The Schur-Horn theorem for operators and frames with prescribed norms and frame operator

Let $\mathcal H$ be a Hilbert space. Given a bounded positive definite operator $S$ on $\mathcal H$, and a bounded sequence $\mathbf{c} = \{c_k \}_{k \in \mathbb N}$ of non negative real numbers, the pair $(S, \mathbf{c})$ is frame admissible, if there exists a frame $\{f_k \}_{k \in \mathbb{N}}$ on $\mathcal H$ with frame operator $S$, such that $\|f_k \|^2 = c_k$, $k \in \mathbb {N}$. We relate the existence of such frames with the Schur-Horn theorem of majorization, and give a reformulation of the extended version of Schur-Horn theorem, due to A. Neumann. We use it to get necessary conditions (and to generalize known sufficient conditions) for a pair $(S, \mathbf{c})$, to be frame admissible.Comment: To appear in Illinois Journal of Mat

Digital receiver study and implementation

Computer software was developed which makes it possible to use any general purpose computer with A/D conversion capability as a PSK receiver for low data rate telemetry processing. Carrier tracking, bit synchronization, and matched filter detection are all performed digitally. To aid in the implementation of optimum computer processors, a study of general digital processing techniques was performed which emphasized various techniques for digitizing general analog systems. In particular, the phase-locked loop was extensively analyzed as a typical non-linear communication element. Bayesian estimation techniques for PSK demodulation were studied. A hardware implementation of the digital Costas loop was developed

MERLIN radio detection of an interaction zone within a binary Orion proplyd system

Presented here are high angular resolution MERLIN 5 GHz (6 cm) continuum observations of the binary proplyd system, LV 1 in the Orion nebula, which consists of proplyd 168--326SE and its binary proplyd companion 168--326NW (separation 0.4 arcsec). Accurate astrometric alignment allows a detailed comparison between these data and published HST PC Halpha and [Oiii] images. Thermal radio sources coincide with the two proplyds and originate in the ionized photoevaporating flows seen in the optical emission lines. Flow velocities of approx 50 km/s from the ionized proplyd surfaces and \geq 100 km/s from a possible micro-jet have been detected using the Manchester Echelle spectrometer. A third radio source is found to coincide with a region of extended, high excitation, optical line emission that lies between the binary proplyds 168--326SE/326NW . This is modelled as a bowshock due to the collision of the photoevaporating flows from the two proplyds. Both a thermal and a non-thermal origin for the radio emission in this collision zone are considered.Comment: 23 pages, 9 figures, accepted by Ap

Test of nuclear level density inputs for Hauser-Feshbach model calculations

The energy spectra of neutrons, protons, and alpha-particles have been measured from the d+59Co and 3He+58Fe reactions leading to the same compound nucleus, 61$Ni. The experimental cross sections have been compared to Hauser-Feshbach model calculations using different input level density models. None of them have been found to agree with experiment. It manifests the serious problem with available level density parameterizations especially those based on neutron resonance spacings and density of discrete levels. New level densities and corresponding Fermi-gas parameters have been obtained for reaction product nuclei such as 60Ni,60Co, and 57Fe

Understanding the effect of seams on the aerodynamics of an association football

The aerodynamic properties of an association football were measured using a wind tunnel arrangement. A third scale model of a generic football (with seams) was used in addition to a 'mini-football'. As the wind speed was increased, the drag coefficient decreased from 0.5 to 0.2, suggesting a transition from laminar to turbulent behaviour in the boundary layer. For spinning footballs, the Magnus effect was observed and it was found that reverse Magnus effects were possible at low Reynolds numbers. Measurements on spinning smooth spheres found that laminar behaviour led to a high drag coefficient for a large range of Reynolds numbers, and Magnus effects were inconsistent, but generally showed reverse Magnus behaviour at high Reynolds number and spin parameter. Trajectory simulations of free kicks demonstrated that a football that is struck in the centre will follow a near straight trajectory, dipping slightly before reaching the goal, whereas a football that is struck off centre will bend before reaching the goal, but will have a significantly longer flight time. The curving kick simulation was repeated for a smooth ball, which resulted in a longer flight time, due to increased drag, and the ball curving in the opposite direction, due to reverse Magnus effects. The presence of seams was found to encourage turbulent behaviour, resulting in reduced drag and more predictable Magnus behaviour for a conventional football, compared with a smooth ball. © IMechE 2005

