In this paper, the $L^p(\mathbb{R})\times L^q(\mathbb{R})\rightarrow L^r(\mathbb{R})$ boundedness of the bilinear oscillatory integral along parabola

\begin{equation*}T_\beta(f, g)(x)=p.v.\int_{{\mathbb R}} f(x-t)g(x-t^{2})\,{\rm e}^{i |t|^{\beta}}\,\frac{{\rm d}t}{t}\end{equation*}

$\frac{1}{p}+\frac{1}{q}=\frac{1}{r}$

$\frac{1}{2}\lt r\lt\infty$

$L^\infty\times L^2\to L^2$

A ship's perception of risk is an important basis for collision avoidance. To improve such perception, several risk measurement parameters on the ship domain are determined, including the approach factor, the time to domain violation (TDV) and the possible collision domain. Then, a risk hierarchy prewarning (RHP) model based on the violation detection of a ship domain is proposed, in which a two-level alarm scheme is adopted accordingly. A low-intensity alarm will be activated by reaching the minimum approach factor and the TDV threshold, and a high-intensity alarm will be activated by the factor of the possible collision domain and the TDV threshold. Subsequently, a novel guard zone in ARPA radar utilising the RHP model has been developed to establish a ship's risk perception system for officers on watch at sea. The model proposed in this paper can not only enhance the veracity of risk assessment around our own ship, but also be used as a decision support system for collision avoidance.

This paper uses population synthesis to investigate the possible origin of isolated millisecond pulsars as born from the coalescence of a neutron star and a white dwarf. Results show that the galactic birth rate of isolated millisecond pulsars is likely to lie between 5.8×10−5 yr−1 and 2.0×10−4 yr−1, depending on critical variables, such as the stability of mass transfer via the Roche lobe and the value of kick velocity. In addition to this, this paper estimates that the solar mass of isolated millisecond pulsars can range from 1.5 and 2.0 Mʘ, making them more massive than other ‘normal’ pulsars. Finally, the majority of isolated millisecond pulsars in our simulations have spin periods ranging from several to 20 ms, which is consistent with previous observations.

Gravitational lensing is one of most promising tools to probe dark energy and dark matter in our Universe. Lensing by larger-scale structures distorts the shape of background galaxies. For ground-based observations the shape is further distorted by atmospheric turbulence and optical distortions. Many algorithms were proposed to measure the shear signal but the systematic biases are still too large to be acceptable for the larger-sky surveys in the future. I will present our new algorithms for PSF reconstruction and shape measurements based on several sets of basis functions.

A Gw-level high-power CO2 laser system has been developed. A short laser pulse is cut out with a double Pockels cell electrooptical shutter from a hybrid CO2 laser oscillator and amplified with a three-stage dual-path TEA preamplifier, a two-stage TEA preamplifier, a large aperture TEA amplifier, and an electron beam-controlled final amplifier. All parts of the laser system are controlled with a control system. The laser output power is up to 3.2 × 109 W and laser pulse width is 4 ns full width at half maximum.