DIGITAL LIBRARY OF MATHEMATICAL FUNCTIONS
We would like to introduce you to a challenging project under development in ITL's Mathematical and Computational Sciences Division. An interdisciplinary team of NIST scientists is designing, editing, and constructing a Digital Library of Mathematical Functions (DLMF) ( http://dlmf.nist.gov/), an interactive, richly linked, and network-based resource of mathematical reference data from a variety of fields. Associate editors, authors, and validators from the U.S. and abroad contribute their expertise to the project. Co-funded by the National Science Foundation and five NIST organizations, the DLMF will provide some of the basic infrastructure needed by the technical community to integrate modern information technology more fully into its day-to-day work.
The digital library will replace the classic Handbook of Mathematical Functions, Applied Mathematics Series 55 (AMS 55), edited by Abramowitz and Stegun, and published by the National Bureau of Standards (now NIST) in 1964. Still in print and widely used throughout the worldwide scientific community, this important reference contains formulas, graphs, and tables, which characterize the higher functions of applied mathematics. These functions (often known as special functions) are used extensively in mathematical analysis in many fields, such as physics and chemistry, and they are essential tools in modern computational modeling of phenomena in the physical sciences and engineering. For example, they aid in analysis and computation in areas as diverse as astronomy, atmospheric modeling, metallurgy, ocean engineering, optical fibers, radar, statistics, underwater acoustics, and the modeling of the microstructure of materials.
The new DLMF will be an electronic publication freely distributed on the Web. It will take advantage of advanced communications and computational resources to present not only static data but also made-to-order dynamic information such as graphs, tables of numerical values, and symbolic transformations. With an emphasis on practical matters, the digital library will offer downloadable formulas, interactive graphics, math-enabled search tools, and links to references and software. The authoritative status of the existing handbook, and its orientation toward applications in science, statistics, engineering, and computation, will be preserved. An applications component will be included for electromagnetism and quantum physics to provide access to mathematical information in these fields, to coordinate and standardize definitions and notation, and to serve as a prototype applications component for other fields.
Thus the utilitarian value of the handbook will be extended far beyond its original scope and the traditional limitations of printed media. The term digital library has gained acceptance for this type of information resource, and our choice of project title reflects our hope that the NIST DLMF will be a vehicle for revolutionizing the way applicable mathematics in general is practiced and delivered.
Our Approach
In 1997, we initiated planning meetings for the development of the digital library. As a starting point, we thoroughly reviewed Abramowitz and Stegun's Handbook of Mathematical Functions with regard to the needs of today's scientific, engineering, and technical communities. For example, was the overall structure still appropriate? Were there functions not presently covered that should be added? Were there functions that should be removed? Was there specific information about each function that needed to be added or removed? And, were there important new mathematical formulas to be added?
It was clear that more emphasis needed to be placed on computational aspects. Ideally, static tables of numerical values should be replaced by software that can generate custom tables on demand. The same is true for graphical representations. Would technology and resources permit us to do this? What was the proper role for symbolic software? These kinds of questions were considered with the assistance of qualified professionals from around the world.
In July 1997, NIST hosted an Invitational Workshop on Mathematical Functions, which was attended by well-known experts in the theory and application of special functions. The concept of the DLMF project, to develop a successor to AMS 55 by conducting a thorough survey of the pertinent scientific literature and to take advantage of the latest relevant advances in information technology, was developed in broad outline at this meeting. We then assessed interest in the project in the larger scientific community and obtained enthusiastic support for our plan. Finally, we assembled our Editorial Board and developed an outline of the technical material to be included in the DLMF.
Our Project Team
To take advantage of expertise in diverse areas, we assembled a project team consisting of 12 NIST staff members. Our team consists of four editors, three Web specialists, two experts in visualizations, two physicists who are developing the physics application modules, and one expert in math algorithms and software. External project participants include ten associate editors, three for special functions, two for physics, and one each in chemistry, combinatorics, numerical analysis, statistics, and computer algebra. Thirty-four authors from around the world will contribute their expertise and validators will review their chapters.
Content of the DLMF
The core mathematical material for the DLMF is being developed from a thorough review of the relevant literature of the past 40 years and is being enriched by current computational methods and typical scientific applications. The Table of Contents reflects the scope of the project:
MP - Mathematical and Physical Constants
AL - Algebraic and Analytical Methods
AS - Asymptotic Approximations
NM - Numerical Methods
CA - Computer Algebra
EF - Elementary Functions
GA - Gamma Function
EX - Exponential Integral, Logarithmic Integral, Sine and Cosine Integrals
ER - Error Functions, Dawson's Integral, Fresnel Integrals
IG - Incomplete Gamma Functions and Generalized Exponential Integral
AI - Airy and Related Functions
BS - Bessel Functions
ST - Struve Functions and Anger-Weber Functions
CH - Confluent Hypergeometric Functions
CW - Coulomb Wave Functions
PC - Parabolic Cylinder Functions
LE - Legendre Functions and Spherical Harmonics
HY - Hypergeometric Functions
GH - Generalized Hypergeometric Functions and Meijer G-Function.
