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Mathematics & Statistics

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Displaying 426 - 450 of 473

Algorithms and Codes for the Macdonald Function: Recent Progress and Comparisons

February 1, 2003

Author(s)

B R. Fabijonas, Daniel W. Lozier, J M. Rappoport

The modified Bessel function K iŅχ, also known as the Macdonald function, finds application in the Kontorovich-Lebedev integral transform when χ and Ņ are real and positive. In this paper, a comparison of three codes for computing this function is made

Dealing with Degeneracy in Triangulation

November 1, 2002

Author(s)

Francis Sullivan, Isabel M. Beichl

This is a tutorial article on a quick method for dealing with degeneracy in geometric computations with specific reference to triangulation. The type degeneracy targeted by this article that of four or more points on a circle and five or more points on a

Lattice Matching (LM)-Prevention of Inadvertent Duplicate Publications of Crystal Structures

October 1, 2002

Author(s)

Alan D. Mighell

Lattice-matching techniques have proved to be an extremely effective for the identification of unknown crystalline materials. A commonly employed lattice-matching strategy is based on matching the reduced cell of an unknown against a database of known

Reconstructing Images of Bar Codes for Construction Site Object Recognition

September 1, 2002

Author(s)

David E. Gilsinn, Geraldine S. Cheok, Dianne M. O'Leary

This paper discusses a general approach to reconstructing ground truth intensity images of bar codes that have been distorted by LADARoptics. The first part of this paper describes the experimental data collection of several bar code images along with

Conventional Cells--The Last Step Toward General Acceptance of Standard Conventional Cells for the Reporting of Crystallographic Data

August 1, 2002

Author(s)

Alan D. Mighell

The Absolute Integrating Sphere Method is now used at NIST for the detector-based calibration of total luminous flux of lamps, as well as for the realization of the lumen. This method has many benefits for high-accuracy applications, allowing for

Comparative Statistical Analysis of Test Parts Manufactured in Production Environments

June 1, 2002

Author(s)

David E. Gilsinn, Alice V. Ling

Estimating error uncertainties arising in parts produced on machine tools in production machine shops is not a well understood process. The current study details a process of estimating these error uncertainties. A part with significant features was

Shape-Preserving, Multi-Scale Fitting of Bivariate Data by Cubic L 1 Smoothing Splines

May 10, 2002

Author(s)

David E. Gilsinn, J E. Lavery

Bivariate cubic L1 smoothing splines are introduced. The coefficients of a cubic L1 smoothing spline are calculated by minimizing the weighted sum of the L1 norms ofsecond derivatives of the spline and the l1 norm of the residuals of the data-fitting

Estimating Critical Hopf Bifurcation Parameters for a Second Order DelayDifferential Equation with Application to Machine Tool Chatter

May 1, 2002

Author(s)

David E. Gilsinn

Nonlinear time delay differential equations are well known to have arisen in models in physiology, biology and population dynamics. They have also arisen in models of metal cutting processes. Machine tool chatter, from a process called regenerative chatter

The Role of Rendering in the Competence Project in Measurement Science for Optical Reflection and Scattering

May 1, 2002

Author(s)

H B. Westlund, G W. Meyer, Fern Y. Hunt

Rendering is the process of producing a synthetic image using a computer. The best known application is animation and simulation of scenes for the entertainment industry but recognition of its value as a tool for product design in other areas is increasing

Lattice Symmetry and Identification--The Fundamental Role of Reduced Cells in Materials Characterization

February 1, 2002

Author(s)

Alan D. Mighell

In theory, physical crystals can be represented by idealized mathematical lattices. Under appropriate conditions, these representations can be used for a variety of purposes such as identifying, classifying, and understanding the physical properties of

The Relegation Algorithm

March 3, 2001

Author(s)

A Deprit, E Deprit, Jesuus Palacian

Given a perturbed Hamiltonian system, normalization yields a Lie transformation which converts the main part of the Hamiltonian into an integral of the transformed system. An extension of the normalization method--the relegation algorithm--does the same

Constructing Sibson Elements for a Rectangular Mesh

February 1, 2001

Author(s)

David E. Gilsinn

This paper documents the construction of a finite element, called the Sibson element. The shape function of this element is formed on rectangular grids by C 1 splines defined on a triangulation of each subrectangle by dividing it into four subtriangles

Analytic Continuation, Singular Value Expansions, and Kramers-Kronig Analysis

January 17, 2001

Author(s)

