Discrete bilinear Radon transforms along arithmetic functions with many common values

We prove that for a large class of functions $P$ and $Q$, there exists $d\in (0,1)$ such that the discrete bilinear Radon transform $$B^{\rm dis}_{P,Q}(f,g)(n)=\sum_{m\in\mathbb{Z}\setminus\{0\}} f(n-P(m))g(n-Q(m))\frac{1}{m}$$ is bounded from $l^2\times l^2$ into $l^{1+\epsilon}$ for any $\epsilon\in (d,1)$. In particular, the boundedness holds for any $\epsilon\in (0,1)$ when $P$ (or $Q$) is the Euler totient function $\phi(|m|)$ or the prime counting function $\pi(|m|)$

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 $\nu$-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 $1$ 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$_2$-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