Measuring the cosmic proper distance from fast radio bursts

The cosmic proper distance $d_P$ is a fundamental distance in the Universe. Unlike the luminosity and angular diameter distances, which correspond to the angular size, the proper distance is the length of light path from the source to observer. However, the proper distance has not been measured before. The recent redshift measurement of a repeat fast radio burst (FRB) can shed light on the proper distance. We show that the proper distance-redshift relation can indeed be derived from dispersion measures (DMs) of FRBs with measured redshifts. From Monte Carlo simulations, we find that about 500 FRBs with DM and redshift measurements can tightly constrain the proper distance-redshift relation. We also show that the curvature of our Universe can be constrained with a model-independent method using this derived proper distance-redshift relation and the observed angular diameter distances. Owing to the high event rate of FRBs, hundreds of FRBs can be discovered in the future by upcoming instruments. The proper distance will play an important role in investigating the accelerating expansion and the geometry of the Universe.Comment: 9 pages, 4 figures, proof versio

Design of a 2.4 GHz High-Performance Up-Conversion Mixer with Current Mirror Topology

In this paper, a low voltage low power up-conversion mixer, designed in a Chartered 0.18 μm RFCMOS technology, is proposed to realize the transmitter front-end in the frequency band of 2.4 GHz. The up-conversion mixer uses the current mirror topology and current-bleeding technique in both the driver and switching stages with a simple degeneration resistor. The proposed mixer converts an input of 100 MHz intermediate frequency (IF) signal to an output of 2.4 GHz radio frequency (RF) signal, with a local oscillator (LO) power of 2 dBm at 2.3 GHz. A comparison with conventional CMOS up-conversion mixer shows that this mixer has advantages of low voltage, low power consumption and high-performance. The post-layout simulation results demonstrate that at 2.4 GHz, the circuit has a conversion gain of 7.1 dB, an input-referred third-order intercept point (IIP3) of 7.3 dBm and a noise figure of 11.9 dB, while drawing only 3.8 mA for the mixer core under a supply voltage of 1.2 V. The chip area including testing pads is only 0.62×0.65 mm2

Log-Harnack Inequality for Stochastic Differential Equations in Hilbert Spaces and its Consequences

A logarithmic type Harnack inequality is established for the semigroup of solutions to a stochastic differential equation in Hilbert spaces with non-additive noise. As applications, the strong Feller property as well as the entropy-cost inequality for the semigroup are derived with respect to the corresponding distance (cost function)

Formation of Hydrogenated Graphene Nanoripples by Strain Engineering and Directed Surface Self-assembly

We propose a new class of semiconducting graphene-based nanostructures: hydrogenated graphene nanoripples (HGNRs), based on continuum-mechanics analysis and first principles calculations. They are formed via a two-step combinatorial approach: first by strain engineered pattern formation of graphene nanoripples, followed by a curvature-directed self-assembly of H adsorption. It offers a high level of control of the structure and morphology of the HGNRs, and hence their band gaps which share common features with graphene nanoribbons. A cycle of H adsorption/desorption at/from the same surface locations completes a reversible metal-semiconductor-metal transition with the same band gap.Comment: 11 pages, 5 figure