scholarly journals A domain mapping approach for elliptic equations posed on random bulk and surface domains

2020 ◽  
Vol 146 (1) ◽  
pp. 1-49
Author(s):  
Lewis Church ◽  
Ana Djurdjevac ◽  
Charles M. Elliott
2020 ◽  
Vol 57 (1) ◽  
pp. 68-90 ◽  
Author(s):  
Tahir S. Gadjiev ◽  
Vagif S. Guliyev ◽  
Konul G. Suleymanova

Abstract In this paper, we obtain generalized weighted Sobolev-Morrey estimates with weights from the Muckenhoupt class Ap by establishing boundedness of several important operators in harmonic analysis such as Hardy-Littlewood operators and Calderon-Zygmund singular integral operators in generalized weighted Morrey spaces. As a consequence, a priori estimates for the weak solutions Dirichlet boundary problem uniformly elliptic equations of higher order in generalized weighted Sobolev-Morrey spaces in a smooth bounded domain Ω ⊂ ℝn are obtained.


2018 ◽  
Vol 2 (2) ◽  
pp. 70-82 ◽  
Author(s):  
Binglu Wang ◽  
Yi Bu ◽  
Win-bin Huang

AbstractIn the field of scientometrics, the principal purpose for author co-citation analysis (ACA) is to map knowledge domains by quantifying the relationship between co-cited author pairs. However, traditional ACA has been criticized since its input is insufficiently informative by simply counting authors’ co-citation frequencies. To address this issue, this paper introduces a new method that reconstructs the raw co-citation matrices by regarding document unit counts and keywords of references, named as Document- and Keyword-Based Author Co-Citation Analysis (DKACA). Based on the traditional ACA, DKACA counted co-citation pairs by document units instead of authors from the global network perspective. Moreover, by incorporating the information of keywords from cited papers, DKACA captured their semantic similarity between co-cited papers. In the method validation part, we implemented network visualization and MDS measurement to evaluate the effectiveness of DKACA. Results suggest that the proposed DKACA method not only reveals more insights that are previously unknown but also improves the performance and accuracy of knowledge domain mapping, representing a new basis for further studies.


Sign in / Sign up

Export Citation Format

Share Document