Variables fractional change

Significance of risk contribution may be done by ordering the risk contributors from most-to-least (rank order), but because of the arbitrariness of variation of the variables, this may be meaningless A more systematic approach is to calculate the fractional change in risk or reliability for a fractional change in a variable. 

The dimensionless model equations are programmed into the ISIM simulation program HOMPOLY, where the variables, M, I, X and TEMP are zero. The values of the dimensionless constant terms in the program are realistic values chosen for this type of polymerisation reaction. The program starts off at steady state, but can then be subjected to fractional changes in the reactor inlet conditions, Mq, Iq, Tq and F of between 2 and 5 per cent, using the ISIM interactive facility. The value of T in the program, of course, refers to dimensionless time. 

These equations simply give the fractional change in volume of a liquid as pressure is changed at constant temperature. The partial derivative is used rather than die ordinary derivative because only one independent variable, pressure, is permitted to vary. Remember that the subscript T indicates that temperature is held constant. 

The methods of FBA and elementary flux modes study interactions between different routes in a metabolic network and the quantification of flux distributions but do not evaluate how fluxes are controlled. In Metabolic Control Analysis (MCA), the control exerted by the rate of a reaction over a substrate flux or any other system parameter (e.g., metabolite concentration or cell proliferation) can be described quantitatively as a control coefficient. The control coefficient is a relative measure of how much a perturbation affects a system variable and is defined as the fractional change in the system property over the fractional change in the reaction rate [e.g., Bums et al. 1985],... 

Then any of the dichotomous models could be expanded to include the additional dummy variable. For example, using a fractional change model clearance could be modeled as... 

Although Eqs. 8.2-8 through 8.2-11 are well suited for calculations in which temperature, pressure, and the partial molar properties are the independent variables, it is usually more convenient to have T, P, and the mole fractions x-, as the independent variables. A change of variables is accomplished by realizing that for a C-component mixture there are only C — 1 independent mole fractions (since XLt Thus we... 

Local velocity of fetal blood in x-direction, cm/sec Local velocity of maternal blood in the x-direction, cm/sec Fractional change in velocity = V2/V 0rmab dimensionless Variable length, cm Dimensioness axial distance... 

The 8 Cxco2 varied considerably in geologic history. Generally, three explanations are given for changes of 8 Cxco2 distribution in the ocean (1) changes in the surface-ocean productivity which cause variable fractionation between surface and deep water carbon isotopic composition, (2)... 

A sensitivity function describes the functional relationship between the change in an integral parameter caused by a fractional change in some input parameter, when the latter is expressed as a function of independent variables. For most applications a linear functional relationship is desirable. Perturbation theory formulations provide such a linear relationship. A sensitivity function can be defined for any integral parameter it can correspond to variations in any of the input parameters and it can be expressed in terms of any of the independent variables. Thus, the total number of sensitivity functions for a given system can be very large, and can be expressed in terms of different combinations of the independent variables. When the input parameter has discrete variations only, we shall refer to the sensitivity functions as sensitivity coefficients. 

The sensitivity coefficients defined by equation (43) relate the absolute change in a solution variable (species concentration) to an absolute change in a parameter (rate constant), and thus have units that depend on the units of the rate constant, which in turn depend on the overall reaction order. The scaled sensitivity coefficients defined by equation (51) relate fractional changes in a solution variable to fractional changes in a parameter. Thus, for example, if <7, = 1, then a 10% increase in parameter dj will lead to a 10% increase in solution variable Likewise, if [Pg.236]

A critical step in the data analysis procedure is the correction of the calculated apparent viscosity for the influences of pressure and viscous heating. The key element in this procedure is the approximation that the fractional change in the viscosity of the polymer solution due to pressure and viscous heating effects is equal to the corresponding fractional change in the viscosity of a hypothetical Newtonian fluid which exhibits the same rheological properties as the polymer solution at low-shear rates where it approaches Newtonian behavior. The hypothetical Newtonian fluid would have a constant viscosity at all shear rates equal to the viscosity of the polymer solution at low-shear rates, and the influence of temperature and pressure on the viscosity of this Newtonian fluid would be identical to the influence of these variables on the low-shear rate viscosity of the polymer solution. 

The labelling procedure which introduces iodine atoms onto the tyrosine radicals of the molecule alters the hormone physicochemically. It may also produce changes in immunochemical behaviour which are detectable in radioimmunoassay when iodination surpasses a certain level Further, during iodination some damage inevitably occurs. A variable fraction of the hormone is involved, depending on the nature of the antigen and the specific sample of iodine used. 

Sensitivity analyses were conducted to determine the impact of variations in input parameters upon selected output parameters. Input parameters were varied by 1% and the resultant sensitivity coefficients were determined. Coefficients presented here are normalized to both the response variable and the parameter being varied and, thus, are defined as fractional change in response per fractional change in input. A negative coefficient indicates a decrease in the response variable with an increase in the input parameter, and a coefficient greater than 1 in absolute value indicates a larger than one to one relationship between the response and input. 

FIGURE 6.14 Same as Figure 6.6, but both the composition variable changed to mass fraction and the volume variable are changed from Uters per mol to liters per unit mass. 

A second factor influencing the distribution of cofactor forms is solvent acidity. With one exception, the principal 2 1 distribution is uninfluenced by this variable. Thus, changes in solvent acidity appear to produce subsets of cofactor species with the following properties (1) Different reduction potentials for the major fraction of oxidized cofactor in acid (E a = -0.36 V) solution (2) changes in the number (Rs-r versus Ns-r and Ws-r) and EPR spectroscopic properties of semi-reduced cofactor species (3) formation of additional forms (Aox, Aox", Aox" ) of electroactive FeMoco(ox). These observations are summarized in Scheme 1. 

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