37,386 research outputs found
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
A Conditional Approach to Panel Data Models with Common Shocks
This paper studies the effects of common shocks on the OLS estimators of the slopes’ parameters in linear panel data models. The shocks are assumed to affect both the errors and some of the explanatory variables. In contrast to existing approaches, which rely on using results on martingale difference sequences, our method relies on conditional strong laws of large numbers and conditional central limit theorems for conditionally-heterogeneous random variables
Stability Analysis of Optimal Velocity Model for Traffic and Granular Flow under Open Boundary Condition
We analyzed the stability of the uniform flow solution in the optimal
velocity model for traffic and granular flow under the open boundary condition.
It was demonstrated that, even within the linearly unstable region, there is a
parameter region where the uniform solution is stable against a localized
perturbation. We also found an oscillatory solution in the linearly unstable
region and its period is not commensurate with the periodicity of the car index
space. The oscillatory solution has some features in common with the
synchronized flow observed in real traffic.Comment: 4 pages, 6 figures. Typos removed. To appear in J. Phys. Soc. Jp
Spin and Charge Structure of the Surface States in Topological Insulators
We investigate the spin and charge densities of surface states of the
three-dimensional topological insulator , starting from the continuum
description of the material [Zhang {\em et al.}, Nat. Phys. 5, 438 (2009)]. The
spin structure on surfaces other than the 111 surface has additional complexity
because of a misalignment of the contributions coming from the two sublattices
of the crystal. For these surfaces we expect new features to be seen in the
spin-resolved ARPES experiments, caused by a non-helical spin-polarization of
electrons at the individual sublattices as well as by the interference of the
electron waves emitted coherently from two sublattices. We also show that the
position of the Dirac crossing in spectrum of surface states depends on the
orientation of the interface. This leads to contact potentials and surface
charge redistribution at edges between different facets of the crystal.Comment: Use the correct spin operator. Changes affect the surface states spin
structure, but not the spectru
Pupillometry, a bioengineering overview
The pupillary control system is examined using a microprocessor based integrative pupillometer. The real time software functions of the microprocessor include: data collection, stimulus generation and area to diameter conversion. Results of an analysis of linear and nonlinear phenomena are presented
Fully automated urban traffic system
The replacement of the driver with an automatic system which could perform the functions of guiding and routing a vehicle with a human's capability of responding to changing traffic demands was discussed. The problem was divided into four technological areas; guidance, routing, computing, and communications. It was determined that the latter three areas being developed independent of any need for fully automated urban traffic. A guidance system that would meet system requirements was not being developed but was technically feasible
Topological Insulators
Topological insulators are electronic materials that have a bulk band gap
like an ordinary insulator, but have protected conducting states on their edge
or surface. The 2D topological insulator is a quantum spin Hall insulator,
which is a close cousin of the integer quantum Hall state. A 3D topological
insulator supports novel spin polarized 2D Dirac fermions on its surface. In
this Colloquium article we will review the theoretical foundation for these
electronic states and describe recent experiments in which their signatures
have been observed. We will describe transport experiments on HgCdTe quantum
wells that demonstrate the existence of the edge states predicted for the
quantum spin Hall insulator. We will then discuss experiments on Bi_{1-x}Sb_x,
Bi_2 Se_3, Bi_2 Te_3 and Sb_2 Te_3 that establish these materials as 3D
topological insulators and directly probe the topology of their surface states.
We will then describe exotic states that can occur at the surface of a 3D
topological insulator due to an induced energy gap. A magnetic gap leads to a
novel quantum Hall state that gives rise to a topological magnetoelectric
effect. A superconducting energy gap leads to a state that supports Majorana
fermions, and may provide a new venue for realizing proposals for topological
quantum computation. We will close by discussing prospects for observing these
exotic states, a well as other potential device applications of topological
insulators.Comment: 23 pages, 20 figures, Published versio
Thermodynamics, strange quark matter, and strange stars
Because of the mass density-dependence, an extra term should be added to the
expression of pressure. However, it should not appear in that of energy
according to both the general ensemble theory and basic thermodynamic
principle. We give a detail derivation of the thermodynamics with
density-dependent particle masses. With our recently determined quark mass
scaling, we study strange quark matter in this new thermodynamic treatment,
which still indicates a possible absolute stability as previously found.
However, the density behavior of the sound velocity is opposite to the previous
finding, but consistent with one of our recent publication. We have also
studied the structure of strange stars using the obtained equation of state.Comment: 6 pages, 6 PS figures, REVTeX styl
Power-law behavior in the power spectrum induced by Brownian motion of a domain wall
We show that Brownian motion of a one-dimensional domain wall in a large but
finite system yields a power spectrum. This is successfully
applied to the totally asymmetric simple exclusion process (TASEP) with open
boundaries. An excellent agreement between our theory and numerical results is
obtained in a frequency range where the domain wall motion dominates and
discreteness of the system is not effective.Comment: 4 pages, 4 figure
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