A note on log-convexity of q-Catalan numbers

The q-Catalan numbers studied by Carlitz and Riordan are polynomials in q with nonnegative coefficients. They evaluate, at q=1, to the Catalan numbers: 1, 1, 2, 5, 14,..., a log-convex sequence. We use a combinatorial interpretation of these polynomials to prove a q-log-convexity result. The sequence of q-Catalan numbers is not q-log-convex in the narrow sense used by other authors, so our work suggests a more flexible definition of q-log convex be adopted

Robotic and automatic welding development at the Marshall Space Flight Center

Welding automation is the key to two major development programs to improve quality and reduce the cost of manufacturing space hardware currently undertaken by the Materials and Processes Laboratory of the NASA Marshall Space Flight Center. Variable polarity plasma arc welding has demonstrated its effectiveness on class 1 aluminum welding in external tank production. More than three miles of welds were completed without an internal defect. Much of this success can be credited to automation developments which stabilize the process. Robotic manipulation technology is under development for automation of welds on the Space Shuttle's main engines utilizing pathfinder systems in development of tooling and sensors for the production applications. The overall approach to welding automation development undertaken is outlined. Advanced sensors and control systems methodologies are described that combine to make aerospace quality welds with a minimum of dependence on operator skill

Stationary and Axisymmetric Solutions of Higher-Dimensional General Relativity

We study stationary and axisymmetric solutions of General Relativity, i.e. pure gravity, in four or higher dimensions. D-dimensional stationary and axisymmetric solutions are defined as having D-2 commuting Killing vector fields. We derive a canonical form of the metric for such solutions that effectively reduces the Einstein equations to a differential equation on an axisymmetric D-2 by D-2 matrix field living in three-dimensional flat space (apart from a subclass of solutions that instead reduce to a set of equations on a D-2 by D-2 matrix field living in two-dimensional flat space). This generalizes the Papapetrou form of the metric for stationary and axisymmetric solutions in four dimensions, and furthermore generalizes the work on Weyl solutions in four and higher dimensions. We analyze then the sources for the solutions, which are in the form of thin rods along a line in the three-dimensional flat space that the matrix field can be seen to live in. As examples of stationary and axisymmetric solutions, we study the five-dimensional rotating black hole and the rotating black ring, write the metrics in the canonical form and analyze the structure of the rods for each solution.Comment: 43 pages, v2: typos fixed, refs adde

Potential formulation of the dispersion relation for a uniform, magnetized plasma with stationary ions in terms of a vector phasor

The derivation of the helicon dispersion relation for a uniform plasma with stationary ions subject to a constant background magnetic field is reexamined in terms of the potential formulation of electrodynamics. Under the same conditions considered by the standard derivation, the nonlinear self-coupling between the perturbed electron flow and the potential it generates is addressed. The plane wave solution for general propagation vector is determined for all frequencies and expressed in terms of a vector phasor. The behavior of the solution as described in vacuum units depends upon the ratio of conductivity to the magnitude of the background field. Only at low conductivity and below the cyclotron frequency can significant propagation occur as determined by the ratio of skin depth to wavelength.Comment: 10 pages, 6 figures, major revision, final version, to appear in Po

Immigration Enforcement and Fairness to Would-Be Immigrants

This chapter argues that governments have a duty to take reasonably effective and humane steps to minimize the occurrence of unauthorized migration and stay. While the effects of unauthorized migration on a country’s citizens and institutions have been vigorously debated, the literature has largely ignored duties of fairness to would-be immigrants. It is argued here that failing to take reasonable steps to prevent unauthorized migration and stay is deeply unfair to would-be immigrants who are not in a position to bypass visa regulations. Importantly, the argument here is orthogonal to the debate as to how much and what kinds of immigration ought to be allowed

Horn-Coupled, Commercially-Fabricated Aluminum Lumped-Element Kinetic Inductance Detectors for Millimeter Wavelengths

We discuss the design, fabrication, and testing of prototype horn-coupled, lumped-element kinetic inductance detectors (LEKIDs) designed for cosmic microwave background (CMB) studies. The LEKIDs are made from a thin aluminum film deposited on a silicon wafer and patterned using standard photolithographic techniques at STAR Cryoelectronics, a commercial device foundry. We fabricated twenty-element arrays, optimized for a spectral band centered on 150 GHz, to test the sensitivity and yield of the devices as well as the multiplexing scheme. We characterized the detectors in two configurations. First, the detectors were tested in a dark environment with the horn apertures covered, and second, the horn apertures were pointed towards a beam-filling cryogenic blackbody load. These tests show that the multiplexing scheme is robust and scalable, the yield across multiple LEKID arrays is 91%, and the noise-equivalent temperatures (NET) for a 4 K optical load are in the range 26\thinspace\pm6 \thinspace \mu \mbox{K} \sqrt{\mbox{s}}

Macrophage migration inhibitory factor downregulation: a novel mechanism of resistance to anti-angiogenic therapy.

