350,261 research outputs found
Painlev\'e V and time dependent Jacobi polynomials
In this paper we study the simplest deformation on a sequence of orthogonal
polynomials, namely, replacing the original (or reference) weight
defined on an interval by It is a well-known fact that under
such a deformation the recurrence coefficients denoted as and
evolve in according to the Toda equations, giving rise to the
time dependent orthogonal polynomials, using Sogo's terminology. The resulting
"time-dependent" Jacobi polynomials satisfy a linear second order ode. We will
show that the coefficients of this ode are intimately related to a particular
Painlev\'e V. In addition, we show that the coefficient of of the
monic orthogonal polynomials associated with the "time-dependent" Jacobi
weight, satisfies, up to a translation in the Jimbo-Miwa -form of
the same while a recurrence coefficient is up to a
translation in and a linear fractional transformation
These results are found
from combining a pair of non-linear difference equations and a pair of Toda
equations. This will in turn allow us to show that a certain Fredholm
determinant related to a class of Toeplitz plus Hankel operators has a
connection to a Painlev\'e equation
Macroscale boundary conditions for a non-linear heat exchanger
Multiscale modelling methodologies build macroscale models of materials with
complicated fine microscale structure. We propose a methodology to derive
boundary conditions for the macroscale model of a prototypical non-linear heat
exchanger. The derived macroscale boundary conditions improve the accuracy of
macroscale model. We verify the new boundary conditions by numerical methods.
The techniques developed here can be adapted to a wide range of multiscale
reaction-diffusion-advection systems
Strongly Coupled Inflaton
We continue to investigate properties of the strongly coupled inflaton in a
setup introduced in arXiv:0807.3191 through the AdS/CFT correspondence. These
properties are qualitatively different from those in conventional inflationary
models. For example, in slow-roll inflation, the inflaton velocity is not
determined by the shape of potential; the fine-tuning problem concerns the dual
infrared geometry instead of the potential; the non-Gaussianities such as the
local form can naturally become large.Comment: 12 pages; v3, minor revision, comments and reference added, JCAP
versio
Spin Structure of the Nucleon - Status and Recent Results
After the initial discovery of the so-called "spin crisis in the parton
model" in the 1980's, a large set of polarization data in deep inelastic
lepton-nucleon scattering was collected at labs like SLAC, DESY and CERN. More
recently, new high precision data at large x and in the resonance region have
come from experiments at Jefferson Lab. These data, in combination with the
earlier ones, allow us to study in detail the polarized parton densities, the
Q^2 dependence of various moments of spin structure functions, the duality
between deep inelastic and resonance data, and the nucleon structure in the
valence quark region. Together with complementary data from HERMES, RHIC and
COMPASS, we can put new limits on the flavor decomposition and the gluon
contribution to the nucleon spin. In this report, we provide an overview of our
present knowledge of the nucleon spin structure and give an outlook on future
experiments. We focus in particular on the spin structure functions g_1 and g_2
of the nucleon and their moments.Comment: 69 pages, 46 figures. Report to be published in "Progress in Particle
and Nuclear Physics". v2 with added references and minor edit
Using Variable Dwell Time to Accelerate Gaze-Based Web Browsing with Two-Step Selection
In order to avoid the "Midas Touch" problem, gaze-based interfaces for
selection often introduce a dwell time: a fixed amount of time the user must
fixate upon an object before it is selected. Past interfaces have used a
uniform dwell time across all objects. Here, we propose a gaze-based browser
using a two-step selection policy with variable dwell time. In the first step,
a command, e.g. "back" or "select", is chosen from a menu using a dwell time
that is constant across the different commands. In the second step, if the
"select" command is chosen, the user selects a hyperlink using a dwell time
that varies between different hyperlinks. We assign shorter dwell times to more
likely hyperlinks and longer dwell times to less likely hyperlinks. In order to
infer the likelihood each hyperlink will be selected, we have developed a
probabilistic model of natural gaze behavior while surfing the web. We have
evaluated a number of heuristic and probabilistic methods for varying the dwell
times using both simulation and experiment. Our results demonstrate that
varying dwell time improves the user experience in comparison with fixed dwell
time, resulting in fewer errors and increased speed. While all of the methods
for varying dwell time resulted in improved performance, the probabilistic
models yielded much greater gains than the simple heuristics. The best
performing model reduces error rate by 50% compared to 100ms uniform dwell time
while maintaining a similar response time. It reduces response time by 60%
compared to 300ms uniform dwell time while maintaining a similar error rate.Comment: This is an Accepted Manuscript of an article published by Taylor &
Francis in the International Journal of Human-Computer Interaction on 30
March, 2018, available online:
http://www.tandfonline.com/10.1080/10447318.2018.1452351 . For an eprint of
the final published article, please access:
https://www.tandfonline.com/eprint/T9d4cNwwRUqXPPiZYm8Z/ful
- …