Rigorous argument

D. D. Clayton, Principles of Stellar Evolution and Nucleosynthesis, McGraw-Hill 1968, University of Chicago Press 1984. This classic text is particularly well written and gives more accurate and rigorous arguments for results derived here often in a somewhat heuristic manner. A more up-to-date (though in some ways less complete) description of nuclear astrophysics is given in... 

The fact that these reactions are indeed a plausible approach to interconnect gas-phase and solution reactivity has been contested by Henchman el al. (1983). The basis for their argument is that for n = 1, reaction (30) yields Br -I- H20 + CH3OH as products, and not the solvated anion. Thus, they conclude that bulk solvent effects cannot be properly extrapolated from the data of reaction (30). While the rigorous argument is correct, the rate constant trend is very useful to show that successive solvation of the reagent anion will slow down the reaction even on a thermochemical basis. 

The determined theorist should make an orderly retreat in the face of the advancing facts. Giant fullerenes have not yet been made in bulk, so I am still free to maintain my original claims in respect of these as yet hypothetical substances. Predictions 2 and 3 were based essentially on my intuitions about the weakness of the expected interaction between big spherical molecules. I buttressed them with some highly over-simplified calculations, not hitherto published. They are more of a speculation than a rigorous argument. 

Present rigorous arguments showing why line OKD in Fig. 2.3.5 must be so drawn that area I matches area II. On what cardinal principle does this case rest ... 

A coefficient of 2 is intimateiy connected with the approximate nature of the derivation, i.e., a one-dimensional random waik with ions being permitted to jump forward and backward oniy. More rigorous arguments may yieid other vaiues for the numericai coefficient, e.g., 6. 

Valentas et al. (VI) also used a coalescence efficiency of exponential form, but gave no rigorous arguments to support their model. 

The friction coefficient y defines the timescale, y of thermal relaxation in the system described by (8.13). A simpler stochastic description can be obtained for a system in which this time is shorter than any other characteristic timescale of our system. This high friction situation is often referred to as the overdamped limit. In this limit of large y, the velocity relaxation is fast and it may be assumed to quickly reaches a steady state for any value of the applied force, that is, v = x = 0. This statement is not obvious, and a supporting (though not rigorous) argument is provided below. If true then Eqs (8.13) and (8.20) yield... 

We shall now derive relation (G.ll) using a more intuitive, albeit less rigorous argument, based on the two exact normalization conditions. 

A list of factors that act to drive risk up or down with respect of a conventional UK lesignalhng system was collected in support of a qualitative but rigorous argument that risk would not be reduced in the long-run by the strategic option of replacing the ACC with a conventional UK resignalling. 

The Ministry of Defence standard which is based upon a mathematical q)ecification and formal proofs or rigorous arguments for compliance has a lot to recommend it [5]. HowevOT, the complete plication of this standard is often not feasible and hence other methods must be u, even within the defence context. Whatever qjproach is taken, the form of the eventual program is vital, since it is an analysis of that which must provide the basis of most of the assurance procedures. This implies that the programming language used for the plication is likely to have a key role. 

---