Operating definition

The appropriate quantum mechanical operator fomi of the phase has been the subject of numerous efforts. At present, one can only speak of the best approximate operator, and this also is the subject of debate. A personal historical account by Nieto of various operator definitions for the phase (and of its probability distribution) is in [27] and in companion articles, for example, [130-132] and others, that have appeared in Volume 48 of Physica Scripta T (1993), which is devoted to this subject. (For an introduction to the unitarity requirements placed on a phase operator, one can refer to [133]). In 1927, Dirac proposed a quantum mechanical operator tf), defined in terms of the creation and destruction operators [134], but London [135] showed that this is not Hermitean. (A further source is [136].) Another candidate, e is not unitary. 

Description of the Method. The operational definition of water hardness is the total concentration of cations in a sample capable of forming insoluble complexes with soap. Although most divalent and trivalent metal ions contribute to hardness, the most important are Ca + and Mg +. Hardness is determined by titrating with EDTA at a buffered pH of 10. Eriochrome Black T or calmagite is used as a visual indicator. Hardness is reported in parts per million CaCOs. 

Equations 11.19-11.21 are defined for a potentiometric electrochemical cell in which the pH electrode is the cathode. In this case an increase in pH decreases the cell potential. Many pH meters are designed with the pH electrode as the anode so that an increase in pH increases the cell potential. The operational definition of pH then becomes... 

We can provide an operational definition for the constant by rearranging Equation (14.23) to give... 

To meet this requirement, a company must define an incident in specific terms for their facility. This includes an operational definition that indicates the number of pounds of the substance used in a particular process that would qualify as a catastrophic event . Defining an incident in site-specific terms also includes defining the terms "could reasonably have resulted in . Appendix C of the regulation provides guidelines for clarifying this point. It includes definitions of "near misses in which a catastrophic failure occurred, but a chemical release did not occur. Clear guidelines should be established that provide the employee with a quantifiable means of defining those incidents that require a violation report. 

The potentiostat is particularly useful in determining the behaviour of metals that show active-passive transition. Knowledge of the nature of passivity and the probable mechanisms involved has accumulated more rapidly since the introduction of the potentiostatic technique. Perhaps of more importance for the subject at hand are the practical implications of this method. We now have a tool which allows an operational definition of passivity and a means of determining the tendency of metals to become passive and resist corrosion under various conditions. 

The current-potential relationship ABCDE, as obtained potentiosta-tically, has allowed a study of the passive phenomena in greater detail and the operational definition of the passive state with greater preciseness. Bonhoeffer, Vetter and many others have made extensive potentiostatic studies of iron which indicate that the metal has a thin film, composed of one or more oxides of iron, on its surface when in the passive state . Similar studies have been made with stainless steel, nickel, chromium and other metals... 

Gaddum equation for, 122, 125 nonsurmountable, 99 operational classifications of, 127 operational definition of, 99 orthos teric... 

Returning to our two definitions of an acid, the first, the operational definition, gives clearcut instructions on how to decide whether a given substance is an acid. Dissolve it in water and see if it has certain properties. The second (conceptual) definition, however, has the deeper significance since it includes our knowledge of why an acid has these particular properties. It provides a basis for finding hidden likenesses between acid-base reactions in water and other reactions in other solvents. Each type of definition has its merit neither is the definition. 

OH molecules, reaction between, 282 Oil-drop experiment, 241 Oil of wintergreen, 346 Oleomargarine, 407 Open hearth furnace, 404 Operational definition, 195 Orbital representation of chemical bonding, 278 Orbitals atomic, 262, 263 dand/, 262... 

Clean and Polluted Air. In the development of atmospheric chemistry, there has been an historic separation between those studying processes in the natural or unpolluted atmosphere, and those more concerned with air pollution chemistry. As the field has matured, these distinctions have begun to disappear, and with this disappearance has come the realization that few regions of the troposphere are completely unaffected by anthropogenic emissions. An operational definition of clean air could be based upon either the NMHC concentration, or upon the NOjj concentration. 

A definition of clean air based upon NOj concentrations is more difficult to obtain, because of the ubiquitous natural source in lightning (56,154), and because NO may influence HO concentration even at the lowest tropospheric NO levels (a few ppt) that have been observed. An operational definition might require that the rate of the H02 self-reaction R33 be much faster than its reaction with NO, R13. At NO concentrations below about 1 ppb, [H02 ] is relatively independent of [NO ], while [HO ] may increase with [NO ]. Above this level, both [HO2 ] and [HO ] fall with increasing [NOJ. These [HOJ dependencies on [NO ] are shown in Figure 4 (58) and discussed further in the last section. 

