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The Effects of Incremental Change

For example, if we consider the function y =AX) — x3, the incremental change in y that accompanies a change in Ax in x is given as  [Pg.110]

For sufficiently small values of Ax, the power terms in Ax decrease very rapidly in magnitude. Thus, for example, if Ax= 10 2, then Ax2 = 10-4 and Ax3 = 10-6. This may be expressed algebraically as  [Pg.110]

The appearance of 3x2 in this expression is no accident. If we rewrite the expression for Ay as  [Pg.110]

An infinitesimal change in x, known as the differential dx, gives rise to a corresponding change in y that is well represented by the differential dy  [Pg.111]

The concept of an infinitesimal change is not soundly based mathematically we interpret such changes as being very, very small (non-zero) increments in the specified variable. [Pg.111]


Figure 2 illustrates the effect of incremental changes in ruthenium catalyst content upon the production of acetic acid and its C1--C2 alkyl acetate esters. Acetic acid production is maximized at Ru/Co ratios of ca. 1.0 1.5 however, the data in Figure 2 do show an approximate first order dependence of lOAc (acetic acid plus acetate esters) upon initial ruthenium content—at least up to the 2/1, Ru/Co stoichiometry under the chosen conditions. Selectivity to acetic acid in the liquid product peaks at 92 wt % (carbon efficiency 95 mol %) for a catalyst combination with initially low Ru/Co ratios (e.g. 1 4). The formation of C1-C2 alkanols and their acetate esters rapidly exceeds acetic acid productivity when the Ru/Co atomic ratio is raised above 1.5, although two-carbon oxygenates continue to be the predominant fraction. Smaller quantities of glycol may also be in evidence. [Pg.99]

A search for related work has shown several papers on the traceability problem related to CIA. Another topic of research that is published extensively is the effect of incremental changes e.g. in object-oriented development. We have also seen some publications on research on the effect of process change. However, we have seen no papers on the problems of change impact analysis in agile development of safety critical software apart from one of our own recent papers [11]. The closest is a quote from a paper by Jose Luis de la Vara and Rajwinder Kaur Panesar-Walawege on their meta-model SafetyMet [12] where they identify this topic as an area of future research. [Pg.446]

Most modem spectrometers have interactive software that permits the operator to vary a particular weighting parameter and immediately observe the effect of this change on the final spectmm. The first increment generally is selected to see what the effects of weighting parameters are on the 2 data. With the first FID displayed, the operator can then shift the midpoint of the sine bell function toward the S/N (left) part of the FID, until the best compromise is reached between sensitivity and resolution. It is important for the operator to remember that the weighting function must have a zero value at the right end of the FID so that it drives the FID to zero intensity at the end of (i) in 2 and (ii) the effective (ni/swi) in i. [Pg.246]

Once the initial composition has been prepared and its reaction rate measured, vary the oxidizer/fuel ratio up and down in small increments and observe the effect on the reaction rate. This will give you an insight into the effect of small changes in composition on the reactivity of the composition, as well as an indication of whether you are close to the actual stoichiometric point for the primary reaction that is occurring when the test material is ignited. [Pg.25]

Physical chemistry is concerned to a great extent with the effect that a change in one variable of a system will have on the other variables of the system. For example, how will a change in the pressure or temperature of a system affect its volume or energy Differential calculus is the mathematics of incremental changes. It is based primarily on the mathematical concept known as the derivative. The derivative of a variable y with respect to a variable jc, where y must be a function of x, is defined as... [Pg.19]

Fig. 3. The effect of crack growth on potential energy in a loaded body where (a) is a cracked body of arbitrary shape with a load P appHed, and (b) is the change in potential energy in the body owing to incremental crack growth, Sa. Other terms are defined in text. Fig. 3. The effect of crack growth on potential energy in a loaded body where (a) is a cracked body of arbitrary shape with a load P appHed, and (b) is the change in potential energy in the body owing to incremental crack growth, Sa. Other terms are defined in text.
Refractive Index. The effect of mol wt (1400-4000) on the refractive index (RI) increment of PPG in ben2ene has been measured (167). The RI increments of polyglycols containing aUphatic ether moieties are negative drj/dc (mL/g) = —0.055. A plot of RI vs 1/Af is linear and approaches the value for PO itself (109). The RI, density, and viscosity of PPG—salt complexes, which maybe useful as polymer electrolytes in batteries and fuel cells have been measured (168). The variation of RI with temperature and salt concentration was measured for complexes formed with PPG and some sodium and lithium salts. Generally, the RI decreases with temperature, with the rate of change increasing as the concentration increases. [Pg.354]

