Recently, a Hamiltonian regularised shallow water (Saint-Venant) system has been introduced by Clamond and Dutykh (2018). This is Galilean invariant, linearly non-dispersive conserves formally an H1-like energy. In this paper, we extend regularisation in two directions. First, consider the more general barotropic Euler system, equations being very special case. Second, introduce class regularis...

The paper belongs to the field of ultrafast optics. Acousto-optic pulse shaping has been studied experimentally for binary intensity modulation in a chirped amplification laser system. Direct time-domain measurement rise/fall time with picosecond streak camera was performed Ti:sapphire regenerative amplifier. It discovered that sign second order dispersion produced by acousto-optic delay line a...

A set of nonnegative integers is called a Sidon if there no 4-tuple, i.e., (a, b, c, d) in with + b = c d and {a, b} ∩ {c, d} ∅. Cameron Erdős proposed the problem determining number sets [n]. Results Kohayakawa, Lee, Rodl Samotij, Saxton Thomason have established that between 2 (1.16+o(1))√n (6.442+o(1))√n . An α-generalized [n] at most α 4-tuples. One way to extend estimate We show (n/ log4 n...

In this paper, we prove a sparse random analogue of the Van der Waerden Theorem. We show that, for all $r > 2$ and $q_1 \geq q_2 \dotsb q_r 3 \in \mathbb{N}$, $n^{-\frac{q_2}{q_1(q_2-1)}}$ is threshold following property: For every $r$-coloring $p$-random subset $\{1,\dotsc,n\}$, there exists monochromatic $q_i$-term arithmetic progression colored $i$, some $i$. This extends results Rödl Ruc...

Meadow, S. R., Cameron, J. S., Ogg, C. S., and Saxton, H. M. (1971). Archives of Disease in Childhood, 46, 221. Children referred for acute dialysis. Acute unexplained renal failure of infancy and childhood is a rewarding condition to treat. Of 27 children referred for acute dialysis, only 3 died. Half were managed without dialysis, and of those dialysed, 6 recovered full or adequate renal func...

Phase-retrieval measurements of point-spread functions from the pre- and post-repair Hubble Space Telescope are presented. The primary goal was to determine the aberrations present in the second wide-field and planetary camera (WFPC2) to align and validate its corrective optics. With both parametric model-fitting techniques and iterative (Gerchberg-Saxton) methods, accurate measurements have be...

The discrete sampling of a wave-front using a Shack-Hartmann sensor limits the maximum spatial frequency we can measure and impacts sensitivity to frequencies at the high end of the correction band due to aliasing. Here we present Wiener filters for wave-front reconstruction in the spatial-frequency domain, ideally suited for systems with a high number of degrees of freedom. We develop a theore...

The two-headed motor protein kinesin hydrolyzes nucleotide to move unidirectionally along its microtubule track at speeds up to 1000 nm/s (Saxton et al., 1988) and develops forces in excess of 5 pN (Hunt et al., 1994; Svoboda et al., 1994a). Individual kinesin molecules have been studied recently in vitro, and their behavior has been characterized in terms of force-velocity curves and variance ...

We present a new formulation of a family of proximity operators that generalize the projector step for phase retrieval. These proximity operators for noisy intensity measurements can replace the classical "noise-free" projection in any projection-based algorithm. They are derived from a maximum-likelihood formulation and admit closed form solutions for both the Gaussian and the Poisson cases. I...