KDI: Mathematical Foundations for a Networked Scientific Knowledge Base

KDI：网络科学知识库的数学基础

• 批准号: 9980036
• 负责人: Daniel Lozier
• 金额: $ 130万
• 依托单位: NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY
• 依托单位国家: 美国
• 项目类别: Interagency Agreement
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-09-01 至 2005-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9980036&HistoricalAwards=false
• 关键词: KDI; Mathematical; Foundations; Networked; Scientific

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.

9980036这个项目解决了数学概念的生成，验证，组织，分布和使用的问题。 覆盖范围是应用数学的特殊功能。 研究者及其同事开发了数字功能的数字库（DLMF），这是一个可通过对档案文献的全新调查获得的经过验证的数学数据的知识库。 DLMF以经典的NBS数学功能手册（Abramowitz and Stegun，编辑）的简洁方式提供参考信息，但在基于语义的表示，元数据，交互式特征和内部/外部链接的丰富结构中。 它支持各种用户需求，例如简单查找，复杂的搜索和检索，公式验证和发现，自动规则生成，交互式可视化，按需自定义数据以及对软件的指针以及评估的数值方法。 作为NBS手册的继任者，DLMF提供了可追溯到NIST定义的数学概念的权威来源。 基础研究问题与人类和其他代理商与DLMF知识库的内容，表示和相互作用有关。 此类问题包括对相关材料的识别和验证；开发基于语义的数学信息表示；元数据的结构；在数学数据库中进行搜索和检索；以及适用于组成，显示和计算的格式之间数学数据的转换。 这些问题由国际专家团队解决，由编辑委员会监督。 DLMF将以CD-ROM以及将在NIST中无限期维护的免费Web服务的印刷版中传播。项目人员正在构建数字数字函数库（DLMF），该数字库提供了NIST认证的参考数据和相关信息，以提供较高的应用数学功能。 这些功能具有大量重要和高度技术性的特性，工程师，科学家，统计学家和其他人使用，以帮助在各种应用中构建和分析材料和过程的计算模型。 THEDLMF协助其用户找到公式，算法和软件；通过交互式图形和典型应用理解复杂的关系；在将数学定义和属性追踪到NIST标准中；并以完全的可靠性和准确性将复杂的数学信息转录为文档和计算机程序。 例如，软件公司将能够使用DLMF生产大量改进的库和软件包。 这是非常重要的，因为软件为从业者提供了最有效的手段，可以轻松，可靠地采用数学方法。 NIST在1950年代由NSF支持开发的当前数学函数标准参考非常过时。 从那时起，无数的新属性，功能，应用和计算技术就已经登上了重要性。 需要填补这一差距，并以充分利用现代信息技术的方式进行。 这些数据是在最先进的全球网站上介绍的，该网站将成为研究人员和数学功能技术的用户以及CD-ROM的书籍的重点。 预计DLMF将成为其他类似类型的项目的模型。 这个KDI项目得到了数学科学和信息和智能系统的部门的支持。