Tractability of multivariate problems for standard and linear information in the worst case setting: part II

We study QPT (quasi-polynomial tractability) in the worst case setting for linear tensor product problems defined over Hilbert spaces. We assume that the domain space is a reproducing kernel Hilbert space so that function values are well defined. We prove QPT for algorithms that use only function values under the three assumptions: 1) the minimal errors for the univariate case decay polynomially fast to zero, 2) the largest singular value for the univariate case is simple and 3) the eigenfunction corresponding to the largest singular value is a multiple of the function value at some point. The first two assumptions are necessary for QPT. The third assumption is necessary for QPT for some Hilbert spaces

"Mariage des Maillages": A new numerical approach for 3D relativistic core collapse simulations

We present a new 3D general relativistic hydrodynamics code for simulations of stellar core collapse to a neutron star, as well as pulsations and instabilities of rotating relativistic stars. It uses spectral methods for solving the metric equations, assuming the conformal flatness approximation for the three-metric. The matter equations are solved by high-resolution shock-capturing schemes. We demonstrate that the combination of a finite difference grid and a spectral grid can be successfully accomplished. This "Mariage des Maillages" (French for grid wedding) approach results in high accuracy of the metric solver and allows for fully 3D applications using computationally affordable resources, and ensures long term numerical stability of the evolution. We compare our new approach to two other, finite difference based, methods to solve the metric equations. A variety of tests in 2D and 3D is presented, involving highly perturbed neutron star spacetimes and (axisymmetric) stellar core collapse, demonstrating the ability to handle spacetimes with and without symmetries in strong gravity. These tests are also employed to assess gravitational waveform extraction, which is based on the quadrupole formula.Comment: 29 pages, 16 figures; added more information about convergence tests and grid setu

The optimal polarizations for achieving maximum contrast in radar images

There is considerable interest in determining the optimal polarizations that maximize contrast between two scattering classes in polarimetric radar images. A systematic approach is presented for obtaining the optimal polarimetric matched filter, i.e., that filter which produces maximum contrast between two scattering classes. The maximization procedure involves solving an eigenvalue problem where the eigenvector corresponding to the maximum contrast ratio is an optimal polarimetric matched filter. To exhibit the physical significance of this filter, it is transformed into its associated transmitting and receiving polarization states, written in terms of horizontal and vertical vector components. For the special case where the transmitting polarization is fixed, the receiving polarization which maximizes the contrast ratio is also obtained. Polarimetric filtering is then applies to synthetic aperture radar images obtained from the Jet Propulsion Laboratory. It is shown, both numerically and through the use of radar imagery, that maximum image contrast can be realized when data is processed with the optimal polarimeter matched filter

Determination of the magnetic anisotropy axes of single-molecule magnets

Simple methods are presented allowing the determination of the magnetic anisotropy axes of a crystal of a single-molecule magnet (SMM). These methods are used to determine an upper bound of the easy axis tilts in a standard Mn12-Ac crystal. The values obtained in the present study are significately smaller than those reported in recent high frequency electron paramagnetic resonance (HF-EPR) studies which suggest distributions of hard-axes tilts.Comment: 10 pages, 6 figure

Radius Dependent Luminosity Evolution of Blue Galaxies in GOODS-N

We examine the radius-luminosity (R-L) relation for blue galaxies in the Team Keck Redshift Survey (TKRS) of GOODS-N. We compare with a volume-limited, Sloan Digital Sky Survey sample and find that the R-L relation has evolved to lower surface brightness since z=1. Based on the detection limits of GOODS this can not be explained by incompleteness in low surface-brightness galaxies. Number density arguments rule out a pure radius evolution. It can be explained by a radius dependent decline in B-band luminosity with time. Assuming a linear shift in M_B with z, we use a maximum likelihood method to quantify the evolution. Under these assumptions, large (R_{1/2} > 5 kpc), and intermediate sized (3 < R_{1/2} < 5 kpc) galaxies, have experienced Delta M_B =1.53 (-0.10,+0.13) and 1.65 (-0.18, +0.08) magnitudes of dimming since z=1. A simple exponential decline in star formation with an e-folding time of 3 Gyr can result in this amount of dimming. Meanwhile, small galaxies, or some subset thereof, have experienced more evolution, 2.55 (+/- 0.38) magnitudes. This factor of ten decline in luminosity can be explained by sub-samples of starbursting dwarf systems that fade rapidly, coupled with a decline in burst strength or frequency. Samples of bursting, luminous, blue, compact galaxies at intermediate redshifts have been identified by various previous studies. If there has been some growth in galaxy size with time, these measurements are upper limits on luminosity fading.Comment: 34 Total pages, 15 Written pages, 19 pages of Data Table, 13 Figures, accepted for publication in Ap