Accounting for Federalism in State Courts - Exclusion of Evidence Obtained Lawfully By Federal Agents

After the terrorist attacks on September 11th, Congress greatly enhanced federal law enforcement powers through enactment of the U.S.A. Patriot Act. The Supreme Court also has provided more leeway to federal officers in the past few decades, for example by limiting the scope of the exclusionary rule. At the same time, many states have interpreted their constitutions to provide greater individual protections to their citizens than provided by the federal constitution. This phenomenon has sometimes created a wide disparity between the investigatory techniques available to federal versus state law enforcement officers. As a result, state courts sometimes must decide whether to suppress evidence obtained legally by federal law enforcement officers but in violation of state law. In deciding these cases the states usually rely on a state evidentiary basis ignoring federalism concerns. This article proposes a framework by which state courts may suppress this evidence while recognizing notions of federalism

Transnational social capital: the socio‐spatialities of civil society

Civil society remains a contested concept, but one that is widely embedded in global development processes. Transnationalism within civil society scholarship is often described dichotomously, either through hierarchical dependency relations or as a more amorphous networked global civil society. These two contrasting spatial imaginaries produce very particular ideas about how transnational relations contribute to civil society. Drawing on empirical material from research with civil society organizations in Barbados and Grenada, in this article I contend that civil society groups use forms of transnational social capital in their work. This does not, however, resonate with the horizontal relations associated with grassroots globalization or vertical chains of dependence. These social relations are imbued with power and agency and are entangled in situated historical, geographical and personal contexts. I conclude that the diverse transnational social relations that are part of civil society activity offer hope and possibilities for continued civil society action in these unexpected spatial arrangements

3D Reconstruction of the Density Field: An SVD Approach to Weak Lensing Tomography

We present a new method for constructing three-dimensional mass maps from gravitational lensing shear data. We solve the lensing inversion problem using truncation of singular values (within the context of generalized least squares estimation) without a priori assumptions about the statistical nature of the signal. This singular value framework allows a quantitative comparison between different filtering methods: we evaluate our method beside the previously explored Wiener filter approaches. Our method yields near-optimal angular resolution of the lensing reconstruction and allows cluster sized halos to be de-blended robustly. It allows for mass reconstructions which are 2-3 orders-of-magnitude faster than the Wiener filter approach; in particular, we estimate that an all-sky reconstruction with arcminute resolution could be performed on a time-scale of hours. We find however that linear, non-parametric reconstructions have a fundamental limitation in the resolution achieved in the redshift direction.Comment: 11 pages, 6 figures. Accepted for publication in Ap

Oxygen-rich dust production in IC 10

We report the detection of oxygen-rich circumstellar envelopes in stars of the nearby (700 kpc) starburst galaxy IC 10. The star formation history and the chemical environment of this galaxy makes it an ideal target to observe dust production by high-mass stars in a low-metallicity environment. The goal of this study is to identify oxygen-rich stars in IC 10 and to constrain their nature between asymptotic giant branch stars (AGBs), red supergiants (RSGs), and other infrared bright sources. We examine the mass-loss rate of the stars and compare to results obtained for the Magellanic Clouds. Our objectives are to (1) assess whether RSGs can be significant dust producers in IC 10, and (2), solve the discrepancy between the star formation history of IC 10 and the relatively low number of RSGs detected in the optical. We search for silicate dust in emission by using the spectral map observed with the Infrared Spectrograph on board the Spitzer Space Telescope. The optical (UBVRI) and infrared (JHK, Spitzer/IRAC and Spitzer/MIPS) photometry is used to assert the membership of the stars to IC 10 and disentangle between AGBs and RSGs. Radiative models are used to infer mass-loss rates and stellar luminosities. The luminosity and colors of at least 9 silicate emission sources are consistent with stars within IC 10. Furthermore, the photometry of 2 of these sources is consistent with RSGs. We derive dust mass-loss rates similar to the values found in the Magellanic Clouds. Accounting for the sample completeness, RSGs are not important contributors to the dust mass budget in IC 10.Comment: Accepted for publication in A&