Qualitative and Quantitative Reasoning

After all the causal events are listed on a fault tree, the FTA allows the analyst to evaluate each event separately or in combination with other events on the tree. This provides the user with a powerful tool capable of determining, through deduction, which event or set of events led to the top event. When more than one contributing event is identified, as is usually the case, their respective locations on the fault tree are collectively referred to as a cutset. Identification and qualification of one or multiple cutsets within a fault tree facilitates the evaluation process. Essentially, the cutset isolates specific events in the system and allows for a qualitative examination of the relationship between the cutset, as a whole, and its effect on the top event. 

When the likelihood of an event is known and a probability value has been assigned, then analysis of these events on a fault tree will also yield quantitative results. As cutsets are identified, the probability of occurrence as a result of cutset interactions can be quantified and the associated risk can be more readily evaluated. 

---

Qualitative and quantitative relations between enthalpy and entropy were observed several times in the 1920 s, and their importance was rightly recognized by some authors. However, some ideas from this early work seem to have been overlooked later, perhaps because they were connected with obsolete theories or because they were developed independently in the fields of organic chemistry, catalysis, and pure physical chemistry. For this reason, a brief historical survey seems appropriate. 

The theory of electrolytic dissociation was not immediately recognized universally, despite the fact that it could qualitatively and quantitatively explain certain fundamental properties of electrolyte solutions. For many scientists the reasons for spontaneous dissociation of stable compounds were obscure. Thus, an energy of about 770kJ/mol is required to break up the bonds in the lattice of NaCl, and about 430kJ/mol is required to split H l bonds during the formation of hydrochloric acid solution. Yet the energy of thermal motions in these compounds is not above lOkJ/mol. It was the weak point of Arrhenius s theory that this mismatch could not be explained. 

The EC mechanism (Scheme 2.1) associates an electrode electron transfer with a first-order (or pseudo-first-order) follow-up homogeneous reaction. It is one of the simplest reaction schemes where a heterogeneous electron transfer is coupled with a reaction that takes place in the adjacent solution. This is the reason that it is worth discussing in some detail as a prelude to more complicated mechanisms involving more steps and/or reactions with higher reaction orders. As before, the cyclic voltammetric response to this reaction scheme will be taken as an example of the way it can be characterized qualitatively and quantitatively. 

The combined UPS and XPS facilities available in the Vacuum Generators ESCA-3 Spectrometer (the name by which the prototype became known) provided a powerful means (5, 3a) of exploring solids, their surfaces, and in turn the reasons for their inherent chemical reactivities. We shall see that XPS and UPS enable both qualitative and quantitative characterization of the solid surface at the atomic level, the chemical environment of a particular... 

The radical addition and hydrogen transfer mechanisms of inhibition by chain-breaking antioxidants are now reasonably well understood in both qualitative and quantitative terms. The electron-transfer mechanism of inhibition deserves greater attention. 

Mathematica, Interactive Physics, Spartan, and Odyssey are all available with protocols and content (sometimes from third parties) for subject-specific topics. The learning objectives, however, go beyond those of specific content. Being very different from memorization aids, method-based learning environments have at least the potential to familiarize students with the process and the principles of science. It is precisely the use of a multi-purpose tool that makes students invoke the generic reasoning skills, both qualitatively and quantitatively, that are the hallmark of a scientifically literate mind. Sometimes there is value in using fewer applications for more purposes ... 

Never use your personal financial situation as a reason for requesting more money. Comments like "I need more money to afford my mortgage, rent, or car payments" do not concern the employer. Instead, focus on the value you offer the company and be prepared to offer qualitative and quantitative information to support your statements. Your chances of receiving the salary you re seeking increases dramatically by proving to an employer you re worth it. 

The separation between qualitative and quantitative knowledge is not always as great as has been suggested. Give an example where qualitative reasoning and quantitative reasoning have interacted in classroom studies or work experience. 

In a second phase, alternative sites to locate the consolidated site were evaluated. Four sites were considered with one of the alternatives involving a co-location at an existing site and the others requiring the construction of a new site. To reflect the nature of the decision problem the objective hierarchy described above was modified to include the net present value of the alternatives in addition to the qualitative criteria. On this basis trade-offs between qualitative and quantitative objectives were analyzed. In the case example it turned out that co-locating the plant at the existing site is both the most attractive option financially (mainly because no property rent or acquisition was required) and from a qualitative perspective (mainly due to proximity of the existing site to major customers). It should be noted that no major utilities infrastructure was required for the value chain considered and hence constructing a new site could not be ruled out up front for financial reasons. 

At the present time it is hardly possible to make a final judgement about the influence of such manipulations in order to promote qualitative and quantitative changes in the biological activity. Specifications are often lacking in this matter. The clarification of the commercial use of the analogues synthesized in the laboratories of some firms is surely one reason for the few results reported so far. On the other hand many of the published results can only be interpreted very carefully, because the biological models used are different. 

No single species is a satisfactory indicator for all qualitative and quantitative effects of a compound in man. The substance is given to various species by appropriate routes. If the pattern of regression lines is similar for a variety of mammalian species, there is reason to assume a similar pattern would apply to man. However, species differences usually are found. 

---