Anti-angiogenic therapies for cancer such as VEGF neutralizing antibody bevacizumab have limited durability. While mechanisms of resistance remain undefined, it is likely that acquired resistance to anti-angiogenic therapy will involve alterations of the tumor microenvironment. We confirmed increased tumor-associated macrophages in bevacizumab-resistant glioblastoma patient specimens and two novel glioblastoma xenograft models of bevacizumab resistance. Microarray analysis suggested downregulated macrophage migration inhibitory factor (MIF) to be the most pertinent mediator of increased macrophages. Bevacizumab-resistant patient glioblastomas and both novel xenograft models of resistance had less MIF than bevacizumab-naive tumors, and harbored more M2/protumoral macrophages that specifically localized to the tumor edge. Xenografts expressing MIF-shRNA grew more rapidly with greater angiogenesis and had macrophages localizing to the tumor edge which were more prevalent and proliferative, and displayed M2 polarization, whereas bevacizumab-resistant xenografts transduced to upregulate MIF exhibited the opposite changes. Bone marrow-derived macrophage were polarized to an M2 phenotype in the presence of condition-media derived from bevacizumab-resistant xenograft-derived cells, while recombinant MIF drove M1 polarization. Media from macrophages exposed to bevacizumab-resistant tumor cell conditioned media increased glioma cell proliferation compared with media from macrophages exposed to bevacizumab-responsive tumor cell media, suggesting that macrophage polarization in bevacizumab-resistant xenografts is the source of their aggressive biology and results from a secreted factor. Two mechanisms of bevacizumab-induced MIF reduction were identified: (1) bevacizumab bound MIF and blocked MIF-induced M1 polarization of macrophages; and (2) VEGF increased glioma MIF production in a VEGFR2-dependent manner, suggesting that bevacizumab-induced VEGF depletion would downregulate MIF. Site-directed biopsies revealed enriched MIF and VEGF at the enhancing edge in bevacizumab-naive patients. This MIF enrichment was lost in bevacizumab-resistant glioblastomas, driving a tumor edge M1-to-M2 transition. Thus, bevacizumab resistance is driven by reduced MIF at the tumor edge causing proliferative expansion of M2 macrophages, which in turn promotes tumor growth

Induced hyperlipaemia and immune challenge in locusts

Injections of immunogens, such as β-1,3-glucan or lipopolysaccharide (LPS), bring about a marked hyperlipaemia with associated changes in lipophorins and apolipophorin-III in the haemolymph of Locusta migratoria. These changes are similar to those observed after injection of adipokinetic hormone (AKH). The possibility that endogenous AKH is released as part of the response to these immunogens is investigated using passive immunisation against AKH-I, and measurement of AKH-I titre in the haemolymph after injection of immunogens. The data presented show that, despite the similarity of the changes brought about by the presence of immunogens in the haemolymph to those brought about by AKH, there is no release of endogenous AKH after injection of laminarin or LPS. A direct effect of the immunogens on release of neutral lipids by the fat body cannot be demonstrated in vitro, and the mechanism by which hyperlipaemia is induced during immune challenge remains uncertain

A LEKID-based CMB instrument design for large-scale observations in Greenland

We present the results of a feasibility study, which examined deployment of a ground-based millimeter-wave polarimeter, tailored for observing the cosmic microwave background (CMB), to Isi Station in Greenland. The instrument for this study is based on lumped-element kinetic inductance detectors (LEKIDs) and an F/2.4 catoptric, crossed-Dragone telescope with a 500 mm aperture. The telescope is mounted inside the receiver and cooled to $<\,4$ K by a closed-cycle $^4$He refrigerator to reduce background loading on the detectors. Linearly polarized signals from the sky are modulated with a metal-mesh half-wave plate that is rotated at the aperture stop of the telescope with a hollow-shaft motor based on a superconducting magnetic bearing. The modular detector array design includes at least 2300 LEKIDs, and it can be configured for spectral bands centered on 150~GHz or greater. Our study considered configurations for observing in spectral bands centered on 150, 210 and 267~GHz. The entire polarimeter is mounted on a commercial precision rotary air bearing, which allows fast azimuth scan speeds with negligible vibration and mechanical wear over time. A slip ring provides power to the instrument, enabling circular scans (360 degrees of continuous rotation). This mount, when combined with sky rotation and the latitude of the observation site, produces a hypotrochoid scan pattern, which yields excellent cross-linking and enables 34\% of the sky to be observed using a range of constant elevation scans. This scan pattern and sky coverage combined with the beam size (15~arcmin at 150~GHz) makes the instrument sensitive to $5 < \ell < 1000$ in the angular power spectra