Limit of Fractional Power Sobolev Inequalities

We derive the Moser-Trudinger-Onofri inequalities on the 2-sphere and the 4-sphere as the limiting cases of the fractional power Sobolev inequalities on the same spaces, and justify our approach as the dimensional continuation argument initiated by Thomas P. Branson.Comment: 17 page

Some higher order isoperimetric inequalities via the method of optimal transport

In this paper, we establish some sharp inequalities between the volume and the integral of the $k$-th mean curvature for $k+1$-convex domains in the Euclidean space. The results generalize the classical Alexandrov-Fenchel inequalities for convex domains. Our proof utilizes the method of optimal transportation.Comment: 21 page

Strange metal in paramagnetic heavy-fermion Kondo lattice: Dynamical large-N fermionic multi-channel approach

The mechanism of strange metal (SM) with unconventional charge transport near magnetic phase transitions has become an outstanding open problem in correlated electron systems. Recently, an exotic quantum critical SM phase was observed in paramagnetic frustrated heavy-fermion materials near Kondo breakdown. We establish a controlled theoretical framework to this issue via a dynamical large-N fermionic multichannel approach to the two-dimensional Kondo-Heisenberg lattice model, where KB transition separates a heavy-Fermi liquid from fermionic spin-liquid state. With Kondo fluctuations being fully considered, we find a distinct SM behavior with quasi-linear-in-temperature scattering rate associated with KB. When particle-hole symmetry is present, signatures of a critical spin-liquid SM phase as $T \rightarrow 0$ are revealed with $\omega/T$ scaling extended to a wide range. We attribute these features to the interplay of critical bosonic charge (Kondo) fluctuations and gapless fermionic spinons. The implications of our results for the experiments are discussed.Comment: 6 pages, 4 figure

Are there contagion effects in the REIT market? The case of Brexit

On June 23, 2016 the Brexit event that tremendously surprised and shocked investors around the world was considered the largest black swan with a political earthquake in 2016, and even spread to the international financial market and real estate market. This study uses the heteroscedasticity biases based on correlation coefficients by Forbes and Rigobon and the GJR-GARCH model to examine the contagion effects of the Brexit event on global REITs markets. The data are collected at the daily interval covering the time period from June 23, 2015 to December 30, 2016. Evidence reveals that no REITs markets suffered from Brexit, suggesting no transmission of Brexit across REITs markets, even the neighbouring markets, is found

Performance Analysis of a Near-Field Thermophotovoltaic Device with a Metallodielectric Selective Emitter and Electrical Contacts for the Photovoltaic Cell

A near-field thermophotovoltaic (TPV) system with a multilayer emitter of alternate tungsten and alumina layer is proposed in this paper. The fluctuational electrodynamics along with the dyadic Green function for a multilayered structure is applied to calculate the spectral heat flux, and the charge transport equations are solved to get the photocurrent generation and electrical power output. The spectral heat flux is much enhanced when plain tungsten emitter is replaced with multilayer emitter. The mechanism of surface plasmon polariton coupling in the tungsten thin film, which is responsible for the heat flux enhancement, is analyzed. In addition, the invalidity of effective medium theory to predict the optical properties of multilayer structure in near-field radiation is discussed. The tungsten and alumina layer thicknesses are optimized to match the spectral heat flux with the bandgap of TPV cell. Practically, with a gold reflector placed on the back of TPV cell, which also acts as the back electrode, and a 5-nm-thick indium tin oxide (ITO) layer as the front contact, when the emitter and receiver temperature are respectively set as 2000 K and 300 K, the conversion efficiency and electrical power output can be achieved to 23.7% and 0.31 MW/m2 at a vacuum gap distance of 100 nm

Optimal Real-time Spectrum Sharing between Cooperative Relay and Ad-hoc Networks

Optimization based spectrum sharing strategies have been widely studied. However, these strategies usually require a great amount of real-time computation and significant signaling delay, and thus are hard to be fulfilled in practical scenarios. This paper investigates optimal real-time spectrum sharing between a cooperative relay network (CRN) and a nearby ad-hoc network. Specifically, we optimize the spectrum access and resource allocation strategies of the CRN so that the average traffic collision time between the two networks can be minimized while maintaining a required throughput for the CRN. The development is first for a frame-level setting, and then is extended to an ergodic setting. For the latter setting, we propose an appealing optimal real-time spectrum sharing strategy via Lagrangian dual optimization. The proposed method only involves a small amount of real-time computation and negligible control delay, and thus is suitable for practical implementations. Simulation results are presented to demonstrate the efficiency of the proposed strategies.Comment: One typo in the caption of Figure 5 is correcte