The monic integer transfinite diameter

We study the problem of finding nonconstant monic integer polynomials, normalized by their degree, with small supremum on an interval I. The monic integer transfinite diameter t_M(I) is defined as the infimum of all such supremums. We show that if I has length 1 then t_M(I) = 1/2. We make three general conjectures relating to the value of t_M(I) for intervals I of length less that 4. We also conjecture a value for t_M([0, b]) where 0 < b < 1. We give some partial results, as well as computational evidence, to support these conjectures. We define two functions that measure properties of the lengths of intervals I with t_M(I) on either side of t. Upper and lower bounds are given for these functions. We also consider the problem of determining t_M(I) when I is a Farey interval. We prove that a conjecture of Borwein, Pinner and Pritsker concerning this value is true for an infinite family of Farey intervals.Comment: 32 pages, 5 figure

Preliminary Candidate Advanced Avionics System (PCAAS)

Specifications which define the system functional requirements, the subsystem and interface needs, and other requirements such as maintainability, modularity, and reliability are summarized. A design definition of all required avionics functions and a system risk analysis are presented

Coupled and separable iterations in nonlinear estimation

This thesis deals with algorithms to fit certain statistical models. We are concerned with the interplay between the numerical properties of the algorithm and the statistical properties of the model fitted. Chapter 1 outlines some results, concerning the construction of tests and the convergence of algorithms, based on quadratic approximations to the likelihood surface. These include the relationship between statistical curvature and the convergence of the scoring algorithm, separable regression, and a Gauss-Seidel process which we called coupled iterations. Chapters 2, 3 and 4 are concerned with varying parameter models. Chapter 2 proposes an extension of generalized linear models by including a linear predictor for (a function of) the dispersion parameter also. Chapter 3 deals with various ways to go outside this extended generalized linear model framework for normally distributed data. Chapter 4 briefly describes how coupled iterations may be applied to autoregressive and multinormal models. Chapters 5 to 8 apply a generalization of Prony's classical parametrization to solve separable regression problems which satisfy a linear homogeneous difference equation. Chapter 5 introduces the problem, specifies the assumptions under which asymptotic results are proved, and shows that the reduced normal equations may be expressed as a nonlinear eigenproblem in terms of the Prony parameters. Chapter 6 describes the algorithm which results from solving the eigenproblem, including some computational details. Chapter 7 proves that the algorithm is asymptotically stable. Chapter 8 compares the convergence of the algorithm with that of Gauss-Newton by way of simulations

Aging of poled ferroelectric ceramics due to relaxation of random depolarization fields by space-charge accumulation near grain boundaries

Migration of charged point defects triggered by the local random depolarization field is shown to plausibly explain aging of poled ferroelectric ceramics providing reasonable time and acceptor concentration dependences of the emerging internal bias field. The theory is based on the evaluation of the energy of the local depolarization field caused by mismatch of the polarizations of neighbor grains. The kinetics of charge migration assumes presence of mobile oxygen vacancies in the material due to the intentional or unintentional acceptor doping. Satisfactory agreement of the theory with experiment on the Fe-doped lead zirconate titanate is demonstrated.Comment: theory and experiment, 22 pages, 3 figure

Analysis of United Kingdom Off-Highway Construction Machinery Market and Its Consumers Using New-Sales Data

The off-highway construction machinery market and its consumers have attracted minimal previous research. This study addresses that void by analyzing annual United Kingdom (UK) (volume/portfolio) new-sales data for the 10 most popular products within that market, 1990–2010 inclusive. Graphical, descriptive statistical, Pearson-correlational, autocorrelational, and elementary modeling are employed to identify contrasts in sales regarding (1) high- and low-volume items; (2) growth trends and significant recessionary effects on volumes; (3) a demand change point circa 1997, since when annual product portfolio has changed little; and (4) product associations in consumer demand. Significant association is demonstrated between demand and construction output, especially with the value of new housing. Subsequently, consumption of wheeled loaders is modeled using construction volume, and demand for mini and crawler excavators is modeled using new-housing data. Time series trends for these machinery types are presented and forecast through 2015. The primary contribution of this study is a deeper understanding of the UK new-machinery market and the predilections of its consumers over the last two decades (to present)