Remote sensing of ocean waves by polarimetric SAR

A new method to measure ocean wave slope spectra using fully polarimetric synthetic aperture radar (POLSAR) data was developed without the need for a complex hydrodynamic modulation transform function. There is no explicit use of a hydrodynamic modulation transfer function. This function is not clearly known and is based on hydrodynamic assumptions. The method is different from those developed by Schuler and colleagues or Pottier but complements their methods. The results estimated from NASA Jet Propulsion Laboratory (JPL) Airborne Synthetic Aperture Radar (AIRSAR) C-band polarimetric SAR data show that the ocean wavelength, wave direction, and significant wave height are in agreement with buoy measurements. The proposed method can be employed by future satellite missions such as RADARSAT-2.

Decompositions of spaces of measures

Let M be the Banach space of sigma-additive complex-valued measures on an abstract measurable space. We prove that any closed, with respect to absolute continuity norm-closed, linear subspace L of M is complemented and describe the unique complement, projection onto L along which has norm 1. Using this fact we prove a decomposition theorem, which includes the Jordan decomposition theorem, the generalized Radon-Nikodym theorem and the decomposition of measures into decaying and non-decaying components as particular cases. We also prove an analog of the Jessen-Wintner purity theorem for our decompositions.

Extended spectral decompositions of the Renyi map

We present new general methods to obtain spectral decompositions of dynamical systems in rigged Hilbert spaces and investigate the existence of resonances and the completeness of the associated eigenfunctions. The results are illustrated explicitly for the simplest chaotic endomorphism, namely the Renyi map.

The first polarimetric signatures of infrared jets in X-ray binaries

We present near-infrared linear spectropolarimetry of a sample of persistent X-ray binaries, Sco X-1, Cyg X-2, and GRS 1915+105. The slopes of the spectra are shallower than what is expected from a standard steady state accretion disk, and can be explained if the near-infrared flux contains a contribution from an optically thin jet. For the neutron star systems, Sco X-1 and Cyg X-2, the polarization levels at 2.4 mu m are 1.3% +/- 0.10% and 5.4% +/- 0.7%, respectively, which is greater than the polarization level at 1.65 mu m. This cannot be explained by interstellar polarization or electron scattering in the anisotropic environment of the accretion flow. We propose that the most likely explanation is that this is the polarimetric signature of synchrotron emission arising from close to the base of the jets in these systems. In the black hole system GRS 1915+105 the observed polarization, although high (5.0% +/- 1.2% at 2.4 mu m), may be consistent with interstellar polarization. For Sco X-1 the position angle of the radio jet on the sky is approximately perpendicular to the near-infrared position angle (electric vector), suggesting that the magnetic field is aligned with the jet. These observations may be a first step toward probing the ordering, alignment, and variability of the outflow magnetic field in a region closer to the central accreting object than is observed in the radio band.

Polarimetric signatures of infrared jets in X-ray binaries

We present near-infrared linear spectropolarimetry of a sample of persistent X-ray binaries, Sco X-1, Cyg X-2 and GRS 1915+105. For Sco X-1 and Cyg X-2, the polarization levels at 2.4 µm are 1.3+/-0.10% and 5.4+/-0.7%, respectively, which is greater than the polarization level at 1.65 µm. This cannot be explained by interstellar polarization or electron scattering in the anisotropic environment of the accretion flow. We propose that the most likely explanation is that this is the polarimetric signature of synchrotron emission arising from close to the base of the jet. For Sco X-1 the position angle of the radio jet on the sky is approximately perpendicular to the near-infrared position angle (electric vector), suggesting that the magnetic field is aligned with the jet. These observations may be a first step towards probing the ordering, alignment, and variability of the outflow magnetic field, in a region closer to the central accreting object than is observed in the radio band.

Fast Moving Window Algorithm for QR and Cholesky Decompositions

This paper proposes a fast moving window algorithm for QR and Cholesky decompositions by simultaneously applying data updating and downdating. The developed procedure is based on inner products and entails a similar downdating to that of the Chambers’ approach. For adding and deleting one row of data from the original matrix, a detailed analysis shows that the proposed algorithm outperforms existing ones in terms or computational efficiency, if the number of columns exceeds 7. For a large number of columns, the proposed algorithm is numerically superior compared to the traditional sequential technique.

New techniques for enhanced medial axis based decompositions in 2-D

New techniques are presented for using the medial axis to generate high quality decompositions for generating block-structured meshes with well-placed mesh singularities away from the surface boundaries. Established medial axis based meshing algorithms are highly effective for some geometries, but in general, they do not produce the most favourable decompositions, particularly when there are geometry concavities. This new approach uses both the topological and geometric information in the medial axis to establish a valid and effective arrangement of mesh singularities for any 2-D surface. It deals with concavities effectively and finds solutions that are most appropriate to the geometric shapes. Methods for directly constructing the corresponding decompositions are also put forward.