Definitions and Equations

There are a number of equations and definitions associated with the principles behind the working of the pulse oximeter. 

Step 4—assign dependent variables of scientific equations and definitions as outputs... 

Details of the Pitzer equations and definitions of the notations utilized in this paper and in PHRQPITZ are given in the literature (3-lOL As the focus of this report is on the capabilities and limitations of PHRQPITZ in relation to its application to geochemical problems, only selected aspects of the implementation of the Pitzer equations in PHRQPITZ are presented. 

The application of the above equations and definitions and the resulting implications are best illustrated by using a relatively simple tviK>-co(nponent sample. We shall deal with the case where all constituents Involved are monovalent weak electrolytes. Although essentially immaterial, we shall consider a separation compartment of uniform dimensions at a constant electrical driving current and at constant temperature. The separation process and some relevant information are given in Fig. 1. For more detailed information is referred to the references [5a and 5b]. 

The tortuosity describes the ratio of the (average) incremental distance that an ion/molecule must travel to cover the direct distance in the direction of diffusion (Berner, 1980) and is thus the factor, which describes the increase in travel distance in the porous medium. Since the definitions of tortuosity in literature indicate small however substantial differences (an excellent overview of different procedures, equations and definitions is given by Boudreau (1997)), the definition used here is described briefly. The diffusion coefficient is corrected by the squared tortuosity. The square of the tortuosity is called tortuosity factor (Carman, 1937). This factor represents the... 

Derivation of Young s Equation and Definition of Contact Angle... 

On the other hand, the equations and definitions presented above are the most fundamental ones for adsorption science although more than fifty years have elapsed since their publication. As it can be seen in the further considerations a large part of modern adsorption theory is derived directly from the equations discussed above. Moreover, these equations play a fundamental role in the studies of structure of most industrial adsorbents and solid catalysts. 

When a chemical reaction occurs, the chemical identities of the system are changing. Although most of the equations and definitions we have considered so far are still directly applicable, we need to expand the applicability of AL/and AH. 

There are some subtleties with respect to the physicochemical meaning of the contact angle equation, and these are taken up in Section X-7. The preceding, however, serves to introduce the conventional definitions to permit discussion of the experimental observations. 

This makes it desirable to define other representations in addition to the electronically adiabatic one [Eqs. (9)-(12)], in which the adiabatic electronic wave function basis set used in the Bom-Huang expansion (12) is replaced by another basis set of functions of the electronic coordinates. Such a different electronic basis set can be chosen so as to minimize the above mentioned gradient term. This term can initially be neglected in the solution of the / -electionic-state nuclear motion Schrodinger equation and reintroduced later using perturbative or other methods, if desired. This new basis set of electronic wave functions can also be made to depend parametrically, like their adiabatic counterparts, on the internal nuclear coordinates q that were defined after Eq. (8). This new electronic basis set is henceforth refened to as diabatic and, as is obvious, leads to an electronically diabatic representation that is not unique unlike the adiabatic one, which is unique by definition. 

The natural laws in any scientific or technological field are not regarded as precise and definitive until they have been expressed in mathematical form. Such a form, often an equation, is a relation between the quantity of interest, say, product yield, and independent variables such as time and temperature upon which yield depends. When it happens that this equation involves, besides the function itself, one or more of its derivatives it is called a differential equation. 

Proc., 65(3), 45 (1986)] is preferred. To use this and alternate models, dimensional characteristics of structured packing must be defined. Figure 14-51 shows nomenclature and definitions of key dimensions. Not shown, but also important, is the angle the corrugations make with the horizontal (usu y 45 or 60°). Then the Rocha et al. predictive equation is ... 

Basic Equations In Background and Definitions, the basic equation for gas permeation was derived with the major assumptions noted. Equation (22-62) may be restated as ... 

All the early work was concerned with atoms, with Sir William Hartree regarded as the father of the technique. His son, Douglas R. Hartree, published the definitive book, The Calculation of Atomic Structures, in 1957, and in this he derived the atomic HF equations and described numerical algorithms for their solution. Charlotte Froese Fischer was a research student working under the guidance of D. R. Hartree, and she published her own definitive book. The Hartree—Fock Method for Atoms A Numerical Approach in 1977. The Appendix lists a number of freely available atomie structure programs. Most of these can be obtained from the Computer Physics Communications Program Library. 

See nomenclature for definition of symbols and units. The units presented are English engineering units, unless a conversion is required. The friction factor is the only experimental variable that must be determined by reference to the above equations and it is represented by Figure 2-3. Note that this may sometimes be referred to as the Fanning formula, and may be modified to )held a fric-... 

FIGURE 10.7 Figure illustrating the comparison of concentration-response curves to two full agonists. Equations describe response in terms of the operational model (variable slope version equation see Section 10.6.1). Schematic indicates the interacting species in this case, two full agonists A1 and A2 activating a common receptor R to produce response. Boxes show the relevant measurements (EPMRs) and definitions of the parameters of the model used in the equation. 

Thus, from an investigation of the compressibility of a gas we can deduce the values of its critical constants. We observe that, according to van der Waals theory, liquid and gas are really two distant states on the same isotherm, and having therefore the same characteristic equation. Another theory supposes that each state has its own characteristic equation, with definite constants, which however vary with the temperature, so that both equations continuously coalesce at the critical point. The correlation of the liquid and gaseous states effected by van der Waals theory is, however, rightly regarded as one of the greatest achievements of molecular theory. 

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