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We present new results concerning the approximation of the total variation, ∫Ω∣∇u∣, of a function u by non-local, non-convex functionals of the form $$ \Lambda_\delta u = \int_{\Omega} \int_{\Omega} \frac{\delta \varphi \big( |u(x) - ...
An increasing number of knowledge brokers work at the interface between research, policy and practice. Their function is to facilitate processes to foster mutual learning among research, policy and practice. For some knowledge brokers, practical methodolog ...
The amount of controversial issues being discussed on the Web has been growing dramatically. In articles, blogs, and wikis, people express their points of view in the form of arguments, i.e., claims that are supported by evidence. Discovery of arguments ha ...
In this paper we consider the Holm-Staley b-family of equations in the Sobolev spaces H-s (R) for s > 3/2. Using a geometric approach we show that, for any value of the parameter b, the corresponding solution map, u(0) bar right arrow u(T), is nowhere loca ...
In this article, we establish novel decompositions of Gaussian fields taking values in suitable spaces of generalized functions, and then use these decompositions to prove results about Gaussian multiplicative chaos. We prove two decomposition theorems. Th ...
We establish improved versions of the Hardy and Caffarelli-Kohn-Nirenberg inequalities by replacing the standard Dirichlet energy with some nonlocal nonconvex functionals which have been involved in estimates for the topological degree of continuous maps f ...
Device for testing a material response, such as a tissue response, to a compound; said device comprising material impedance measuring means which are adapted to measure the material impedance at the compound action site. ...
There are many situations where fixed-wing drones may be required to track ground moving agents, such as humans or cars, which are typically slower than drones. Some control strategies have been proposed and validated in simulations using the average dista ...
In this thesis we investigate the class of supramenable groups. In the first part we give an overview of some analogous characterizations of amenable and supramenable groups. This is followed by the study of two properties close to supramenability: megamen ...
In this paper we make a survey of some recent developments of the theory of Sobolev spaces W-1,W-q (X, d, m), 1 < q < infinity, in metric measure spaces (X, d, m). In the final part of the paper we provide a new proof of the reflexivity of the Sobolev spac ...
