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doi: 10.1007/BF03170732pmid: N/A
(1) The rotatory dispersion of stereoisomoric 4-chloro-o-toluidino-, 5-iodo-o-toluidino-, and 3-nitro-p-toluidino-methylene camphors is found, in all the six solvents, to oboy the Drude’s one-term equation, $$[a] = \frac{K}{{\lambda ^2 - \lambda _0 ^2 }}$$ ; it is therefore simple. (2) Within the limits of experimental error, thed- andl-forms of theso compounds possess identical rotatory power. (3) In accordance with the polar series, deduced from specific inductive capacities, the NO3 group is considered to possess positive polarity and the CH3 group negative polarity. Subject to minor variations, the NO2 group is found to raise, and the CH3 group to lower the rotatory power of the parent compound. (4) The sequence (decreasing or increasing) of rotatory power of these compounds in the different solvents does not run strictly parallel with that of the dielectric constant of the solvent in which the rotatory power is determined.
doi: 10.1007/BF03170733pmid: N/A
The Dirac-matrices generate an algebra consisting of sixteen linearly independent elements. A formula is given for expressing the product of any two elements as a linear combination of these sixteen. This determines the structure of the algebra completely. It is shown that certain known identities concerning these matrices can be obtained comparatively casily by the present method. Some new identifies are also deduced.
doi: 10.1007/BF03170734pmid: N/A
It is shown in this paper that the non-zero characters of the classes of the form (n 1,n 2,…n k ) come only from partitions belonging to P1, P2,…P k . Using the recurrence relations between S-functions the characters of the classes (n 1,n 2,n 3) are expressed in terms of the known characters of the classes (n 1,n 2).
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