Periodic subvarieties of a projective variety under the action of a maximal rank abelian group of positive entropy

We determine positive-dimensional G-periodic proper subvarieties of an n-dimensional normal projective variety X under the action of an abelian group G of maximal rank n-1 and of positive entropy. The motivation of the paper is to understand the obstruction for X to be G-equivariant birational to the quotient variety of an abelian variety modulo the action of a finite group.Comment: Asian Journal of Mathematics (to appear), Special issue on the occasion of Prof N. Mok's 60th birthda

Mobile robot localization using robust extended H-infinity filtering

This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2009 Institution of Mechanical Engineers.In this paper, a novel methodology is provided for accurate localization of a mobile robot using autonomous navigation based on internal and external sensors. A new robust extended H∞ filter is developed to deal with the non-linear kinematic model of the robot and the non-linear distance measurements, together with process and measurement noises. The proposed filter relies on a two-step prediction-correction structure, which is similar to a Kalman filter. Simulations are provided to demonstrate the effectiveness of the proposed method.EPSRC, the Nuffield Foundation, and the Alexander von Humboldt Foundation

Secure thermal infrared communications using engineered blackbody radiation

The thermal (emitted) infrared frequency bands, from 20–40 THz and 60–100 THz, are best known for applications in thermography. This underused and unregulated part of the spectral range offers opportunities for the development of secure communications. The ‘THz Torch' concept was recently presented by the authors. This technology fundamentally exploits engineered blackbody radiation, by partitioning thermally-generated spectral noise power into pre-defined frequency channels; the energy in each channel is then independently pulsed modulated and multiplexing schemes are introduced to create a robust form of short-range secure communications in the far/mid infrared. To date, octave bandwidth (25–50 THz) single-channel links have been demonstrated with 380 bps speeds. Multi-channel ‘THz Torch' frequency division multiplexing (FDM) and frequency-hopping spread-spectrum (FHSS) schemes have been proposed, but only a slow 40 bps FDM scheme has been demonstrated experimentally. Here, we report a much faster 1,280 bps FDM implementation. In addition, an experimental proof-of-concept FHSS scheme is demonstrated for the first time, having a 320 bps data rate. With both 4-channel multiplexing schemes, measured bit error rates (BERs) of < 10(−6) are achieved over a distance of 2.5 cm. Our approach represents a new paradigm in the way niche secure communications can be established over short links

Properties of solutions of stochastic differential equations driven by the G-Brownian motion

In this paper, we study the differentiability of solutions of stochastic differential equations driven by the $G$-Brownian motion with respect to the initial data and the parameter. In addition, the stability of solutions of stochastic differential equations driven by the $G$-Brownian motion is obtained

On cross-beam monitoring of atmospheric winds and turbulence with two orbiting telescopes

Crossed beam monitoring of atmospheric winds and turbulence with two orbiting astronomical telescopes mounted on single spacecraf