International Cooperation
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Grant: 20-22230L
from 01/01/2020
to 31/12/2022
Grantor: Austrian Science Foundation (FWF) - Czech Science Foudation
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Banach spaces of continuous and Lipschitz functions
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Objectives:
The supreme goal of this project is to study Banach spaces of continuous and Lipschitz functions over compact spaces from the points of view of various branches of mathematics. Since every Banach space can be isometrically embedded into a Banach space of continuous functions on a compact space, such spaces constitute one of the most important classes of Banach spaces and thus their better understanding will lead to sourcing broader knowledge and comprehension of all Banach spaces in general. We propose to apply mathematical techniques and methods originating from different areas of modern analysis, geometry, topology, and logic. Such a universal approach will allow us to obtain more profound insight into the structure of Banach spaces and related objects, aiming at solving several open problems in this area. Expected results will offer new tools for studying and classifying the topology and geometry of spaces of continuous and Lipschitz functions, as well as the corresponding compact and metric spaces.
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Grant: GC19-06175J
from 01/01/2019
to 31/12/2021
Grantor: Czech Science Foundation
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Compositional Methods for the Control of Concurrent Timed Discrete-Event Systems
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Objectives:
Current approaches for control of timed discrete-event systems (DES) with dense real time only deal with monolithic plants, which means that their control suffers from high complexity and even decidability issues (non existence of finite state controllers). In order to face these issues, it is important to develop computationally efficient compositional approaches, such as modular control. We will investigate modular and coordination control of timed DES modeled by timed Petri nets or by (max,+)-automata.
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