Full factors

Standard correlation spectroscopy (COSY) experiments were run on the same four samples and the results are displayed in Figure 8.2.16. Since the acquisition time was approximately an order of magnitude less than the recycle delay, a full factor of four for improvement in throughput was achieved in fact, the number of coils could be increased for yet further improvements in temporal efficiency. No signal bleedthrough was observed from one spectrum to another. Similar results were reported in this paper with a two-coil probe used at 500 MHz [19]. 

Full factorial designs Such designs are the best choice when the number of variables is four, or less. A full four-variable factorial design gives estimates of all main effects and two-variable interaction effects, and also an estimate of the experimental enor variance. This is obtained firom the residual sum of squares after a least squares fit of a second-order interaction model, see (Example Catalytic hydrogenation, p. 112). A full factoral design should be used if individual estimates of the interaction effects are desired. Otherwise, it is recommended first to run a half fraction 2 " (I = 1234), and then run the complementary fraction, if necessary, (see Example Synthesis of a semicarbazide, p. 135). 

UFs = 3 (subchronic to chronic exposure extrapolation full factor of 10 not used because a chronic oral study is available)... 

Cyanogen Chloride (CK). RfDe = 3 x 10 mg kg d . Data were not available to derive an RfDe directly from studies conducted on CK. Because the systemic toxicity of CK results from its transformation to free cyanide, CK is expected to elicit the same toxic effects as cyanide. Therefore, an oral RfDe for CK was derived from studies conducted on cyanide. Two studies were considered cocritical in the derivation of the RfDe one animal study and one human epidemiological study. In the animal study, a NOAEL was identified and a total uncertainty factor of 300 was applied to account for protection of sensitive subpopulations (10), animal-to-human extrapolation (10), and extrapolation from a subchronic to chronic exposure (3). A full factor of 10 was not used for the latter UF because chronic oral data were also available which showed that the subchronic NOAEL was adequately protective. In the human epidemiological study, a LOAEL was identified and a total uncertainty factor of 30 was applied to account for extrapolation from a subchronic to chronic exposure (3) and extrapolating from a LOAEL to a NOAEL (10). A uncertainty factor for sensitive human subpopulations was not used because the subject population... 

Specific factorial designs can be considered if the resources are insufficient to run all tests prescribed by the complete factorial design (see for example, Feng et al, 2013). This, in particular, is true for the experiments with the number of factors k>3. These designs include fractional factorial designs such as 2 and 2 which are called one-half and one-quarter designs, respectively, because they require respectively a half or a quarter of the total number of tests of the full factor experiment. 

Drawdown and build-up surveys are typically performed once a production well has been completed, to establish the reservoir property of permeability (k), the well completion efficiency as denoted by its skin factor (S), and the well productivity index (PI). Unless the routine production tests indicate some unexpected change in the well s productivity, only SBHP surveys may be run, say once a year. A full drawdown and build-up survey would be run to establish the cause of unexplained changes in the well s productivity. 

Since this is a purely mechanical operation it can be performed using the above equation, or by looking up the appropriate discount factor in discount tables. Two types of discount factors are presented for full year and half year discounting. 

If the reference date is set at the beginning of the year (e.g. 1.1.98) then full year discount factors imply that t is a whole number and that cashflows occur in lump sums at the end of each year. If the cashflow occurs uniformly throughout the year and the reference date is the beginning of the year then mid-year discount factors are more appropriate, in which case the discounting equation would be ... 

Figure 2 Flow diagram of the DHT with N=8, P=3. Broken lines represent transfer factors -1 while full lines represent unity transfer factor. The crossover boxes perform the sign reversal called for by the shift theorem which also requires the sine and cosine factors Sn, Cn.

A further advantage is the Selenium halflife of 120 days, which is 60% more when compared to iridium and a factor of approx. 4 when compared to Ytterbium. These differences turn out to be an important economical aspect when comparing the different sources, as they are a direct measure of the useful life of sources. The short halflife and the very high costs for Ytterbium sources have been the main factors for the rather low importance of Ytterbium in the full range of gamma radiography. 

Quantitative determined visual recognition for usual inspections, indicate that for indications with lengths over about 1.5 mm tbe probability of recognition is about 100 %. This is also applied to the penetrant inspection. This does not include the so called "human factor" which means that it cannot be guaranted that the inspector detects all indications for instance not always observing the inspection surface with full concentration. 

They must be coupled by separate radial factors in a full calculation [2] but, to the extent that non-adiabatic coupling between the upper and lower... 

We also describe a tracing method to obtain the phases after a full cycling. We shall further consider wave functions whose phases at the completion of cycling differ by integer multiples of 2jc (a situation that will be written, for brevity, as 2Nn ). Some time ago, these wave functions were shown to be completely equivalent, since only the phase factor (viz., is observable... 

The first and second terras contain phase factors identical to those previously met in Eq. (82). The last term has the new phase factor [Though the power of q in the second term is different from that in Eq. (82), this term enters with a physics-based coefficient that is independent of k in Eq. (82), and can be taken for the present illustration as zero. The full expression is shown in Eq. (86) and the implications of higher powers of q are discussed thereafter.] Then a new off-diagonal matrix element enlarged with the third temi only, multiplied by a (new) coefficient X, is... 

Tracing the arctan over a full revolution by the method described in Section rV and noting the factor 1 /2 in Eq. (171) establishes our result. (The case that E — m needs more careful consideration, since it leads to a breakdown of the adiabatic theorem. However, this case will be of no consequence for the results.)... 

Replacing the nuclear and electronic momenta by the modifications shown above in the kinetic energy terms of the full electronic and nuclear-motion hamiltonian results in the following additional factors appearing in H ... 

Many systems that cannot be represented by a first-order empirical model can be described by a full second-order polynomial equation, such as that for two factors. 

A solution which obeys Raoult s law over the full range of compositions is called an ideal solution (see Example 7.1). Equation (8.22) describes the relationship between activity and mole fraction for ideal solutions. In the case of nonideal solutions, the nonideality may be taken into account by introducing an activity coefficient as a factor of proportionality into Eq. (8.22). 

Gasohol in the United States. Over 90% of the fuel ethanol in the United States is produced from com. Typically, 0.035 m (1 bushel) of com yields 9.5 L (2.5 gal) of ethanol. Ethanol is produced by either dry or wet milling (87). Selection of the process depends on market demand for the by-products of the two processes. More than two-thirds of the ethanol in the United States is produced by wet milling. Depending on the process used, the full cost of ethanol after by-product credits has been estimated to be between 0.25—0.53/L ( 1—2/gal) for new plants (88). Eeedstock costs are a significant factor in the production of fuel ethanol. A change in com price of 0.29/m ( 1.00/bushel) affects the costs of ethanol by 0.08/L ( 0.30/gal). 

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