The geometric mean is a Bernstein function

In the paper, the authors establish, by using Cauchy integral formula in the theory of complex functions, an integral representation for the geometric mean of $n$ positive numbers. From this integral representation, the geometric mean is proved to be a Bernstein function and a new proof of the well known AG inequality is provided.Comment: 10 page

One-way cloak based on nonreciprocal photonic crystal

We propose a physical concept of non-reciprocal transformation optics, by which a one-way invisible cloak is designed. The one-way invisible cloak is made of a coordinate-transformed nonreciprocal photonic crystal, showing a perfect cloaking for wave incident from one direction but acting as a perfect reflector for wave from the counter direction. The proposed design shows a high promise of applications in military, as protecting the own information to be detected but efficiently grabbing the information from the “enemy” side

A universal approach to coverage probability and throughput analysis for cellular networks

This paper proposes a novel tractable approach for accurately analyzing both the coverage probability and the achievable throughput of cellular networks. Specifically, we derive a new procedure referred to as the equivalent uniformdensity plane-entity (EUDPE)method for evaluating the other-cell interference. Furthermore, we demonstrate that our EUDPE method provides a universal and effective means to carry out the lower bound analysis of both the coverage probability and the average throughput for various base-station distribution models that can be found in practice, including the stochastic Poisson point process (PPP) model, a uniformly and randomly distributed model, and a deterministic grid-based model. The lower bounds of coverage probability and average throughput calculated by our proposed method agree with the simulated coverage probability and average throughput results and those obtained by the existing PPP-based analysis, if not better. Moreover, based on our new definition of cell edge boundary, we show that the cellular topology with randomly distributed base stations (BSs) only tends toward the Voronoi tessellation when the path-loss exponent is sufficiently high, which reveals the limitation of this popular network topology

Spin Decomposition of Electron in QED

We perform a systematic study on the spin decomposition of an electron in QED at one-loop order. It is found that the electron orbital angular momentum defined in Jaffe-Manohar and Ji spin sum rules agrees with each other, and the so-called potential angular momentum vanishes at this order. The calculations are performed in both dimensional regularization and Pauli-Villars regularization for the ultraviolet divergences, and they lead to consistent results. We further investigate the calculations in terms of light-front wave functions, and find a missing contribution from the instantaneous interaction in light-front quantization. This clarifies the confusing issues raised recently in the literature on the spin decomposition of an electron, and will help to consolidate the spin physics program for nucleons in QCD.Comment: 8 page