Phase Retrieval from Sampled Gabor Transform Magnitudes: Counterexamples

We consider the recovery of square-integrable signals from discrete, equidistant samples of their Gabor transform magnitude and show that, in general, signals can not be recovered from such samples. In particular, we show that for any lattice, one can construct functions in $$L^2({\mathbb {R}})$$ L 2 ( R ) which do not agree up to global phase but whose Gabor transform magnitudes sampled on the lattice agree. These functions have good concentration in both time and frequency and can be constructed to be real-valued for rectangular lattices.

Near-zero surface pressure assembly of rectangular lattices of microgels at fluid interfaces for colloidal lithography

Rectangular lattices of microgels at interfaces self-assemble at near zero surface pressure due to attractive quadrupolar capillary interactions and steric repulsion. They can be used for soft colloidal lithography.

Relativistic energy-dispersion relations of 2D rectangular lattices

An exactly solvable relativistic approach based on inseparable periodic well potentials is developed to obtain energy-dispersion relations of spin states of a single-electron in two-dimensional (2D) rectangular lattices. Commutation of axes transfer matrices is exploited to find energy dependencies of the wave vector components. From the trace of the lattice transfer matrix, energy-dispersion relations of conductance and valence states are obtained in transcendental form. Graphical solutions of relativistic and nonrelativistic transcendental energy-dispersion relations are plotted to compare how lattice parameters [Formula: see text], core and interstitial size of the rectangular lattice affects to the energy-band structures in a situation core and interstitial diagonals are of equal slope.