Conditions for validity

The conditions for validation of an analytical method for the determination of residues in air are the same as the requirements given in Section 4.2.5. 

V. Conditions for Valid Measurement and Interpretation of Limiting Currents. . 252... 

Since current can be measured with ease and precision, the limiting-current technique provides a convenient and, under certain conditions, accurate method for measuring mass-transfer rates. The conditions for valid measurement and correct interpretation of limiting currents are discussed in the following sections. 

The Feynman-Hibbs and QFH models perform quite well in free energy calculations as long as the quantum corrections are modest. The conditions for validity of the approximations are given above. 

The condition for valid results in this work is the fact that the system is in the gel-state that is, it is in a state of inner equilibrium, and not in the glass state. Measurements of Hellwege, Knappe, and Lehmann (5) on pure PVC show the expected discontinuity in the compressibility vs. pressure curve at the melting point transition in the glass state. It is inferred from this study that the glass temperature for pure PVC and for the plasticized, gel-type PVC does not rise above 110° C. at pressures of 200 atm. (Figure 7). Our study showed that the system is always in a state of inner equilibrium. 

The conditions for validity of the harmonic approximation in eq. 13 (i.e. that the potential bequad-ratic within a few de Broglie wavelengths h//2 -mkT in all directions from the saddl point) are somewhat opposed to its conditions of validity in eq. 12 (i.e. 

So far the form of 4, has not been specified. While the Schrodinger equation defines clear conditions for valid state functions of the system, it does not offer a practical method to actually obtain the exact solution VP or vPel. As a consequence, iterative procedures have been developed that start with some trial wavefunction, and subsequently improve their quality until some predefined convergence criterion is fulfilled. 

Most of the observations reported so far suggest, that there are certain ranges of time, quench depth and wave numbers q where unmixing progresses to a good approximation in the linear branch, i.e. non-linearity is very weak. The conditions for validity of the linear theory can be specified more precisely as follows ... 

T is the bath temperature the conditions for validity of eq. (23), which scarcely ever fail and which apply in practice at all pressures of the systems, have been described elsewhere.lsb Figure 8 shows the form which /( ) exhibits the distribution functions are for C2, C4, and C4-d , formed by association of two Ci (methyl) radicals, two C2 radicals, and two Ci-dz radicals, respectively. The association complexes are complex 3, Table I, for C2, and complex 5, Table II, and the complex described in Table VI, for the C4 molecules. It is evident that increasing in the number of degrees of freedom of the reactants, and lowering the vibrational frequencies broadens the distribution. 

ISO 9000 2000 [16] Confirmation, through the provision of objective evidence (3.8.1.), that the requirements (3.1.2) for a specific intended use or application have been fulfilled NOTE 1 The term validated is used to designate the corresponding status NOTE 2 The use conditions for validation can be real or simulated. 

Theorem 3.5 A necessary (but not sufficient) condition for validity is that of convexity of the function n(mk) with respect to k ... 

This is essentially just the neutral stability condition for direct-mode buoyancy-driven convection. In the Ra, Ra plane, this is a straight line that defines a possible stability boundary. Note, however, that we do not get conditions for validity of the assumption aImag = 0. For this, we must examine the other case, crjmag / 0. 

The same type of difficulty that is resolved by use of equation (35) for the partial-equilibrium approximation may also arise in connection with the steady-state approximation. For example, part of the sum of terms that contribute to the production rate of a primary species, to which the steady-state approximation is not applied, may be a constant multiple of (D, for an intermediary that is subject to the steady-state approximation, and the remaining terms in the production rate may be smaller than even though c j is small compared with. Under this condition, inaccurate results for the concentration history of the primary species will be obtained by use of the steady-state approximation for the intermediary unless a substitution analogous to equation (35) is employed. In the absence of appropriate substitutions, the previously stated condition for validity of the steady-state approximation, although necessary, is not sufficient in all respects. Often less complicated criteria are stated for the validity of steady-state approximations for example, it is frequently suggested that the steady state for an intermediary will be acceptable if its concentration is small compared with the concentrations of the major species. These simple criteria, which are useful for obtaining insights and estimates, usually are necessary but not sufficient. Especially when combinations of steady-state and partial-equilibrium approximations are employed, correct specification of necessary and sufficient conditions can become complex. 

The assumptions made in deriving (18.41) require that aG/u < x/u. Thus the condition for validity of the result is... 

To see the conditions for validity of this expression note that the first and the exponential terms in the asymptotic series expansion for... 

The integral may be evaluated graphically from experimental data. If P( ) =1 then the integral is 8/3 and equation (55) is reduced to equation (18). The general condition for validity of this simplified theory is, for spheres, that 2[Pg.35]

Conditions for validity Adiabatic mixing negligible heat absorbed by the solution container, negligible dependence of heat capacities on temperature between 25°C and Tao for A, 25°C and Tbo for B, and 25°C and for the solution. 

Ff = Ff" is generally more likely to be valid than the corresponding condition for validity of Equation [8.86] that pertains to external calibration using clean solutions of analytical standard plus SIS however, this is not always a valid assumption (Section 4.2), e.g., if the native analyte is somehow occluded in the sample matrix (Boyd 1996) or strongly bound to another component in the analytical sample (Ke 2000). 

Noyes, R. (1978). Generalized kinetics of chemical change some conditions for validity of the steady state approximation. Supplement of the Progr. Theor. Phys., 64, 295-306. 

The conditions for validity of the NFE model break down for conductivity values near the loffe-Regel limit, that is, o-(O) 07. As discussed in Sec. 2.3.2, electronic transport in this situation is best described as diffusion of electrons from atom to atom, even though the system is stiD metallic with delocalized electron states. In this connection, it is interesting that near the range where cr(0) 07, the temperature coefiScient d n.(r(Q)/d nT)y is clearly positive (Freyland, 1981 Freyland et al., 1974). 

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