60,604 research outputs found
Strong laws of large numbers for sub-linear expectations
We investigate three kinds of strong laws of large numbers for capacities
with a new notion of independently and identically distributed (IID) random
variables for sub-linear expectations initiated by Peng. It turns out that
these theorems are natural and fairly neat extensions of the classical
Kolmogorov's strong law of large numbers to the case where probability measures
are no longer additive. An important feature of these strong laws of large
numbers is to provide a frequentist perspective on capacities.Comment: 10 page
Multi chiral-doublets in one single nucleus
Adiabatic and configuration-fixed constraint triaxial relativistic mean field
(RMF) approaches are developed for the first time and a new phenomenon, the
existence of multi chiral-doublets (MD), i.e., more than one pairs of
chiral doublets bands in one single nucleus, is suggested for nuclei in A~100
region, typically for Rh, based on the triaxial deformations together
with their corresponding proton and neutron configurations.Comment: 10 pages, 4 figure
An Invariance Principle of G-Brownian Motion for the Law of the Iterated Logarithm under G-expectation
The classical law of the iterated logarithm (LIL for short)as fundamental
limit theorems in probability theory play an important role in the development
of probability theory and its applications. Strassen (1964) extended LIL to
large classes of functional random variables, it is well known as the
invariance principle for LIL which provide an extremely powerful tool in
probability and statistical inference. But recently many phenomena show that
the linearity of probability is a limit for applications, for example in
finance, statistics. As while a nonlinear expectation--- G-expectation has
attracted extensive attentions of mathematicians and economists, more and more
people began to study the nature of the G-expectation space. A natural question
is: Can the classical invariance principle for LIL be generalized under
G-expectation space? This paper gives a positive answer. We present the
invariance principle of G-Brownian motion for the law of the iterated logarithm
under G-expectation
Progress on tilted axis cranking covariant density functional theory for nuclear magnetic and antimagnetic rotation
Magnetic rotation and antimagnetic rotation are exotic rotational phenomena
observed in weakly deformed or near-spherical nuclei, which are
respectivelyinterpreted in terms of the shears mecha-nism and two shearslike
mechanism. Since their observations, magnetic rotation and antimagnetic
rotation phenomena have been mainly investigated in the framework of tilted
axis cranking based on the pairing plus quadrupole model. For the last decades,
the covariant density functional theory and its extension have been proved to
be successful in describing series of nuclear ground-states and excited states
properties, including the binding energies, radii, single-particle spectra,
resonance states, halo phenomena, magnetic moments, magnetic rotation,
low-lying excitations, shape phase transitions, collective rotation and
vibrations, etc. This review will mainly focus on the tilted axis cranking
covariant density functional theory and its application for the magnetic
rotation and antimagnetic rotation phenomena.Comment: 53 pages, 19 figure
- …