Related papers: Phase space localization of antisymmetric function…
The entropy region is a fundamental object in information theory. An outer bound for the entropy region is defined by a minimal set of Shannon-type inequalities called elemental inequalities also referred to as the Shannon region. This…
A floating hemisphere under forced harmonic oscillation at very high and very low frequencies is considered. The problem is reduced to an elliptic one, that is, the Laplace operator in the exterior domain with standard Dirichlet and Neumann…
How can one fully harness the power of physics encoded in relativistic $N$-body phase space? Topologically, phase space is isomorphic to the product space of a simplex and a hypersphere and can be equipped with explicit coordinates and a…
The quadratic phase Fourier transform has gained much popularity in recent years because of its applications in image and signal processing. However, the QPFT is inadequate for localizing the quadratic phase spectrum which is required in…
We analyze the asymptotic behavior of solutions to wave equations with strong damping terms. If the initial data belong to suitable weighted $L^1$ spaces, lower bounds for the difference between the solutions and the leading terms in the…
The dimension function D_psi of a band-limited wavelet is bounded by n if the support of its Fourier transform is contained in the interval [-{2^(n+2)/3}pi, {2^(n+2)/3}pi]. For each positive integer n and for each epsilon > 0, we construct…
The Wigner function shares several properties with classical distribution functions on phase space, but is not positive-definite. The integral of the Wigner function over a given region of phase space can therefore lie outside the interval…
We show that the behaviour in phase space of the Wigner function associated to the electromagnetic modes carries the information of both, the entanglement properties between matter and field, and the regions in parameter space where quantum…
Process of the nonlinear deformation of the surface wave in shallow water is studied. Main attention is paid to the relation between the Fourier-spectrum and wave steepness. It is shown that the spectral harmonics of the initially sine wave…
In a recent paper [PRE 62, 4665 (2000)] (quant-ph/0203102) Manfredi and Feix proposed an alternative definition of quantum entropy based on Wigner phase-space distribution functions and discussed its properties. They proposed also some…
We use entropy numbers in combination with the polynomial method to derive a new general lower bound for the n-th minimal error in the quantum setting of information-based complexity. As an application, we improve some lower bounds on…
We consider universal approximations of symmetric and anti-symmetric functions, which are important for applications in quantum physics, as well as other scientific and engineering computations. We give constructive approximations with…
Most statistical tools used to characterize the complex structures of the interstellar medium can be related to the power spectrum, and therefore to the Fourier amplitudes of the observed fields. To tap into the vast amount of information…
We derive expressions for the phase-space of a particle of momentum $p$ decaying into $N$ particles, that are valid for any number of dimensions. These are the imaginary parts of so-called `sunset' diagrams, which we also obtain. The…
Localization of a particle in the wells of an asymmetric double-well (DW) potential is investigated here. Information entropy-based uncertainty measures, such as Shannon entropy, Fisher information, Onicescu energy, etc., and phasespace…
For the zone of moderate deviation probabilities the local asymptotic minimax lower bound of asymptotic efficiency of estimators is established. The estimation parameter is multidimensional. The lower bound admits the interpretation as the…
The bending energy of any freely deformable closed surface is quadratic in its curvature. In the absence of constraints, it will be minimized when the surface adopts the form of a round sphere. If the surface is confined within a…
Properties of the four families of recently introduced special functions of two real variables, denoted here by $E^\pm$, and $\cos^\pm$, are studied. The superscripts $^+$ and $^-$ refer to the symmetric and antisymmetric functions…
We consider a homogenization of elliptic spectral problem stated in a perforated domain, Fourier boundary conditions being imposed on the boundary of perforation. The presence of a locally periodic coefficient in the boundary operator gives…
The halfspace depth is a well studied tool of nonparametric statistics in multivariate spaces, naturally inducing a multivariate generalisation of quantiles. The halfspace depth of a point with respect to a measure is defined as the infimum…