Deterministic variation coefficient

In order to solve the multi-objectives optimization problem proposed, several numerical applications have been carried out for specific levels of the main system and filter characteristics. These parameters, stochastically expressed by the mean and the variation coefficient, are considered deterministically known. The principle aim is to incorporate uncertainties in both the load and the structural model parameters. All data with certain and uncertain parameters are listed in Table 1, as above ... 

Table 6.1 Determination of the coefficient of variation Q, for the deterministic and stochastic models.

In all previous dissolution models described in Sections 5.1 and 5.2, the variability of the particles (or media) is not directly taken into account. In all cases, a unique constant (cf. Sections 5.1, 5.1.1, and 5.1.2) or a certain type of time dependency in the dissolution rate constant (cf. Sections 5.1.3, 5.2.1, and 5.2.2) is determined at the commencement of the process and fixed throughout the entire course of dissolution. Thus, in essence, all these models are deterministic. However, one can also assume that the above variation in time of the rate or the rate coefficient can take place randomly due to unspecified fluctuations in the heterogeneous properties of drug particles or the structure/function of the dissolution medium. Lansky and Weiss have proposed [130] such a model assuming that the rate of dissolution k (t) is stochastic and is described by the following equation ... 

The stochastic error is expressed in (9.23) by the variance Var [Aj (t)] and co-variance Cov [Nj (t) Nk (t)] that did not exist in the deterministic model. This error could also be named spatial stochastic error, since it describes the process uncertainty among compartments for the same t and it depends on the number of drug particles initially administered in the system. For the sake of simplicity, assume riQi = uq for each compartment i. From the previous relations, the coefficient of variation CVj (t) associated with a time curve Nj (t) in compartment 3 is... 

As previously, initial conditions for the compartmental model and the enzymatic reaction were set to tiq = [100 50], and so = 100, eo = 50, and cq = 0, respectively. Figures 9.31 and 9.32 show the deterministic prediction, a typical run, and the average and confidence corridor for 100 runs from the stochastic simulation algorithm for the compartmental system and the enzyme reaction, respectively. Figures 9.33 and 9.34 show the coefficient of variation for the number of particles in compartment 1 and for the substrate particles, respectively. 

In this article a simplified mass balance has been used to describe the net transport of sand over an accreting mud bottom. The combination of these two sedimentary processes controls the transition from sand to mud on the floor of the Sound. The distribution of sand may be described with three parameters an advection velocity of sand grains, an eddy-diffusion coefficient for mobile sand, and a rate of accumulation of marine mud. (Only the ratios of these quantities are needed if the distribution is in a steady state.) The motion of sand is thereby represented with both a deterministic part and a statistical part. The net, one-way advection of sand is the result of the superposition of an estuarine circulation on the tidal stream, and unpredictable variations in the rate of sand transport are represented as an eddy-diffusion process. Sand is immobilized when it is incorporated into the permanent deposit of marine mud. 

Cheng [ 19] studies the TWK due date rule under the objective of minimizing total squared lateness. Both for deterministic and random processing times (with known means and equal coefficient of variation), he finds the optimal value of the parameter a and shows that the optimal sequencing policy is SPT. Further extensions of this work are presented in [20] and [23]. 

Observe that the coefficient of variation is a decreasing function of r. This means, that at very long times the Poisson process can be regarded as deterministic. We shall come back to this point later. 

Step 6. The lateral load pattern for conventional pushover analyses was based on the first vibration mode (Eq. 15). Eor simplicity, the stmc-ture was analyzed in the Y direction only (see Eig. 1). The pushover curves for all stmctural models from Step 4 are presented in Eig. 2. An extensive scatter can be observed in the case of the deformation capacity of the realized stmctural models, whereas the difference in the strength is less. However, no significant differences can be observed between the deterministic model and the so-called median pushover curve. The limit-state top displacement and the corresponding base share are highlighted for the DL, SD, and NC limit states. The high coefficient of variation of the limit-state top displacement, which increases gradually with respect to the severity of the limit state, is partly the consequence of the high coefficient of variation of the input parameters and partly the consequence of the formation of different system failure modes, which were observed from pushover analyses. 

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