Three Basic Approaches

There are now hundreds of programs designed to compute chemical equilibrium in complex, multi-component systems. These are too numerous to summarize completely here, but thorough reviews are available in the literature (Van Zeggeren and Storey, 1970 Nordstrom etal., 1979b Wolery, 1979,1983 Smith and Missen, 1982 Reed, 1982 Nordstrom and Ball, 1984 Nordstrom and Munoz, 1985, Appendix E De Capitani and Brown, 1987). 

There are three general categories or types of algorithm used those that use equilibrium constants (as in our rote method above) those that use the free energy of each species and find that set of activities which minimizes the free energy of the entire system and those that follow reaction progress in small steps towards a state of final equilibrium. We will summarize these methods briefly in the following sections. 

---

Three basic approaches have been used to solve the equations of motion. For relatively simple configurations, direct solution is possible. For complex configurations, numerical methods can be employed. For many practical situations, particularly three-dimensional or one-of-a-kind configurations, scale modeling is employed and the results are interpreted in terms of dimensionless groups. This section outlines the procedures employed and the limitations of these approaches (see Computer-aided engineering (CAE)). 

The low concentration of initiator residues in polymers formed by radical polymerization means that they can usually only be observed directly in exceptional circumstances or in very low molecular weight polymers (Section 3.5.3). Thus, the study of the reactions of initiator-derived radicals with monomers has seen the development of some novel techniques. Three basic approaches have been employed. These involve ... 

There are three basic approaches to identify the ion series. The most straightforward approach is based on a-ions linked to b-ions. If there is at least one or two mass shifts of 28 Da associated with any of the already identified peaks, there is a high probability that we found a b-ion series. However, this can only be considered speculation. 

In terms of waste definition, there are three basic approaches (as it pertains to petroleum, petroleum products, and nonpetroleum chemicals) to defining petroleum or a petroleum product as hazardous (1) a qualitative description of the waste by origin, type, and constituents (2) classification by characteristics based on testing procedures and (3) classification as a result of the concentraUon of specific chemical substances. 

Oceanographers follow three basic approaches to collecting data for the study of biogeo-chemical processes (1) they measure concentrations over time and space, (2) they make direct measurements of chemical fluxes, and (3) they perform laboratory experiments... 

Originally we evolved three basic approaches or strategies ... 

Three basic approaches are used to control viral diseases vaccination, antiviral chemotherapy, and stimulation of host resistance mechanisms. Vaccination has been used successfully to prevent measles, rubella, mumps, poliomyelitis, yellow fever, smallpox, chickenpox, and hepatitis B. Unfortunately, the usefulness of vaccines appears to be limited when many stereotypes are involved (e.g., rhinoviruses, HIV). Furthermore, vaccines have little or no use once the infection has been established because they cannot prevent the spread of active infections within the host. Passive immunization with human immune globulin, equine antiserum, or antiserum from vaccinated humans can be used to assist the body s own defense mechanisms. Intramuscular preparations of immune globulin may be used to prevent infection following viral exposure and as replacement therapy in individuals with antibody deficiencies. Peak plasma concentrations of intramuscular immune globulins occur in about 2 days. In contrast, intravenously administered immune globulin provides immediate passive immunity. 

There are three basic approaches to defeat segregation (6) ... 

Various methods can be employed in modeling chemical or physical processes. There are three basic approaches in the scale-up procedure (Mukhyonov et al., 1979) (a) mathematical modehng, (b) physical modeling, and (c) experimental scale-up. 

There are three basic approaches to measuring transport processes, which include diffusion, dispersion, and bulk flow phenomena. These are the following ... 

Since international justice is possible, nations should be concerned about global health inequalities and how best to respond to them. The decision on how to respond to health inequalities depends on the approach adopted to international justice. There are three basic approaches, which mirror approaches to national justice libertarianism. 

Real catalytic reactions upon solid surfaces are of great complexity and this is why they are inherently very difficult to deal with. The detailed understanding of such reactions is very important in applied research, but rarely has such a detailed understanding been achieved neither from experiment nor from theory. Theoretically there are three basic approaches kinetic equations of the mean-field type, computer simulations (Monte Carlo, MC) and cellular automata CA, or stochastic models (master equations). 

