A control system design approach for flexible spacecraft

A control system design approach for flexible spacecraft is presented. The control system design is carried out in two steps. The first step consists of determining the ideal control system in terms of a desirable dynamic performance. The second step consists of designing a control system using a limited number of actuators that possess a dynamic performance that is close to the ideal dynamic performance. The effects of using a limited number of actuators is that the actual closed-loop eigenvalues differ from the ideal closed-loop eigenvalues. A method is presented to approximate the actual closed-loop eigenvalues so that the calculation of the actual closed-loop eigenvalues can be avoided. Depending on the application, it also may be desirable to apply the control forces as impulses. The effect of digitizing the control to produce the appropriate impulses is also examined

On elliptic curves with an isogeny of degree 7

We show that if $E$ is an elliptic curve over $\mathbf{Q}$ with a $\mathbf{Q}$-rational isogeny of degree 7, then the image of the 7-adic Galois representation attached to $E$ is as large as allowed by the isogeny, except for the curves with complex multiplication by $\mathbf{Q}(\sqrt{-7})$. The analogous result with 7 replaced by a prime $p > 7$ was proved by the first author in [7]. The present case $p = 7$ has additional interesting complications. We show that any exceptions correspond to the rational points on a certain curve of genus 12. We then use the method of Chabauty to show that the exceptions are exactly the curves with complex multiplication. As a by-product of one of the key steps in our proof, we determine exactly when there exist elliptic curves over an arbitrary field $k$ of characteristic not 7 with a $k$-rational isogeny of degree 7 and a specified Galois action on the kernel of the isogeny, and we give a parametric description of such curves.Comment: The revision gives a complete answer to the question considered in Version 1. Version 3 will appear in the American Journal of Mathematic

Electrostatically shaped membranes

Disclosed is a method and apparatus for electrostatically shaping a membrane suitable for use in antennas or the like, comprising an electrically conductive thin membrane where the periphery of said membrane is free to move in at least one direction, a first charge on the electrically conductive thin membrane to electrostatically stiffen the membrane, a second charge which shapes the electrostatically stiffened thin membrane and a restraint for limiting the movement of at least one point of the thin membrane relative to the second charge. Also disclosed is a method and apparatus for adaptively controlling the shape of the thin membrane by sensing the shape of the membrane and selectively controlling the first and second charge to achieve a desired performance characteristic of the membrane

Global associations between UVR exposure and current eczema prevalence in children from ISAAC Phase Three

We sought to examine the relationship globally between UV dose exposure and current eczema prevalences. ISAAC Phase Three provided data on eczema prevalence for 13-14 year-olds in 214 centres in 87 countries and for 6-7 year-olds in 132 centres in 57 countries. Linear and non-linear associations between (natural log transformed) eczema prevalence and the mean, maximum, minimum, standard deviation and range of monthly UV dose exposures were assessed using linear mixed-effects regression models. For the 13-14 year olds, the country-level eczema prevalence was positively and linearly associated with country-level monthly mean (prevalence ratio: 1.31, 95% confidence interval: [1.05, 1.63] per kJ/m2) and minimum (1.25 [1.06, 1.47] per kJ/m2) UV dose exposure. Linear and non-linear associations were also observed for other metrics of UV. Results were similar in trend, but non-significant, for the fewer centres with 6-7 year-olds (e.g. 1.24 [0.96, 1.59] per kJ/m2 for country-level monthly mean UV). No consistent within-country associations were observed (e.g. 1.05 [0.89, 1.23] and 0.92 [0.71, 1.18] per kJ/m2 for center-level monthly mean UV, for the 13-14 and 6-7 year-olds, respectively). These ecological results support a role for UV exposure in explaining some of the variation in global childhood eczema prevalence

Submillimeter wavelength survey of the galactic plane from l = -5 deg to l = +62 deg: Structure and energetics of the inner disk

Results from a large scale survey of the first quadrant of the Milky Way galactic plane at wavelengths of 150, 250, and 300 microns with a 10x10 arcmin beam are presented. The emission detected in the survey arises from compact sources, most of which are identified with known peaks of 5 GHz and/or CO emission, and from an underlying diffuse background with a typical angular width of approximately 0.9 deg (FWHM) which accounts for most of the emission. A total of 80 prominent discrete sources were identified and characterized, of which about half were not previously reported at far infrared wavelengths. The total infrared luminosity within the solar circle is approximately 1 to 2x10 to the 10th power L sub 0, and is probably emitted by dust that resides in molecular clouds

The First Brown Dwarf Discovered by the Backyard Worlds: Planet 9 Citizen Science Project

The Wide-field Infrared Survey Explorer (WISE) is a powerful tool for finding nearby brown dwarfs and searching for new planets in the outer solar system, especially with the incorporation of NEOWISE and NEOWISE-Reactivation data. So far, searches for brown dwarfs in WISE data have yet to take advantage of the full depth of the WISE images. To efficiently search this unexplored space via visual inspection, we have launched a new citizen science project, called "Backyard Worlds: Planet 9," which asks volunteers to examine short animations composed of difference images constructed from time-resolved WISE coadds. We report the discovery of the first new substellar object found by this project, WISEA J110125.95+540052.8, a T5.5 brown dwarf located approximately 34 pc from the Sun with a total proper motion of $\sim$0.7 as yr$^{-1}$. WISEA J110125.95+540052.8 has a WISE $W2$ magnitude of $W2=15.37 \pm 0.09$, this discovery demonstrates the ability of citizen scientists to identify moving objects via visual inspection that are 0.9 magnitudes fainter than the $W2$ single-exposure sensitivity, a threshold that has limited prior motion-based brown dwarf searches with WISE.Comment: 9 pages, 4 figures, 1 table. Accepted for publication in the Astrophysical Journal Letter

Realizing orders as group rings

An order is a commutative ring that as an abelian group is finitely generated and free. A commutative ring is reduced if it has no non-zero nilpotent elements. In this paper we use a new tool, namely, the fact that every reduced order has a universal grading, to answer questions about realizing orders as group rings. In particular, we address the Isomorphism Problem for group rings in the case where the ring is a reduced order. We prove that any non-zero reduced order $R$ can be written as a group ring in a unique ``maximal'' way, up to isomorphism. More precisely, there exist a ring $A$ and a finite abelian group $G$, both uniquely determined up to isomorphism, such that $R\cong A[G]$ as rings, and such that if $B$ is a ring and $H$ is a group, then $R\cong B[H]$ as rings if and only if there is a finite abelian group $J$ such that $B\cong A[J]$ as rings and $J\times H\cong G$ as groups. Computing $A$ and $G$ for given $R$ can be done by means of an algorithm that is not quite polynomial-time. We also give a description of the automorphism group of $R$ in terms of $A$ and $G$