# Publications Portal

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Topic Area: Math

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Displaying records 61 to 70 of 235 records.

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61.

**Optimality Conditions for a Hierarchical Control Problem Governed by a PDE**
**Topic:** Math

**Published:** 11/15/2011

**Author:** Anthony J Kearsley

**Abstract:** We consider the approximate pointwise control of a linear parabolic system with multiple targets.
Assuming a hierarchy among the objectives, we derive optimality conditions for a particular test problem and provide numerical results.

http://www.nist.gov/manuscript-publication-search.cfm?pub_id=910100
62.

**Mean Value Formulas for Twisted Edwards Curves**
**Topic:** Math

**Published:** 11/3/2011

**Author:** Dustin Moody

**Abstract:** R. Feng and H.Wu recently established a certain mean-value formula for the coordinates of the n-division points on an elliptic curve given inWeierstrass form (A mean value formula for elliptic curves, 2010, available at http://eprint.iacr.org/2009/58

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http://www.nist.gov/manuscript-publication-search.cfm?pub_id=907010
63.

**A Special Functions Handbook for the Digital Age**
**Topic:** Math

**Published:** 8/1/2011

**Authors:** Ronald F Boisvert, Charles W Clark, Daniel W Lozier, Frank William John Olver

**Abstract:** The NIST Digital Library of Mathematical Functions (DLMF) is a reference work providing information on the properties of the special functions of applied mathematics. It is a successor to the highly successful NBS Handbook of Mathematical Functions (

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http://www.nist.gov/manuscript-publication-search.cfm?pub_id=906771
64.

**Only non-informative Bayesian prior distributions agree with the GUM Type A evaluations of input quantities**
**Topic:** Math

**Published:** 6/21/2011

**Author:** Raghu N Kacker

**Abstract:** The Guide to the Expression of Uncertainty in Measurement (GUM) is self-consistent when Bayesian statistics is used for the Type A evaluations and the standard deviation of the posterior state-of-knowledge distribution is used as the Bayesian standar

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http://www.nist.gov/manuscript-publication-search.cfm?pub_id=907999
65.

**Rapid Monte Carlo SI Mulations Using Parallel Computing and a Client-server Model **
**Topic:** Math

**Published:** 6/21/2011

**Authors:** Raghu N Kacker, Ruediger Kessel

**Abstract:** Processors with multiple CPU cores have become widely available. Therefore it is useful to parallelize the Monte Carlo simulation process in the context of metrology. Different approaches for parallel computing including Monte Carlo simulations are a

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http://www.nist.gov/manuscript-publication-search.cfm?pub_id=909264
66.

**Division Polynomials for Jacobi Quartic Curves**
**Topic:** Math

**Published:** 6/13/2011

**Author:** Dustin Moody

**Abstract:** In this paper we find division polynomials for Jacobi quartics. These curves are an alternate model for elliptic curves to the more common Weierstrass equation. Division polynomials for Weierstrass curves are well known, and the division polynomials

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http://www.nist.gov/manuscript-publication-search.cfm?pub_id=908330
67.

**On Parameter Differentiation for Integral Representations of Associated Legendre Functions**
**Topic:** Math

**Published:** 5/24/2011

**Author:** Howard S Cohl

**Abstract:** 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 associate

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http://www.nist.gov/manuscript-publication-search.cfm?pub_id=907710
68.

**Bayesian uncertainty analysis for a regression model versus application of GUM Supplement 1 to the least-squares estimate**
**Topic:** Math

**Published:** 5/5/2011

**Authors:** Blaza Toman, Clemens Elster

**Abstract:** 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 esti

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http://www.nist.gov/manuscript-publication-search.cfm?pub_id=907685
69.

**Reconstructing the Past From Imprecise Knowledge of the Present: Some Examples of Non Uniqueness
in Solving Parabolic Equations Backward in Time**
**Series:** NIST Interagency/Internal Report (NISTIR)

**Report Number:** 7783

**Topic:** Math

**Published:** 4/13/2011

**Author:** Alfred S Carasso

http://www.nist.gov/manuscript-publication-search.cfm?pub_id=908362
70.

**A Survey of Binary Covering Arrays**
**Topic:** Math

**Published:** 4/7/2011

**Authors:** James F Lawrence, Raghu N Kacker, Yu Lei, David R Kuhn, Michael Forbes

**Abstract:** 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 im

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http://www.nist.gov/manuscript-publication-search.cfm?pub_id=51256