 

In the droplet bulk, one can evaluate the dissipative integral using the circular cap solution valid when gravity and other external forces can be neglected, this will be just a spherical cup approximated by a parabola ... 

Find an approximate solution, valid for long times, to the linear parabolic partial differential equation, describing mass or heat transport ffom/to a sphere with constant physical properties, such as thermal conductivity and diffusion coefficient... 

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