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Mathematics & Statistics

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Displaying 201 - 225 of 872

Elliptic Curves Arising from Triangular Numbers

February 1, 2019
Author(s)
Abhishek Juyal, Shiv D. Kumar, Dustin Moody
We study the Legendre family of elliptic curves E_t : y^2 = x(x − 1)(x − ∆t), parametrized by triangular numbers ∆t = t(t + 1)/2. We prove that the rank of E_t over the function field Q(t) is 1, while the rank is 0 over Q(t). We also produce some infinite

Compositional Models for Complex Systems

January 19, 2019
Author(s)
Spencer J. Breiner, Ram D. Sriram, Eswaran Subrahmanian
In this chapter we argue for the use of representations from category theory to support better models for complex systems, and provide an example of such an application might look like. Our approach rests on the well known observation that complex system

Categorical Models for Process Planning

November 19, 2018
Author(s)
Spencer J. Breiner, Eswaran Subrahmanian, Albert W. Jones
Process plans provide a structure for 1) identifying the tasks involved in a given process, 2) the resources needed to accomplish them, and 3) a variety of relationships and constraints between these. This information guides important operational decisions

True value and uncertainty in measurement

September 3, 2018
Author(s)
Raghu N. Kacker
We will discuss the concept of true value and its connection with the uncertainty in measurement as defined in the Guide to the Expression of Uncertainty in Measurement (GUM), and three subsequent documents from the Joint Committee for Guides in Metrology

Federal Office of Research and Technology Applications Survey Results

August 9, 2018
Author(s)
Nicole K. Gingrich
This publication serves as a formal reporting of the data presented at the 2017 Federal Laboratory Consortium’s National Meeting. It presents summary data collected through a survey conducted by NIST in conjunction with the Interagency Working Group on

THREE APPROACHES TO QUANTIFICATION OF NDE UNCERTAINTY AND A DETAILED EXPOSITION OF THE EXPERT PANEL APPROACH USING THE SHEFFIELD ELICITATION FRAMEWORK

July 15, 2018
Author(s)
Jeffrey T. Fong, Nathanael A. Heckert, James J. Filliben, Steven R. Doctor
The ASME Boiler & Pressure Vessel Code Section XI Committee is currently developing a new Division 2 nuclear code entitled the "Reliability and Integrity Management (RIM) program," with which one is able to arrive at a risk-informed, NDE-based engineering

RFC: DLMF Content Dictionaries

July 12, 2018
Author(s)
Bruce R. Miller
This note presents a proposed set of (virtual) OpenMath Content Dictionaries to characterize the mathematical special functions as used in the Digital Library of Mathematical Functions.

Shape Analysis, Lebesgue Integration and Absolute Continuity Connections

July 10, 2018
Author(s)
Javier Bernal
As shape analysis of the form presented in Srivastava and Klassen’s textbook “Functional and Shape Data Analysis” is intricately related to Lebesgue integration and absolute continuity, it is advantageous to have a good grasp of the latter two notions