Point interactions for 3D sub-Laplacians

In this paper we show that, for a sub-Laplacian Δ on a 3-dimensional manifold M, no point interaction centered at a point $q_0\in M$ exists. When M is complete w.r.t. the associated sub-Riemannian structure, this means that Δ acting on $C_0^{\infty }(M?\{q_0\})$ is essentially self-adjoint in $L^2(M)$. A particular example is the standard sub-Laplacian on the Heisenberg group. This is in stark contrast with what happens in a Riemannian manifold N, whose associated Laplace-Beltrami operator acting on $C_0^{\infty }(N?\{q_0\})$ is never essentially self-adjoint in $L^2(N)$, if $\dim ?N\le 3$. We then apply this result to the Schrödinger evolution of a thin molecule, i.e., with a vanishing moment of inertia, rotating around its center of mass.     

PASE synthesis of 1-azolyl-1H-1,2,4-triazoles by the reaction of diazoazoles with ethyl isocyanoacetate

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Reversible C=C Bond Activation by an Intramolecularly Coordinated Antimony(I) Compound

The reaction of N,C,N-chelated stibinidene ArSb ( 1 ) (Ar=C₆H₃-2,6-(CH=NtBu)₂) with selected N-alkyl/aryl-maleimides RN(C(O)CH)₂ (R=Me, tBu, Ph) gave the addition products with bridged bicyclic [2.2.1] structure containing an antimony atom at the bridgehead position, fused with a 6-membered benzene and a 5-membered N-alkyl/aryl-pyrrolidine ring. These compounds were completely characterized. More importantly, additional studies showed that these reactions are reversible in solution, thereby representing an unprecedented reversible activation of a C=C bond by an antimony(I) compound.     

Binuclear copper(II) complex with 2-imidazolylbenzothiazole and bridged chloride ligands

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Unexpected formation of dinaphthoaza-17-crown-5 ether containing γ-aminopiperidine subunit

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Benchmarking culture in Europe: A data envelopment analysis approach to identify city-specific strengths

Culture is an integral part of a city's quality of life, a driver of urban change, and a genuine economic sector. To support benchmarking of urban culture and facilitate peer learning amongst policymakers, the European Commission has recently created the ‘Cultural and Creative Cities Index’. While this index builds on a standardised method to aggregate 29 indicators for the 155 selected cities, it is explicitly acknowledged that a ‘gold standard’ for a ‘Cultural and Creative City’ does not exist. Instead, different approaches should be allowed for in capturing cities’ cultural and creative vitality. This is the point of departure for this paper, which employs a Benefit-of-the-Doubt (BoD) modelling approach to allow cities to combine such respect for performance diversity with peer learning and benchmarking. Expert-based weights are used to provide expert-consistent bounds for the shares of key dimensions in a city's final BoD index value. We identify three city clusters, amongst which there are large performance differences. Accordingly, we focus on the within-group identification of peer cities and target values, which we illustrate in more detail for Bilbao, Krak?w and Umeå, towards the formulation of fit-for-purpose policy measures that can support culture-led development.