A caution

We have seen in the previous section that the definition of a set of OjS is intimately bound up with some choice of function space. The reader is cautioned, however, that not all function spaces can be used to define OjjS appropriate for a given point group. For example, the functions cosXi, sinx cosx and sinx, do not forma basis for a representation of the (symmetric tripod) point group xl and xt are the coordinates introduced before (see Fig. 5-2.2). 

The four functions do define a function space, since the general function is 

However, if we consider the C, operation of (clockwise rotation by 2tt-/3 about e,), then 

CJonsequently, this function space does not provide a basis for a representation of the sv point group. 

A set of five real d-orbitals defines a function space. In spherical polar coordinates r, 0, and f , they consist of a common radial function times a combination of spherical harmonics 7 (0, f ), l 2 and m =0, 1, 2. The combinations of the five spherical harmonics are chosen such that the orbitals are real. 

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Another potential problem is due to rotor instability caused by gas dynamic forces. The frequency of this occurrence is non-synchronous. This has been described as aerodynamic forces set up within an impeller when the rotational axis is not coincident with the geometric axis. The verification of a compressor train requires a test at full pressure and speed. Aerodynamic cross-coupling, the interaction of the rotor mechanically with the gas flow in the compressor, can be predicted. A caution flag should be raised at this point because the full-pressure full-speed tests as normally conducted are not Class IASME performance tests. This means the staging probably is mismatched and can lead to other problems [22], It might also be appropriate to caution the reader this test is expensive. 

It may be somewhat surprising that there is so lithe variation in CPU time among the various jobs. However, most of these jobs are dominated by computational overhead since they are so small. Only the largest basis set jobs even approach typical research-sized problems. This table should serve as a caution against drawing performance conclusions from such small, toy jobs. 

As a caution, the rolling of tubes into their tubesheets is a very special job that requires experience and feel, even though today there are electronically controlled rolling and expanding tools. The tubes must be just right, not over nor under expanded, to give a good joint and seal. 

However, in the course of this brief commentary, I would like to issue a caution regarding the extent to which the periodic table, for example, is truly explained by quantum mechanics so that chemical educators might refrain from overstating the success of this approach. I would also like to raise an issue which, to the best of my knowledge, has only recently been explicitly pointed out in the literature (/). 

As a caution, however, one must carefully purify the sample since small amounts of low molecular weight impurities can contribute significantly to II, even though their mass percentage in the sample is small. 

A Caution Hydrogen fluoride and fluorine are dangerous materials. Exposure to them will cause severe, painful, and perhaps fatal injury. Exposure may not be evident for several hours. The procedures described here pose the risk of exposure to hydrogen fluoride and to elemental fluorine and should only be carried out by, or under the direct supervision of, qualified professionals. Qualified first aid treatment and professional medical resources must be established prior to working in the area. Prompt treatment is necessary to reduce the severity of damage from exposure and should be sought immediately following exposure or suspected exposure. Material safety data sheets are available from HF and fluorine suppliers. Their recommendations should be followed scrupulously. 

Bates, M. and Avdalovic, N., The value of Dowex -50 in fractionation of nucleotides from acid-soluble pool. A caution, Anal. Biochem., 61, 508, 1974. 

There are different restriction enzymes that cut DNA at different sites. The previous sequence can be repeated several times for the same DNA sample. From a study of each restriction enzyme, a probability that another person will have the same profile is assigned. Thus, one restriction enzyme may have the possibility that another person has the same match of 1 in 100 or 1%. A second restriction enzyme may have the probability of 1 in 1000 or 0.1%. A third restriction enzyme may have a probability for a match of 1 in 500 or 0.2%. If there is a match with all three restriction enzymes, the probability would be 0.01 x 0.001 x 0.002 or 0.00000002% or 0.000002% or 1 part in 50,000,000. There is a caution to using the multiplication rule, in that DNA sequences are not totally random. In fact, DNA sequence agreements generally diverge as one s ancestors are less closely related. 

The conclusion drawn from this analysis is that classes A and C are separated, while class B may be overlapped with classes A and/or C. For illustrative purposes, assume that additional information is available that confirms our assertion that the unusual class B samples are actually mislabeled class A samples. These unusual class B samples will henceforth be labeled as belonging tO class A. Caution Do not make class assignments based solely on the score plots. Known class information drives the supervised methods and. therefore, it is vcn- imponant that ihc clas,s desiunati[Pg.78]

Hepatotoxicity. Duloxetine is rarely associated with increases in serum transaminase levels, typically in the first 2 months of treatment. In controlled trials in major depressive disorder, elevations of alanine aminotransferase (ALT) to greater than three times the upper limit of normal occurred in 0.9% (8 of 930) of the duloxetine-treated patients and in 0.3% (2 of 652) of the placebo-treated patients. Current product labeling contains a caution regarding the use of duloxetine in patients with significant alcohol use or chronic liver disease. Postmarketing reports have indicated that increases in transaminases have occurred in some patients with chronic liver disease (Cymbalta 2005). 

Finally, a caution about the Redhead equation. The requirement n=l is not explicit in the equation. For this reason nothing prevents that the equation is applied in situations where the order of the desorption is unknown or, even worse, when the order is known to be different from 1. To describe E obtained in this fashion as an approximation is an understatement, completely wrong is a better description. 

Cyclopropylcarbenes (see Section 2.4 for more on this reaction, and a caution) ring expand to give cyclobutenes in what is likely a concerted reaction. When a vinyl group is attached to the cyclopropane ring in the proper way, new products appear that are best rationalized by diradical intermediate 26 (Scheme 7.16). ... 

In studies of reaction pathways, nitrosyl radicals are frequently used as spin traps to provide evidence for free radical pathways. A caution in interpretation of these results is that the probe or products will interact with the transition metal complex in the reaction and affect the reactivity of the probe with the organic substrate or free radicals produced. A number of reactions of the stable free radicals RNO and R2NO with platinum(II) complexes have been carried out which show that such reactions must indeed be considered (equations 473-... 

A caution has been noted for chiral PTC alkylations involving alkyl halides that can be easily reduced. Attempted alkylation of 35 with (bromomethyl)cyclooctatetraene with a chiral cinchona-derived catalyst gave only racemic product [20]. 

As a caution to the reader Of course, Avogadro s hypotheses and the gas laws assume that gases are all ideal gases. The gases in the real world are not all ideal gases the molar volume at S.T.P. is most often a little below the 22.414 L indicated here. In the remainder of this chapter, the rounded value 22.4L/mol will be used for all gases and, if not so identified, all the gases are ideal. 

It s also for a caution to lawyers to consider any documents that could be material to patentability and not just those that are prior art. 

Because of the potential teratogenic effects of high-dose vitamin A, caution must be taken in the treatment of severe vitamin A deficiency among pregnant women as well as women of reproductive age. Women of reproductive age should be treated with 200,000 IU only when they display active corneal xerophthalmia. For... 

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