Concentration dependence of thermal isomerization process of methyl orange in ethanol

The thermal isomerization (TI) rates of methyl orange (MO) and 4-dimethylaminoazobenzene (DMAAB) in ethanol (EtOH) are measured. Usually TI rates of azobenzene dyes are known to be concentration independent. However, the TI rate of MO showed a concentration dependence whereas that of DMAAB did not. The TI rate of DMAAB in EtOH became larger by the addition of alkali halide. This phenomenon is caused mainly by the interaction between DMAAB and cation. MO is a derivative of DMAAB in which one end of the azobenzene is substituted by a SO3-Na+ group. The interaction with the dissociated Na+ ion is considered to be an origin of the concentration dependence of the TI rate of MO

Convergence of excursion point processes and its applications to functional limit theorems of Markov processes on a half-line

Invariance principles are obtained for a Markov process on a half-line with continuous paths on the interior. The domains of attraction of the two different types of self-similar processes are investigated. Our approach is to establish convergence of excursion point processes, which is based on It\^{o}'s excursion theory and a recent result on convergence of excursion measures by Fitzsimmons and the present author.Comment: Published in at http://dx.doi.org/10.3150/08-BEJ132 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Wiener integral for the coordinate process under the σ \sigma -finite measure unifying Brownian penalisations

Wiener integral for the coordinate process is defined under the $\sigma$-finite measure unifying Brownian penalisations, which has been introduced by Najnudel, Roynette and Yor. Its decomposition before and after last exit time from 0 is studied. This study prepares for the author's recent study of Cameron--Martin formula for the $\sigma$-finite measure

Functional limit theorems for processes pieced together from excursions

A notion of convergence of excursion measures is introduced. It is proved that convergence of excursion measures implies convergence in law of the processes pieced together from excursions. This result is applied to obtain homogenization theorems of jumping-in extensions for positive self-similar Markov processes, for Walsh diffusions and for the Brownian motion on the Sierpi\'nski gasket