Three basic approaches have been employed to conduct the TBA test on foods. It can be performed (1) on aqueous acid extracts of food samples (see Basic Protocol 1 Tarladgis et al., 1964 Witte et al., 1970 Siu and Draper, 1978 Caldironi and Bazan, 1982 Salih et al., 1987 Bedinghaus and Ockerman, 1995), (2) on an aliquot of a steam distillate of food samples (see Alternate Protocol 1 Tarladgis et al., 1960 Igene et al., 1979 Yamauchi et al., 1982 Ke et al., 1984), and (3) on the extracted lipid portion of food samples (see Alternate Protocol 2 You-nathan and Watts, 1960 Pikul etal., 1983). The chromophore formed by the reaction of malonaldehyde with TBA is then quantified spectro-photometrically. 

Of these three basic approaches, the aqueous acid extraction TBA test (see Basic Protocol 1) may be considered the better assay for estimating the malonaldehyde content in food. In this technique, the food sample is not subjected to heat and less sample autoxidation takes place the malonaldehyde content of the sample should not be overestimated. For this reason, the extraction assay has been listed as the basic protocol to determine TBA values of foodstuffs. 

Supported liquid membranes were one of the first types of liquid membranes published in 1967 [1, 2]. There are several types of SLM, which have an origin in three basic approaches ... 

With regard to the stereochemistry, the three basic approaches are illustrated in Figure 30.2. In this figure a tick symbol (S) represents a stereogenic center where we can be assured that the stereochemistry is rigorously defined. A question mark symbol ( ) means that we can be concerned of the rigor of the stereocontrol in the chemistry, and a frown symbol ( ) means we expect a problem with the stereocontrol. 

Nitrogen regeneration can also be measured by monitoring the flow of a labeled compound from a source pool to a target pool. In the case of DON release, N-labeled NH4+ or NOs is added to a sample and the appearance of N in the DON pool is monitored over time (Bronk and Glibert, 1991). To measure a DON flux, DON must be isolated prior to mass spectrometric analysis. There are three basic approaches used to isolate DON (1) wet chemistry (e.g., Axler and Reuter, 1986 Bronk and Ward, 1999 Slawyk and Raimbault, 1995), (2) ion retardation (Bronk and GHbert, 1991 Nagao and Miyazaki, 1999), and (3) dialysis (Feuerstein et al., 1997) aU three approaches are discussed in more detail in Chapter 28 by McCarthy and Bronk (this volume). 

DON At present, there are three basic approaches used to isolate DON for tracer experiments wet chemical isolation, ion retardation or dialysis, described above. The suitability of a method is judged by its ability to remove aU of the DIN forms (NH4+, NOs", and N02 ) and to isolate the DON pool with high efSciency. Ultrafiltration is not a suitable isolation method for use in determining DON release rates because it only isolates the higher MW fraction and thus allows the LMW moieties, which are likely important short-term release products, to be lost. 

Three basic approaches have been developed for the formation of these unsaturated systems. Two of these involve direct ring-formation reactions and generally give only one of the isomers. The third method involves reaction of a preformed ring system and yields both of the possible isomers. 

Three basic approaches may be used to generate man-made radionuclides, two of which involve neutron irradiation of suitable target materials in a nuclear reactor. In one case this is to... 

There are three basic approaches (Scheme 26) to make Type 4 ligands. 

Three basic approaches underlie these gene-lnactlvatlon techniques (1) replacing a normal gene with other sequences ... 

The first high-pressure NMR studies were performed by Benedek and Purcell in the mid nineteen-fifties. They discovered that the beryllium-copper alloy Berylco-25 is nonmagnetic and that it is very suitable for high-pressure equipment for magnetic studies. Their pressurizable NMR probe (see Fig. 4.19) was similar to designs used today, and it was used at pressures up to 1 GPa (10000 atm) to study the variation with viscosity of proton relaxation times and self-diffusion eonstants in a series of liquids. Since then a variety of systems for variable-pressure experiments have been developed. Three basic approaches have been used ... 

There are three basic approaches to solving second-order sensing problems. The first method, called rank annihilation, was investigated in the 1970s as a technique to subtract a known response matrix of a pure component from a matrix of responses due to the component of interest and other interfering compounds [41]. With this technique, the known matrix of the pure component, which is of rank one, is subtracted from the complex matrix of rank greater than one. The rank of the complex matrix decreases as the amount (concentration) of the pure matrix is subtracted. When the rank drops one value, i.e. from five to four, the amount of the pure component has been completely removed and the concentration of that component is the amount subtracted. This is an iterative process which consumes a lot f time. 

Thus, the study of the reactions of initiator-derived radicals with monomers has seen the development of some novel techniques. Three basic approaches have been employed. These involve ... 

---