Observed ratio

Catalytic hydrogenation of 1 4 dimethylcyclopentene yields a mixture of two products Iden tify them One of them is formed in much greater amounts than the other (observed ratio =10 1) Which one is the major product" ... 

Both side-chain and main-chain scission products are observed when polyacrylates are irradiated with gamma radiation (60). The nature of the alkyl side group affects the observed ratio of these two processes (61,62). 

The most serious problem with ensemble average approaches is that they introduce many more parameters into the calculation, making the parameter-to-observable ratio worse. The effective number of parameters has to be restrained. This can be achieved by using only a few confonners in the ensemble and by determining the optimum number of confonners by cross-validation [83]. A more indirect way of restraining the effective number of parameters is to restrict the conformational space that the molecule can search... 

Radium occurs only in association with uranium (Chapter 31) the observed ratio Ra/U is 1 mg per 3 kg, leading to a terrestrial abundance for Ra of 10 ppm. As uranium ores normally contain only a few hundred ppm of U, it follows that about 10 tonnes of ore must be processed for 1 mg Ra. The total amount of Ra available worldwide is of the order of a few kilograms, but its use in cancer therapy has been superseded by the use of other isotopes, and the... 

The procedure comprises the addition of a constant amount of internal standard to a fixed volume of several synthetic mixtures which contain varying known amounts of the component to be determined. The resulting mixtures are chromatographed and a calibration curve is constructed of the percentage of component in the mixtures against the ratio of component peak area/standard peak area. The analysis of the unknown mixture is carried out by addition of the same amount of internal standard to the specified volume of the mixture from the observed ratio of peak areas the solute concentration is read off using the calibration curve. 

The observed ratio / = Lp/Ln, is quite different from that reported for subcooled flow boiling of water in tubes of 17-22 mm inner diameter. Prodanovic et al. (2002) reported that this ratio was typically around 0.8 for experiments at 1.05-3 bar. The situation considered in experiments carried out by Hetsroni et al. (2003) is however different as the bubbles undergo a significant volume change and the flow is unstable. Ory et al. (2000) studied numerically the growth and collapse of a bubble in a narrow tube filled wifh a viscous fluid. The situation considered in that study is also quite different from experiments by Hetsroni et al. (2003) as, in that case, heat was added to the system impulsively, rather than continuously as we do here. 

Crystallographic refinement is a procedure which iteratively improves the agreement between structure factors derived from X-ray intensities and those derived from a model structure. For macro molecular refinement, the limited diffraction data have to be complemented by additional information in order to improve the parameter-to-observation ratio. This additional information consists of restraints on bond lengths, bond angles, aromatic planes, chiralities, and temperature factors. 

The cyclization constant (7, which may be evaluated from the observed ratio of the two products at a given concentration c, affords a measure of the tendency for a given bifunctional compound to cyclize. A plot of log C vs. the ring size n for the lactonization of w-hydroxy acids... 

Van der Voet [21] advocates the use of a randomization test (cf. Section 12.3) to choose among different models. Under the hypothesis of equivalent prediction performance of two models, A and B, the errors obtained with these two models come from one and the same distribution. It is then allowed to exchange the observed errors, and c,b, for the ith sample that are associated with the two models. In the randomization test this is actually done in half of the cases. For each object i the two residuals are swapped or not, each with a probability 0.5. Thus, for all objects in the calibration set about half will retain the original residuals, for the other half they are exchanged. One now computes the error sum of squares for each of the two sets of residuals, and from that the ratio F = SSE/JSSE. Repeating the process some 100-2(K) times yields a distribution of such F-ratios, which serves as a reference distribution for the actually observed F-ratio. When for instance the observed ratio lies in the extreme higher tail of the simulated distribution one may... 

This expression is relatively imprecise because of the scarcity of data. Also, the oxidation state of Pb in these experiments is not known. However, it is interesting that for those experiments in which both Dpb and Dsr have been determined, the Dpb/Dsr ratio is consistently less than would be predicted from the 2+ lattice strain model using parameters presented above. As in the case of clinopyroxene, increasing the effective Vlll-fold ionic radius of Pb in plagioclase, to 1.38 A, does retrieve the observed ratios. Thus one can... 

Alternatively, the exudation of the soyasapogenols, which are probably not differentially localized in the root, could represent a more active process. According to the data in Table II, by day 15 approximately 94% of the soyasapogenol E synthesized in the root has been released into the root exudate. In contrast, only 69% of the soyasapogenol B synthesized in the root is found in root exudate. Thus, the differential secretion of soyasapogenol B and E may account for the observed ratio of soyasapogenol B to E within the root. 

The observed ratio of m to r isomers, m,/r remaining during the (n-Bu)3SnH reduction of DCP (see Figure 2) are plotted in Figure 4. Substituting this data into Equation (2) yields a ratio of k0m/k0r = 1.3. Apparently m-W diads are 30% more reactive toward (n-Bu)3SnH than are r-W diads. 

