Propositional

The greater the positive NPV for a project, the more economically attractive it is. A project with a negative NPV is not a profitable proposition. 

Analysis of tlie global statistics of protein sequences has recently allowed light to be shed on anotlier puzzle, tliat of tlie origin of extant sequences [170]. One proposition is tliat proteins evolved from random amino acid chains, which predict tliat tlieir length distribution is a combination of the exponentially distributed random variable giving tlie intervals between start and stop codons, and tlie probability tliat a given sequence can fold up to fonii a compact... 

Corollary 4. In addition to the assumptions in Proposition 2 suppose that... 

The third eigenmeasure 1 3 corresponding to A3 provides information about three additional almost invariant sets on the left hand side in Fig. 8 we have the set corresponding to the oscillation C D, whereas on the fight hand side the two almost invariant sets around the equilibria A and B are identified. Again the boxes shown in the two parts of Fig. 8 approximate two sets where the diserete density of 1/3 is positive resp. negative. In this case we can use Proposition 2 and the fact that A and B are symmetrically lelated to conclude that for all these almost invariant sets 5 > A3 = 0.9891. 

Hence, we just have proven the following proposition ... 

After Strike wrote the first edition and started up the old web site, a lot of new theories came in. The most promising was a proposition from our founding father of cyber chemistry Eleusis. This was his proposal ... 

Use the Simha equation and these data to criticize or defend the following proposition These polymer molecules behave like rods whose diameter is 16 A and whose length is 1.5 A per repeat unit. The molecule apparently exists in fully extended form in this solvent rather than as random coils. 

Once the value of the constant and the a value in Eq. (2.36) have been evaluated for a particular system, viscosity measurements constitute a relatively easy method for determining the molecular weight of a polymer. Criticize or defend the following proposition Since viscosity is so highly dependent on molecular weight for M > M, a 10% error in 17 will result in a 34% error in M above M, but only a 10% error in M below M, . 

Criticize or defend the following proposition In dilute solutions, branching affects viscosity only inasmuch as the branched molecule has a more compact shape. At higher concentrations, the effect of branching is closer to a bulk effect. 

Criticize or defend the following proposition These data display the same trends described in the example and suggest the same interpretation. 

From the data in Fig. 4.8b, estimate the shift factors required to displace the data at 0 = 0.5 (consider only this point) so that all runs superimpose on the experiment conducted at 128 C at 0 = 0.5. Either a ruler or proportional dividers can be used to measure displacements. Criticize or defend the following proposition Whether a buffered aqueous solution of H2O2 and 1. containing small amounts of S2O3 and starch, appears blue or colorless depends on both the time and the temperature. This standard general chemistry experiment could be used to demonstrate the equivalency of time and temperature. The pertinent reactions for the iodine clock are... 

On the basis of these observations, criticize or defend the following propositions ... 

The polymer described in the last problem is commercially called poly (phenylene oxide), which is not a proper name for a molecule with this structure. Propose a more correct name. Use the results of the last problem to criticize or defend the following proposition The experimental data for dimer polymerization can be understood if it is assumed that one molecule of water and one molecule of monomer may split out in the condensation step. Steps involving incorporation of the monomer itself (with only water split out) also occur. 

On the basis of these observations, criticize or defend the following proposition The fact that the separate spots fuse into a single spot of intermediate Rf value proves that block copolymers form between the two species within the blend upon heating. 

At 270°C adipic acid decomposesf to the extent of 0.31 mol % after 1.5 hr. Suppose an initially equimolar mixture of adipic acid and diol achieves a value of p = 0.990 after 1.5 hr. Compare the expected and observed values of n in this experiment. Criticize or defend the following proposition The difference between the observed and expected values would be even greater than calculated above if, instead of the extent of reaction being measured analytically, the value of p expected (neglecting decomposition) after 1.5 hr were calculated by an appropriate kinetic equation. 

For monomers of the AB type, reactions (5.CC) and (5.DD) become AB -> and 2AB AbaB, respectively. If kj. and k are the respective rate constants for these reactions, derive an expression which gives the ring to linear ratio in the product as a function of AB concentration and the two rate constants. Criticize or defend the following proposition To obtain a test of Eq. (5.47) without the complications of intramolecular condensations, a series of otherwise identical polymeriztion reactions could be carried out on monomer mixtures at different concentrations. By... 

Assuming that no other transfer reactions occur, calculate the values missing from the table. Criticize or defend the following proposition The v values obtained from the limit [SX]/[M] 0 show that the AIBN initiates polymerization identically in all solvents. 

Still assuming terminal control, evaluate r and T2 from these data. Criticize or defend the following proposition The copolymer composition equation does not provide a very sensitive test for the terminal control mechanism. 

Randall used C-NMR to study the methylene spectrum of polystyrene. In 1,2,4-trichlorobenzene at 120°C, nine resonances were observed. These were assumed to arise from a combination of tetrads and hexads. Using m and r notation, extend Table 7.8 to include all 20 possible hexads. Criticize or defend the following proposition Assuming that none of the resonances are obscured by overlap, there is only one way that nine methylene resonances can be produced, namely, by one of the tetrads to be split into hexads while the remaining tetrads remain unsplit. 

By combining Eqs. (8.42), (8.49), and (8.60), show that Vi°(52 - 5i) = (l/2)RTj., where T. is the critical temperature for phase separation. For polystyrene with M = 3 X 10, Shultz and Floryf observed T. values of 68 and 84°C, respectively, for cyclohexanone and cyclohexanol. Values of Vi° for these solvents are abut 108 and 106 cm mol", respectively, and 5i values are listed in Table 8.2. Use each of these T. values to form separate estimates of 62 for polystyrene and compare the calculated values with each other and with the value for 62 from Table 8.2. Briefly comment on the agreement or lack thereof for the calculated and accepted 5 s in terms of the assumptions inherent in this method. Criticize or defend the following proposition for systems where use of the above relationship is justified Polymer will be miscible in all proportions in low molecular weight solvents from which they differ in 5 value by about 3 or less. 

Based on these observations, criticize or defend the following proposition Except for two of the values in MEK, the reproducibility of M determinations is quite acceptable. MEK consistently gives erroneous values, probably because the solutions are highly nonideal for this solvent, which is more polar than either benzene or toluene. 

Under 0 conditions occurring near room temperature, [r ] = 0.83 dl g for a polystyrene sample of molecular weight 10. f Use this information to evaluate tg and for polystyrene under these conditions. For polystyrene in ethylcyclohexane, 0 = 70°C and the corresponding calculation shows that (tQ /M) = 0.071 nm. Based on these two calculated results, criticize or defend the following proposition The discrepancy in calculated (rQ /M) values must arise from the uncertainty in T>, since this ratio should be a constant for polystyrene, independent of the nature of the solvent. 

The refractive index of CCI4 at 20°C and 589 nm, the D line of the sodium spectrum, is 1.4607. At this temperature the density of this compound is 1.59 g cm . Use this information to calculate a for CCI4. Criticize or defend the following proposition The prediction that = f(R/X) may have been premature. The consideration of Eq. (10.3) which led to this conclusion could just as well predict = f(a /X). 

Using the original Hc2/r values, recalculate M using the various refractive index gradients. On the basis of self-consistency, estimate the molecular weight of this polymer and select the best value of dn/dc2 in each solvent. Criticize or defend the following proposition Since the extension of the Debye theory to large particles requires that the difference between n for solute and solvent be small, this difference should routinely be minimized for best results. 

Propofol Propofol [2078-54-8] Proportional counters Proposition 65 Propoxides Propoxur [114-26-1]... 

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