Monotonic increasing

Snch a generalization is consistent with the Second Law of Thennodynamics, since the //theorem and the generalized definition of entropy together lead to the conchision that the entropy of an isolated non-eqnilibrium system increases monotonically, as it approaches equilibrium. 

Knowledge-based systems typically use quaHtative methods rather than quantitative ones. For example, consider a simple tank system. The equation describing the flow rate of Hquid out of the tank is given below, where C is the orifice coefficient, d is the diameter of the orifice, and h is the height of Hquid in the tank. Based solely on the form of the equation, a human reasoner can infer that the flow rate F increases monotonically with the height b of Hquid in the tank. 

Several features of ISS quantitative analysis should be noted. First of all, the relative sensitivities for the elements increase monotonically with mass. Essentially none of the other surface spectroscopies exhibit this simplicity. Because of this simple relationship, it is possible to mathematically manipulate the entire ISS spectrum such that the signal intensity is a direct quantitative representation of the surface. This is illustrated in Figure 5, which shows a depth profile of clean electrical connector pins. Atomic concentration can be read roughly as atomic percent direcdy from the approximate scale at the left. 

We can see, in Table 12 that there is a monotonic relationship between the SSR and the concentration of the interferring 5,h component in each sample of the validation set A5. In Figure 63 we can see that the relationship is approximately linear with the square root of the SSR. The important thing is not the linearity of the relationship, but that it exists at all and increases monotonically. It gives us a very useful way of flagging samples which our... 

The effect of changing solvent composition (polarity) on molecular weight dispersity is noteworthy. Mw/Mn is quite low (1.69) in the experiment carried out by the use of 100% CH2C12 and it increases monotonically with increasing n-C6H14 content. It is very difficult to interpret these data at this time. 

Koulkes-Pujo and coworkers5 5 studied the formation of methane in the reaction of OH radicals and H atoms with aqueous DMSO in acidic media. In the radiolysis of deaerated acidic aqueous solution of DMSO they found that G(CH4) increases monotonously with CH4 concentration up to 0.8 m DMSO. Similar results were obtained for C2H6 but the yields of C2H6 are much lower than that of CH4. 

So, Tg/ increases monotonically with medium density, but in the beginning the increase corresponds to gap filling, and in the end to general narrowing of the spectrum. 

The dependence of the measured rise in fluid mixed-cup temperature on Reynolds number is illustrated in Fig. 3.12. The difference between outlet and inlet temperatures increases monotonically with increasing Re at laminar and turbulent flows. Under conditions of the given experiments, the temperature rise due to energy dissipation is very significant AT = 15—35 K at L/ i = 900—1,470 and Re = 2,500. The data on rising temperature in long micro-tubes can be presented in the form of the dependence of dimensionless viscous heating parameter Re/[Ec(L/(i)] on Reynolds number (Fig. 3.13). 

In the low-hnmidity regime (RH < A), Ac ) increases monotonically. When RH = A, the K salts show a decrease in Ac ), followed by a constant platean for RH > A. For NaCl, Ac ) continnes to increase bnt at a lower rate. The response time t also shows a different behavior below and above A, which is manifested by a change in the slope of log(T). 

The influence of parameter a on tumor size, as judged from classic sensitivity analysis, seems to increase monotonically to a plateau, reaching about 50% of its effect no sooner than day 13 conversely, MCCC indicates a fast increase of effect of parameter a up to a peak at about day 3 or 4, with a subsequent decrease and attainment of the plateau from above. 

More specifically, the reduced variable Kj = kjA is defined on [0, ti]. Generally, the error in an FD approximation (or rather its dispersion relation, Eq. (36)) increases with Kj. The Taylor series approach outlined above, which leads to the standard Lagrangian FD approximations, is essentially perfect for very small Kj but quickly deviates from the correct, quadratic dependence, Eq. (37). The generic behavior is that the error increases monotonically with Kj. Instead of requiring that the fit be perfect in the limit of very small Kj, we require that the error be no greater than s from Kj = 0 up to some... 

Extensive data are given in the Uterature for the potentiometric titration of polymer acids which may be used to study the behaviour of polyelectrolyte systems under different conditions. For poly(a-D) galacturonic acid there are few data of this kind, especially in connection with the occurrence of a conformational transition induced by pH variations, or with the effect brought about by the addition or the exchange of counterions. Since for a polyacid not exhibiting a conformational transition in the course of titration, pK K denoting the apparent dissociation constant) increases monotonously with degree... 

Pr, Nd, and Sm) samples increased monotonously with an increase in ionic radius of A (Figure 1). T10% is the temperature at which methane conversion reaches 10%, and was lowered with an increase in ionic radius of A (Figure 1). 

Relatively detailed study has been done for the reaction pathways over Au/Ti02 catalysts mainly because of simplicity in catalytic material components. The rate of PO formation at temperatures around 323 K does not depend on the partial pressure of C3H6 up to 20vol% and then decreases with an increase, while it increases monotonously with the partial pressure of O2 and H2 [57]. A kinetic isotope effect of H2 and D2 was also observed [63]. These rate dependencies indicate that active oxygen species are formed by the reaction of O2 and H2 and that this reaction is rate-determining [57,63,64]. 

Figure 18 shows the dependence of the roughness function on the two dimensionless parameters K]h and Kjh. In accord with the limits considered above, the roughness function increases monotonically with both variables. 

The concentration versus lactose conversion (X) plots have maxima for B and C, while the concentrations of D, E, F and G increase monotonously with conversion E, F and G showing a steep decrease at high lactose conversions. 

The improved method guarantees that the EoS will calculate the correct VLE not only at the experimental data but also at any other point that belongs to the same isotherm. The question that arises is what happens at temperatures different than the experimental. As seen in Figure 14.10 the minima of the stability function increase monotonically with respect to temperature. Hence, it is safe to assume that at any temperature between the lowest and the highest one, the EoS predicts the correct behavior of the system. However, below the minimum experimental temperature, it is likely that the EoS will predict erroneous liquid phase separation. 

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