Homogeneous distribution population

The consequences of being on the receiving end of an enemy attack with EA 3167 could be severe. Multiple low dose attacks over a period of several days could produce an insidious build-up of cognitive defects. Distributed attacks would also tend to result in a more homogeneous distribution of dosage, since members of the population would probably change their locations at various times and total exposure would thus tend to be more uniform. 

We have so far been able to obtain exact explicit analytic solutions for (a) the case where only processes (i) and (ii) are significant, and (b) the case where only processes (ii) and (iii) are significant. We have also obtained an approximate analytic solution for the case where all three processes (i), (ii) and (iii) occur, but where the loss of radicals occurs predominantly by process (ii) rather than by prodess (iii). As a generalisation of case (a), we have obtained a general solution which covers the case where the parameters which characterise the processes (i) and (ii) are themselves time-dependent. The general solution to case (b) requires modification if processes of type (ii) do not occur. Complete solutions have been obtained for three special cases of (b), namely, decay from a Stockmayer-01Toole distribution of locus populations, decay from a Poisson distribution of locus populations, and decay from a homogeneous distribution of locus populations. 

The steady-state rate of population of state 2 thus has a Lorentzian dependence on the energy gap 12. As we discussed in Qiap. 2, the Lorentzian function can be equated to the homogeneous distribution of 12 when the mean value of 12 is zero and state 2 has a lifetime of 2/2. Note that, according to Eq. (10.29b), T2II — when pure dephasing is negUgible. If we identily the time ccaistant T2 in Eq. (10.35) with 2T in Eq. (2.71), and identify the energy difference 12 with ( — ), then the factor in the second set of parentheses in Eq. (10.35) must be lulh times the distribution function Re[G( )] in Eq. (2.71). 

First an ensemble (a statistical population) of societies - each of which consists of one homogeneous (human) population of 2 members - will be considered and the probability distribution over their socio-configurations will be defined. Thus the function... 

For the results shown in Figs. 4.2 a, b weak internal and external sympathy parameters are assumed. Figure 4.2 a shows that all mean values trend into the stable focus P(0, 0). This focus represents a homogeneous distribution of both populations over both city areas. Correspondingly the stationary probability distribution shown in Fig. 4.2 b concentrates around this stable focus. 

The binomial distribution describes a population whose members have only certain, discrete values. A good example of a population obeying the binomial distribution is the sampling of homogeneous materials. As shown in Example 4.10, the binomial distribution can be used to calculate the probability of finding a particular isotope in a molecule. 

Few populations, however, meet the conditions for a true binomial distribution. Real populations normally contain more than two types of particles, with the analyte present at several levels of concentration. Nevertheless, many well-mixed populations, in which the population s composition is homogeneous on the scale at which we sample, approximate binomial sampling statistics. Under these conditions the following relationship between the mass of a randomly collected grab sample, m, and the percent relative standard deviation for sampling, R, is often valid. ... 

---