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Without resorting to complex numbers or any advanced topological arguments, we show that any real polynomial of degree greater than two always has a real quadratic polynomial factor, which is equivalent to the fundamental theorem of algebra. The proof uses ...
In this paper we study the moments of polynomials from the Askey scheme, and we focus on Askey-Wilson polynomials. More precisely, we give a combinatorial proof for the case where d = 0. Their values have already been computed by Kim and Stanton in 2015, h ...
Generalized algebraic data types (GADTs) are a powerful tool allowing to express invariants leveraging the type system. Scala 3 considerably improves the support of GADTs with respect to its predecessor Scala 2. A unique feature of Scala 3, compared to lan ...
Model-checking intends to verify whether a property is satisfied by a model, or not. Model-checking of high-level models, e.g. SysML models, usually first requires a model transformation to a low level formal specification. The present papers proposes a ne ...
It is well known that hyperedge-replacement grammars can generate NP-complete graph languages even under seemingly harsh restrictions. This means that the parsing problem is difficult even in the non-uniform setting, in which the grammar is considered to b ...
In the first chapter of this thesis, the macrocyclization of a new type of bifunctional substrates, omega-isocyanoaldehyde derivatives, is described. Ten different omega-isocyanoaldehydes in terms of different ring sizes and functional groups were prepared ...
Most logic synthesis algorithms work on graph representations of logic functions with nodes associated with arbitrary logic expressions or simple logic functions and iteratively optimize such graphs. While recent multilevel logic synthesis efforts focused ...
Many natural optimization problems are NP-hard, which implies that they are probably hard to solve exactly in the worst-case. However, it suffices to get reasonably good solutions for all (or even most) instances in practice. This paper presents a new algo ...
We provide a counterexample to the performance guarantee obtained in the paper "Il'ev, V., Linker, N., 2006. Performance guarantees of a greedy algorithm for minimizing a supermodular set function on comatroid", which was published in Volume 171 of the Eur ...
Motivated by applications in shared mobility, we address the problem of allocating a group of agents to a set of resources to maximize a cumulative welfare objective. We model the welfare obtainable from each resource as a monotone DR-submodular function w ...
