Remarks on the boundary curve of a constant mean curvature topological disc

We discuss some consequences of the existence of the holomorphic quadratic Hopf differential on a conformally immersed constant mean curvature topological disc with analytic boundary. In particular, we derive a formula for the mean curvature as a weighted average of the normal curvature of the boundary curve, and a condition for the surface to be totally umbilic in terms of the normal curvature.Comment: 6 pages, 1 figure. Version 2: comments and references adde

Please Lower Small Cell Antenna Heights in 5G

In this paper, we present a new and significant theoretical discovery. If the absolute height difference between base station (BS) antenna and user equipment (UE) antenna is larger than zero, then the network capacity performance in terms of the area spectral efficiency (ASE) will continuously decrease as the BS density increases for ultra-dense (UD) small cell networks (SCNs). This performance behavior has a tremendous impact on the deployment of UD SCNs in the 5th-generation (5G) era. Network operators may invest large amounts of money in deploying more network infrastructure to only obtain an even worse network performance. Our study results reveal that it is a must to lower the SCN BS antenna height to the UE antenna height to fully achieve the capacity gains of UD SCNs in 5G. However, this requires a revolutionized approach of BS architecture and deployment, which is explored in this paper too.Comment: Final version in IEEE: http://ieeexplore.ieee.org/document/7842150/. arXiv admin note: substantial text overlap with arXiv:1608.0669

Single-index copulae

We introduce so-called "single-index copulae". They are semi-parametric conditional copulae whose parameter is an unknown "link" function of a univariate index only. We provide estimates of this link function and of the finite dimensional unknown parameter. The asymptotic properties of the latter estimates are stated. Thanks to some properties of conditional Kendall's tau, we illustrate our technical conditions with several usual copula families.Comment: Revised version: correction of Assumption 3 and some minor induced modification

Quantum point contacts as heat engines

The efficiency of macroscopic heat engines is restricted by the second law of thermodynamics. They can reach at most the efficiency of a Carnot engine. In contrast, heat currents in mesoscopic heat engines show fluctuations. Thus, there is a small probability that a mesoscopic heat engine exceeds Carnot's maximum value during a short measurement time. We illustrate this effect using a quantum point contact as a heat engine. When a temperature difference is applied to a quantum point contact, the system may be utilized as a source of electrical power under steady state conditions. We first discuss the optimal working point of such a heat engine that maximizes the generated electrical power and subsequently calculate the statistics for deviations of the efficiency from its most likely value. We find that deviations surpassing the Carnot limit are possible, but unlikely.Comment: 9 pages, 2 figures. Contribution to the Physica E special issue on "Frontiers in quantum electronic transport" in memory of Markus Buttiker. Published versio