The 5C 6 and 5C 7 surveys of radio sources

5C 6 and 5C 7 continue the series of deep surveys made at 408 and 1407 MHz with the One-Mile telescope at Cambridge. They were intended (1) to provide a sample of faint radio sources suitable for further study; (2) to improve the statistics of source counts N(S) and spectral-index distributions at low flux densities; (3) to study the isotropy of the distribution of faint sources. Each observed field is about 4° in diameter at 408 MHz and 1° in diameter at 1407 MHz, and the field-centres are a α = 02ʰ14ᵐ, δ = 32° (5C 6) and α = 08ᵏ17ᵐ, δ = 27° (5C 7). The synthesized beamwidths (FWHM) are 80 arcsec (408 MHz) and 23 arcsec (1407 MHz). The techniques of observation and data-analysis followed closely those used for 5C 5 (Pearson, T. J., 1975. Mon. Not. R. astr. Soc., 171, 475), with some minor variations which are noted in Section 2

A New Approximation of the Schur Complement in Preconditioners for PDE Constrained Optimization

Saddle point systems arise widely in optimization problems with constraints. The utility of Schur complement approximation is now broadly appreciated in the context of solving such saddle point systems by iteration. In this short manuscript, we present a new Schur complement approximation for PDE constrained optimization, an important class of these problems. Block diagonal and block triangular preconditioners have previously been designed to be used to solve such problems along with MINRES and non-standard Conjugate Gradients respectively; with appropriate approximation blocks these can be optimal in the sense that the time required for solution scales linearly with the problem size, however small the mesh size we use. In this paper, we extend this work to designing such preconditioners for which this optimality property holds independently of both the mesh size and of the Tikhonov regularization parameter \beta that is used. This also leads to an effective symmetric indefinite preconditioner that exhibits mesh and \beta-independence. We motivate the choice of these preconditioners based on observations about approximating the Schur complement obtained from the matrix system, derive eigenvalue bounds which verify the effectiveness of the approximation, and present numerical results which show that these new preconditioners work well in practice

Fast iterative solvers for convection-diffusion control problems

In this manuscript, we describe effective solvers for the optimal control of stabilized convection-diffusion problems. We employ the local projection stabilization, which we show to give the same matrix system whether the discretize-then-optimize or optimize-then-discretize approach for this problem is used. We then derive two effective preconditioners for this problem, the �first to be used with MINRES and the second to be used with the Bramble-Pasciak Conjugate Gradient method. The key components of both preconditioners are an accurate mass matrix approximation, a good approximation of the Schur complement, and an appropriate multigrid process to enact this latter approximation. We present numerical results to demonstrate that these preconditioners result in convergence in a small number of iterations, which is robust with respect to the mesh size h, and the regularization parameter β, for a range of problems

f(R) as a dark energy fluid

We study the equations for the evolution of cosmological perturbations in $f\left(\mathcal{R}\right)$ and conclude that this modified gravity model can be expressed as a dark energy fluid at background and linearised perturbation order. By eliminating the extra scalar degree of freedom known to be present in such theories, we are able to characterise the evolution of the perturbations in the scalar sector in terms of equations of state for the entropy perturbation and anisotropic stress which are written in terms of the density and velocity perturbations of the dark energy fluid and those in the matter, or the metric perturbations. We also do the same in the much simpler vector and tensor sectors. In order to illustrate the simplicity of this formulation, we numerically evolve perturbations in a small number of cases.Comment: 12 pages, 5 figure

Parametric oscillator tuning curve from observations of total parametric fluorescence

Measurements of total emitted parametric fluorescence power are presented and used to fix one point on the predicted tuning curve of a parametric oscillator. The method is particularly useful for predicting the tuning curve of infrared pumped parametric oscillators. Experimental results, which verify the usefulness of the technique in a 1.06-μ-pumped oscillator, are presented

Frequency analysis via the method of moment functionals

Several variants are presented of a linear-in-parameters least squares formulation for determining the transfer function of a stable linear system at specified frequencies given a finite set of Fourier series coefficients calculated from transient nonstationary input-output data. The basis of the technique is Shinbrot's classical method of moment functionals using complex Fourier based modulating functions to convert a differential equation model on a finite time interval into an algebraic equation which depends linearly on frequency-related parameters

Robust Iterative Solution of a Class of Time-Dependent Optimal Control Problems

The fast iterative solution of optimal control problems, and in particular PDE-constrained optimization problems, has become an active area of research in applied mathematics and numerical analysis. In this paper, we consider the solution of a class of time-dependent PDE-constrained optimization problems, specifically the distributed control of the heat equation. We develop a strategy to approximate the (1,1)-block and Schur complement of the saddle point system that results from solving this problem, and therefore derive a block diagonal preconditioner to be used within the MINRES algorithm. We present numerical results to demonstrate that this approach yields a robust solver with respect to step-size and regularization parameter

Organic-inorganic spatial relationships in carbonaceous chondrites

The use of a novel technique to determine the spatial relationships of organic and aqueously produced inorganic phases in carbonaceous chondrites, in order to support proposals of a genetic link between the two

Results from the National Aeronautics and Space Administration remote sensing experiments in the New York Bight, 7-17 April 1975

A cooperative operation was conducted in the New York Bight to evaluate the role of remote sensing technology to monitor ocean dumping. Six NASA remote sensing experiments were flown on the C-54, U-2, and C-130 NASA aircraft, while NOAA obtained concurrent sea truth information using helicopters and surface platforms. The experiments included: (1) a Radiometer/Scatterometer (RADSCAT), (2) an Ocean Color Scanner (OCS), (3) a Multichannel Ocean Color Sensor (MOCS), (4) four Hasselblad cameras, (5) an Ebert spectrometer; and (6) a Reconafax IV infrared scanner and a Precision Radiation Thermometer (PRT-5). The results of these experiments relative to the use of remote sensors to detect, quantify, and determine the dispersion of pollutants dumped into the New York Bight are presented