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Mathematics & Statistics

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Displaying 501 - 525 of 872

Fourier, Gauss, Fraunhofer, Porod and the Shape from Moments Problem

January 17, 2012
Author(s)
Gregg M. Gallatin
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 Gauss can

Social and Physical Aspects of Seismic Risk

December 31, 2011
Author(s)
Carmen D. Gon?alves, Antonio Possolo
Seismic risk has social and physical aspects: although very different in nature, they are intertwined and share striking similarities. Seismic risk assessment involves models and data, and judgments of the potential impact of earthquakes, which must be

Counting the Leaves of Trees

December 19, 2011
Author(s)
Brian D. Cloteaux, Luis A. Valentin
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 algorithm

Linear Algebra and Sequential Importance Ssampling for Network Reliability

December 11, 2011
Author(s)
David G. Harris, Francis Sullivan, Isabel M. Beichl
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 sizes

Combining Results from Multiple Evaluations of the Same Measurand

December 1, 2011
Author(s)
Raghu N. Kacker, Klaus-Dieter Sommer
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 the

Computing Network Reliability Coefficients

December 1, 2011
Author(s)
Elizabeth R. Moseman, Isabel M. Beichl, Francis Sullivan
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 coefficients

A Special Functions Handbook for the Digital Age

August 1, 2011
Author(s)
Ronald F. Boisvert, Charles W. Clark, Daniel W. Lozier, Frank W. Olver
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

Division Polynomials for Jacobi Quartic Curves

June 13, 2011
Author(s)
Dustin Moody
In this paper we fi nd 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 we fi