Practical Reasons

The general attributes of the capillary rise method may be summarized as follows. It is considered to be one of the best and most accurate absolute methods, good to a few hundredths of a percent in precision. On the other hand, for practical reasons, a zero contact angle is required, and fairly large volumes of solution are needed. With glass capillaries, there are limitations as to the alkalinity of the solution. For variations in the capillary rise method, see Refs. 11, 12, and 22-26. 

A set of pendant drop profiles is shown in Fig. 11-17 as an illustration of the range of shapes that may be observed. It has been pointed out that for practical reasons, the size of the tip from which the drop is suspended should be such that rja is about 0.5 or less [66]. 

The two sources of stochasticity are conceptually and computationally quite distinct. In (A) we do not know the exact equations of motion and we solve instead phenomenological equations. There is no systematic way in which we can approach the exact equations of motion. For example, rarely in the Langevin approach the friction and the random force are extracted from a microscopic model. This makes it necessary to use a rather arbitrary selection of parameters, such as the amplitude of the random force or the friction coefficient. On the other hand, the equations in (B) are based on atomic information and it is the solution that is approximate. For ejcample, to compute a trajectory we make the ad-hoc assumption of a Gaussian distribution of numerical errors. In the present article we also argue that because of practical reasons it is not possible to ignore the numerical errors, even in approach (A). 

Each of these tools has advantages and limitations. Ab initio methods involve intensive computation and therefore tend to be limited, for practical reasons of computer time, to smaller atoms, molecules, radicals, and ions. Their CPU time needs usually vary with basis set size (M) as at least M correlated methods require time proportional to at least M because they involve transformation of the atomic-orbital-based two-electron integrals to the molecular orbital basis. As computers continue to advance in power and memory size, and as theoretical methods and algorithms continue to improve, ab initio techniques will be applied to larger and more complex species. When dealing with systems in which qualitatively new electronic environments and/or new bonding types arise, or excited electronic states that are unusual, ab initio methods are essential. Semi-empirical or empirical methods would be of little use on systems whose electronic properties have not been included in the data base used to construct the parameters of such models. 

Criteria 1 through 5 must be obeyed in order to obtain reasonable results in subsequent calculations using the function. Criteria 6 through 10 are desirable for practical reasons. Finding a function that meets these criteria requires skill and experience, and no small amount of patience. 

For practical reasons, the application of the adsorption method to the study of surface area and porosity has to be limited to bodies which are either very finely divided or possess an extensive pore system. It is helpful to consider the case of finely divided bodies first. 

Section 3.7, the gas adsorption method breaks down for practical reasons. Since the angle of contact of mercury with solids is 140° (see later), and therefore more than 90°, an excess pressure Ap is required to force liquid mercury into the pores of a soh d. The idea of using mercury intrusion to measure pore size appears to have been first suggested by Washburn who put forward the basic equation... 

LC can be combined with all kinds of mass spectrometers, but for practical reasons only quadrapolar, magnetic/electric-sector, and TOP instruments are in wide use. A variety of interfaces are used, including thermospray, plasmaspray, electrospray, dynamic fast-atom bombardment (FAB), particle beam, and moving belt. 

For practical reasons, the blast furnace hearth is divided into two principal zones the bottom and the sidewalls. Each of these zones exhibits unique problems and wear mechanisms. The largest refractory mass is contained within the hearth bottom. The outside diameters of these bottoms can exceed 16 or 17 m and their depth is dependent on whether underhearth cooling is utilized. When cooling is not employed, this refractory depth usually is determined by mathematical models these predict a stabilization isotherm location which defines the limit of dissolution of the carbon by iron. Often, this depth exceeds 3 m of carbon. However, because the stabilization isotherm location is also a function of furnace diameter, often times thermal equiHbrium caimot be achieved without some form of underhearth cooling. 

Both phases are siibstantiaUy in plug flow. Dispersion measurements of the hquid phase usuaUy report Peclet numbers, Uid /D, less than 0.2. With the usual smaU particles, the waU effect is negligible in commercial vessels of a meter or so in diameter, but may be appreciable in lab units of 50 mm (1.97 in) diameter. Laboratory and commercial units usuaUy are operated at the same space velocity, LHSy but for practical reasons the lengths of lab units may be only 0.1 those of commercial units. 