A crucial point is the use of a reliable force field, and various parameters for Ni11 have been developed and employed successfully 379,386-392 As an example, molecular mechanics calculations (MOMEC87 program) have been used to predict the isomer distributions of Ni11 complexes of chiral (95) and (96), and isomer ratios were in good agreement with observed ratios.393... 

Table V. Calculated and Observed Ratios of Carbon Atoms in MTF, PTF, and BTF...

B) Compare the expected and observed largest-to-smallest intensity ratios. Accidental degeneracies (or am/ line-width dependence) may cause the observed ratio to be bigger than expected. It is rarer (but not unknown) to find a smaller ratio than expected. 

The observed ratio aaiioy/aNi agreed well with the Ni content predicted.) As discussed later, it was believed that hydrogen chemisorption was proportional to the surface nickel concentration (see Section IV). It is clear, however, that chemisorption as a method of surface area measurement must be used with discretion in the case of alloy films. 

A radiochemical method for the determination of Rn-220 in fumarolic gas is studied. Both condensed water and non-condensing gas are collected together and Pb-212 is precipitated as PbS. After dissolving the precipitate in conc.HCI, it is mixed with an emulsion scintillator solution for activity measurements. As Pb-214 is simultaneously measured, the observed ratio of Pb-212 /Pb-214 gives Rn-220/Rn-222. This method is superior to the method of directly measuring Rn-220 for the samples in which Rn-220/Rn-222 ratios are less than unity. This method and the previously proposed direct method were applied in the field, and new data obtained. An attempt was also made to understand the formation and transport of radon underground. 

Moreover, the observed excess of C compared to the dilution models in the N-rich dwarfs suggests that maybe an additional source of 12C does exist a similar suggestion is provided by the 12C/13C ratios. The observed ratios of 7-8 in NGC 6752 are compatible with about 60% of the observed C being produced by triple-a burning. 

The partitioning of [1+] between addition of solvent and deprotonation was discussed in Section 2, where it was suggested that the observed ratio of kjkp = 60 in 50/50 (v/v) trifluoroethanol/water underestimates the relative chemical barriers for ks and kp. This is because the addition of solvent is limited by rotational reorganization of solvent, ks = reorg 1011 s-1.21 Use of the larger value of (ks)chem = 1012 s 1 estimated for the addition of solvent that is prepositioned to react with [1+]21 gives kjkp = 600. The latter ratio is close... 

The difference in the values of ATadd = 900 for hydration of [2] and Kadd 40 for hydration of X-[7] (Table 1) shows that an a-aryl substituent provides substantial stabilization of an alkene relative to the alcohol. The value of kjkp = 1400 for partitioning of Me-[6+]14 is slightly larger than (ks)chem/kp = 600 for partitioning of [1+] that can be calculated by correcting the observed ratio of ks/kp = 60 (Table 1) for the difference in the values of ks = fcreorg = 1011 s -1 for solvent addition that is limited by solvent reorganization and ( s)chem = 1012 s I estimated for chemical bond formation between solvent and [1+] (see previous section). 

Vinylcarbenes. The use of diazoalkenes as vinylcarbene precursors is often precluded by rapid cyclization, with formation of pyrazoles. However, on photochemical generation of the diazoalkenes in situ, cyclization and nitrogen extrusion can proceed competitively. Photolysis of 1,3-diphenylpropenone to-sylhydrazone sodium salt (5) in MeOD afforded 3,5-diphenylpyrazole (9) and l,3-diphenyl-3-methoxypropene (10) in similar amounts.17 If 10 is formed by way of the 1,3-diphenylallyl cation (8), the deuterium should be distributed between C-l and C-3 of 10 (Scheme 6). The observed ratio of 10a to 10b was 66 34 the methoxy group is bound preferentially to the deuterated site, which originates from the divalent carbon of 7 (for a discussion of this effect, see below). 

There have been fewer measurements of H02 in the MBL. The agreement between modelled and measured [H02] is variable. Some studies show a reasonable agreement with the measurements (within 25%), but generally the models tend to overestimate [H02] by a factor of 2 or more (Carslaw et al., 1999, 2002 Kanaya et al., 2000, 2001). In PEM Tropics B Tan et al. (2001) reported a modelled to observed ratio of 1.12 for H02 near the surface. 

For unpolarized light, this relation is a very good approximation for incidence angles d., < 15°. When f < 1, the observed ratio is x - (R-/R+) "4 < x°. If r12 were small, then the fact that f would compress the waveform symmetrically about the value R could be used to find x°, and hence Note that this analysis would also... 

In many monosaccharides the proportion of the a-anomer in aqueous solution is higher than the expected ratio only based on steric inteactions. In particular, while the predicted ratio in aqueous solution at 25 °C based on the A value for axial vs. equatorial cyclohexanol is 11/89, the observed ratio for D-glucose is 36/64 for a-pyranose/p-pyranose.10 Based on... 

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