19,013 research outputs found
Discrete bilinear Radon transforms along arithmetic functions with many common values
We prove that for a large class of functions and , there exists such that the discrete bilinear Radon transform is bounded from into
for any . In particular, the boundedness
holds for any when (or ) is the Euler totient
function or the prime counting function
Energy Efficiency in Multiuser Transmission Over Parallel Frequency Channels
Energy efficiency is an important design criterion for wireless
communications. When parallel frequency channels are used for multiuser
transmission, the channel bandwidths and user power are adjusted to maximize
the sum information rate with the bandwidth budget, the transmit power budget,
and the user-specific rate requirements. The maximum sum rate is used in
measuring the energy efficiency. With fixed or flexible bandwidths of the
frequency channels, practical methods are developed to find the total transmit
power with the unique optimal resource (bandwidth and power) allocation for
maximum energy efficiency. This resource allocation ensures that, while each
user's minimum rate requirement is satisfied, all the excess resource of the
spectrum and transmit power is dedicated to the one user with the best channel
quality. Simulation results validate the optimal solutions of total transmit
power and resource allocation that support the energy-efficient multiuser
transmission.Comment: 10 pages, 9 figure
Second-Order Necessary Conditions for Optimal Control with Recursive Utilities
The necessary conditions for an optimal control of a stochastic control
problem with recursive utilities is investigated. The first order condition is
the the well-known Pontryagin type maximum principle. When the optimal control
satisfying such first-order necessary condition is singular in some sense,
certain type of the second-order necessary condition will come in naturally.
The aim of this paper is to explore such kind of conditions for our optimal
control problem
On second variation of Perelman's Ricci shrinker entropy
In this paper we provide a detailed proof of the second variation formula,
essentially due to Richard Hamilton, Tom Ilmanen and the first author, for
Perelman's -entropy. In particular, we correct an error in the stability
operator stated in Theorem 6.3 of [2]. Moreover, we obtain a necessary
condition for linearly stable shrinkers in terms of the least eigenvalue and
its multiplicity of certain Lichnerowicz type operator associated to the second
variation.Comment: 13 pages; final version; to appear in Math. An
Aronson-B\'enilan estimates for the fast diffusion equation under the Ricci flow
We study the fast diffusion equation (FDE) with a linear forcing term under
the Ricci flow on complete manifolds with bounded curvature and nonnegative
curvature operator. We prove Aronson-B\'enilan and Li-Yau-Hamilton type
differential Harnack estimates for positive solutions of the FDE. In addition,
we use similar method to prove certain Li-Yau-Hamilton estimates for the heat
equation and conjugate heat equation which extend those obtained by X. Cao and
R. Hamilton, X. Cao, and S. Kuang and Q. Zhang to noncompact setting
Aronson-B\'enilan estimates for the porous medium equation under the Ricci flow
In this paper we study the porous medium equation (PME) coupled with the
Ricci flow on complete manifolds with bounded nonnegative curvature operator.
In particular, we derive Aronson-B\'enilan and Li-Yau-Hamilton type
differential Harnack estimates for positive solutions to the PME, with a linear
forcing term, under the Ricci flow.Comment: Minor changes to the abstract and remark 1.
Natural Hazards Twitter Dataset
With the development of the Internet, social media has become an important
channel for posting disaster-related information. Analyzing attitudes hidden in
these texts, known as sentiment analysis, is crucial for the government or
relief agencies to improve disaster response efficiency, but it has not
received sufficient attention. This paper aims to fill this gap by focusing on
investigating attitudes towards disaster response and analyzing targeted relief
supplies during disaster response. The contributions of this paper are
fourfold. First, we propose several machine learning models for classifying
public sentiment concerning disaster-related social media data. Second, we
create a natural disaster dataset with sentiment labels, which contains nearly
50,00 Twitter data about different natural disasters in the United States
(e.g., a tornado in 2011, a hurricane named Sandy in 2012, a series of floods
in 2013, a hurricane named Matthew in 2016, a blizzard in 2016, a hurricane
named Harvey in 2017, a hurricane named Michael in 2018, a series of wildfires
in 2018, and a hurricane named Dorian in 2019). We are making our dataset
available to the research community:
https://github.com/Dong-UTIL/Natural-Hazards-Twitter-Dataset. It is our hope
that our contribution will enable the study of sentiment analysis in disaster
response. Third, we focus on extracting public attitudes and analyzing the
essential needs (e.g., food, housing, transportation, and medical supplies) for
the public during disaster response, instead of merely targeting on studying
positive or negative attitudes of the public to natural disasters. Fourth, we
conduct this research from two different dimensions for a comprehensive
understanding of public opinion on disaster response, since disparate hazards
caused by different types of natural disasters.Comment: 3 pages. The dataset is available on GitHub at this address: :
https://github.com/Dong-UTIL/Natural-Hazards-Twitter-Datase
Orbital Insulators and Orbital Order-disorder Induced Metal-Insulator Transition in Transition-Metal Oxides
The role of orbital ordering on metal-insulator transition of
transition-metal oxides is investigated by the cluster self-consistent field
approach in the strong correlation regime. A clear dependence of the insulating
gap on the orbital order parameter is found in the single-particle excitation
spectra. The thermal fluctuation drives the orbital order-disorder transition,
diminishes the gap and leads to the metal-insulator transition. The interplay
between spins and orbits results in unusual temperature dependence of the
orbital polarization in the orbital insulator, which can be seen in the
resonant x-ray scattering intensity.Comment: Published versio
Behavior of ZnO-coated alumina dielectric barrier discharge in atmospheric pressure air
A complete investigation of the discharge behavior of dielectric barrier
discharge device using ZnO-coated dielectric layer in atmospheric pressure is
made. Highly conductive ZnO film was deposited on the dielectric surface.
Discharge characteristic of the dielectric barrier discharge are examined in
different aspects. Experimental result shows that discharge uniformity is
improved definitely in the case of ZnO-coated dielectric barrier discharge. And
relevant theoretical models and explanation are presented to describing its
discharge physics.Comment: 4 pages,10 figures,1 tabl
Atmospheric Escape From TOI-700 d: Venus versus Earth Analogs
The recent discovery of an Earth-sized planet (TOI-700 d) in the habitable
zone of an early-type M-dwarf by the Transiting Exoplanet Survey Satellite
constitutes an important advance. In this Letter, we assess the feasibility of
this planet to retain an atmosphere -- one of the chief ingredients for surface
habitability -- over long timescales by employing state-of-the-art
magnetohydrodynamic models to simulate the stellar wind and the associated
rates of atmospheric escape. We take two major factors into consideration,
namely, the planetary atmospheric composition and magnetic field. In all cases,
we determine that the atmospheric ion escape rates are potentially a few orders
of magnitude higher than the inner Solar system planets, but TOI-700 d is
nevertheless capable of retaining a bar atmosphere over gigayear timescales
for certain regions of the parameter space. The simulations show that the
unmagnetized TOI-700 d with a 1 bar Earth-like atmosphere could be stripped
away rather quickly ( 1 gigayear), while the unmagnetized TOI-700 d with a 1
bar CO-dominated atmosphere could persist for many billions of years; we
find that the magnetized Earth-like case falls in between these two scenarios.
We also discuss the prospects for detecting radio emission of the planet
(thereby constraining its magnetic field) and discerning the presence of an
atmosphere.Comment: ApJ Letters, in press, 8 pages, 3 figures, and 1 tabl
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