Invalid.Part

There remain the small, homogeneous reactors. For such reactors the Taylor expansion which breaks off at the third term is invalid— partly because the kernels are no longer displacement kernels, partly because the Taylor series does not converge well. The second consideration suggests that the higher moments of the kernel G x — A ) are important—i.e., that for small reactors, the full spatial dependence of the kernels must be considered. 

In production you need to ensure that only those personnel, equipment, materials, and facilities that were qualified are employed in the process, otherwise you will invalidate the qualification and inject uncertainty into the results. If subcontracting special processes you need to ensure that the subcontractor only employs qualified personnel and has qualified process equipment and facilities (see Part 2 Chapters 6 and 18). 

That all actual processes are irreversible does not invalidate the results of thermodynamic reasoning with reversible processes, because the results refer to equilibrium states. This procedure is exactly analogous to the method of applying the principle of Virtual Work in analytical statics, where the conditions of equilibrium are derived from a relation between the elements of work done during virtual i.e., imaginary, displacements of the parts of the system, whereas such displacements are excluded by the condition of equilibrium of the system. 

The decrease of 0.04 A. in the double bond distance requires that the resonance curve be revised. It is fortunate that this revision invalidates none of the earlier conclusions, for the reason that only the part of the curve from 0 to 50% double-bond character was made use of, and the new curve does not differ appreciably from the old one in this region. 

Several doubts about the correctness of the usual statistical treatment were expressed already in the older literature (31), and later, attention was called to large experimental errors (142) in AH and AS and their mutual dependence (143-145). The possibility of an apparent correlation due only to experimental error also was recognized and discussed (1, 2, 4, 6, 115, 116, 119, 146). However, the full danger of an improper statistical treatment was shown only by this reviewer (147) and by Petersen (148). The first correct statistical treatment of a special case followed (149) and provoked a brisk discussion in which Malawski (150, 151), Leffler (152, 153), Palm (3, 154, 155) and others (156-161) took part. Recently, the necessary formulas for a statistical treatment in common cases have been derived (162-164). The heart of the problem lies not in experimental errors, but in the a priori dependence of the correlated quantities, AH and AS. It is to be stressed in advance that in most cases, the correct statistical treatment has not invalidated the existence of an approximate isokinetic relationship however, the slopes and especially the correlation coefficients reported previously are almost always wrong. 

The district court thus concluded that selection of compound (2) as a "lead compound" was "taught away" from by the prior art, and the Federal Circuit agreed. Because, in part, selecting compound (2) as a "lead compound" was "taught away" from, Alphapharm s attempt to invalidate the 777 patent was thwarted. 

One area of research related to abuse or neglect has to do with how well a person fits within his or her social environment. One researcher, Marsha Linehan (1993), has talked about how a poor fit with the social environment (viz., not fitting into the family, school life, or other important social networks) may cause psychiatric problems if the poorness of fit causes the person to feel like an outsider or to feel constandy invalidated or put down. Many of my clients have told me that they have not felt part of their families or that they did not fit well into society in general, or have described themselves as black sheep. Abuse and neglect lead to an invalidating environment, but so can mismatches of personalities within families or mismatches of behavioral patterns with social norms. Furthermore, there is evidence that the way emotion is expressed in families can be associated with a poorness of fit that can influence the course of drug problems. 

Xr from the robust approach, as expected, still gives the correct answer however, the conventional approach fails to provide a good estimate of the process variables. Although the main part of the data distribution is Gaussian, the conventional approach fails in the task because of the presence of just one outlier. In a strict sense, the presence of this outlier results in the invalidation of the statistical basis of data reconciliation,... 

There are instances where some or all parts of the concept of equal reactivity of functional groups are invalid [Kronstadt et al., 1978 Lovering and Laidler, 1962], The assumption of equal reactivities of all functional groups in a polyfunctional monomer may often be incorrect. The same is true for the assumption that the reactivity of a functional group is... 

Chemical systems in those days were little more than assemblies of more or less independent rules and concepts, lacking the interdependent structure of a coherent system of concepts and practice we would today call a theory. The rejection of one part did not necessarily invalidate any of the others. This is certainly the case with the chemistry of Rouelle, whose teaching nonetheless colored the attitudes and writings of his pupils. The two major expressions of Rouelle s influence are found in the writings of Gabriel-Fran ois Venel (1723-1775), the principle contributor of the chemical articles in the Encyclopedie of Denis Diderot (1713-1784), and the textbook and Dictionary of Pierre-Joseph Macquer (1718-1784). 

The validity of RSP has been discussed by Exner O. Exner, J. Chem. Soc, Perkin Trans. 2, 5, 973 (1993). For a given reaction series four types of behavior are possible (i) a valid RSP when the selectivity decreases with reactivity (ii) anti-RSP when the reverse is true (iii) indifferent behavior when the change in selectivity is negligible (iv) a cross-over when RSP is valid in one part of the series and invalid in the other. 

It is the outer portion of the double layer that interests us most as far as colloidal stability is concerned. The existence of a Stern layer does not invalidate the expressions for the diffuse part of the double layer. As a matter of fact, by lowering the potential at the inner boundary of the diffuse double layer, we enhance the validity of low-potential approximations. The only problem is that specific adsorption effects make it difficult to decide what value to use for J/6. 

In order to explain the field effects observed for the cationic polymerizations, we have earlier proposed a kinetic scheme based on the two-state polymerization mechanism and on the field-facilitated dissociation hypothesis (11). Though the assumptions involved in the proposed interpretation turn out to be partly invalid in the light of the experimental data accumulated most recently (15), it is still necessary to give an outline of the scheme. We assumed that, by the initiation reaction between initiator molecules (C) and monomer molecules (M), active species of an ion-pair type (My) are produced, a portion of which dissociates into active species of a free ion type (Mf) and gegenions (C ). The propagation, monomer transfer and termination can be effected by the free ions and ion pairs. A dissociation equilibrium is established between the free ions and ion pairs, which can be characterized by a dissociation constant K. Then we have ... 

The effect of the difference between El and E2 on the force at break is shown in Figure 8.7. The approximate average stress is /2(A+B) which is the apparent tensile strength and may be considerably less than the true tensile strength, A. The discrepancy may be as much as 33%66 and will vary with the steepness of the final part of the stress/strain curve. Although this may not be serious in pure quality control testing, the variation with slope of the stress/strain curve could make comparisons between different rubbers invalid. 

It should be noted, however, that we need to check whether Tkh(x) < 0 is quasi-convex at each iteration. If the quasi-convexity condition is not satisfied, then the obtained lower bound by OA/ER may not be a valid one that is, it may be above the global solution of the MINLP model. This may happen due to the potential invalid linearizations which may cut off part of the feasible region. 

---