Propagation terminology

In Figure 1.15, the propagator of free self-diffusion is shown. Actually, selfdiffusion was the first case where the propagator terminology was discussed in the NMR context by Karger (see also Chapter 3.1). The propagator of free diffusion is of... 

We envisage the propagation step as the addition of the components of the ester across the double bond of the monomer in modern terminology this is an insertion reaction. Whether this reaction occurs through a 4-centre or a 6-centre transition state, as shown below, is not clear. 

Another important contribution of the referenced terminology was the fault - error - failure -. .. chain, which provides a deeper understanding of fault propagation, fault containment and fault consequences in critical systems A fault in a hardware part, component or subsystem may lead to an erroneous state of this element of the system, which may lead to a failure of this element (the fault is the cause of the error respectively failure, the failure the consequence of the fault respectively error). The failing component constitutes a fault of the subsystem where it is embedded, and so on. This is... 

The waves that can propagate in a solid depend upon both the properties of the solid and its boundaries [1], Figure 2.1 shows schematically the waves that can propagate in an unbounded solid, a semi-infinite solid having a single plane boundary, and in a solid plate that has two plane boundaries. The terminology, definitions and analyses that follow in this chapter are used to determine the nature of these wave motions and the phase velocities of the waves in particular solids. 

As noted, the transient nature of most free radical species is a major consideration in ESR studies of free radicals. Free radical chemistry [77] involves an initiation step in which the free radicals are formed, often followed by one or more propagation (chain) reactions before termination. Because most radical-radical termination reactions are fast, the majority of free radicals decay rapidly by self reaction, i.e., they are transient even in the absence of another species. (In non-transient, i.e., persistent, radicals the radical center is sterically hindered, thereby inhibiting self-reaction.) A comment on terminology may be appropriate at this point many transient radicals are frequently described as stable or unreactive, which can lead to some confusion. The source of this confusion is that reactivity and stability are often used to denote... 

It should be noted that in the literature the term single-file diffusion has sometimes been used to indicate only the mutual steric hindrance of the molecules in zeolite channels and not the additional constraint of an absolute exclusion of their mutual passage. Such terminology is clearly misleading since in this case molecular propagation would also be subjected to Pick s laws. 

Analysis of Green s functions can be useful in seeking to establish model hamil-tonians with the property of giving approximately correct propagators, when put in the equations of motion. In this section, we explore a particularly simple model in order to familiarize the reader with various molecular orbital concepts using the terminology of Green s function theory. We employ the Hartree-Fock approximation and seek the molecular Fock operator matrix elements... 

In order to mathematically describe the IPUE, Fukuda defined two additional reactivity ratios in the PUM, that is, 1 = 211/ 111 and 52= 122/ 222- When this terminology is used to describe the average propagation rate constant as a function of the monomer feed composition, the expressions as shown in eqns [33] and [34] apply ... 

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