A final word

A final word may be said about appraising the accuracy of a computed root. No usable rigorous bound to the errors is known that does not require approximations to all roots and vectors. Suppose, then, that X is a matrix whose columns are approximations to the characteristic vectors, and form... 

A final word Can frequency response methods replace root locus ... 

A final word of caution on aromatic systems - the electron donating groups (notably those in which oxygen is the shielding entity) can cause problems, because their ortho- and para- effects are so similar. Consider the following example - you are presented with a sample known to be one of the two isomers shown in Structure 5.3 ... 

A final word, quoted from The Dow Chemical Company, a leader in the field of reactive chemistry ... 

A final word of caution regarding the use of single-temperature equilibrium constants. Although this is a rather expeditious method to derive reaction enthalpies, the obtained values may be quite inaccurate. For instance, a small 10 J K I mol-1 error in the estimated Ar,Vy. yields a 3 kJ mol-1 error in Ar at 298.15 K. 

A final word needs to be said about the supposedly unique features of enzymes, namely, their ability to produce enantiomerically pure products. This is not the place to speculate about the stereospecificity of enzymes, a problem that has been discussed elegantly by Comforth (15). It cannot be denied that the high (>99.9%) enantiomeric purity achieved by enzymes may be uniquely useful in the case of liquid products. However, when crystalline products are obtained in an asymmetric synthesis and the e.e. exceeds 80%, crystallization to enantiomeric purity without excessive loss of material is routinely achieved. 

A final word about IUPAC nomenclature of organic compounds ... 

A final word concerns the n-body problem with n > 3. Here the main problem is the rate of convergence of the EHF and corr series expansions, which we have discussed in Section IV.C. Although we may consider the knowledge of the potential-energy surface in its full dimensionality to be of fundamental importance in the case of four or five atoms, we suspect that the same may not be true for systems with a larger number of atoms, since the main role in the system chemical reactivity may then be attributed to three, four, or five atoms which define the active molecular center. Currently under way are studies for the H03 and 04 systems, and we hope, by using the DMBE... 

A final word about the order of names of joint inventors which appear on a granted patent. The sequence of names follows the order in which they appear in the application oath. In the eyes of the law, the first name on a patent does not imply in any way a greater contribution or lesser or what have you. All joint inventors are considered as jointly making the invention somewhat in the manner of a joint tenancy holding real estate. Each has an undivided part in the whole as well as in the part. 

A final word on the value of patents. A patent can greatly increase the value of a business. So when starting a business there are good reasons to try to patent the essential parts. However, a patent on its own - without a business - is seldom worth much. Most patents cost money. Most firms need patents to keep on working. They may use them to have a position in negotiations. They may licence (part of) their patents. Only a few firms, mainly development ones, regard patents as core business. 

A final word about the capping rule concerns a limitation. The [Os8(CO)22]2 cluster has the bicapped Structure shown in (16-XX). However, two other isomeric bicapped Mg structures, (16-XXI) and (16-XXII), are possible and the capping rule per se cannot predict which one to expect, nor can any other rule presently known. The mww-capped structure (16-XXI) is known for [Re8C(CO)24]2 , but no example of (16-XXII) has yet been reported. It may be that when the steric requirements of the CO groups are considered, this cis-capped arrangement is, for that reason, not possible. 

A final word of caution extends to the quality of the lamp. Xe lamps darken quite quickly with age, so long before the lamp should be replaced (say at lOOOh), the far-UV output will have diminished. This makes the head-room for absorbing species much less. Opening the slits can help, but then spectral resolution is lost. Always using two or three cuvettes for setting up these measurements will provide confirming evidence that the measurements are real. 

A final word should be said about the variety of porous materials. Porous catalysts cover a rather narrow range of possibilities. Perhaps the largest variation is between monodisperse and bidisperse pellets, but even these differences are small in comparison with materials such as freeze-dried beef, which is like an assembly of solid fibers, and freeze-dried fruit, which appears to have a structure like an assembly of ping-pong balls with holes in the surface to permit a continuous void phase. ... 

Presented text does not give a final word about what model is the best suited for applications in the zeolite science. We have attempted to show that the choice of the model depends primarily on the property under investigation. It is important to stress that other factors must be also taken into consideration, e. g., software and hardware limitations. It is always a difficult decision to find a suitable compromise among the size of the model and reliability of the method (under the constraint of available computational resources). It is equally difficult to judge the reliability of any computational study in the zeolite science. We hope that the present manuscript helps the reader to acquire some initial orientation in the computational zeolite science. 

A final word of caution is that very often a reaction cannot be studied with a simple SCF calculation the transition state of many reactions will require a higher level treatment (some correlation). Nevertheless very many reactions can be and have been successfully modeled by MINDO/3, MNDO, AMI, and SINDOl. The latter has even been used to model photochemical processes. 

We may say, as a final word of caution, that even the more-sophisticated kinds of calculation discussed in this subsection are not to be treated as Gospel-truth, for the figures cited above are valid only within the approximations relevant to the particular methods used to calculate them. The point we wish to emphasise, however, is that, without these methods, we really would not have any understanding of phenomena such as hyperconjugation. The reader may feel that, in this subsection, we have been alternatively an optimist and a pessimist this would be fair comment and one can only answer that, in this game, one has to be NJ0... 

As a final word, there is the pranise in some quarters that AIDS and cancer are somehow connected, both being immunologically deficient diseases. There may be even more to consider. The AIDS virus is considered to mutate, to be ever-changing, so that no treatment can pin it down. This, however, is a characteristic known as pleomorphism, a phenomenon that has been connected with cancer-causing viruses or microbes, and one about which there is much disagreement (Walters, 1993, p. 16 Moss, 1992, pp. 490-492). 

However, a final word of caution should be added. The above conclusions have been drawn for H + H., and similar reactions for which the vibrational-energy separations are large. Deviations from the predictions of activated complex theory are more likely for very low energy barriers, or when the energy barrier is large in comparison with the vibrational quanta and is situated in the product valley. There is indeed theoretical evidence, and evidence from molecular beam and chemiluminescence studies, that such is the case for a number of reactions. 

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