Monotone and boolean unitary Brownian motions

The additive monotone (respectively boolean) unitary Brownian motion is a non-commutative stochastic process with monotone (respectively boolean) independent and stationary increments which are distributed according to the arcsine law (respectively Bernoulli law). We introduce the monotone and boolean unitary Brownian motions and derive a closed formula for their associated moments. This provides a description of their spectral measures. We prove that, in the monotone case, the multiplicative analog of the arcsine distribution is absolutely continuous with respect to the Haar measure on the unit circle, whereas in the boolean case the multiplicative analog of the Bernoulli distribution is discrete. Finally, we use quantum stochastic calculus to provide a realization of these processes as the stochastic exponential of the correspending additive Brownian motions.

APLIKASI SIMULASI BERBASIS WEB UNTUK SUHU DAN KALOR PADA MATA PELAJARAN FISIKA BAGI SISWA SMA KELAS X

Physics is one of the subjects studied in high school . Many argue that one of the lessons of physics become less desirable , one reason because physics contains many abstract concepts and magnitudes . One material that is in high school physics is fluid mechanics , including fluid static and dynamic fluid . Static fluid include law pascal and archimedes law , while the law include the dynamic fluid continuity and Bernoulli law . During this learning method is applied mostly still conventional , inside delivery media still use the board as well as the extent of the image of the book . Still at least the lack of visualization of dynamic and interactive learning media that makes the lack of interest in learning physics , it made for a multimedia -based simulation applications of fluid mechanics in physics . The method used in the design and manufacture of this application is the waterfall methodology and multimedia development stages. Software used in the making of this application is Adobe Flash CS3 with actionscript 2.0 programming language for multimedia applications . While web applications built using PHP and MySQL software .