The Algebraic Theory of Matrix Polynomials

A matrix S is a solvent of the matrix polynomial M(X)=A₀Xᵐ +...+ Am if M(S)=O where A, X, and S are square matrices. In this paper we develop the algebraic theory of matrix polynomials and solvents. We define division and interpolation, investigate the properties of block Vandermonde matrices, and define and study the existence of a complete set of solvents. We study the relation between the matrix polynomial problem and the lambda-matrix problem, which is to find a scalar A₀λᵐ + A₁λᵐ⁻¹ +...+ Am is singular. In a future paper we extend Traub’s algorithm for calculating zeros of scalar polynomials to matrix polynomials and establish global convergence properties of this algorithm for a class of matrix polynomials

Algorithms for Solvents of Matrix Polynomials

In an earlier paper we developed the algebraic theory of matrix polynomials. Here we introduce two algorithms for computing "dominant" solvents. Global convergence of the algorithms under certain conditions is established

The impact of analyst sentiment on UK stock recommendations and target prices

© 2015 Taylor & Francis. The aim of this paper is to investigate the relationship between narrative sentiment in analysts' company reports and their recommendation and target price outputs. We study an industry-balanced sample of 275 UK quoted company sell-side analyst reports over the period 2006-2010 using a content analysis methodology to measure net sentiment for a range of themes. We then model analysts' outputs against themed sentiment scores to analyse the impact of the Global Financial Crisis. We find that themed sentiments impact upon analysts' outputs, but their magnitude and direction vary over the pre-crisis, crisis and post-crisis periods. In particular, before the crisis we find a strong negative relationship between the macroeconomic and regulatory environment and report outputs, though this effect diminishes somewhat with the onset of the crisis, to be restored thereafter. Growth sentiment exerts a weak positive impact before the crisis which disappears thereafter. Financial performance sentiment becomes a significant positive driver of outputs following the crisis. There is evidently a "back to basics" approach following the crisis which restores financial fundamentals to the heart of stock analysis. Our findings provide some insight into the thought processes of analysts by identifying the dynamic relation between analysts' outputs and themed sentiments

LpL^p-Spectral theory of locally symmetric spaces with QQ-rank one

We study the $L^p$-spectrum of the Laplace-Beltrami operator on certain complete locally symmetric spaces $M=\Gamma\backslash X$ with finite volume and arithmetic fundamental group $\Gamma$ whose universal covering $X$ is a symmetric space of non-compact type. We also show, how the obtained results for locally symmetric spaces can be generalized to manifolds with cusps of rank one

Very High Resolution Solar X-ray Imaging Using Diffractive Optics

This paper describes the development of X-ray diffractive optics for imaging solar flares with better than 0.1 arcsec angular resolution. X-ray images with this resolution of the \geq10 MK plasma in solar active regions and solar flares would allow the cross-sectional area of magnetic loops to be resolved and the coronal flare energy release region itself to be probed. The objective of this work is to obtain X-ray images in the iron-line complex at 6.7 keV observed during solar flares with an angular resolution as fine as 0.1 arcsec - over an order of magnitude finer than is now possible. This line emission is from highly ionized iron atoms, primarily Fe xxv, in the hottest flare plasma at temperatures in excess of \approx10 MK. It provides information on the flare morphology, the iron abundance, and the distribution of the hot plasma. Studying how this plasma is heated to such high temperatures in such short times during solar flares is of critical importance in understanding these powerful transient events, one of the major objectives of solar physics. We describe the design, fabrication, and testing of phase zone plate X-ray lenses with focal lengths of \approx100 m at these energies that would be capable of achieving these objectives. We show how such lenses could be included on a two-spacecraft formation-flying mission with the lenses on the spacecraft closest to the Sun and an X-ray imaging array on the second spacecraft in the focal plane \approx100 m away. High resolution X-ray images could be obtained when the two spacecraft are aligned with the region of interest on the Sun. Requirements and constraints for the control of the two spacecraft are discussed together with the overall feasibility of such a formation-flying mission

Magnetic Reversal on Vicinal Surfaces

We present a theoretical study of in-plane magnetization reversal for vicinal ultrathin films using a one-dimensional micromagnetic model with nearest-neighbor exchange, four-fold anisotropy at all sites, and two-fold anisotropy at step edges. A detailed "phase diagram" is presented that catalogs the possible shapes of hysteresis loops and reversal mechanisms as a function of step anisotropy strength and vicinal terrace length. The steps generically nucleate magnetization reversal and pin the motion of domain walls. No sharp transition separates the cases of reversal by coherent rotation and reversal by depinning of a ninety degree domain wall from the steps. Comparison to experiment is made when appropriate.Comment: 12 pages, 8 figure

The Layer 0 Inner Silicon Detector of the D0 Experiment

This paper describes the design, fabrication, installation and performance of the new inner layer called Layer 0 (L0) that was inserted in the existing Run IIa Silicon Micro-Strip Tracker (SMT) of the D0 experiment at the Fermilab Tevatron collider. L0 provides tracking information from two layers of sensors, which are mounted with center lines at a radial distance of 16.1 mm and 17.6 mm respectively from the beam axis. The sensors and readout electronics are mounted on a specially designed and fabricated carbon fiber structure that includes cooling for sensor and readout electronics. The structure has a thin polyimide circuit bonded to it so that the circuit couples electrically to the carbon fiber allowing the support structure to be used both for detector grounding and a low impedance connection between the remotely mounted hybrids and the sensors.Comment: 28 pages, 9 figure

The charismatic leadership of the ECB presidency:A language-based analysis

There is little doubt that the European Central Bank (ECB), and in particular its presidency, has taken the lead in tackling the euro crisis. But can this leadership be also characterised as charismatic? This article answers the question by focusing on language – a key component as well as a reliable indicator of charisma. By means of a software‐assisted content analysis of the entire corpus of ECB presidential speeches, it is found that the crisis has indeed led to the emergence of the Bank's presidency as a charismatic euro leader. This in turn confirms the recent politicisation of the ECB, but at the same time might be seen as mitigating the problems related to the Bank's democratic deficit, to the extent that charisma can be seen, from a Weberian standpoint, as an alternative source of political legitimacy

Accretion, Outflows, and Winds of Magnetized Stars

Many types of stars have strong magnetic fields that can dynamically influence the flow of circumstellar matter. In stars with accretion disks, the stellar magnetic field can truncate the inner disk and determine the paths that matter can take to flow onto the star. These paths are different in stars with different magnetospheres and periods of rotation. External field lines of the magnetosphere may inflate and produce favorable conditions for outflows from the disk-magnetosphere boundary. Outflows can be particularly strong in the propeller regime, wherein a star rotates more rapidly than the inner disk. Outflows may also form at the disk-magnetosphere boundary of slowly rotating stars, if the magnetosphere is compressed by the accreting matter. In isolated, strongly magnetized stars, the magnetic field can influence formation and/or propagation of stellar wind outflows. Winds from low-mass, solar-type stars may be either thermally or magnetically driven, while winds from massive, luminous O and B type stars are radiatively driven. In all of these cases, the magnetic field influences matter flow from the stars and determines many observational properties. In this chapter we review recent studies of accretion, outflows, and winds of magnetized stars with a focus on three main topics: (1) accretion onto magnetized stars; (2) outflows from the disk-magnetosphere boundary; and (3) winds from isolated massive magnetized stars. We show results obtained from global magnetohydrodynamic simulations and, in a number of cases compare global simulations with observations.Comment: 60 pages, 44 figure