36,497 research outputs found
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 -finite measure unifying Brownian penalisations
Wiener integral for the coordinate process is defined under the -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 -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
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