A behavioral view of Nevanlinna-Pick interpolation

The classical Nevanlinna-Pick (NP) interpolation problem is about finding a rational function that satisfies given interpolation conditions, along with a norm condition. In this paper we address the NP problem using concepts from behavioral systems theory and quadratic differential forms (QDFs). The NP problem is solved using a certain “dualization of data”. We address system theoretic motivations for this dualization and the advantages gained in this process. Finally, we address the problem of constructing interpolating functions that satisfy a “frequency dependent” norm condition

Interpolation with bilinear differential forms

We present a recursive algorithm for modeling with bilinear differential forms. We discuss applications of this algorithm for interpolation with symmetric bivariate polynomials, and for computing storage functions for autonomous systems

Vector-exponential time-series modeling for polynomial J-spectral factorization

An iterative algorithm to perform the J-spectral factorization of a para-Hermitian matrix is presented. The algorithm proceeds by computing a special kernel representation of an interpolant for a sequence of points and associated directions determined from the spectral zeroes of the to-be factored matrix

Comparative study of different scattering geometries for the proposed Indian X-ray polarization measurement experiment using Geant4

Polarization measurements in X-rays can provide unique opportunity to study the behavior of matter and radiation under extreme magnetic fields and extreme gravitational fields. Unfortunately, over past two decades, when X-ray astronomy witnessed multiple order of magnitude improvement in temporal, spatial and spectral sensitivities, there is no (or very little) progress in the field of polarization measurements of astrophysical X-rays. Recently, a proposal has been submitted to ISRO for a dedicated small satellite based experiment to carry out X-ray polarization measurement, which aims to provide the first X-ray polarization measurements since 1976. This experiment will be based on the well known principle of polarization measurement by Thomson scattering and employs the baseline design of a central low Z scatterer surrounded by X-ray detectors to measure the angular intensity distribution of the scattered X-rays. The sensitivity of such experiment is determined by the collecting area, scattering and detection efficiency, X-ray detector background, and the modulation factor. Therefore, it is necessary to carefully select the scattering geometry which can provide the highest modulation factor and thus highest sensitivity within the specified experimental constraints. The effective way to determine optimum scattering geometry is by studying various possible scattering geometries by means of Monte Carlo simulations. Here we present results of our detailed comparative study based on Geant4 simulations of five different scattering geometries which can be considered within the weight and size constraints of the proposed small satellite based X-ray polarization measurement experiment.Comment: 14 pages, 6 figures, accepted for publication in "Nuclear Inst. and Methods in Physics Research, A

Anti-correlated hard X-ray time lags in Galactic black hole sources

We investigate the accretion disk geometry in Galactic black hole sources by measuring the time delay between soft and hard X-ray emissions. Similar to the recent discoveries of anti-correlated hard X-ray time lags in Cyg X-3 and GRS 1915+105, we find that the hard X-rays are anti-correlated with soft X-rays with a significant lag in another source: XTE J1550-564. We also find the existence of pivoting in the model independent X-ray spectrum during these observations. We investigate time-resolved X-ray spectral parameters and find that the variation in these parameters is consistent with the idea of a truncated accretion disk. The QPO frequency, which is a measure of the size of truncated accretion disk, too changes indicating that the geometric size of the hard X-ray emitting region changes along with the spectral pivoting and soft X-ray flux. Similar kind of delay is also noticed in 4U 1630-47.Comment: 14 pages, 7 figures, accepted for publication in Ap