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Item type:Publication, Access status: with files , Duality for evolutionary equations with applications to null controllabilityWe study evolutionary equations in exponentially weighted (Formula presented.) -spaces as introduced by Picard in 2009. First, for a given evolutionary equation, we explicitly describe the (Formula presented.) -adjoint system, which turns out to describe a system backwards in time. We prove well-posedness for the (Formula presented.) -adjoint system. We then apply the obtained duality to introduce and study notions of null controllability for evolutionary equations.Publicationtype: Journal Article27 17 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Generalized fractional entropy functions with an application in hierarchical clustering(2023-06); We establish novel entropy functions based on some types of generalized fractional derivatives. Classic entropy functions are included in the results obtained in this paper. As an application in information theory and probability theory, we use these entropy functions to measure the uncertainty and similarity of data collected from crop-sown areas in 32 regions. For doing this, the approach of hierarchical clustering with the average-linkage method is used and three visual dendrograms are offered in the end.Publicationtype: Journal Article47 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Conceptual modelling: Towards detecting modelling errors in engineering applications(2020-02); ; ; Rapid advancements of modern technologies put high demands on mathematical modelling of engineering systems. Typically, systems are no longer “simple” objects, but rather coupled systems involving multiphysics phenomena, the modelling of which involves coupling of models that describe different phenomena. After constructing a mathematical model, it is essential to analyse the correctness of the coupled models and to detect modelling errors compromising the final modelling result. Broadly, there are two classes of modelling errors: (a) errors related to abstract modelling, eg, conceptual errors concerning the coherence of a model as a whole and (b) errors related to concrete modelling or instance modelling, eg, questions of approximation quality and implementation. Instance modelling errors, on the one hand, are relatively well understood. Abstract modelling errors, on the other, are not appropriately addressed by modern modelling methodologies. The aim of this paper is to initiate a discussion on abstract approaches and their usability for mathematical modelling of engineering systems with the goal of making it possible to catch conceptual modelling errors early and automatically by computer assistant tools. To that end, we argue that it is necessary to identify and employ suitable mathematical abstractions to capture an accurate conceptual description of the process of modelling engineering systems.Publicationtype: Journal Article86