Related papers: $\theta$-splitting Densities and Reflection Positi…
The theory of total positivity for reductive groups is here extended to the case of symmetric spaces.
A variety of statistics based on sample spacings has been studied in the literature for testing goodness-of-fit to parametric distributions. To test the goodness-of-fit to a nonparametric class of univariate shape-constrained densities,…
A new method to extract the density of partition function zeroes (a continuous function) from their distribution for finite lattices (a discrete data set) is presented. This allows direct determination of the order and strength of phase…
A stationary subset $S$ of a regular uncountable cardinal $\kappa$ {\it reflects fully} at regular cardinals if for every stationary set $T \subseteq \kappa$ of higher order consisting of regular cardinals there exists an $\alpha \in T$…
Consider a real Gaussian stationary process $f_\rho$, indexed on either $\mathbb{R}$ or $\mathbb{Z}$ and admitting a spectral measure $\rho$. We study $\theta_{\rho}^\ell=-\lim\limits_{T\to\infty}\frac{1}{T}…
We consider Gaussian states of fermionic systems and study the action of the partial transposition on the density matrix. It is shown that, with a suitable choice of basis, these states are transformed into a linear combination of two…
The determination of density profiles with knowing the phase information of complex reflection coefficient for neutron specularly reflected from a film, yields unique results. Recently it has been shown that the phase can be determined by…
In this paper we study the notion of strong non-reflection, and its contrapositive weak reflection. We say theta strongly non-reflects at lambda iff there is a function F: theta ---> lambda such that for all alpha < theta with cf(alpha)=…
Weak gravitational lensing of distant galaxies can probe the total projected mass distribution of foreground gravitational structures on all scales and has been used successfully to map the projected mass distribution of rich intermediate…
The generalized entropic measure, which is optimized by a given arbitrary distribution under the constraints on normalization of the distribution and the finite ordinary expectation value of a physical random quantity, is considered and its…
A new differential test for series of positive terms is proved. Let f(x) be a positive continuous function corresponded to a series of positive terms f(k), and g(x) is a derivative of reciprocal of f(x). Then, the convergence and divergence…
A measure of complexity based on a probabilistic description of physical systems is proposed. This measure incorporates the main features of the intuitive notion of such a magnitude. It can be applied to many physical situations and to…
This paper proposes a novel method for testing observability in Gaussian models using discrete density approximations (deterministic samples) of (multivariate) Gaussians. Our notion of observability is defined by the existence of the…
The positivity of the Gram-Charlier probability density function has been a subject of extensive study for decades. Since Barton and Dennis (1952) introduced numerical positivity conditions, no analytic closed-form expression was available…
The long-standing issues of determination of the mass distribution and nature of the center of our Galaxy could be probed by a lensing experiment capable of testing the spatial and velocity distributions of stars nearby and beyond it. We…
We construct mesures supported on a compact subset E of the real line having zero principal value of their Cauchy integral a.e. on E with respect to Lebesgue measure and having singular components. E is sufficiently regular (Widom property…
Gravitational Lensing is a UNIQUE tool to constrain the mass distribution of collapsed structures, this is particularly true for galaxies, either on a case by case basis using multiple images of background sources (such as quasars), or…
A simple method to describe spatially dispersive metasurfaces is proposed where the angle-dependent surface susceptibilities are explicitly used to formulate the zero thickness sheet model of practical metasurface structures. It is shown…
We provide necessary and sufficient conditions for a tempered distribution $F\in S'(R)$ to be positive definite. A generalized Cauchy transform $\widetilde{F}$ of $F$ is used as a numerical continuation of $F$ to the open upper and lower…
We consider the lateral shift of a light beam reflecting from a dielectric slab backed by a metal. It is found that the lateral shift of the reflected beam can be negative while the intensity of reflected beam is almost equal to the…