It seems that the effect of the induction of phenol-content increment by high oxygen atmospheres is affected also by the exposure time of the product to the given atmosphere (Ayala-Zavala and others 2007). Awad and others found no losses of flavonoids in apples stored under conventional or controlled atmosphere (Awad and others 2000). No changes in the concentration of simple phenols, flavonoids, and anthocyanins were observed for Delicious and Ralls apples held for 4 to 5 months under refrigeration (Ju and others 1996). However, they found a decrease in simple phenols in earlier harvested apples after 3 months of cold storage. However, after 7 days at 20°C storage, phenols and flavonoid content decreased rapidly. [Pg.315]

Different surfactants are usually characterised by the solubility behaviour of their hydrophilic and hydrophobic molecule fraction in polar solvents, expressed by the HLB-value (hydrophilic-lipophilic-balance) of the surfactant. The HLB-value of a specific surfactant is often listed by the producer or can be easily calculated from listed increments [67]. If the water in a microemulsion contains electrolytes, the solubility of the surfactant in the water changes. It can be increased or decreased, depending on the kind of electrolyte [68,69]. The effect of electrolytes is explained by the HSAB principle (hard-soft-acid-base). For example, salts of hard acids and hard bases reduce the solubility of the surfactant in water. The solubility is increased by salts of soft acids and hard bases or by salts of hard acids and soft bases. Correspondingly, the solubility of the surfactant in water is increased by sodium alkyl sulfonates and decreased by sodium chloride or sodium sulfate. In the meantime, the physical interactions of the surfactant molecules and other components in microemulsions is well understood and the HSAB-principle was verified. The salts in water mainly influence the curvature of the surfactant film in a microemulsion. The curvature of the surfactant film can be expressed, analogous to the HLB-value, by the packing parameter Sp. The packing parameter is the ratio between the hydrophilic and lipophilic surfactant molecule part [70] ... [Pg.193]

The optimum values of the parameters a, / , y are found by fitting measured values of Cp over a range of temperatures to equation (5.5). Thus, if we know the value of Cp at one temperature, we can evaluate it at another temperature, and thereby determine the effect of that incremental (or decremental) change in temperature, AT, upon Cp, given by ACp. Alternatively, we can use the properties of differentials given in equation (5.4) to evaluate the differential of Cp, dCp, in terms of the differential d T as ... [Pg.112]

It may be noted that the variation in increments shown in Scheme 12 represents differences in interaction energies between the OH group and the hydrocarbon fragment of the alcohol molecule. When pAR values are compared between different carbocations, they include the effect of the structural change upon the alcohol. Thus the difference in values for /-butyl and isopropyl cations underestimates the relative stabilities of the carbocations as measured by their HIAs by 1.5 log units (2.0/1.364). [Pg.42]

Table 11.2 Illustration of the effect of changing the composition of injected solution on incremental oil recovery in an enhanced oil-recovery process. ... [Pg.273]


See other pages where The Effects of Incremental Change is mentioned: [Pg.268]    [Pg.110]    [Pg.23]    [Pg.268]    [Pg.110]    [Pg.23]    [Pg.452]    [Pg.288]    [Pg.54]    [Pg.361]    [Pg.204]    [Pg.144]    [Pg.68]    [Pg.386]    [Pg.34]    [Pg.481]    [Pg.538]    [Pg.6]    [Pg.820]    [Pg.120]    [Pg.498]    [Pg.148]    [Pg.502]    [Pg.490]    [Pg.96]    [Pg.61]    [Pg.151]    [Pg.572]    [Pg.577]    [Pg.202]    [Pg.405]    [Pg.37]    [Pg.175]    [Pg.382]    [Pg.240]    [Pg.226]    [Pg.272]    [Pg.312]    [Pg.213]    [Pg.60]   


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