Analytic proposition

Even beyond the intellectual and argumentative use of words for scientific or analytic propositions, there is a need to be sensitive to their values and appropriateness for the matter on hand. Again T. S. Eliot (Four Quartets, Burnt Norton, lines 149-58) says,... 

At 270°C adipic acid decomposesf to the extent of 0.31 mol % after 1.5 hr. Suppose an initially equimolar mixture of adipic acid and diol achieves a value of p = 0.990 after 1.5 hr. Compare the expected and observed values of n in this experiment. Criticize or defend the following proposition The difference between the observed and expected values would be even greater than calculated above if, instead of the extent of reaction being measured analytically, the value of p expected (neglecting decomposition) after 1.5 hr were calculated by an appropriate kinetic equation. 

The nature of the adsorbed species can be inferred from the usual chemical parameters, i.e. chemical shifts, linewidths and relaxation times. These latter allow the study of the mobility on the surfaces. As an analytical tool, C-NMR spectroscopy can also be used to determine the concentration of reactants or products as a function of time and hence kinetic constants can easily be determined. As a conclusion, a rather complete kinetic study can be carried out involving the nature of interaction between the admolecule and the surface and eventually the nature of the surface active centers. One can finally arrive at the proposition of a reaction mechanism. 

We have had a number of successful projects with Oak Ridge in both ceramics and analytical development. These projects shared four common characteristics They met a defined business need for Dow and met the mission of the laboratory, each had a champion in Dow and at Oak Ridge, each had defined deliverables, and there was a win-win proposition for both Oak Ridge and Dow. 

For the Greeks and particularly for Plato, episteme and techne represented knowledge of an order completely different from metis. Technical knowledge, or techne, could be expressed precisely and comprehensively in the form of hard-and-fast rules (not rules of thumb), principles, and propositions. At its most rigorous, techne is based on logical deduction from self-evident first principles. As an ideal type, it radically differs from metis in terms of how it is organized, how it is codified and taught, how it is modified, and the analytical precision it exhibits. 

A major step forward in the theory of pseudopotentials was the introduction of a norm-conservation condition with the proposition by Hamann, Schliiter and Chiang [155] of a set of conditions to ensure transferability of pseudopotentials. Different recipes for constructing pseudopotentials satisfying these conditions have been proposed. They can be either analytic [155,156] or numeric [157] and also differ by the way valence wave functions are made smooth in the core region. 

The Choice of the Optimal Starting Set of Analytical Techniques. Seldom is a solids and surfaces problem presented in pure analytical terms. Therefore, the first step is to derive a working hypothesis which can relate the observed behavior of a material to its possible composition and structure. This should result in a microscopic model, which can range from a complete, quantitative proposition to a mere classification of the problem area. The detail of the model, in general, reflects the detail of the desired analytical result. 

Definition 5 and Proposition 2 set up the category of affine varieties in precise analogy with the category of topological spaces, differentiable manifolds, and analytic spaces. There are, however, some very categorical differences between these examples. Consider the following statement ... 

The balancing procedures described above start with a raw output composition vector and seek to produce a corrected output composition vector whose molar contents and atomic balances are such that they present a solution closest to a perfect balance in each of the components. The adjustments made to the raw data will in principle remove the analytical error present in the raw data and will quickly alert the operator to the presence of systematic or unusual random errors in the analysis. The procedures used for this purpose are based cm the self-evident proposition that mass and atomic balances must all close between the input and the output of the reactor. 

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