Download A Spectroscopic Criterion for the Benzenoid Structure in by Gibbs R.C., Shapiro C.V. PDF

By Gibbs R.C., Shapiro C.V.

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Extra resources for A Spectroscopic Criterion for the Benzenoid Structure in Some Types of Triphenylmethane Derivatives

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Proof Take any such arrangement a in a space s. Procedure. Find any deepest space in a. It can be found with a finite search since in any given a the number of crosses, and thereby the number of spaces, is finite. THEOREMS 1, 2 Call the space Sd. Now Sd is either contained in a cross or not contained in a cross. If sa is not contained in a cross, then Sd is s and there is no cross in s, and so a is already simple. If Sd is in a cross c&, then c

Let tokens of constant form 1 indicate instructions to cross the boundary of the first distinction according to the conventions already called. Call any token of variable form after its form. Call any token of constant form cross. Let indications used in the description of theorem 8 be taken out of context so that T\ P = Calí this the form of position. A CALCULUS TAKEN OUT OF THE CALCULUS Let indications used in the description of theorem 9 be taken out of context so that Call this the form of transposition.

Case 1. In this case Cd condenses with the other empty cross. Thereby, one cross is eliminated from a. Case 2. In this case Cd cancels with the other cross. Thereby, two crosses are eliminated from a. Now, since each repetition of the procedure used in case 1 or case 2 (that is to say, the procedure for an arrangement which is not simple) results in a new arrangement with one or two fewer crosses, there will come a time when, after a finite number of repetitions, a has been either reduced to one cross or eliminated completely.

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