# Publications Portal

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Topic Area: Math

Displaying records 41 to 50 of 220 records.

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41.

**Families of Elliptic Curves with Rational 3-torsion**
**Topic:** Math

**Published:** 1/30/2012

**Authors:** Dustin Moody, Hongfeng Wu

**Abstract:** In this paper we look at three families of elliptic curves with rational 3-torsion over a finite field. These families include Hessian curves, twisted Hessian curves, and a new family we call generalized DIK curves. We find the number of Fq-isogeny

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http://www.nist.gov/manuscript-publication-search.cfm?pub_id=909543
42.

**Fourier, Gauss, Fraunhofer, Porod and the Shape from Moments Problem**
**Topic:** Math

**Published:** 1/17/2012

**Author:** Gregg M. Gallatin

**Abstract:** We show how the Fourier transform of a shape in any number of dimensions can be simplified using Gauss' law and evaluated explicitly for polygons in two dimensions, polyhedra three dimensions, etc. We also show how this combination of Fourier and Gau

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http://www.nist.gov/manuscript-publication-search.cfm?pub_id=909668
43.

**Mathematical Optimization of Procedures for Cryoprotectant Equilibration Using a Toxicity Cost Function**
**Topic:** Math

**Published:** 1/10/2012

**Authors:** Adam Zachary Higgins, James Benson, Anthony J Kearsley

**Abstract:** Cryopreservation nearly universally depends on the equilibration of cells and tissues with high concentrations of permeating chemicals known as cryoprotective agents, or CPAs. Despite their protective properties, CPAs can cause damage as a result of

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http://www.nist.gov/manuscript-publication-search.cfm?pub_id=910486
44.

**Counting the Leaves of Trees**
**Topic:** Math

**Published:** 12/19/2011

**Authors:** Brian Dale Cloteaux, Luis A. Valentin

**Abstract:** A number of important combinatorial counting problems can be reformulated into the problem of counting the number of leaf nodes on a tree. Since the basic leaf-counting problem is #P-complete, there is strong evidence that no polynomial time algorith

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http://www.nist.gov/manuscript-publication-search.cfm?pub_id=908869
45.

**Linear Algebra and Sequential Importance Ssampling for Network Reliability**
**Topic:** Math

**Published:** 12/11/2011

**Authors:** David G. Harris, Francis Sullivan, Isabel M Beichl

**Abstract:** The reliability polynomial of a graph gives the probability that a graph is connected as a function of the probability that each edge is connected. The coefficients of the reliability polynomial count the number of connected subgraphs of various size

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http://www.nist.gov/manuscript-publication-search.cfm?pub_id=909109
46.

**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
47.

**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
48.

**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
49.

**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
50.

**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