We show that for @math and for measurable subsets of the unit square with Lebesgue measure @math there exist bi-Lipschitz maps with bounded Lipschitz constant (uniformly over all such sets) which are identity on the boundary and increases the Lebesgue measure of the set to at least @math .
The question considered in this paper has connections to several different problems in analysis, an interested reader is referred to @cite_5 and the references therein for more details.
@cite_5
1786941226
Document authors commonly use tables to support arguments presented in the text. But, because tables are usually separate from the main body text, readers must split their attention between different parts of the document. We present an interactive document reader that automatically links document text with corresponding table cells. Readers can select a sentence (or tables cells) and our reader highlights the relevant table cells (or sentences). We provide an automatic pipeline for extracting such references between sentence text and table cells for existing PDF documents that combines structural analysis of tables with natural language processing and rule-based matching. On a test corpus of 330 (sentence, table) pairs, our pipeline correctly extracts 48.8 of the references. An additional 30.5 contain only false negatives (FN) errors -- the reference is missing table cells. The remaining 20.7 contain false positives (FP) errors -- the reference includes extraneous table cells and could therefore mislead readers. A user study finds that despite such errors, our interactive document reader helps readers match sentences with corresponding table cells more accurately and quickly than a baseline document reader. Reading academic paper is a daily task for researchers and graduate students. However, reading effectively can be challenging, particularly for novices in scientific research. For example, when readers are reading the related work section that cites a fair number of references in limited page space, they often need to flip back and forth between the text and the references and may also frequently search elsewhere for more information about the references. This increases the difficulty of understanding a paper. In this paper, we propose a narrative visualization system that helps the reading of academic papers. As a first step, we adopt narrative visualization to present literature review as interactive slides. Specifically, we propose a narrative structure with three levels of granularities that the reader can drill down or roll up freely. The logic flow of a slideshow can be organized based on the paper's presentation or citations. We demonstrate the effectiveness of our system through several case studies and user studies. The results show that the system allows users to quickly track and glance related work, making paper reading more effective and enjoyable. Scholars are increasingly citing electronic “web references” which are not preserved in libraries or full text archives. WebCite is a new standard for citing web references. To “webcite” a document involves archiving the cited Web page through www.webcitation.org and citing the WebCite permalink instead of (or in addition to) the unstable live Web page. This journal has amended its “instructions for authors” accordingly, asking authors to archive cited Web pages before submitting a manuscript. Almost 200 other journals are already using the system. We discuss the rationale for WebCite, its technology, and how scholars, editors, and publishers can benefit from the service. Citing scholars initiate an archiving process of all cited Web references, ideally before they submit a manuscript. Authors of online documents and websites which are expected to be cited by others can ensure that their work is permanently available by creating an archived copy using WebCite and providing the citation information including the WebCite link on their Web document(s). Editors should ask their authors to cache all cited Web addresses (Uniform Resource Locators, or URLs) “prospectively” before submitting their manuscripts to their journal. Editors and publishers should also instruct their copyeditors to cache cited Web material if the author has not done so already. Finally, WebCite can process publisher submitted “citing articles” (submitted for example as eXtensible Markup Language [XML] documents) to automatically archive all cited Web pages shortly before or on publication. Finally, WebCite can act as a focussed crawler, caching retrospectively references of already published articles. Copyright issues are addressed by honouring respective Internet standards (robot exclusion files, no-cache and no-archive tags). Long-term preservation is ensured by agreements with libraries and digital preservation organizations. The resulting WebCite Index may also have applications for research assessment exercises, being able to measure the impact of Web services and published Web documents through access and Web citation metrics. @PARASPLIT [J Med Internet Res 2005;7(5):e60] There were 20 scholars interviewed about their citation motives in recently published articles. Their 437 citations were scaled along 1 or more of the following 7 citer motives: currency, negative credit, operational information, persuasiveness, positive credit, reader alert, and social consensus. The majority (70.7 ) of the references were attributed to more than 1 motive. Analysis of the clustering of the citer motives showed 3 groupings: (1) persuasiveness, positive credit, currency, and social consensus, (2) negative credit, and (3) reader alert and operational information. Negative credit references were often found to be used with a countervailing positive credit, currency, or social consensus reference. This is considered to be empirical evidence of MacRoberts and MacRoberts' [8] hypothesis that scholars dissemble when giving negative references. © 1986 John Wiley & Sons, Inc.