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Mathematics & Statistics

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Displaying 676 - 700 of 872

Approximating Periodic Solutions of Autonomous Delay Differential Equations

November 30, 2006
Author(s)
David E. Gilsinn
Machine tool chatter has been characterized as isolated periodic solutions or limit cycles of delay differential equations. Determining the amplitude and frequency of the limit cycle is sometimes crucial to understanding and controlling the stability of

Integral Operators and Delay Differential Equations

October 1, 2006
Author(s)
David E. Gilsinn, Florian A. Potra
We begin this expository essay by reviewing with examples what a typical engineer already knows about statistics. We then consider a central question in engineering decision making, i.e., given a computer simulation of high-consequence systems, how do we

Minimum-Phase Calibration of Sampling Oscilloscopes

August 15, 2006
Author(s)
Andrew M. Dienstfrey, Paul D. Hale, Darryl A. Keenan, Tracy S. Clement, Dylan F. Williams
We describe an algorithm for determining the minimum phase of a linear time-invariant response function from its magnitude. The procedure is based on Kramers Kronig relations in combination with auxiliary direct measurements of the desired phase response

Calculation of the uncertainty of the mean of autocorrelated measurements

August 4, 2006
Author(s)
Nien-Fan Zhang
When repeated measurements are autocorrelated, it is not appropriate to use the traditional approach to calculate the uncertainty of the average of the measurements, which assumes that the measurements are statistically independent. In this paper, we

Pseudo-Exhaustive Testing for Software

April 28, 2006
Author(s)
David R. Kuhn, Vadim Okun
Pseudo-exhaustive testing uses the empirical observation that, for broad classes of software, a fault is likely triggered by only a few variables interacting. The method takes advantage of two relatively recent advances in software engineering: algorithms

Bayesian Alternative to the Guide's Use of the Welch-Satterthwaite Formula

January 3, 2006
Author(s)
Raghu N. Kacker
The Guide to the Expression of Uncertainty in Measurement suggests that to account for the statistical uncertainty in a combined standard uncertainty that arises when one or more of its components are evaluated from a limited number of independent normally

Coefficient of Contribution to the Combined Standard Uncertainty

January 1, 2006
Author(s)
Raghu N. Kacker, Rudiger Kessel, Michael Berglund
The International Organization for Standardization (ISO) Guide to the Expression of Uncertainty in Measurement (GUM) describes a generic procedure for determining an estimate for the measurand and its associated combined standard uncertainty from the