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.     

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.     

Oleogels—Their Applicability and Methods of Characterization

Oleogels or, more precisely, non-triglyceride structured lipid phases have been researched excessively in the last decade. Yet, no comprehensive knowledge base has emerged, allowing technology elevation from the laboratory bench into the industrial food application. That is partly due to insufficient characterization of the structuring systems studied. Examining a single composition decided upon by arbitrary methods does not stimulate progress in the research and technology area. A framework that gives much better guidance to product applications can easily be derived. For example, the incremental structure contribution concept is advocated as a parameter to compare the potency of structuring systems. These can straightforwardly be determined by combining solubility data and structural measurements in the recommended manner. The current method to determine the oil-binding capacity suffers from reproducibility and relevance. A newly developed method is suggested to overcome these shortcomings. The recommended new characterization of oleogels should contribute to a more comprehensive knowledge base necessary for product innovations.     

Acrolein and Copper as Competitive Effectors of α-Synuclein

Mounting evidence supports the role of amyloidogenesis, oxidative stress, and metal dyshomeostasis in the development of neurodegenerative disorders. Parkinson's Disease is characterized by α-synuclein (αSyn) accumulation and aggregation in brain regions, also promoted by Cu²⁺. αSyn is modified by reactive carbonyl species, including acrolein (ACR). Notwithstanding these findings, the interplay between ACR, copper, and αSyn has never been investigated. Therefore, we explored more thoroughly the effects of ACR on αSyn using an approach based on LC-MS/MS analysis. We also evaluated the influence of Cu²⁺ on the protein carbonylation and how the ACR modification impacts the Cu²⁺ binding and the production of Reactive Oxygen Species (ROS). Finally, we investigated the effects of ACR and Cu²⁺ ions on the αSyn aggregation by dynamic light scattering and fluorescence assays. Cu²⁺ regioselectively inhibits the modification of His50 by ACR, the carbonylation lowers the affinity of His50 for Cu²⁺ and ACR inhibits αSyn aggregation both in the presence and in the absence of Cu²⁺.     

Organic Cage Dumbbells

Molecular dumbbells with organic cage capping units were synthesised via a multi-component imine condensation between a tri-topic amine and di- and tetra-topic aldehydes. This is an example of self-sorting, which can be rationalised by computational modelling.     

Surface and structural analysis of epitaxial La1−xSrx (Mn1−yCoy)zO3 films

In the present study were studied the ferromagnetic La_1−xSr_x (Mn_1−yCo_y)_zO₃ (LSMCO) films with Co content y = 0 to 0.18, grown on LaAlO₃ substrates by advantageous pulsed-injection metalorganic chemical vapor deposition technique. The LSMCO films exhibit negative colossal magnetoresistance effect; therefore, they are interesting as potential material for the applications in magnetic field sensing. The changes of lattice volume in the investigated LSMCO films were monitored by X-ray diffraction measurements revealing a transition from tensile to compressive strain with increase of Co content. Additionally, from the atomic force microscopy images, the surface smoothening with increase of y was determined. Despite the reduction of the out-of-plane lattice parameter of LSMCO, the increase of lattice volume in the whole Co-doping range was observed. The X-ray photoelectron spectroscopy combined with Ar⁺ ion sputtering was used for the investigation of chemical composition of the LSMCO films and demonstrated the change and redistribution of oxidation states of Mn and Co on the surface and in the volume of the films. Regardless of the structural changes and charge distribution of Co and Mn cations, epitaxial LSMCO exhibits ferromagnetic properties and magnetoresistance values increases with augmenting Co content in the range of y = 0 to 0.18.     

Widened derangements and generalized Laguerre polynomials

The Ramanujan Journal - Let $$D_h$$ , $$E_k$$ and $$F_{\alpha }$$ be sets of size $$h,k,\alpha $$ respectively, with $$k \le h$$ . We define a strongly widened derangement to be a permutation of...