We prove that there exists an extremal function to the Airy Strichartz inequality ‖e−t∂3 xf‖L8t,x(R×R) ≤ C‖f‖L2(R), by using the linear profile decomposition. Furthermore we show that, if f is an extremal, then f is exponentially decaying in the Fourier space and so f can be extended to be an entire function on the complex domain.

Owing to the distinguishing properties of nondiffraction, self-healing, and transverse acceleration, Airy beams have attracted much attention in the past decade. To date, a simple approach for exquisitely fabricating cubic phase plates with both continuous variation of phase and micro size still remains challenging, which limits the generation of high-quality Airy beams for integrated micro-opt...

Here we study systematically the self-focusing dynamics and collapse of vortex Airy optical beams in a Kerr medium. The collapse is suppressed compared to a non-vortex Airy beam in a Kerr medium due to the existence of vortex fields. The locations of collapse depend sensitively on the initial power, vortex order, and modulation parameters. The collapse may occur in a position where the initial ...

We have investigated the effect of Airy illumination on the image quality and depth penetration of digitally scanned light-sheet microscopy in turbid neural tissue. We used Fourier analysis of images acquired using Gaussian and Airy light-sheets to assess their respective image quality versus penetration into the tissue. We observed a three-fold average improvement in image quality at 50 μm dep...

A field emitter array held at the threshold of emission by a dc gate potential from which current pulses are triggered by the application of a laser pulse on the backside of the semiconductor may produce electron bunches ~‘‘density modulation’’! at gigahertz frequencies. We develop an analytical model of such optically controlled emission from a silicon tip using a modified Wentzel– Kramers–Bri...

In this research, mechanical buckling of rectangular plates of functionally graded materials (FGMs) is considered. Equilibrium and stability equations of a FGM rectangular plate under uniform in-plane compression are derived. For isotropic materials, convergent buckling loads have been presented for non-uniformly compressed rectangular plates based on a rigorous superposition fourier solution f...

The equilibrium of a membrane shell is governed by Pucher’s equation that described in terms the relations among external load, shape shell, and Airy stress function. Most existing funicular form-finding algorithms take discretized network as input find shape. When resulting does not meet user’s expectation, there no direct clue on how to revise input. paper utilizes method radial basis functio...

The localization of fluorescent microspheres is often employed for drift correction and image registration in single molecule microscopy, and is commonly carried out by fitting a point spread function to the image of the given microsphere. The mismatch between the point spread function and the image of the microsphere, however, calls into question the suitability of this localization approach. ...