A qualitative listing of the hardness of some acids and bases is given in Table 8.3. The treatment has also been made quantitative, with the following operational definition ... 

Practical activities should embody as best as possible the scientifie proeesses that have been preseribed by the American Association for the Advancement of Science observation, elassification, numerieal relations, measurements, time-spaee relations, eommunieation (oral, pictorial, written), deriving of conclusions, prediction ( what would happen if. .hypothesis making, production of operational definitions, identifieation and control of variables, experiment and explanation of experimental data. Different theoretical perspectives should be used with the aim to optimize the positive eognitive and affeetive outcomes. The use, sometimes together, sometimes separately, of different perspeetives can act complimentarily and can lead to positive results (Niaz, 1993 Tsaparhs, 1997). 

COMMENT It might be advisable to stiek to more operational definitions in talking about these eompounds. One runs a risk if compounds have not been tested in people, and to refer to a eompound as hallueinogenie when it is operative. A drug diserimination test might lead you to certain assumptions about the drug that are not true. 

OPERATIONAL DEFINITIONS IN SOC10-BEHAV10RAL DRUG USE RESEARCH 1975. Jack Elinson, Ph.D., and David Nurco, Ph.D., eds. 

Thermodynamics describes the behaviour of systems in terms of quantities and functions of state, but cannot express these quantities in terms of model concepts and assumptions on the structure of the system, inter-molecular forces, etc. This is also true of the activity coefficients thermodynamics defines these quantities and gives their dependence on the temperature, pressure and composition, but cannot interpret them from the point of view of intermolecular interactions. Every theoretical expression of the activity coefficients as a function of the composition of the solution is necessarily based on extrathermodynamic, mainly statistical concepts. This approach makes it possible to elaborate quantitatively the theory of individual activity coefficients. Their values are of paramount importance, for example, for operational definition of the pH and its potentiometric determination (Section 3.3.2), for potentiometric measurement with ion-selective electrodes (Section 6.3), in general for all the systems where liquid junctions appear (Section 2.5.3), etc. 

Under these conditions, an operational definition must be used, i.e. a definition based on the method by which the quantity pH is measured. Obviously, the operational definition must be formulated as closely as possible to the absolute equation (1.4.39). In this way, a practical scale of pH is obtained that is very similar to the absolute scale but is not identical... 

Nasmyth I m confused by what you mean by a stem cell. What is your operational definition ... 

In whole tissue or cell monolayer experiments, transcellular membrane resistance (Rm = Pm1) lumps mucosal to serosal compartment elements in series with aqueous resistance (R = P ). The operational definition of Lm depends on the experimental procedure for solute transport measurement (see Section VII), but its magnitude can be considered relatively constant within any given experimental system. Since the Kp range dwarfs the range of Dm, solute differences in partition coefficient dominate solute differences in transcellular membrane transport. The lumped precellular resistance and lumped membrane resistance add in series to define an effective resistance to solute transport ... 

Hund E, Massart DL, Smeyers-Verbeke J (2001) Operational definitions of uncertainty. Trends Anal Chem 29 394... 

In general, all observed intemuclear distances are vibrationally averaged parameters. Due to anharmonicity, the average values will change from one vibrational state to the next and, in a molecular ensemble distributed over several states, they are temperature dependent. All these aspects dictate the need to make statistical definitions of various conceivable, different averages, or structure types. In addition, since the two main tools for quantitative structure determination in the vapor phase—gas electron diffraction and microwave spectroscopy—interact with molecular ensembles in different ways, certain operational definitions are also needed for a precise understanding of experimental structures. 

Similar operational definitions have to be taken into account for every experimental tool of structural chemistry to define the meaning of the observables that it provides6. In microwave spectroscopy, for example, structural information is obtained from the rotational constants... 

Operational definitions of molecular structure are needed to clarify experimental significance. In addition, some statistical notation is needed to clarify physical meaning. All statistical definitions hinge on the minimum of potential energy in a bound electronic state, which defines the equilibrium geometry or r,-intemuclear distance type. 

One more step provides an operational definition. The HOMO level lies, I = ionization energy, below the vacuum level, while the LUMO level lies, A = electron affinity, below it. Thus, the chemical hardness lies midway in the gap and usually is given in units of eV. 

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