p-Nitrophenylazo-, o-nitrophenylazo-, and 2,4-dinitrophenylaso derivatives of 9-phenylfluorene and triphenylmethane have been prepared and the kinetics of their decomposition in toluene has been studied. In each case the phenylfluorenyl derivative decomposed more rapidly than the corresponding triphenylmethyl derivative, and with lower activation energy. This is ascribed to and cited as evidence for the greater resonance stabilization of phenylfluorenyl as compared with triphenylmethyl radical. The partially compensating energies and entropies of activation are discussed. The relevance of these results to the dissociation of the related hexaarylethanes is discussed. Attempts to prepare azo compounds as sources of 9-fluorenyl radical, for comparison with diphenylmethyl, are described.

The exchange of (CgHgkCH• with (CgHg)2CH2 was studied by decomposition of (CjH5)2CH-N=N-CHfCgHs)» (I) in (C6H5)2C14H2 at 60°and examination of the (CeH5)2CH-CH(CgH5)2 (II) produced for radioactivity. Little or no exchange was observed. Thiophenol, ca. 0.04 mole/1., led to diminished yield of II and 17% exchange, apparently via the reactions (CgH5)2CH• + CgHsSH (CgHg)2CH2 + CgHsS•. Irradiation of diphenyl disulfide in (CgHghCLB led to II. A few experiments with -mercaptotoluene and 2-mercaptomesitylene led to little if any exchange. Thiophenol and I in both benzene and (C6H5)2CH2 led also, in low yield, to compound III, apparently 2,2,3,3-tetraphenylethylenimine, which was also formed by decomposition of I in benzene in the presence of benzophenone azine. Analysis and interpretation of the results are given.

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We propose a novel online regularization scheme for revenue-maximization in high-dimensional dynamic pricing algorithms. The online regularization scheme equips the proposed optimistic online regularized maximum likelihood pricing (OORMLP) algorithm with three major advantages: encode market noise knowledge into pricing process optimism; empower online statistical learning with alwaysvalidity over all decision points; envelop prediction error process with time-uniform non-asymptotic oracle inequalities. This type of non-asymptotic inference results allows us to design safer and more robust dynamic pricing algorithms in practice. In theory, the proposed OORMLP algorithm exploits the sparsity structure of highdimensional models and obtains a logarithmic regret in a decision horizon. These theoretical advances are made possible by proposing an optimistic online LASSO procedure that resolves dynamic pricing problems at the process level, based on a novel use of non-asymptotic martingale concentration. In experiments, we evaluate OORMLP in different synthetic pricing problem settings and observe that OORMLP performs better than RMLP proposed in [13].Preprint. Under review.

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