Quantitative criterion for

Stability of an enzyme is defined as its ability to retain catalytic activity under specified conditions (Martinek and Berezin, 1978). The quantitative criterion for stability is the value of the first-order rate constant of monomolecular inactivation, king k-. 

The quantitative criterion for adiabacity is given by a parameter x defined as 47tV2 e-Sli... 

In industrialized nations, a significant portion of the population is overweight. The Body-Mass-Index (BMI) provides a reliable and simple quantitative criterion for assessing this condition it is calculated as follows ... 

The significant conclusion of this work is that although mixing of the fluid in the direction of flow has a strong influence on the stability of a continuous flow reactor, as can be seen by the way the parameters of the residence-time distribution are involved, the quantitative criterion for stability is independent of the mechanism by which such mixing occurs. The criterion applies equally well to imperfectly-... 

A more quantitative criterion for the allowed spread in residence time is given by the following equation... 

A more quantitative criterion for the operation of a cation radical cycloaddition mechanism has been carried out for a Diels-Alder reaction system consisting of various substituted derivatives of /ran -stilbene (as the ionizable dienophile) and 2,3-dimethyl-1,3-butadiene (Scheme 37) [71]. 

The relative amount of proximate bonded molecules estimated for small extents of surface coverage serves as a quantitative criterion for distinguishing between different types of distributions. Indeed, differences between distributions are especially marked for small loading (Fig.l). 

The key then is to somehow calculate the probability with which a specific quantum state contributes to the average values. As far as thermal systems in thermodynamic equilibrium are concerned, this is the central problem addressed by statistical thermodynamics. W( therefore begin our discuasion of some core elements of statistical thermodynamics at the quantum level but will eventually turn to the classic limit, because the phenomena addressed by this book occur under conditions where a classic description turns out to be adequate. We shall see this at the end of this chapter in Section 2.5 where we introduce a quantitative criterion for the adequacy of such a classic description. 

In free disperse systems, in particular those with low concentration of dispersed phase, the nature of colloid stability and conditions under which the collapse occurs, are to a great extent dependent on thermal motion of dispersed particles, which may contribute to both stability and destabilization. For example, the necessary condition for sedimentation stability is sufficiently small particle size, so that the tendency of particles to distribute within the entire volume of disperse system due to the Brownian motion (an increase in entropy) would not be affected by gravity. As a quantitative criterion for the presence of noticeable amount of dispersed particles in equilibrium with a sediment one, for instance, may use the... 

Berezin162 has argued that vibrational force constants are a quantitative characteristic of the properties of the electron shells of molecules and has proposed that the coefficients of influence (where the matrix of the coefficients of influence is the inverse of that of the force constants) may serve as a quantitative criterion for aromaticity. The coefficients of influence for benzene, pyridine, pyrazine, s-triazine, and s-tetrazine have been calculated from the force constants of the molecules and the sum of the diagonal coefficients of influence of all six internal ring angles and seem to increase as Balaban s K values (Section II,F, 1) for these compounds decrease. 

Sergeeva, K. Martinek, Denaturation capacity - a new quantitative criterion for selection of organic-solvents as reaction media in biocatalysis, Eur.J. Biochem. 1991,... 

A quantitative criterion for the degree of order can be laid down. Imagine 2n lattice points all unoccupied. For the perfectly ordered state n specific points are reserved for copper and n for zinc. In the actual state let a fraction p of the zinc atoms occupy their own reserved points, the remainder intruding into the places reserved for copper. For perfect order, p = 1 for complete randomness p = J, since there is then an equal chance for the zinc to find one of its own sites or a copper site. The formula [Pg.309]

Our approach to derive a quantitative criterion for the roughness characteristics of ultra-hydrophobic surfaces with stochastic roughness properties is based on roughness analysis by power spectral density (PSD) functions and subsequent data reduction algorithm [11]. 

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. 

In a critical appraisal, Jones early on expressed the view that diamagnetic susceptibility exaltation provides a qualitative rather than a quantitative criterion for aromatic character. He argued that the uncertainties in the value used for the diamagnetic constants for atoms and bonds, the need to use constitutive corrections, and in particular the uncertainties in the origin of the susceptibility, which are clearly related to the problems of the ring current model, prevent the meaningful use of this phenomenon as a quantitative criterion. ... 

To arrive at a quantitative criterion for quasidiabaticity, it has been proposed to minimize the integral of F(3) 2 which is the Euclidean norm for matrices, over the nuclear coordinates. This natural requirement leads to the simple equation ... 

In DVS guideline 2225-4, as discussed in the previous section, thickness reduction Sr alone is used as a criterion for seam quality. In view of our previous considerations it is obvious that this criterion cannot guarantee a perfect seam. When the melt depth is small, a thickness reduction conforming to the guideline can still be achieved by extensively driving the melt out from the seam. However, one will then most likely produce an unsatisfactory seam and an experienced welder will recognise this. Only the ratio of to the melt depth Lq of a certain range of values represents a quantitative criterion for the seam quality. 

Khmelnitsky, Y. L., V. V. Mozhaev, A. B. Belova, M. V. Sergeeva, and K. Martinek. 1991. Denaturation Capacity A New Quantitative Criterion for Selection of Organic Solvents as Reaction Media in Biocatalysis. European Journal of Biochemistry 198 (1) 31-41. 

It is now clear that the relativistic screening effect of the 6s electrons as well as the other s electrons tends to promote an itinerant nature of the 4f electrons in a crystal. It is difficult at present, however, to predict correctly in which cerium compounds the 4f electrons may be itinerant, because the strong correlations between the 4f electrons make it difficult to derive a quantitative criterion for the itinerancy of the 4f electrons theoretically. 

Ellison was in defence of the use of the correlation coefficient, stating that it has valid application as a routine criterion for acceptable fit if used with due care." He pointed out that (1) the useful relationship between the correlation coefficient and the residual standard deviation can be used to relate the correlation coefficient approximately to the standard error of prediction, and therefore to the approximate uncertainty of interpolated values and (2) the relationship among calibrated range, residual standard deviation and correlation coefficient indicated that either r or r can be used as a quantitative criterion for calibration curve quality. 

This equation, due to Higbie, was originally derived to describe mass transfer between rising gas bubbles and a surrounding liquid Tran. AIChE, 31,368 [1935]). It applies quite generally to situations where the contact time between the phases is short and the penetration (or depletion) depth is so small that transfer may be viewed as taking place from a plant to a semiinfinite domain. In Section 4.1.2.3 we will provide a quantitative criterion for this approach, which is also referred to as the Penetration Theory. It also describes both the short- and long-term behavior in diffusion between a plane and a semi-infinite space, and we used this property in Chapter 1, Table 1.4, to help us set upper and lower bounds to mass transfer coefficients and "film" thickness Zp j. 

Let us reflect on the net directional movement of species 1 and species 2 in this countercurrent column. It is clear that the lighter species 1, H2, moves up the column and the heavier species 2, N2, moves down the counter-current column. One could argue that, in effect, the concentration wave velocity, i j, of species 1 is positive vis-a-vis the z-coordinate in Figure 8.1.1, whereas that for species 2, N2, is negative. We illustrate the quantitative criterion for this type of species movement in a counter-current system of two immiscible phases in Section 8.1.1.3, where we illustrate also that only two species may be separated in such a countercurrent column having steady state flow. 

From the above it follows that the problem of finding quantitative criterion for conclusive attributing the situation of ships meeting to the head-on situation on reciprocal courses over ground or to the situation of ship s meeting on sharply crossing courses over the ground as before remains on actual problem that needs to be resolved. 

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