Fraction of occurrence

The average atomic weight of a hypothetical element M, Am, is computed by adding fraction-of-occurrence—atomic weight products for all its isotopes that is,... 

In this expression, is the fraction-of-occurrence of isotope i for element M (i.e., the percentage-... 

Indium has two naturally occurring isotopes with an atomic weight of 112.904 amu and with an atomic weight of 114.904 amu. If the average atomic weight for In is 114.818 amu, calculate the fraction-of-occurrences of these two isotopes. 

With the inclusion of in Equation 5.15, the economic feasibility of the BTS in aU potential scenarios is assessed. Each fraction of occurrence represents the time fraction of which a scenario occurs. This time fraction is calculated by dividing the duration of a scenario s with the total duration (time horizon) considered. Thus, the sum of these fractions must equal to one as shown in Equation 5.16. Note that the duration of scenario s is dependent on the raw material supply and energy demand profiles. For instance, if the raw material supply and energy demand profiles are uniform in terms of duration (e.g. hourly, weekly, monthly basis, etc.), the time fraction of occurrence for scenario s can be obtained as shown in Figure 5.2a. As for dynamic profiles where supply and demand profiles are not uniform, the duration of scenario s can be broken down to smaller intervals and obtained as shown in Figure 5.2b. With this consideration, optimization constraints between scenarios can be established. Such feature is useful when deahng with seasonal variations. In practice, these fractions can be estimated subjectively based on the historical and projected information in variations of raw material supply, energy demand, product prices, etc. 

Table 5.3 Synthesis of Biomass-Based Tri-generation Systems 115 Fraction of occurrence for low, mid- and high seasons ... 

Selling cost of exporting excess energy in USD/kW h Capital cost for technology j in USD Capital cost for technology / in USD Fraction of occurrence for scenario s Capital recovery factor... 

The existence of the amorphous phase of the fiber is confirmed in x-ray examination by the occurrence of a distinct intensity maximum of the radiation scattered diffusively at 2Q = 21.6 . The fraction of the amorphous phase in the fiber depends on manufacturing conditions and a possible further refining treatment. It is estimated to vary from 0.25 to 0.60. With an increase of the draw ratio and following the thermal treatment of the fiber, the proportion of the amorphous phase only reaches the lower values of this interval,... 

NMR measurements indicate that the equilibrium constant varies with the polarity of the solvent and temperature. The more polar the solvent, the greater the fraction of sulfoxide at equilibrium which is consistent with the greater dipole moment of the sulfoxide as compared with the sulfenate. Increasing temperature results in a reverse effect, due to the steric hindrance in the sulfoxide which becomes more marked at higher temperatures. These results are the first published evidence for the reversibility of the sulfenate-sulfoxide rearrangement and illustrate the occurrence of the rearrangement unsuccessfully attempted by Cope39. 

The conclusions on the occurrence of ion-molecule reaction in the radiolysis of ethylene are not seriously affected by the uncertainties in the neutralization mechanism. It must be assumed that neutralization results in the complex species which constitute the ionic polymer, — i.e., the fraction of the ethylene disappearance which cannot be accounted for by the lower molecular weight products containing up to six carbon atoms. 

It is also apparent that the sequence of monomer units in an ideal copolymer must necessarily be random. That is to say, the likelihood of occurrence of an Mi unit immediately following an M2 unit is the same as for an Mi to follow an Mi unit. The probability of either unit at any place in the chain is always equal to its mole fraction in an ideal copolymer. ... 

A detailed discussion of the modes of occurrence and biological importance of the polynucleotides is outside the scope of this article. However, in examining the structures of polynucleotides, it is necessary to take into consideration the origins of the materials studied. The pioneer researches of Caspersson114 indicated that deoxyribonucleic acids are present exclusively in the nucleus, whereas ribonucleic acids are found chiefly in the cytoplasm and only to a small extent in the nucleus. This general outline of the distribution of nucleic acids within the cell has been confirmed and extended by more recent work,116 and it has been possible to isolate both types of nucleic acid from different cellular fractions of the same tissue.116... 

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