Operational terms

The differential operator terms ean be reeast in several ways using... 

As of the year 1998, small quantities of sassafras oil are still being sold on retail shelves without any scrutiny. Usually in 1-4oz sizes. Anything larger is usually sold only through distributors and manufacturers. And as of 1998, the DEA has informed most of these distributors that they (the DEA) want lists kept or sales reported of most, if not all, sassafras oil purchases. Mind you it is not illegal to buy the oil. It s just that you will be put on a list if you do. The operative term here is Watched Substance . Solution have someone else buy it for you. 

In the following sections, an attempt is made to provide a critical outline of experimental aspects of investigations directed to biodegradation and biotransformation, with particular emphasis on outstanding issues to which sufficient attention has not always been paid, and which have not therefore received ultimate resolution. Before proceeding further, it is desirable to define clearly some operational terms ... 

In operational terms, the disk filter is similar to the drum filter, but filtration is conducted by using a series of large-diameter filter disks that carry the filter medium on both sides of the disk. They are connected to the main horizontal shaft and partly immersed in the feed slurry. The central shaft is connected by a set of valves which serve to provide vacuum and air, as in drum filters. As the disk sections are immersed during rotation, a vacuum is applied to form a cake on both sides of the disk. The cycle of operation is similar to that in a drum filter. This system is used extensively in the iron ore industry for dewatering magnetite concentrates. 

In operational terms, with fluorescence measurements made at intervals t apart,... 

It is now necessary to evaluate the integrals in Eq. (10C) using the UCpert operator. Terms to first order in Sz will be retained. For the first integral,... 

We then wish to discover how tj depends on reaction and particle characteristics in order to use equation 8.5-5 as a rate law in operational terms. To do this, we first consider the relatively simple particle shape of a rectangular parallelepiped (flat plate) and simple kinetics. 

Substrate-limited growth in terms of reduced availability of both the electron donor and the electron acceptor is common in wastewater of sewer systems. Based on the concept of Michaelis-Menten s kinetics for enzymatic processes, Monod (1949) formulated, in operational terms, the relationship between the actual and the maximal specific growth rate constants and the concentration of a limiting substrate [cf. Equation (2.14)] ... 

In actual practice, the latter mode is technically more demanding and affords results that are much higher in sensitivity. Recent developments in NMR-spectrometer hardware and technique have made this more-sensitive-mode of operation, termed as inverse-detection , rather readily applicable to modem analysis. 

For a nonracemic mixture of enantiomers prepared by resolution or asymmetric synthesis, the composition of the mixture was given earlier as percent optical purity (equation 1), an operational term, which is determined by dividing the observed specific rotation (Mobs) of a particular sample of enantiomer with that of the pure enantiomer ( max), both of which were measured under identical conditions. Since at the present, the amount of enantiomers in a mixture is often measured by nonpolarimetric methods, use of the term percent optical purity is obsolete, and in general has been replaced by the term percent enantiomeric excess (ee) (equation 2) introduced in 197163, usually equal to the percent optical purity, [/ ] and [5] representing the relative amounts of the respective enantiomers in the sample. 

This definition refers to an enantiomeric mixture produced in an asymmetric synthesis. In some cases where a diastereomeric mixture is produced, the definition has to be altered accordingly. Percent optical purity is an operational term that depends on optical rotation measurements. It is not necessarily equal to the percent enantiomeric purity (13), which is a more meaningful term and is the extent to which one enantiomer is formed in excess over the other ... 

In physical terms the site inhomogeneous component may be conceived of either as slightly different protein binding sites for chromophores or as a distribution of protein conformational substates [127] at any one site. In operational terms the spectral forms are represented by the sub-bands of a gaussian or lorentzian decomposition analysis of absorption or fluorescence spectra. 

This materialization is achieved by first defining the increment to be extracted - an operation termed increment delimitation. After this, the increment must be physically extracted. These two operations are sampling processes each associated with potential errors which are termed the increment delimitation error (IDE) and the increment extraction error (lEE) respectively. 

All the operator terms in square brackets in eqn, (365) contain terms CL on their extreme right operating on peq, and CLpeq = kp q (S — k ) = kpt(lbS where SS is the difference between the sink (or reaction) term and its equilibrium averaged value. Since z and L commute (i.e. do not affect each other), the binomial expression of eqn. (365) can be regrouped,... 

It is simplistic to suppose that only an infinite system warrants macroscopic designation. We suspect that certain quite small systems (e.g., 1 mm3 of He gas) might be satisfactorily macroscopic for thermodynamic purposes. Let us frame the definition of macroscopic in more precise and operational terms that allow a realistic finite limit to be established. 

Due to the non-linearity of these equations and the complexity of the operator terms, the set (5.2.5) to (5.2.7) cannot be solved exactly and we have to cut off this hierarchy at some finite m. 

The equations derived above, describing the A + B —> B reaction kinetics in terms of the correlation functions g and g2, have the form of the nonlinear generalised multi-dimensional diffusion equation. Ignoring the multidimensionality of the operator terms in (5.2.11), these equations could be formally considered as similar to the basic non-linear equations for the A + B — 0 reaction (Section 5.1). Equations studied in both Sections 5.1 and 5.2 are derived with the help of the Kirkwood superposition approximation, the use of which leads to several equations for the correlation functions of similar and dissimilar reactants. 

Individual operator terms in these sums are given by (14.15) and (14.16), and here we have introduced additional subscripts of the operators to indicate the space of shells in which they are defined. 

Before the effective hamiltonian can be used in actual calculations some means must be found for expressing the terms Gcore [equation (33)] and the projection operator terms in equations (31) or (34) in a form which is convenient for computing matrix elements this is the subject of parameterization, which is dealt with in Section 3. Two other formal problems remain at this level. Firstly there is the need to modify equation (29) and, as a result, equations (31) and (34) if the atomic calculations on the separate atoms are of the open shell kind as is usually the case. In order not to bias the later molecular calculation the core operators and projection terms can be derived for some average of all the possible open-shell configurations,25 although care should be exercised in the choice of the hamiltonian for which the... 

Matrix elements for the valence functions were taken with the effective core potential the coulomb and exchange terms were handled exactly, numerically, without any parameterization and a Phillips-Kleinman projection operator term was also used. Spin-orbit coupling effects amongst the valence orbitals were treated semi-empirically using the operator... 

Westerners do not accept the existence of conscious processes for which they have no operational term. The attitude which is prevalent is - if you can t label it, and if it is beyond current notions of space-time and personality, then it is not open for investigation. Thus we see the ego-loss experience confused with schizophrenia. Thus we see present-day psychiatrists solemnly pronouncing the psychedelic keys as psychosis-producing and dangerous. 

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