QH - q-Hypergeometric Functions
CP - Classical Orthogonal Polynomials
OO - Other Orthogonal Polynomials
EL - Elliptic Integrals
JA - Jacobian Elliptic Functions and Theta Functions
WE - Weierstrass Elliptic Functions
BP - Bernoulli and Euler Numbers and Polynomials
ZE - Zeta and Related Functions
CM - Combinatorial Analysis
NT - Functions of Number Theory
SM - Statistical Methods and Distributions
MA - Mathieu Functions and Hill's Equation
LA - Lame Functions; Spheroidal Wave Functions
HE - Heun Functions and Hill's Equation
PT - Painleve Transcendents
IC - Integrals with Coalescing Saddles
WA - Wavelets
TJ3j, 6j, 9j Symbols
To view a sample chapter on Airy Functions, see http://dlmf.nist.gov/Contents/AI/.
Conclusion
Revising and updating the mathematical reference data in AMS 55 through the DLMF will ensure that this popular and well-respected NIST product remains useful well into the 21st century. Making the revised and up-to-the-minute data freely available on the Web will not only greatly increase its utility in the research community by saving countless hours of searching time, but also make it available to new audiences, such as small businesses and college students, who may have had limited access to this data in the past. Finally, advancing the technology for display, search, and interaction with mathematical reference data will make the product more usable. We hope that the DLMF will serve as a prototype for treating other branches of mathematics as well as science in a similar way.
The completion date of the project is 2003. However, the Web site will be available in a beta version in 2002 and will grow as chapters are finalized. A hardcopy version of the DLMF with a CD-ROM will also be published in 2003. For more information, contact Dr. Daniel Lozier, DLMF General Editor, at (301) 975-2706, e-mail daniel.lozier@nist.gov.
UPDATE ON NEW PUBLICATIONS
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Formalizing the NIST 4-D/RCS Reference Model Architecture Using an Architectural Description Language
By C. Dabrowski, H. Huang, E. Messina, and J. HorstThe 4-D/Real-Time Control System (RCS) Reference Model Architecture provides a well-defined strategy for the development of software components for applications in robotics, automated manufacturing, and autonomous vehicles. We conducted an investigation into the use of Architectural Description Languages (ADLs) as a means of providing a more formal, rigorous definition of the 4-D/RCS architecture and specifying software components for 4-D/RCS systems. This report describes the results of an experiment into the use of an ADL to specify 4-D/RCS systems and assesses the potential value of ADLs as specification and development tools for RCS domain experts.
Distortion-Tolerant Filter for Elastic-Distorted Fingerprint Matching
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Symposium on the Foundations of Interactive digital TV Application Software Environment (DASE)
A. Mink and R. Snelick, EditorsThis report describes the DASE Symposium 2000. The emergence of interactive digital television (DTV) brings about a host of exciting opportunities for broadcasters, content providers, tool developers, and equipment manufacturers. Interactive DTV combines aspects of traditional television and the Internet that inspires applications in e-commerce, targeted advertising, video-on-demand, and enhanced viewing services. An enabling technology for applying interactive DTV is being developed by the Advanced Television Systems Committee (ATSC) Digital TV Application Software Environment (DASE) standards group. Currently a work-in-progress, the emerging DASE standard and its relationship to DTV were the focus of the symposium.
UPCOMING TECHNICAL CONFERENCES
Biometric Consortium 2000 Conference
The conference will focus on rapid advances in biometrics technologies, measurement, and standards. It will examine how biometrics is being implemented in many personal authentication applications and how it is converging with other authentication technologies (e.g., smart cards and PKI). The audience will be stakeholders in the areas of biometrics and personal authentication technologies, such as government and private industry executives, researchers, vendors, and system integrators.
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This third annual conference will discuss the latest trends, technologies, and standards for electronic books. Topics will include new e-book technologies, digital rights management, e-book applications for libraries, education and government, e-book standards, and interoperability. The audience will be publishers, authors and technologists. Dates: September 25-27, 200023rdNational Information Systems Security Conference
As a leading global forum on computer and information systems security, this annual conference brings together information security and technology professionals from industry, academia, and government. This year's conference theme is "Campaign for Security." The goals of the conference are to provoke debate, dialogue, and action on major information security issues for today and tomorrow; educate the IT community on major information security issues and solutions; promote demand and investment in information security products, solutions, and research; and challenge the IT community to provide solutions, research, and applied technology that are usable, interoperable, scalable, and affordable. Dates: October 16-19, 2000Workshop on Modes of Operation for Symmetric Key Block Cipher Algorithms
The workshop will focus on modes of operation for the protection of data using symmetric key block cipher algorithms. The results of this workshop will be used by NIST in developing a draft modes of operation standard for symmetric key block cipher algorithms. Note that this workshop follows the 23rd National Information Systems Security Conference (see above).
Date: October 20, 2000--------------------------------
Disclaimer: Any mention of commercial products or reference to commercial organizations is for information only; it does not imply recommendation or endorsement by the National Institute of Standards and Technology nor does it imply that the products mentioned are necessarily the best available for the purpose.