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Mathematics & Statistics

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Displaying 526 - 550 of 872

On Parameter Differentiation for Integral Representations of Associated Legendre Functions

May 24, 2011

Author(s)

Howard S. Cohl

For integral representations of associated Legendre functions in terms of modified Bessel functions, we establish justification for differentiation under the integral sign with respect to parameters. With this justification, derivatives for associated

Bayesian Uncertainty Analysis for a Regression Model Versus Application of GUM Supplement 1 to the Least-Squares Estimate

May 5, 2011

Author(s)

Blaza Toman, Clemens Elster

Application of least-squares as, for instance, in curve fitting is an important tool of data analysis in metrology. It is tempting to employ the supplement 1 to the GUM (GUM-S1) to evaluate the uncertainty associated with the resulting parameter estimates

DEoptim: An R Package for Global Optimization by Differential Evolution

May 1, 2011

Author(s)

Katharine M. Mullen, David Ardia , David L. Gil, Donald A. Windover, James P. Cline

This article describes the R package DEoptim which implements the differential evolution algorithm for the global optimization of a real-valued function of a real-valued parameter vector. The implementation of differential evolution in DEoptim interfaces

Reconstructing the Past From Imprecise Knowledge of the Present: Some Examples of Non Uniqueness in Solving Parabolic Equations Backward in Time

April 13, 2011

Author(s)

Alfred S. Carasso

A Survey of Binary Covering Arrays

April 7, 2011

Author(s)

James F. Lawrence, Raghu N. Kacker, Yu Lei, David R. Kuhn, Michael Forbes

Two-valued covering arrays of strength t are 0--1 matrices having the property that for each t columns and each of the possible 2t sequences of t 0's and 1's, there exists a row having that sequence in that set of t columns. Covering arrays are an

Arithmetic Progressions on Edwards Curves

February 8, 2011

Author(s)

Dustin Moody

We look at arithmetic progressions on elliptic curves known as Edwards curves. By an arithmetic progression on an elliptic curve, we mean that the x-coordinates of a sequence of rational points on the curve form an arithmetic progression. Previous work has

Applied and Computational Mathematics Division Summary of Activities for Fiscal Year 2010

February 2, 2011

Author(s)

Ronald F. Boisvert

This report summarizes the technical work of the Applied and Computational Sciences Division (ACMD) of NIST s Information Technology Laboratory. Part I (Overview) provides a high-level overview of the Division s activities, including highlights of

Approximating the Number of Bases for Almost All Matroids

February 1, 2011

Author(s)

Brian D. Cloteaux

We define a class of matroids A for which a fully polynomial randomized approximation scheme (fpras) exists for counting the number of bases of the matroids. We then show that as the number of elements in a matroid increases, the probability that a matroid

Changes

January 3, 2011

Author(s)

Isabel M. Beichl

Recommendation for Password-Based Key Derivation Part 1: Storage Applications

December 22, 2010

Author(s)

Meltem Sonmez Turan, Elaine B. Barker, William E. Burr, Lidong Chen

This Recommendation specifies techniques for the derivation of master keys from passwords or passphrases to protect stored electronic data or data protection keys.

Assessing differences between results determined according to the Guide to the Expression of Uncertainty in Measurement

December 1, 2010

Author(s)

Raghu N. Kacker, Ruediger Kessel, Klaus-Dieter Sommer

When the data consist of multiple results of measurement for a common measurand, often one needs to determine whether the results agree with each other. A result of measurement based on the Guide to the Expression of Uncertainty in Measurement (GUM)

Derivation of Isosceles Trapezoidal Distribution

December 1, 2010

Author(s)

Raghu N. Kacker, James F. Lawrence

It is known that, if the mid-point of a rectangular distribution is specified, the half-width is inexactly known, and the state of knowledge about the half-width may be represented by a narrower rectangular distribution then the resulting distribution

Bochner Subordination, Logarithmic Diffusion Equations, and Blind Deconvolution of Hubble Space Telescope Imagery and Other Scientific Data

November 30, 2010

Author(s)

Alfred S. Carasso

Generalized Linnik processes and associated logarithmic diffusion equations can be constructed by appropriate Bochner randomization of the time variable in Brownian motion and the related heat conduction equation. Remarkably, generalized Linnik