AbstractWe solve the Milne, constant-source, and albedo problems for isotropic scattering in a two-dimensional “Flatland” half-space via the Wiener–Hopf method. The Flatland H-function is derived a...
Infinite media problems have been well studied in Flatland as well as spaces of general dimension @cite_20 @cite_4 @cite_15 @cite_13 @cite_14 @cite_18 @cite_26 @cite_5 @cite_6 and for beams @cite_23 . Some exact solutions have been presented for bounded @cite_25 and layered @cite_24 media, and the singular eigenfunctions for Flatland have been derived @cite_3 . However, to the best of the authors' knowledge, solutions to the classic Milne and albedo problems for the half-space and the @math -function have not been presented. @cite_19 , using an asymptotic analysis, have presented solutions to the classic Milne and albedo problems in two dimensions. The solutions make use of the Flatland equivalent of Chandrasekhar's @math -function, which is left as the solution to an integral equation. We present a complementary derivation of the Milne and albedo problem solutions using the Wiener-Hopf technique. In addition, we present new solutions and benchmark values for @math and provide some Monte Carlo comparisons for the albedo problem.
@cite_18 @cite_14 @cite_4 @cite_26 @cite_6 @cite_3 @cite_24 @cite_19 @cite_23 @cite_5 @cite_15 @cite_13 @cite_25 @cite_20
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AbstractWe solve the Milne, constant-source, and albedo problems for isotropic scattering in a two-dimensional “Flatland” half-space via the Wiener–Hopf method. The Flatland H-function is derived a... In a document network such as a citation network of scientific documents, web-logs, etc., the content produced by authors exhibits their interest in certain topics. In addition some authors influence other authors' interests. In this work, we propose to model the influence of cited authors along with the interests of citing authors. Moreover, we hypothesize that apart from the citations present in documents, the context surrounding the citation mention provides extra topical information about the cited authors. However, associating terms in the context to the cited authors remains an open problem. We propose novel document generation schemes that incorporate the context while simultaneously modeling the interests of citing authors and influence of the cited authors. Our experiments show significant improvements over baseline models for various evaluation criteria such as link prediction between document and cited author, and quantitatively explaining unseen text. A citing sentence is one that appears in a scientific article and cites previous work. Citing sentences have been studied and used in many applications. For example, they have been used in scientific paper summarization, automatic survey generation, paraphrase identification, and citation function classification. Citing sentences that cite multiple papers are common in scientific writing. This observation should be taken into consideration when using citing sentences in applications. For instance, when a citing sentence is used in a summary of a scientific paper, only the fragments of the sentence that are relevant to the summarized paper should be included in the summary. In this paper, we present and compare three different approaches for identifying the fragments of a citing sentence that are related to a given target reference. Our methods are: word classification, sequence labeling, and segment classification. Our experiments show that segment classification achieves the best results. Purpose – The purpose of this paper is to suggest an alternative to the widely used Times Cited criterion for analysing citation networks. The approach involves taking account of the natures of the papers that cite a given paper, so as to differentiate between papers that attract the same number of citations.Design methodology approach – ArticleRank is an algorithm that has been derived from Google's PageRank algorithm to measure the influence of journal articles. ArticleRank is applied to two datasets – a citation network based on an early paper on webometrics, and a self‐citation network based on the 19 most cited papers in the Journal of Documentation – using citation data taken from the Web of Knowledge database.Findings – ArticleRank values provide a different ranking of a set of papers from that provided by the corresponding Times Cited values, and overcomes the inability of the latter to differentiate between papers with the same numbers of citations. The difference in rankings between Times Cited ...