Related papers: Multidimensional Wavelets for Scalable Image Decom…
Multi-time wave functions are wave functions for multi-particle quantum systems that involve several time variables (one per particle). In this paper we contrast them with solutions of wave equations on a space-time with multiple timelike…
The integration of two-dimensional (2D) materials with photonic structures has catalyzed a wide spectrum of optical and optoelectronic applications. Conventional nanophotonic structures generally lack efficient reconfigurability and…
The ideal imaging system would efficiently capture information about all fundamental properties light: intensity, direction, wavelength, and polarization. Most common imaging systems only map the spatial degrees of freedom of light onto a…
Decomposing the field scattered by an object into vector spherical harmonics (VSH) is the prime task when discussing its optical properties on more analytical grounds. Thus far, it was frequently required in the decomposition that the…
We propose a number of variational regularisation methods for the estimation and decomposition of motion fields on the $2$-sphere. While motion estimation is based on the optical flow equation, the presented decomposition models are…
In pursuit of a minimal basis for systems with non-ideal bond angles, in this work we try to pinpoint the exact orientation of the major overlapping orbitals along the nearest neighbouring coordination segments in a given system such that…
This paper aims at presenting a new approach to the electro-sensing problem using wavelets. It provides an efficient algorithm for recognizing the shape of a target from micro-electrical impedance measurements. Stability and resolution…
We analyze several models of atomic detectors in the context of the measurement of coherence properties of matter waves. In particular, we show that an ionization scheme measures normally-ordered correlation functions of the Schr\"odinger…
We develop a general notion of orthogonal wavelets `centered' on an irregular knot sequence. We present two families of orthogonal wavelets that are continuous and piecewise polynomial. We develop efficient algorithms to implement these…
In this note we propose a new set of coordinates to study the hyperbolic or non-elliptic cubic nonlinear Schrodinger equation in two dimensions. Based on these coordinates, we study the existence of bounded and continuous hyperbolically…
Recent investigations (e.g. Han et al. 2001) have shown that fitting the Hipparcos observations with an orbital model when the astrometric wobble caused by the companion is below the noise level can have rather unexpected consequences. With…
Wavelets are widely used in various disciplines to analyse signals both in space and scale. Whilst many fields measure data on manifolds (i.e., the sphere), often data are only observed on a partial region of the manifold. Wavelets are a…
This paper aims at developing new shape functions adapted to smooth vanishing coefficients for scalar wave equation. It proposes the numerical analysis of their interpolation properties. The interpolation is local but high order convergence…
Analysis on the unit sphere $\mathbb{S}^{2}$ found many applications in seismology, weather prediction, astrophysics, signal analysis, crystallography, computer vision, computerized tomography, neuroscience, and statistics. In the last two…
Unparticles are realized by deconstruction in higher extra dimensions. It is shown that in this framework when the scale invariance is broken, the corresponding spectral function of the unparticle is shifted by an amount of the breaking…
Relativistic correction to the Coulomb interaction is considered for strongly correlated electron orbitals. The atomic representation of the Coulomb-Breit interaction and its physical origin are clarified, to generalize a concept of the…
The wavefunction for the multiparticle Schr\"odinger equation is a function of many variables and satisfies an antisymmetry condition, so it is natural to approximate it as a sum of Slater determinants. Many current methods do so, but they…
We develope the tomographic representation ofwavefunctions which are solutions of the generalizednonlinear Schrodinger equation (NLSE) and show itsconnection with the Weyl--Wigner map.In particular, this theory is applied tothe envelope…
In this article we give explicit solutions for the wave equations associated to the modified Schr\"odinger operators with magnetic field on the disc and the upper half plane models of the hyperbolic plane. We show that the modified…
Various definitions of chiral observables in a given Moebius covariant two-dimensional theory are shown to be equivalent. Their representation theory in the vacuum Hilbert space of the 2D theory is studied. It shares the general…