Cumulation coefficient

Cumulation coefficient (C ) is <1 Cumulation coefficient (C ) is within 1-3 Cumulation coefficient (C ) is within 3-5 Cumulation coefficient (C ) is >5... 

For the quantitative assessment of the cumulative affects the cumulation coefficient is used, this is the ratio of the total LD50 (n) obtained in daily administration of a selected part of the LD50 (eg, Vio) in acute experiments to determine the LD50 value. 

A quantitative criterion of cumulative effect can be the cumulation coefficient (C cum), representing the ratio of the summary LDsocn) to the LD50 (Kagan and Stankevich 1964) ... 

If all the animals die the first day, D2 = Dj and Icum = 0- If death occurs later, D2 < Di and Icum tends toward unity (Shtabsky and Kagan 1974). Analysis of cumulative coefficients of organophosphates shows most of these have slightly marked cumulative effects, manifested mainly under regular daily administration of relatively large doses. Reduced daily doses (< 0.1 LD50) do not cause death. 

Cumulation coefficient < 1 Cumulation coefficient 1-3 Cumulation coefficient 3-5 Cumulation coefficient > 5... 

Kagan YS, Stankevich VV (1964) Cumulation coefficient as quantitative criterion for evaluation of cumulative action of toxicant. In Current Problems of Work Hygiene, Industrial Toxicology and Occupational Diseases in Petroleum and Petrochemical Industries, pp 48-49. 

The same result can also be obtained directly from the virial equation of state given above and the low-density fonn of g(r). B2(T) is called the second virial coefficient and the expansion of P in powers of is known as the virial expansion, of which the leading non-ideal temi is deduced above. The higher-order temis in the virial expansion for P and in the density expansion of g(r) can be obtained using the methods of cluster expansion and cumulant expansion. 

Fig. 18. Determining the diffusion coefficient from cumulative transmission.

In turbulent flow, axial mixing is usually described in terms of turbulent diffusion or dispersion coefficients, from which cumulative residence time distribution functions can be computed. Davies (Turbulence Phenomena, Academic, New York, 1972, p. 93), gives Di = l.OlvRe for the longitudinal dispersion coefficient. Levenspiel (Chemical Reaction Engineering, 2d ed., Wiley, New York, 1972, pp. 253-278) discusses the relations among various residence time distribution functions, and the relation between dispersion coefficient and residence time distribution. 

Coefficient of Variation One of the problems confronting any user or designer of crystallization equipment is the expected particle-size distribution of the solids leaving the system and how this distribution may be adequately described. Most crystalline-product distributions plotted on arithmetic-probability paper will exhibit a straight line for a considerable portion of the plotted distribution. In this type of plot the particle diameter should be plotted as the ordinate and the cumulative percent on the log-probability scale as the abscissa. 

In order to be consistent with normal usage, the particle-size distribution when this parameter is used should Be a straight line between approximately 10 percent cumulative weight and 90 percent cumulative weight. By giving the coefficient of variation ana the mean particle diameter, a description of the particle-size distribution is obtained which is normally satisfactory for most industrial purposes. If the product is removed from a mixed-suspension ciystallizer, this coeffi-... 

The toxicological or cumulative effect of illicit drugs on the ecosystems has not been studied yet. Moreover, their fate and transport in the environment is to a big extent still unknown. Due to their physical-chemical properties (octanol-water partition coefficient, solubility, etc.) some of them, such as cannabinoids, are likely to bioaccumulate in organisms or concentrate in sediments whereas the rest, much more polar compounds, will tend to stay in aqueous environmental matrices. However, continuous exposure of aquatic organisms to low aquatic concentrations of these substances, some of them still biologically active (e.g., cocaine (CO), morphine (MOR) and MDMA) may cause undesirable effects on the biota. 

