In this paper we study the relation between module amenability of $theta$-Lau product $A×_theta B$ and that of Banach algebras $A, B$. We also discuss module biprojectivity of $A×theta B$. As a consequent we will see that for an inverse semigroup $S$, $l^1(S)×_theta l^1(S)$ is module amenable if and only if $S$ is amenable.

Abstract Illumination with LEDs is of increasing interest in imaging and lithography. In particular, compared to lasers, are temporally spatially incoherent, so that speckle effects can be avoided by the application LEDs. Besides, LED arrays qualified due their high optical output power. However, have not been widely used for investigating effects, e.g., Lau effect. this paper, we propose an ar...

Talbot and Talbot-Lau effects are frequently used in lensless imaging applications with light, ultrasound, x-rays, atoms and molecules--generally in situations where refractive optical elements are non-existent or not suitable. We here show an experimental visualization of the intriguing wave patterns that are associated with near-field interferometry behind a single periodic diffraction gratin...

We present an electron interferometer based on near-field diffraction from two nanostructure gratings. Lau fringes are observed with an imaging detector, and revivals in the fringe visibility occur as the separation between gratings is increased from 0 to 3 mm. This verifies that electron beams diffracted by nanostructures remain coherent after propagating farther than the Talbot length zT = 2d...