The main objective of this project is to find easily verifiable conditions that characterize embeddings between function spaces or
boundedness or compactness of linear and quasi-linear operators defined on function spaces and to apply the obtained results.
We intend to depart from our results obtained in frame of our previous grants (both domestic and international) and also from
results of other leading scientists, and to continue developing this fruitful research. We shall mainly use real-variable methods,
results of functional analysis, interpolation and extrapolation theorems, and techniques of harmonic analysis including
techniques developed or partly developed by members of the team such as discretization and antidiscretization of weighted
inequalities, characterization of weighted inequalities for supremum operators, characterization of optimal partner spaces or
iteration methods for characterization of higher-order Sobolev spaces. The project is a natural continuation of the project
201/08/0383.
In the light of mathematicians reliance on their discipline's rich published heritage and the key role of mathematics in enabling other scientific disciplines, the European Digital Mathematics Library strives to make the significant corpus of mathematics scholarship published in Europe available online, in the form of an authoritative and enduring digital collection, developed and curated by a network of institutions.
National efforts have led to the digitisation of large quantities of mathematical literature, primarily by partners in this project. Publishers produce new material that needs to be archived safely over the long term, made more visible, usable, and interoperable with the legacy corpus on which it settles. In EuDML, these partners will join together with leading technology providers in constructing the Europe-wide interconnections between their collections to create a document network as integrated and trans-national as the discipline of mathematics itself. They will future-proof their work by providing the organisational and technical infrastructure to accommodate new collections and mathematically rich metadata formats, and will work towards truly open access for the whole European Community to this foundational resource, thereby retaining Europe's leadership in the provision, accessibility and exploitation of electronic mathematical content.
EuDML will design and build a collaborative digital library service that will collate the currently distributed content by the diversity of providers. This will be achieved by implementing a single access platform for heterogeneous and multilingual collections. The network of documents will be constructed by merging and augmenting the information available about each document from each collection, and matching documents and references across the entire combined library. In return for this added value, the rights holders agree to a moving wall policy to secure eventual open access to their full texts.
The aim of the project is to investigate, develop and apply techniques, methods and tools allowing to create proper infrastructure and conditions for implementation of the Czech Digital Mathematical Library (DML-CZ) containing the relevant part of special mathematical literature which has been published in the Czech lands and for its incorporation into the World Digital Mathematical Library (WDML).
The solution will include launching the digitization process and providing access to the digitized material for end users. In this connection research of advanced technologies for search in mathematical documents will start as well as inclusion of born-digital materials.
The project involves a design and an implementation of solutions of interconnected problem circles in the following five regions: acquisition of selected materials to be digitized and handling the IPR, digitization and provision of metadata, creation of structured digital documents, creation of the digital library and its incorporation into the WDML.
The DML-CZ should primarily contain specialized journals of international level published by Czech institutions, such as the Czechoslovak Mathematical Journal and Applications of Mathematics published by the Mathematical Institute AS CR, Kybernetika published by the Institute of Automation and Information Theory AS CR and others. Next, conference proceedings published by the Czech universities and research institutes, selected monographs, textbooks, dissertation theses, research reports etc. will be included. Measures will be taken to complement the digital library with materials which have been digitized earlier (e.g. Commentationes Mathematicae Universitatis Carolinae, Mathematica Bohemica, Archivum Mathematicum digitized by the Göttinger DigitalisierungsZentrum within the project DIEPER). According to preliminary estimate the core of the DML-CZ should contain about 300 000 pages.
grants
