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Displaying 1 - 14 of 14

Semantic Preserving Bijective Mappings of Mathematical Formulae between Word Processors and Computer Algebra Systems

June 28, 2017
Author(s)
Howard S. Cohl, Bonita V. Saunders, Marjorie A. McClain, Moritz Schubotz, Joon Bang, Juergen Gerhardt, Andre Greiner Petter
There are many different approaches to represent mathematical expressions on computers. Word processors like LaTeX offer the ability to render mathematical expressions as one would write these on paper. Using LaTeX, LaTeXML, and tools generated for use in

Digital Repository of Mathematical Formulae KLS Seeding Project

June 23, 2015
Author(s)
Howard S. Cohl, Marjorie A. McClain, Bonita V. Saunders, Moritz Schubotz, Cherry Y. Zou, Alex A. Danoff, Azeem S. Mohammed
One initial goal for the DRMF is to seed our digital compendium with fundamental orthogonal polynomial formulae. We have received permission from Springer-Verlag and the authors to use formulae from Chapters 1, 9, and 14 from the book "Hypergeometric

Digital Repository of Mathematical Formulae

October 17, 2014
Author(s)
Howard S. Cohl, Marjorie A. McClain, Bonita V. Saunders, Moritz Schubotz, Janelle Williams
The purpose of the NIST Digital Repository of Mathematical Formulae (DRMF) is to create a digital compendium of mathematical formulae for orthogonal polynomials and special functions (OPSF) and of associated mathematical data. The DRMF addresses needs of

A Survey of hp-Adaptive Strategies for Elliptic Partial Differential Equations

January 3, 2011
Author(s)
William F. Mitchell, Marjorie A. McClain
The hp version of the finite element method (hp-FEM) combined with adaptive mesh refinement is a particularly efficient method for solving partial differential equations because it can achieve a convergence rate that is exponential in the number of degrees

An Examination of New Paradigms for Spline Approximations

May 1, 2006
Author(s)
Christoph J. Witzgall, David E. Gilsinn, Marjorie A. McClain
Lavery splines are examined in the univariate and bivariate cases. In both instances relaxation based algorithms for approximate calculation of Lavery splines are proposed. Following previous work Gilsinn, et al. [7] addressing the bivariate case, a

Using Nonoscillatory Splines to Model Urban Environments

January 15, 2004
Author(s)
David E. Gilsinn, Marjorie A. McClain, Christoph J. Witzgall
In this paper we introduce the notion of Lavery splines and examine their properties in the univariate case. We also discuss some of the details involved with computing these splines on irregularly spaced data.

A Constrained Monte Carlo Simulation Method for the Calculation of CMM Measurement Uncertainty

January 1, 1999
Author(s)
Steven D. Phillips, Bruce R. Borchardt, Daniel S. Sawyer, William T. Estler, K Eberhardt, M Levenson, Marjorie A. McClain, Ted Hopp
We describe a Monte Carlo simulation technique where known information about a metrology system is employed as a constraint to distinguish the errors associated with the instrument under consideration from the set of all possible instrument errors. The

Practical Aspects of Touch Trigger Probe Error Compensation

July 1, 1997
Author(s)
William T. Estler, Steven D. Phillips, Bruce R. Borchardt, Ted Hopp, M Levenson, K Eberhardt, Marjorie A. McClain
We present extensions of our prior work in modeling and correcting for pretravel variation errors in kinematic seat touch-trigger coordinate measuring machine (CMM) probes with straight styli. A simple correction term is shown to account for a range of

The Calculation of CMM Measurement Uncertainty via The Method of Simulation by Constraints

January 1, 1997
Author(s)
Steven D. Phillips, Bruce R. Borchardt, Daniel S. Sawyer, William T. Estler, David E. Ward, K Eberhardt, M. Levenson, Marjorie A. McClain, B Melvin, Ted Hopp, Y Shen
The calculation of task specific measurement uncertainty when using coordinate measuring machines is an important and challenging task. Current methods to address this issue use simulation techniques (e.g., the virtual CMM) where the propagation of known

Error Compensation for CMM Touch Trigger Probes

October 1, 1996
Author(s)
William T. Estler, Steven D. Phillips, Bruce R. Borchardt, Ted Hopp, G Witzgall, M Levenson, K Eberhardt, Marjorie A. McClain, Y Shen, X Zhang
We present the analysis of a simple mechanical model of a common type of kinematic seat touch trigger probe widely used on modern coordinate measuring machines (CMMs). The model provides a quantitative description of the pretravel variation or probe-lobing