Critical points of inner functions, nonlinear partial differential equations, and an extension of Liouville's theorem

We establish an extension of Liouville's classical representation theorem for solutions of the partial differential equation $\Delta u=4 e^{2u}$ and combine this result with methods from nonlinear elliptic PDE to construct holomorphic maps with prescribed critical points and specified boundary behaviour. For instance, we show that for every Blaschke sequence $\{z_j\}$ in the unit disk there is always a Blaschke product with $\{z_j\}$ as its set of critical points. Our work is closely related to the Berger-Nirenberg problem in differential geometry.Comment: 21 page

Development of Use Cases, Part I

For determining requirements and constructs appropriate for a Web query language, or in fact any language, use cases are of essence. The W3C has published two sets of use cases for XML and RDF query languages. In this article, solutions for these use cases are presented using Xcerpt. a novel Web and Semantic Web query language that combines access to standard Web data such as XML documents with access to Semantic Web metadata such as RDF resource descriptions with reasoning abilities and rules familiar from logicprogramming. To the best knowledge of the authors, this is the first in depth study of how to solve use cases for accessing XML and RDF in a single language: Integrated access to data and metadata has been recognized by industry and academia as one of the key challenges in data processing for the next decade. This article is a contribution towards addressing this challenge by demonstrating along practical and recognized use cases the usefulness of reasoning abilities, rules, and semistructured query languages for accessing both data (XML) and metadata (RDF)

АЗОВСЬКА ГУБЕРНСЬКА КАНЦЕЛЯРІЯ: СТРУКТУРА, ФУНКЦІЇ, ШТАТ (1775-1784)

У статті висвітлюється історія створення та діяльності головної адміністративної установи Азовської губернії – губернської канцелярії (1775–1784 рр.), розкриваються її структура, основні функції та штат.In this article the history of formation and functioning of the main establishment of the Azov province – province office – is illuminated (1775–1784). Such questions as structure, main functions and stat are revealed

Survey over Existing Query and Transformation Languages

A widely acknowledged obstacle for realizing the vision of the Semantic Web is the inability of many current Semantic Web approaches to cope with data available in such diverging representation formalisms as XML, RDF, or Topic Maps. A common query language is the first step to allow transparent access to data in any of these formats. To further the understanding of the requirements and approaches proposed for query languages in the conventional as well as the Semantic Web, this report surveys a large number of query languages for accessing XML, RDF, or Topic Maps. This is the first systematic survey to consider query languages from all these areas. From the detailed survey of these query languages, a common classification scheme is derived that is useful for understanding and differentiating languages within and among all three areas