Galois theory of iterated endomorphisms

Given an abelian algebraic group $A$ over a global field $F$, $\alpha \in A(F)$, and a prime $\ell$, the set of all preimages of $\alpha$ under some iterate of $[\ell]$ generates an extension of $F$ that contains all $\ell$-power torsion points as well as a Kummer-type extension. We analyze the Galois group of this extension, and for several classes of $A$ we give a simple characterization of when the Galois group is as large as possible up to constraints imposed by the endomorphism ring or the Weil pairing. This Galois group encodes information about the density of primes \p in the ring of integers of $F$ such that the order of (\alpha \bmod{\p}) is prime to $\ell$. We compute this density in the general case for several classes of $A$, including elliptic curves and one-dimensional tori. For example, if $F$ is a number field, $A/F$ is an elliptic curve with surjective 2-adic representation and $\alpha \in A(F)$ with $\alpha \not\in 2A(F(A[4]))$, then the density of $\mathfrak{p}$ with (\alpha \bmod{\p}) having odd order is 11/21.Comment: 33 pages; The appendix has been updated, several examples have been redone, and a number of typos corrected. The paper has been accepted for publication in Proceedings of the London Mathematical Societ

A general hospital experience of polymyalgia rheumatica and giant cell arteritis

Imperial Users onl

Hybrid superprism with low insertion losses and suppressed cross-talk

We demonstrate with the two-dimensional finite-difference time-domain method that an adiabatic transition in a superprism with an interface along the [1 [overline 2]] direction enhances the transmission through the superprism to more than 90% (–0.5 dB) over the wavelength range 1.47–1.68 µm, including the telecommunication C and L bands. We also show that diffraction governed by a quasinegative index of refraction inside the superprism can be used to obtain nearly transform-limited beam widths at the output of the superprism. The reduction of the beam width at the output suppresses cross-talk and greatly enhances the achievable frequency resolution of the superprism

A Morse index theorem for elliptic operators on bounded domains

Given a selfadjoint, elliptic operator $L$, one would like to know how the spectrum changes as the spatial domain $\Omega \subset \mathbb{R}^d$ is deformed. For a family of domains $\{\Omega_t\}_{t\in[a,b]}$ we prove that the Morse index of $L$ on $\Omega_a$ differs from the Morse index of $L$ on $\Omega_b$ by the Maslov index of a path of Lagrangian subspaces on the boundary of $\Omega$. This is particularly useful when $\Omega_a$ is a domain for which the Morse index is known, e.g. a region with very small volume. Then the Maslov index computes the difference of Morse indices for the "original" problem (on $\Omega_b$) and the "simplified" problem (on $\Omega_a$). This generalizes previous multi-dimensional Morse index theorems that were only available on star-shaped domains or for Dirichlet boundary conditions. We also discuss how one can compute the Maslov index using crossing forms, and present some applications to the spectral theory of Dirichlet and Neumann boundary value problems.Comment: 21 pages; weaker regularity assumptions than in the first versio

The Ages of A-Stars

Stars with spectral type `A\u27 (also called A-type stars or just A-stars) are bright intermediate mass stars (∼1.5-2.5 M⊙) that make up ∼1% of stars within 25 parsecs, and ∼20% of the brightest stars in the night sky (V \u3c 3 mag). Most A-stars rotate rapidly with rotational velocities that range from ∼100 to ∼200 km/s in most cases, but can exceed 300 km/s. Such rapid rotation not only causes a star\u27s observed properties (flux, temperature, and radius) to be inclination dependent, but also changes how the star evolves both chemically and structurally. Herein we conduct an interferometric survey of nearby A-stars using the CHARA Array. The long baselines of this optical/infrared interferometer enable us to measure the angular sizes of stars as small as ∼0.2 mas, and directly map the oblate shapes of rotationally distorted stars. This in turn allows us to more accurately determine their photospheric properties and estimate their ages and masses by comparing to evolution models that account for rotation. To facilitate this survey, we construct a census of all 232 A-stars within 50 parsecs (the 50PASS) and from that construct a sample of A-stars (the OSESNA) that lend themselves to interferometric observations with the CHARA Array (i.e., are in the northern hemisphere and have no known, bright, and nearby companions - 108 stars in total). The observations are interpreted by constructing a physical model of a rapidly rotating star from which we generate both photometric and interferometric model observations for comparison with actual observations. The stellar properties of the best fitting model are then compared to the MESA evolution models to estimate an age and a mass. To validate this physical model and the adopted MESA code, we first determine the ages of seven members of the Ursa Major moving group, which are expected to be coeval. With the exception of one star with questionable membership, these stars show a 1-σ spread in age of 56 Myr. This agreement validates our technique and provides a new estimate of the age for the group of 414 ± 23 Myr. We apply this validated technique to the directly-imaged `planet\u27 host star κ Andromedae and determine its age to be 47+27-40 Myr. This implies the companion has a mass of 22+8-9 MJup and is thus more likely a brown dwarf than a giant planet. In total, we present new age and mass estimates for 55 nearby A-stars including six members of the Hyades open cluster, five stars with the λ Boötis chemical peculiarity, nine stars which have an infrared excess, possibly from a debris disk, and nine pulsating stars

The Interactive Effects Of Citizenship Pressure And Job Embeddedness On Positive And Negative Outcomes Of Engagement

A more comprehensive understanding of the positive and negative outcomes of engagement could allow for a better conceptualization of the construct. The three goals of this study were: (1) to examine, based on the job demands and resources framework, potential negative antecedent and outcome relationships (i.e., role conflict, role ambiguity, and counterproductive work behaviors); (2) to identify interactions that could negatively impact engagement’s positive outcomes (i.e. citizenship pressure); and (3) to identify interactions that could positively impact engagement’s negative outcomes (i.e. job embeddedness). To accomplish these goals, the study collected data from both employees and their direct supervisors. An employee survey was utilized to collect data on the independent variables (POS, PSS, role conflict, and role ambiguity), moderators (citizenship pressure and job embeddedness), and engagement. An additional survey, which collected data from the employee’s direct supervisor, contained questions pertaining to the dependent variables (Task performance, OCB-O, OCB-I, and CWB). The results supported the effect of perceived supervisor support on engagement and engagement’s partial mediation of the hypothesized antecedent and outcomes relationships. The interaction of citizenship pressure and engagement was found to weaken engagement’s effect on organizational citizenship behavior targeting the organization. Lastly, the interaction of job embeddedness and engagement made engagement’s effect on counterproductive work behaviors less negative