Proof knowledge

The way of discovery and proof the route by which a discipline verifies its knowledge... 

Regarding the "ancestral lineage" on the poster, Democritus, of course, takes first place. Then comes John Dalton (1766-1844), an unassuming religious person whose broad scientific knowledge was self-taught. With his law of multiple proportions of the elements in their different chemical compounds, he rightfully saw indirect proof for the existence of atoms. He represented them as... 

As we explained earlier, the difficulty in this formulation is that generalized coordinates appear explicitly in the form of the Jacobian J, which may be difficult to calculate in many cases. It is therefore desirable to find an expression in which the explicit knowledge of the generalized coordinates is not required. This is done in Sect. 4.4. We end this section with a proof of (4.14). 

Q. But, Professor, the prosecution regards the participation in such meetings as proof of knowledge of the warlike intentions of Hitler. 

To read this book the reader only needs to know the basics of algebraic geometry. For instance the knowledge of [Hartshorne (1)], is certainly enough, but also that of [Eisenbud-Harris (1)] suffices for reading most parts of the book. At some points a certain familiarity with the functor of points (like in the last chapter of [Eisenbud-Harris (1)]) will be useful. Of course we expect the reader to accept some results without proof, like the existence of the Hilbert scheme and obviously the Weil conjectures. 

Note added in proof It is only very recently that it has been recognized that there can be several forms of H20(as). Consequently, not all of the relevant deposition parameters have been adequately controlled in each experiment. Even when pure H20(as) has been made, the form deposited may not be that expected from only a knowledge of the temperature of the substrate. In future experimental studies more attention will have to be given to, e.g. the angle of incidence of the vapor on the substrate, the rate of deposition and the consequent surface temperature, etc. 

Reaction mechanisms are also defined for electroorganic reactions, induced by or including an electron transfer at an electrode. Knowledge of such electrode reaction mechanisms includes, preferably but not exclusively, the potential at which the reaction proceeds, the proof of intermediates, the electron stoichiometry, the kinetics of the various reaction steps, and the transport properties of the species involved. Recently, the terms... 

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