First-order point process definition

A systematic formal kinetic analysis starts with measured concentrationtime curves (e.g., in batch processes, as illustrated in Fig. 2.4 for substrate concentrations). From these data a reaction scheme can be extracted. At this point a clear differentiation must be made between reaction scheme and reaction mechanism. Due to the fictitious character of a mechanism, it may be disproven but never proven. A reaction scheme, on the other hand, can be more or less definitely established and may be extended later only if there is evidence of additional steps. From the shape of the concentration-time curves several conclusions can be made (Moser, 1983b) concerning the interpretation of apparent reaction orders n. Linearity can be a sign for transport limitation or can indicate the presence of a biosorption effect resulting in a reaction order of zero. Half- and first-order reaction can be interpreted as internal transport... 

This analysis can, for example, be applied to multistep radioactive decay reactions and to isomerization reactions. In such multistep processes, every step is by definition a first-order process. An example of multistep radioactive decay is the Actinium series (see Lederer et ah, 1968), in which Bi alpha-decays to ° T1, which beta-decays to ° Pb with respective half-lives of 2.14 and 4.77 min. Therefore, in this two-step consecutive process, k J ki =/9 = 2.14/4.77 = 0.449, very close to the Acme point. Similarly, in the Radium series, Pb beta-decays to which beta-decays to Po, which then alpha-decays very rapidly (with a half-life of only 0.16 ms) to ° Pb. This multistep decay can be closely approximated by two steps, the first with a half-life of 27 min, the second with a half-life... 

Hazardous waste identification begins with an obvious point in order for any material to be a hazardous waste, it must first be a waste. However, deciding whether an item is or is not a waste is not always easy. For example, a material (like an aluminum can) that one person discards could seem valuable to another person who recycles that material. U.S. EPA therefore developed a set of regulations to assist in determining whether a material is a waste. RCRA uses the term solid waste in place of the common term waste. Under RCRA, the term solid waste means any waste, whether it is a solid, semisolid, or liquid. The first section of the RCRA hazardous waste identification regulations focuses on the definition of solid waste. For this chapter, you need only understand in general terms the role that the definition of solid waste plays in the RCRA hazardous waste identification process. 

We shall presently describe the derivation of certain coherent excitations on the basis of definite physical models. Such developments show that random energy supplied to a certain system need not lead to heating but may result in the excitation of ordered (coherent) states. This need not imply that other models could not lead to similar excitations, i.e., that a multicausal situation exists— in other words that experimental verification of the excitation need not necessarily be considered as proof of a particular model. Clearly a situation then arises which requires close collaboration between theory and experiment. Thus, e.g., theory has predicted certain coherent excitations and experiment verifies their existance. This presents a development from the point of view of physics. From the point of view of biology, however, we may ask a question that is prohibited in physics what is the purpose of these excitations Evidence will be presented later in this chapter for the first (physical) stage, but the second, biological question has hardly been touched yet. Its solution will, of course, lead back again to physics, i.e., a certain process has certain consequences. 

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