Andrew M. Dienstfrey, L Greengard

We describe a systematic approach to the recovery of a function analytic in the upper half plane, ${\bfC:^+$, from measurements over a finite interval on the real axis, $D\subset {\bfR}$. Analytic continuation problems of this type are well-known to ill

Lattice Sums and the Two-dimensional, Periodic Green s Function for the Helmholtz Equation

January 16, 2001

Author(s)

Andrew M. Dienstfrey, Fengbo Hang, Jingfang Huang

Many algorithms that are currently used for the solution of the Helmholtz equation in periodic domains require the evaluation of the Green s function, G(x, x0). The fact that the natural representation of G via the method of images gives rise to a

Multiresolution Representation of Urban Terrain By L^1^ Splines, L^2^ Splines, and Piecewise Planar Surfaces

December 11, 2000

Author(s)

J E. Lavery, David E. Gilsinn

Cubic L 1 and L 2 interpolating splines based on C 1 smooth piecewise cubic Sibson elements on a tensor-product grid are investigated. Computational tests were carried out for a 102.4 km area of Fort Hood, Texas represented by a 1025 x 1025 set of 100

Direct Blind Deconvolution II. Substitute Images and the Beak Method

November 1, 2000

Author(s)

Alfred S. Carasso

The BEAK method is an FFT-based direct blind deconvolution technique previously introduced by the author, and applied to a limited but significant class of blurs that can be expressed as convolutions of 2-D symmetric L vy probability density functions

Attractors, Chain Transitive Sets and Invariant Measures

September 15, 2000

Author(s)

Fern Y. Hunt

This paper discusses an easy to implement procedure for approximating the long time behavior of iterates of maps. Applications include to finding the roots of a complex polynomial and approximating attractors. The method uses the theory of Markov chains.

Zoltan: Data-Management Services For Parallel Applications Developer's Guide

June 30, 2000

Author(s)

K Devine, B Hendrickson, E Boman, M St. John, C Vaughan, William F. Mitchell

The Zoltan Dynamic Load-Balancing Library provides critical capability to a number of parallel applications. Zoltan includes a suite of algorithms for dynamically computing partitions of problems over sets of processors; geometric, tree-based and graph

Zoltan: Data-Management Services For Parallel Applications; User's Guide

June 30, 2000

Author(s)

K Devine, B Hendrickson, E Boman, M St. John, C Vaughan, William F. Mitchell

On the Bifurcation From Continuous to Segmented Chip Formation in Metal Cutting

February 6, 2000

Author(s)

Timothy J. Burns, Matthew A. Davies, Christopher J. Evans

We describe a new approach to modeling chip formation in orthogonal machining. Metal cutting is interpreted as a nonlinear dynamical process with thermomechanical feedback, which is similar in many ways to an open chemical reactor. As the cutting speed is

A First Stop Towards Photorealistic Rendering of Coated Surfaces and Computer Based Standards of Appearance

November 1, 1999

Author(s)

Fern Y. Hunt, Egon Marx, G W. Meyer, Theodore V. Vorburger, P A. Walker, H B. Westlund

We seek to explore the feasibility of producing computer graphic images to visualize the color and gloss of surfaces using optical and surface topographical data.

The DLMF Project: A New Initiative in Classical Special Functions

June 1, 1999

Author(s)

Daniel W. Lozier

NIST (formerly, National Bureau of Standards) has started an ambitious project that aims to produce a successor to Abramowitz and Stegun's {\em Handbook of Mathematical Functions}, published by the National Bureau of Standards in 1964 and reprinted by

Stable Quasicrystalline Sphere Packing

March 1, 1999

Author(s)

Eric J. Cockayne, M Mihalkovic

Wills (1990, J. Phys., Paris 51, 1061), found a method relating certain decagonal disk packings to decagonal sphere packings with high packing fractions. Applying this technique to the decagonal rectangle-triangle tiling generated by inflation, we obtain a

Logarithmic Convexity and the 'Slow Evolution' Constraint in Ill-Posed Initial Value Problems

January 15, 1999

Author(s)

Alfred S. Carasso

This paper examines a wide class of ill-posed initial value problems for partial differential equations, and surveys logarithmic convexity results leading to Hoelder-continuous dependence on data for solutions satisfying prescribed bounds. The discussion

On the Distribution of the Limit of Products of I.I.D 2 x 2 Random Stochastic Matrices

January 15, 1999

Author(s)

A Mukherjea, Anastase Nakassis, J S. Ratti

This article extends the results of [3] by establishing sufficient conditions for the limit distribution of products of i.i.d. 2 x 2 random stochastic matrices to be continuous singular, when the support of the distribution of the individual random

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