KDI: Mathematical Foundations for a Networked Scientific Knowledge Base

9980036这个项目解决了一个面向web的数学概念知识库的生成、验证、组织、分布和使用问题。所涵盖的领域是应用数学的特殊函数。研究者和他的同事开发了一个数字数学函数图书馆（DLMF），这是一个通过对档案文献进行全新调查而获得的经过验证的数学数据的网络知识库。DLMF以经典的NBS数学函数手册（Abramowitz和Stegun主编）的简洁风格提供参考信息，但在基于语义的表示、元数据、交互功能和内部/外部链接的丰富结构中。它支持不同的用户需求，例如简单查找、复杂搜索和检索、公式验证和发现、自动规则生成、交互式可视化、按需定制数据，以及指向软件和评估数值方法的指针。作为NBS手册的继承者，DLMF提供了可追溯到NIST定义的数学概念的权威来源。基础研究问题与内容、表示以及人类和其他代理与DLMF知识库的交互有关。这些问题包括识别和验证相关材料；基于语义的数学信息表示的发展元数据结构；数学数据库的检索与检索；以及适合组合、显示和计算的格式之间的数学数据转换。这些问题正在由一个由编辑委员会监督的国际专家小组解决。DLMF将与CD-ROM以及免费的网络服务一起以印刷版的形式传播，该服务将在NIST无限期地维护。项目人员正在构建一个数字数学函数图书馆（DLMF），为应用数学的高级函数提供nist认证的参考数据和相关信息。这些函数具有丰富的至关重要和高度技术性的特性，被工程师、科学家、统计学家和其他人用来帮助在各种应用中构建和分析材料和过程的计算模型。dlmf帮助用户定位公式、算法和软件；通过交互式图形和典型应用理解复杂关系；追踪数学定义和属性到NIST标准；并将复杂的数学信息以完全可靠和准确的方式转录到文件和计算机程序中。例如，软件公司将能够使用DLMF来生产大大改进的库和软件包。这是非常重要的，因为软件为从业者提供了最有效的方法，使他们能够轻松可靠地使用数学方法。目前的数学函数参考标准是由NIST在美国国家科学基金会的支持下于20世纪50年代开发的，已经严重过时。从那时起，无数新的属性、函数、应用和计算技术变得重要起来。这一差距需要通过充分利用现代信息技术来填补。这些数据将在一个最先进的万维网网站上公布，该网站将成为数学函数技术研究人员和用户社区的焦点，此外还将在一本附有CD-ROM的书中公布。预计DLMF将成为其他类似项目的典范。该KDI项目由数学科学部和信息与智能系统部支持。

9980036This project addresses the problems of generation, validation, organization, distribution and use of a Web-oriented knowledge base of mathematical concepts. The field of coverage is the special functions of applied mathematics. The investigator and his colleagues develop a Digital Library of Mathematical Functions (DLMF), a Web-accessible knowledge base of validated mathematical data obtained by a completely new survey of the archival literature. The DLMF delivers reference information in the concise style of the classic NBS Handbook of Mathematical Functions (Abramowitz and Stegun, eds.), but within a rich structure of semantic-based representation, metadata, interactive features, and internal/external links. It supports diverse user requirements such as simple lookup, complex search and retrieval, formula validation and discovery, automatic rule generation, interactive visualization, custom data on demand, and pointers to software and evaluated numerical methodology. As successor to the NBS Handbook, the DLMF provides an authoritative source of mathematical concepts traceable to a NIST definition. The basic research issues are associated with content, representation, and interaction of humans and other agents with the DLMF knowledge base. Such issues include identification and validation of relevant material; development of semantic-based representations of mathematical information; structure of metadata; search and retrieval in mathematical databases; and conversion of mathematical data between formats suitable for composition, display, and computation. These problems are being solved by an international team of experts, overseen by an editorial board. The DLMF will be disseminated in a print edition with CD-ROM as well as from a free Web service that will be maintained indefinitely at NIST.The project personnel are constructing a Digital Library of Mathematical Functions (DLMF) which provides NIST-certified reference data and associated information for the higher functions of applied mathematics. Such functions possess a wealth of critically important and highly technical properties that are used by engineers, scientists, statisticians and others to aid in the construction and analysis of computational models of materials and processes in a wide variety of applications. TheDLMF assists its users in locating formulas, algorithms and software; in understanding complex relationships through interactive graphics and typical applications; in tracing mathematical definitions and properties to a NIST standard; and in transcribing intricate mathematical information into documents and computer programs with complete reliability and accuracy. For example, software companies will be able to use the DLMF to produce vastly improved libraries and software packages. This is very significant because software provides the most effective means for practitioners to employ mathematical methods easily and reliably. The current standard reference for mathematical functions, developed by NIST with NSF support in the 1950s, is seriously out-of-date. A myriad of new properties, functions, applications and computational techniques have come into importance since then. This gap needs to be filled, and done so in a way that takes full advantage of modern information technology. The data are presented at a state-of-the-art World Wide Web site that will become a focus for the community of researchers and users of mathematical function technology, as well as in a book with CD-ROM. It is expected that the DLMF will be a model for other projects of similar type. This KDI project is supported by the Division of Mathematical Sciences and the Division of Information and Intelligent Systems.