Boundary behavior of analytic functions of two variables via generalized models

We describe a generalization of the notion of a Hilbert space model of a function in the Schur class of the bidisc. This generalization is well adapted to the investigation of boundary behavior at a mild singularity of the function on the 2-torus. We prove the existence of a generalized model with certain properties corresponding to such a singularity and use this result to solve two function-theoretic problems. The first of these is to characterise the directional derivatives of a function in the Schur class at a singular point on the torus for which the Carath\'eodory condition holds. The second is to obtain a representation theorem for functions in the two-variable Pick class analogous to the refined Nevanlinna representation of functions in the one-variable Pick class.Comment: 30 page

Nevanlinna representations in several variables

We generalize two integral representation formulae of Nevanlinna to functions of several variables. We show that for a large class of analytic functions that have non-negative imaginary part on the upper polyhalfplane there are representation formulae in terms of densely defined self-adjoint operators on a Hilbert space. We introduce three types of structured resolvent of a self-adjoint operator and identify four different types of representation in terms of these resolvents. We relate the types of representation that a function admits to its growth at infinity.Comment: 37 pages. In this version we have added some references and expanded the introductio

On the Size of Structures in the Solar Corona

Fine-scale structure in the corona appears not to be well resolved by current imaging instruments. Assuming this to be true offers a simple geometric explanation for several current puzzles in coronal physics, including: the apparent uniform cross-section of bright threadlike structures in the corona; the low EUV contrast (long apparent scale height) between the top and bottom of active region loops; and the inconsistency between loop densities derived by spectral and photometric means. Treating coronal loops as a mixture of diffuse background and very dense, unresolved filamentary structures address these problems with a combination of high plasma density within the structures, which greatly increases the emissivity of the structures, and geometric effects that attenuate the apparent brightness of the feature at low altitudes. It also suggests a possible explanation for both the surprisingly high contrast of EUV coronal loops against the coronal background, and the uniform ``typical'' height of the bright portion of the corona (about 0.3 solar radii) in full-disk EUV images. Some ramifications of this picture are discussed, including an estimate (10-100 km) of the fundamental scale of strong heating events in the corona.Comment: To appear in APJ, June 2007; as accepted Feb 200

Case Studies for achieving a Return on Investment with a Hardware Refresh in Organizations with Small Data Centers

Data centers have been highlighted as a major energy consumer and there has been an increasing trend towards the consolidation of smaller data centers into larger facilities. Yet, small data centers exist for a variety of reasons and account for a significant portion of the total number of servers in the US. Frequent refreshes of IT hardware has emerged as a trend in hyper-scale data centers but little attention has been paid to how these savings can be achieved in small data centers. This work provides a comprehensive framework for the energy saving opportunities, while determining when a return on investment can be achieved to enable small data center operators to create credible business cases for hardware refreshes. Various data center deployment scenarios are used as case studies (based on real-life datasets) to validate the proposed concepts

Users manual: Dynamics of two bodies connected by an elastic tether, six degrees of freedom forebody and five degrees of freedom decelerator

The equations of motion and a computer program for the dynamics of a six degree of freedom body joined to a five degree of freedom body by a quasilinear elastic tether are presented. The forebody is assumed to be a completely general rigid body with six degrees of freedom; the decelerator is also assumed to be rigid, but with only five degrees of freedom (symmetric about its longitudinal axis). The tether is represented by a spring and dashpot in parallel, where the spring constant is a function of tether elongation. Lagrange's equation is used to derive the equations of motion with the Lagrange multiplier technique used to express the constraint provided by the tether. A computer program is included which provides a time history of the dynamics of both bodies and the tension in the tether

Computer program for the load and trajectory analysis of two DOF bodies connected by an elastic tether: Users manual

The derivation of the differential equations of motion of a 3 Degrees of Freedom body joined to a 3 Degrees of Freedom body by an elastic tether. The tether is represented by a spring and dashpot in parallel. A computer program which integrates the equations of motion is also described. Although the derivation of the equations of motions are for a general system, the computer program is written for defining loads in large boosters recovered by parachutes

Diagnostic reasoning techniques for selective monitoring

An architecture for using diagnostic reasoning techniques in selective monitoring is presented. Given the sensor readings and a model of the physical system, a number of assertions are generated and expressed as Boolean equations. The resulting system of Boolean equations is solved symbolically. Using a priori probabilities of component failure and Bayes' rule, revised probabilities of failure can be computed. These will indicate what components have failed or are the most likely to have failed. This approach is suitable for systems that are well understood and for which the correctness of the assertions can be guaranteed. Also, the system must be such that changes are slow enough to allow the computation

Planetological implications of mass loss from the early Sun

The element lithium is observed to be underabundant in the Sun by a factor of approx. equal to 100. To account for this depletion, Boothroyd et al. (Ap. J., in press 1991) proposed a model in which the Sun's zero-age-main-sequence mass was approx. 1.1 solar magnitude. If this is the explanation for the lithium depletion, then astronomical observations of F/G dwarfs in clusters suggest that the timescale for mass loss is approx. equal to 0.6 Gyr. Assuming this approximate timescale, the authors investigated several planetological implications of the astrophysical model

Coherent-feedback quantum control with a dynamic compensator

I present an experimental realization of a coherent-feedback control system that was recently proposed for testing basic principles of linear quantum stochastic control theory [M. R. James, H. I. Nurdin and I. R. Petersen, to appear in IEEE Transactions on Automatic Control (2008), arXiv:quant-ph/0703150v2]. For a dynamical plant consisting of an optical ring-resonator, I demonstrate ~ 7 dB broadband disturbance rejection of injected laser signals via all-optical feedback with a tailored dynamic compensator. Comparison of the results with a transfer function model pinpoints critical parameters that determine the coherent-feedback control system's performance.Comment: 4 pages, 4 EPS figure