114,689 research outputs found
Geometric Stable processes and related fractional differential equations
We are interested in the differential equations satisfied by the density of
the Geometric Stable processes
, with stability \ index and asymmetry
parameter , both in the univariate and in the
multivariate cases. We resort to their representation as compositions of stable
processes with an independent Gamma subordinator. As a preliminary result, we
prove that the latter is governed by a differential equation expressed by means
of the shift operator. As a consequence, we obtain the space-fractional
equation satisfied by the density of For some
particular values of and we get some interesting results
linked to well-known processes, such as the Variance Gamma process and the
first passage time of the Brownian motion.Comment: 12 page
From cosmic ray physics to cosmic ray astronomy: Bruno Rossi and the opening of new windows on the universe
Bruno Rossi is considered one of the fathers of modern physics, being also a
pioneer in virtually every aspect of what is today called high-energy
astrophysics. At the beginning of 1930s he was the pioneer of cosmic ray
research in Italy, and, as one of the leading actors in the study of the nature
and behavior of the cosmic radiation, he witnessed the birth of particle
physics and was one of the main investigators in this fields for many years.
While cosmic ray physics moved more and more towards astrophysics, Rossi
continued to be one of the inspirers of this line of research. When outer space
became a reality, he did not hesitate to leap into this new scientific
dimension. Rossi's intuition on the importance of exploiting new technological
windows to look at the universe with new eyes, is a fundamental key to
understand the profound unity which guided his scientific research path up to
its culminating moments at the beginning of 1960s, when his group at MIT
performed the first in situ measurements of the density, speed and direction of
the solar wind at the boundary of Earth's magnetosphere, and when he promoted
the search for extra-solar sources of X rays. A visionary idea which eventually
led to the breakthrough experiment which discovered Scorpius X-1 in 1962, and
inaugurated X-ray astronomy.Comment: This work was presented at the conference "100 Years Cosmic Ray
Physics - Anniversary of the V.F. Hess Discovery", 6-8 August, Bad
Saarow/Pieskow, Germany, where Hess landed on August 7, 1912, after discovery
of the "H\"ohenstrahlung". To be published in the Astroparticle Journa
- …