In addition, the temperature dependence of the diffusion potentials and the temperature dependence of the reference electrode potential itself must be considered. Also, the temperature dependence of the solubility of metal salts is important in Eq. (2-29). For these reasons reference electrodes with constant salt concentration are sometimes preferred to those with saturated solutions. For practical reasons, reference electrodes are often situated outside the system under investigation at room temperature and connected with the medium via a salt bridge in which pressure and temperature differences can be neglected. This is the case for all data on potentials given in this handbook unless otherwise stated. 

Some researchers (e.g., Abramovich,Baturin,Rajaratnam,- and Nielsen and Moller ) consider x to be the distance from a point located at some distance Xq upstream from the diffuser face. Equations for the jet boundaries and velocity profile used in the centerline velocity derivation assume that the jet is supplied from the point source. Addition of the distance Xq to the distance from the outlet corrects for the influence of the outlet size on the jet geometry. For practical reasons some researchers neglect Xq. 

As in the case of equations for the velocity decay computation, in the equations for the temperature decay computation, some researchers consider X to be a distance starting from some virtual source located at some distance X(, from the diffuser face others for practical reasons neglect Xq. 

However, there are practical reasons even in the IT age when it may not be prudent to reissue a document after each change. 

We shall discuss the factors involved in the reverse order for practical reasons. 

A-Bromo- as well as A-chloroamines have been used as starting materials. For practical reasons (greater stability) the easily accessible A-chloro compounds are preferred. 

Although the viscosity of the sample solution may affect the resolution, for practical reasons highly concentrated protein samples will give the best separations in the case of SEC with respect to the process economy. Although the actual loading capacity depends on the separation problem and on the... 

Stable than the parent system 4. Hereinafter, for practical reasons, all five formal dihydroisomers 1-5 will be referred to as indolocarbazoles. 

In practice, reasonable estimates of the limit limc >oo 5 (B) may be obtained for relatively small B. 

There are two practical reasons to err toward the correction of the ICso of an antagonist to estimate the Kb- The first is that an overestimation of antagonist potency will only result in a readjustment of values upon rigorous measurement of antagonism in subsequent analysis. However, more importantly, if the correction is not applied then there is a risk of not detecting weak but still useful antagonism due to an underestimation of potency (due to nonapplication of the correction factor). These reasons support the application of the correction in all cases as a default. 

The complete specification of a random process requires us to have some way of writing down an infinite number of distribution functions. For practical reasons, this is an impossible task unless all the distribution functions can be specified by means of a rule that enables one to calculate any distribution function of interest in terms of a finite amount of prespecified information. The following examples will illustrate these ideas by showing howr some particular stochastic processes of interest can be defined. 

NOTE Generally speaking, the higher the TDS of the RW source to the RO, the higher the applied pressure required to produce a constant permeate water TDS. Also, for practical reasons, the rate of permeate recovery tends to decrease with increase in source water TDS. 

In theory, the chiral center can be anywhere in the molecule, but in practice, reasonable diastereoselectivity is most often achieved when it is in the a position. For examples of high diastereoselectivity when the chiral center is further away, especially in reduction of P-hydroxy ketones, see Narasaka, K. Pai, F. Tetrahedron, 1984, 40, 2233 Hassine, B.B. Gorsane, M. Pecher, J. Martin, R.H. Bull. Soc. Chim. Belg., 1985, 94, 597 Bloch, R. Gilbert, L. Girard, C. Tetrahedron Lett., 1988, 53, 1021 Evans, D.A. Chapman, K.T. Carreira, E.M. J. Am. Chem. Soc., 1988, 110, 3560. 

A particularly interesting case is when a set of hydrogens which are chemically equivalent in the unionized molecule become inequivalent in the positive ion. Obvious examples are Jahn-Teller active molecules, but the same phenomenon may be found also in Jahn-Teller inactive systems. Since deuteration fcr practical reasons must be done before ionization, it may happen that a single deuterated molecule may produce several inequivalent isomers of the radical cation, e.g., upon irradiation. This will obviously influence the recorded ESR spectrum. 

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