Fixed fraction

Notice that both the electric charge and the total number of nuclear particles (nucleons) are conserved in the nuclear decomposition. Careful study of the rate of this nuclear decay shows that in a given period of time a constant fraction of the nuclei present will undergo decomposition. This observation allows us to characterize or describe the rate of nuclear decay in a very simple manner. We simply specify the length of time it takes for a fixed fraction of the nuclei initially present to decay. Normally we pick the time for... 

Now, note that each of the leak-through terms in Eqs. (7.1) and (7.2) is just a fixed fraction of the intensity in its own channel ... 

The result of treating the Flory-Stockmayer ensemble in this way and at the same level of approximation as that of the Cayley tree sketched in the previous section, is that a very similar relaxation spectrum to Eq. (36) is predicted, but with a value for the exponent 0 of 4 rather then 2. A disentanglement transition is also found, as well as the appeafing feature that at each seniority a fixed fraction of the molecules still entangled actually renormalise into linear polymers (like the comb topology) and relax by reptation rather than by further fluctuation [49]. 

C Linewidth Control, This parameter refers to the necessity of maintaining the correct features size across an entire substrate and from one substrate to another. This is important since the successful performance of most devices depends upon control of the size of critical structures, as for example in the gate electrode structure in an MOS device. As feature size is decreased and circuit elements packed closer together, the margin of error on feature size control is reduced. The allowable size variation on structures is generally a fixed fraction of the nominal feature size. A rule of thumb is that the dimensions must be controlled to tolerances of at least 1/5 the minimum feature size. Linewidth control is affected by a variety of parame-... 

A stainless-steel reactor (36 mm i.d.), specifically designed and realized, is employed to test the ATR reaction. At the reactor outlet, a fixed fraction of the exhaust stream is sent to the analysis section after removing water in a cold trap. 

A widely used method described by Shirley (1972) is similar, but it employs instead a summation over the observed electron flux (z)fc, which includes contributions from electrons already scattered. Our own iterative method is based on the assumption of uniform scattering of a fixed fraction of the electrons that would be observed in the complete absence of scat-... 

Consider a hypothetical system that has an initial abundance of a short-lived radionuclide Nr. This nuclide is present as a fixed fraction of the parent element and its abundance can be written as the ratio of the radionuclide to a stable reference isotope of the same element, Ns. When the short-lived nuclide has completely decayed to its daughter nuclide, D, we have ... 

The published figures for Ctm are in general fairly consistent values at 60° C in the range 2-3 x 10 4 have been found by several workers (142,143,179,184, 186). There is a bigger spread in the values reported for Clp, from about 1.2 to 7.0 x 10 4 In some treatments of the problem it is assumed that all terminal double bonds, produced by transfer to monomer, can copolymerize, but that their reactivity is some fixed fraction K of the reactivity of the double bonds of the monomer K is found to be about 0.8 at 60° C. Graessley (143) has assumed as an alternative that only a fraction h of these double bonds can copolymerize at all (presumably those formed by transfer at a monomer acetate group), and that these have the same reactivity as the monomer h was found to be 0.76 at 60° C and 0.88 at 72° C. 

In his PGSE study of polyethylene oxide and polydimethylsiloxane in QHg and CHC13, Tanner 39) also measured the diffusion of a fixed fraction of solvent in the polymers. He concluded that their diffusion rate in polymers of molecular weight lower than their own was approximately equal to that of the polymers. As the polymer molecular weight exceeded that of the solvent, the solvent diffusion rate approached a constant value, independent of polymer molecular weight. Tanner offered semiempirical explanations for this effect. 

When activated, the battery supplies the typical discharge current shown in the discharge curve in Fig. 9.26. The beginning of the discharge in this battery, and more generally in all thermal batteries, is characterized by a peak voltage which falls off as the internal resistance of the cell rises, as a result of a build-up of insoluble products at the electrodes and a fall in temperature of the electrolyte, Usually the life of a thermal battery is measured as the time elapsed to reach a fixed fraction (e.g. 80%) of the peak voltage. 

Some characteristics of a Gaussian peak are summarized in figure 1.4. It can be seen from this figure that the variance of a genuinely Gaussian peak can be determined by measuring the peak width at some fixed fraction of the peak height. The peak width at the... 

Control of the heavies column is simpler. A fixed fraction of the feed is taken as bottom product, in a feedforward manner. The reboiler duty controls the level in the column sump. Note that this arrangement, which is required because of the small bottoms stream, cannot be implemented if a kettle reboiler is used. The column is operated at constant reflux, while the distillate rate controls the condenser level. 

However, it must be considered that an animal is in free fall for a time within each stride, therefore it would be reasonable to think that gravity retains its importance. If the period of falling is a fixed fraction of stride duration and if running speed at transition varies with leg length multiplied by the stride frequency - which is supported by observation - then the respective transition point has to be set by by a fixed Froude number. 

The loss terms in N-cycle models that transform particulate and dissolved organic nitrogen into other forms can include a variety of processes (e.g., phytoplankton exudation, zooplankton grazing, sloppy feeding, phytoplankton and zooplankton mortality, bacterial remineralization, etc.). Different models may differ substantially in terms of which of these are included and their formulation (Christian and Anderson, 2002). Many N-cycle models now include significant phytoplankton exudation loss terms. This is often parameterized by simply specifying that some fixed fraction of the DIN uptake by phytoplankton is shunted directly to the DON pool (e.g., Anderson and Williams, 1998). Sloppy feeding by zooplankton can be similarly accounted for. Many models also include linear loss terms in the phytoplankton equation that represent either natural mortality or phytoplankton respiration (e.g.. Hood et ai, 2001). 

I 1 6 iS A P3 U equilibrium angle = k 6 - 6/6). A fourth-order polynomial enables an independent fit of the barrier to linearity. Such constrained polynomial fittings are rarely done. Instead the bending function is taken to be identical for all atom types, for example a fourth-order polynomial with cubic and quartic constants as a fixed fraction of the harmonic constant. These features are illustrated for H2O in Figure 2.5, where the exact form is taken ... 

The declining-balance method is an accelerated depreciation schedule that allows higher charges in the early years of a project. This helps improve project economics by giving higher cash flows in the early years. In the declining-balance method, the annual depreciation charge is a fixed fraction, Fj, of the book value ... 

The demixtion curves (Fig. 16.2) show us that there exists a range of volume fractions q> (cp < tpc) and of temperatures T(T < Tc) in which solutions are dilute and b is negative. Then for a fixed fraction q>i, the predicted collapse (Chapter 14, Sections 3, 4, and 6) can be observed by lowering the temperature Tdown to the demixtion temperature T((p1). The process is schematically shown in Fig. 16.10. We can see that the smaller measurement require cp to be larger than a minimal value cplm below which observations are no longer possible. 

When S increases, the demixtion curve comes exponentially nearer to the asymptote p = 0. For a fixed fraction cp1( the interval Tc — 7 ([Pg.825]

Consider calcium carbonate, the major compound in marble. It is composed of three elements—calcium, carbon, and oxygen—and each is present in a fixed fraction (or percent) by mass. The following results are obtained for the elemental mass composition of 20.0 g of calcium carbonate (for example, 8.0 g of calcium/20.0 g = 0.40 parts of calcium) ... 

Definite composition. A compound is a combination of a specific ratio of different atoms (postulate 4), each of which has a particular mass (postulate 3). Thus, each element in a compound constitutes a fixed fraction of the total mass. 

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