Figure 4.51. Distribution of experimental data. Six experimental formulations (strengths 1, 2, resp. 3 for formulations A, respectively B) were tested for cumulative release at five sampling times (10, 20, 30, 45, respectively 60 min.). Twelve tablets of each formulation were tested, for a total of 347 measurements (13 data points were lost to equipment malfunction and handling errors). The group means were normalized to 100% and the distribution of all points was calculated (bin width 0.5%, her depicted as a trace). The central portion is well represented by a combination of two Gaussian distributions centered on = 100, one that represents the majority of points, see Fig. 4.52, and another that is essentially due to the 10-minute data for formulation B. The data point marked with an arrow and the asymmetry must be ignored if a reasonable model is to be fit. There is room for some variation of the coefficients, as is demonstrated by the two representative curves (gray coefficients in parentheses, h = peak height, s = SD), that all yield very similar GOF-figures. (See Table 3.4.)...

Figure 4.52. Coefficients of variation that reflect both tablet to tablet and analytical variability. For formulation B, particularly strengths 2 and 3, the drop in CV with higher cumulative release (a - b) is marked, cf. Fig, 4.50. When the dissolution rate is high, individual differences dominate, while towards the end analytical uncertainty is all that remains. The very low CVs obtained with strength 3 of formulation A ( 0.7-0.8%, data offset by +10% for clarity) are indicative of the analytical uncertainty. Because content uniformity is harder to achieve the lower the drug-to-excipient ratio, this pattern is not unexpected.

Figure 3.42 Evolution of a pulse at the entrance of a micro channel for different diffusion coefficients. Calculated concentration profile (left) and cumulative residence time distribution curve (channel 300 pm x 300 pm x 20 mm flow velocity 1 m s f = 10 s) [27],...

Thus, the rate of change for the cumulative mass of diffusant passing through a membrane per unit area, or the flux of diffusant, j, may be evaluated from the steady-state portion of the permeation profile of a drug, as shown in Eq. (3). If the donor concentration and the steady-state flux of diffusant are known, the permeability coefficient may be determined. 

It is noted that the partial derivatives in the above variance expressions depend on time t and therefore the variances should be computed simultaneously with the state variables and sensitivity coefficients. Finally, the confidence intervals of the cumulative production of each well and of the total reservoir are calculated by integration with respect to time (Kalogerakis and Tomos, 1995). 

Koizumi and Higuchi [18] evaluated the mass transport of a solute from a water-in-oil emulsion to an aqueous phase through a membrane. Under conditions where the diffusion coefficient is expected to depend on concentration, the cumulative amount transported, Q, is predicted to follow the relationship... 

The cumulative effect of updating the model and using the new rate coefficient for the reaction 0(1D)+N2 is negligible (<2%). 

The Uj and w, deviates are normal deviates, the deviates vf are log-normal. See text for the description of the computed random variables K represents mineral-liquid partition coefficients, F the fraction of residual melt, x the fraction of a mineral in the cumulate, D bulk solid-liquid partition coefficients. 

Let us consider the behavior of the ith among m trace elements upon partitioning between a homogeneous liquid (labeled liq) and the n phases (labeled j) of the cumulate in a system of finite size. These phases are usually considered as mineral phases but liquid trapped in the cumulate can be handled as an additional phase with partition coefficients equal to unity (Greenland, 1970 Albarede, 1976). 

A basalt contains 150 ppm Ni, 100 ppm Sr, 3 ppm Yb, and 10 ppm Rb. Calculate the concentration of each element after removal of 20 percent of a cumulate containing 30 percent olivine, 20 percent clinopyroxene and 50 percent plagioclase in the residual liquid and in the average cumulate. Assume the partition coefficients given in Table 9.6. 

A mixture t° i1°,nPol"Kl J,K S1 cs an absoi ptitm spei tnnn which i the cumulative effect of both coiiip°,in s < i the molar absorption coefficients of each compound would... 

FIGURE 1-1 Cumulative surface-area distributioii for Figure 7-6, showing the fraction of surface area of daughter branch that has local transfer coefficient equal to or greater than stated value dp 0.088 fim, C/ 100 cm/sec. Reprinted with permission from Bell. 

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