A method for constructing an object support based on K-means clustering of the object-intensity distribution is newly presented in diffractive imaging. This releases the adjustment of unknown parameters in the support construction, and it is well incorporated with the Gerchberg and Saxton diagram. A simple numerical simulation reveals that the proposed method is effective for dynamically constr...

We consider N=2 supersymmetric extensions of the Camassa-Holm and HunterSaxton equations. We show that they admit geometric interpretations as Euler equations on the superconformal algebra of contact vector fields on the 1|2dimensional supercircle. We use the bi-Hamiltonian formulation to derive Lax pairs. Moreover, we present some simple examples of explicit solutions. As a byproduct of our an...

We demonstrate the use of optical pulse-shaping technique in conjunction with difference frequency generation in a non-linear optoelectronic crystal for generating synthesized waveforms at terahertz frequencies. Spectral phase modulations, programmed using Gerchberg-Saxton algorithm and prepared in a spatial light Fourier filter, produce tailored terahertz pulses, including chirped pulses, zero...

The notion of a scalar equation describing pseudo-spherical surfaces is reviewed. It is shown that if an equation admits this structure, the existence of conservation laws, symmetries, and quadratic pseudo-potentials, can be studied by geometrical means. As an application, it is pointed out that the important Camassa–Holm and Hunter–Saxton equations possess features considered to be characteris...

The Papoulis-Gerchberg algorithm has been extensively used to solve the missing data problem in band-limited signals. The interpolation of low-pass signals with this algorithm can be done if the signal bandwidth is known. In practice, the signal bandwidth is unknown and has to be estimated by the user, preventing an automatic application of the Papoulis-Gerchberg algorithm. In this paper, we pr...

In this paper we characterize the regularity structure, as well show global-in-time existence and uniqueness, of (energy) conservative solutions to Hunter-Saxton equation by using method characteristics. The major difference between current work previous results is that are able singularities energy measure their nature in a very precise manner. particular, singularities, whose temporal spatial...