# Publications Portal

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Topic Area: Math

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Displaying records 61 to 70 of 237 records.

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61.

**Combining Results from Multiple Evaluations of the Same Measurand**
**Series:** Journal of Research (NIST JRES)

**Topic:** Math

**Published:** 12/1/2011

**Authors:** Raghu N Kacker, Klaus-Dieter Sommer

**Abstract:** According to the Guide to the Expression of Uncertainty in Measurement (GUM), a result of measurement consists of a measured value together with its associated standard uncertainty. The measured value and the standard uncertainty are interpreted as

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http://www.nist.gov/manuscript-publication-search.cfm?pub_id=905068
62.

**Computing Network Reliability Coefficients**
**Topic:** Math

**Published:** 12/1/2011

**Authors:** Elizabeth R Moseman, Isabel M Beichl, Francis Sullivan

**Abstract:** When a network is modeled by a graph and edges of the graph remain reliable with a given probability p, the probability of the graph remaining connected is called the reliability of the network. One form of the reliability polynomial has as coefficie

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http://www.nist.gov/manuscript-publication-search.cfm?pub_id=908418
63.

**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
64.

**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
65.

**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
66.

**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
67.

**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
68.

**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
69.

**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
70.

**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