Uncertainly

As stated previously, the source of capital is often not known, and hence it is not known whether or not Eq. (A. 10) is appropiiate to represent the cost of capital. Equation (A. 10) is, strictly speaking, only appropriate if the money for capital expenditure is to be borrowed over a fixed period at a fixed rate of interest. Moreover, if Eq. (A. 10) is accepted, then the number of years over which the capital is to be annualized is unknown, as is the rate of interest. However, the most important thing is that even if the source of capital is not known, etc., and uncertain assumptions are necessary, Eq. (A. 10) provides a common basis for the comparison of competing projects. 

Figure 1. Dynamic model of testing of the material as a black box , where IN - loads and actions OUT - response of the material as measuring characteristics N - noise (combination of uncertain factors) ...

The uncertainties in choice of potential function and in how to approximate the surface distortion contribution combine to make the calculated surface energies of ionic crystals rather uncertain. Some results are given in Table VII-2, but comparison between the various references cited will yield major discrepancies. Experimental verification is difficult (see Section VII-5). Qualitatively, one expects the surface energy of a solid to be distinctly higher than the surface tension of the liquid and, for example, the value of 212 ergs/cm for (100)... 

One feature of this inequality warrants special attention. In the previous paragraph it was shown that the precise measurement of A made possible when v is an eigenfiinction of A necessarily results in some uncertainty in a simultaneous measurement of B when the operators /land fido not conmuite. However, the mathematical statement of the uncertainty principle tells us that measurement of B is in fact completely uncertain one can say nothing at all about B apart from the fact that any and all values of B are equally probable A specific example is provided by associating A and B with the position and momentum of a particle moving along the v-axis. It is rather easy to demonstrate that [p, x]=- ih, so that If... 

The scientific shidies of the early 1970s are fiill of concern whether the critical exponents detemiined experimentally, particularly those for fluids, could be reconciled with the calculated values, and at times it appeared that they could not be. However, not only were the theoretical values more uncertain (before RG calculations) than first believed, but also there were serious problems with the analysis of the experiments, in addition to those associated with the Wegner... 

For a RRKM calculation without any approximations, the complete vibrational/rotational Flamiltonian for the imimolecular system is used to calculate the reactant density and transition state s sum of states. No approximations are made regarding the coupling between vibration and rotation. Flowever, for many molecules the exact nature of the coupling between vibration and rotation is uncertain, particularly at high energies, and a model in which rotation and vibration are assumed separable is widely used to calculate the quantum RRKM k(E,J) [4,16]. To illustrate this model, first consider a linear polyatomic molecule which decomposes via a linear transition state. The rotational energy for tire reactant is assumed to be that for a rigid rotor, i.e. 

Manganese(IV) oxide is a dark-brown solid, insoluble in water and dilute acids. Its catalytic decomposition of potassium chlor-ate(V) and hydrogen peroxide has already been mentioned. It dissolves slowly in alkalis to form manganates(lW), but the constitution of these is uncertain. It dissolves in ice-cold concentrated hydrochloric acid forming the complex octahedral hexachloromangan-ate(IV) ion ... 

The mechanism of the reduction remains uncertain. The work of E. D. Williams, K. A. Krieger and A. R. Day (1953) using deuterium-labelled aluminium isopropoxide, shows that hydrogen atoms are transferred predominantly from the central carbon atom of an isopropoxide group to the carbon atom of the carbonyl group undergoing reduction, the process probably involving a cyclic complex ... 

Dissolve 0-5 g. of the phenol in 2 -5 ml. of pyridine, and add one equivalent of dlphenylcarbamyl chloride (or 0- 0-5 g. if the molecular weight is uncertain). Reflux the mixture for 30-60 minutes on a boiling water bath, and then pour into about 25 ml. of water. Filter the derivative, wash with a little sodium bicarbonate solution, and recrystallise from alcohol benzene, light petroleum (b.p. 60-80°) or carbon tetrachloride. 

Out of-plane C—H deformation vibration. This may be the C—C absorption of the Origin uncertain. 

Silicon is present in the sun and stars and is a principal component of a class of meteorites known as aerolites. It is also a component of tektites, a natural glass of uncertain origin. 

In TT-complexes formed from aromatic compounds and halogens, the halogen is not bound to any single carbon atom but to the 7r-electron structure of the aromatic, though the precise geometry of the complexes is uncertain. The complexes with silver ions also do not have the silver associated with a particular carbon atom of the aromatic ring, as is shown by the structure of the complex from benzene and silver perchlorate. ... 

Partial rate factors for the nitration of 4-hydroxyquinoline and its derivatives are given in table 10.6. Comparison with the values for quinolinium (table 10.4) show that the introduction of a 4-hydroxy or a 4-methoxy group into the latter activates the 6-position by factors of 3-3 X 10 and 1-6 X 10 , respectively, and the 8-position by factors of 29-5 and 23, respectively. What has been said above makes the significance of partial rate factors which may be calculated for 4-hydroxy-cinnoline uncertain. 

The digits in a measured quantity, including all digits known exactly and one digit (the last) whose quantity is uncertain. 

Kalantar, A. H. Kerrich s Method for y = ax Data When Both y and X Are Uncertain, /. Chem. Educ. 1991, 68, 368-370. Macdonald, J. R. Thompson, W. J. Least-Squares Litting When Both Variables Contain Errors Pitfalls and Possibilities, Am. J. Phys. 1992, 60, 66-73. 

Since the actual number of protons transferred between the analyte and titrant is uncertain, we define the analyte s equivalent weight (EW) as the apparent formula weight when = 1. The true formula weight, therefore, is an integer multiple of the calculated equivalent weight. 

Some substances under El conditions fragment so readily that either no molecular ions survive or so few survive that it is difficult to be sure that the ones observed do not represent some impurity. Therefore, there is either no molecular mass information or it is uncertain. Under Cl conditions, very little fragmentation occurs and, depending on the reagent gas, ions [M + X]+ (X = H, NH4, NO, etc.) or [M - H] or [M - H]" or [M -1- X] (X = F, Cl, OH, O, etc.) are the abundant quasi-molecular ions, which do give molecular mass information. 

Table 6.7 gives a few other examples of torsional barrier heights. That for ethylene is high, typical of a double bond, but its value is uncertain. The barriers for methyl alcohol and ethane are three-fold, which can be confirmed using molecular models, and fhose of toluene and nifromefhane are six-fold. The decrease in barrier heighf on going fo a higher-fold barrier is fypical. Rofafion abouf fhe C—C bond in toluene and fhe C—N bond in nifromefhane is very nearly free. 

Heisenberg uncertainly principle, as an expectation value. Streitwieser has eloquentiy summarized the importance of such concepts in chemical computations (42) ... 

Produced from Co l. Estimates of the cost of producing methanol from coal have been made by the U.S. Department of Energy (DOE) (12,17) and they are more uncertain than those using natural gas. Experience in coal-to-methanol faciUties of the type and size that would offer the most competitive product is limited. The projected costs of coal-derived methanol are considerably higher than those of methanol produced from natural gas. The cost of the production faciUty accounts for most of the increase (11). Coal-derived methanol is not expected to compete with gasoline unless oil prices exceed 0.31/L ( 50/bbl). Successful development of lower cost entrained gasification technologies could reduce the cost so as to make coal-derived methanol competitive at oil prices as low as 0.25/L ( 40/bbl) (17) (see Coal conversion processes). 

The future for these technologies is uncertain. Economic comparisons with fluorspar-based processes indicate that as long as fluorspar suppHes remain abundant, there is Httle justification to proceed with such processes. 

---