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.     

Groups in which every subgroup of infinite rank is almost permutable

In this paper, the structure of locally finite groups of infinite rank whose subgroups of infinite rank are permutable in a subgroup of finite index is investigated.     

Firing-Induced Microstructural Properties of Quasi-Diamagnetic Carbonate-Based Porous Ceramics: a <Superscript>1</Superscript>H NMR Relaxation Correlation Study

This study deals with the application of two-dimensional proton nuclear magnetic resonance relaxometry (2D ¹H NMR-R) to the characterization of porous ceramics nearly free of magnetic compounds. Different microstructural properties were obtained by firing a diamagnetic mixture of kaolin, calcium, and magnesium carbonate over a wide range of maximum temperatures (600–1100 °C) and firing times at the maximum temperature (soaking times) (0–10 h). The 2D ¹H NMR-R method relies on the correlated measurement of ¹H longitudinal (T ₁) and transverse (T ₂) relaxation times of pore-filling water by which the properties of the interconnected pore space may be investigated. In the absence of significant magnetic susceptibility effect due to para- and ferro-magnetic compounds, the 2D ¹H NMR-R maps allow studying the conjoint effects on pore size distribution and inter-pore coupling due to the variations in both time and temperature of firing. The NMR experiments were performed with a low-field ¹H NMR sensor, which allows non-destructive and in situ analysis. For ceramic specimens fired at 600 and 700 °C, the fraction of smallest pores increases with firing time at the expenses of those with intermediate size. The pore shrinkage occurring at this stage, and likely associated with the transformation of kaolinite in metakaolinite, is affected in a similar way by soaking time and firing temperature, in line with the concept of equivalent firing temperature. At temperatures from 800 to 1100 °C, the structural modifications involving interconnectivity and average pore size are driven primarily by firing temperature and, secondarily, by soaking time. The 2D ¹H NMR-R results are confirmed by more traditional, but destructive, mineralogical, and structural analyses like X-ray powder diffraction, helium pycnometry, mercury intrusion porosimetry, and nitrogen adsorption/desorption method.     

Range conditions for the exponential Radon transform

A new approach to the range conditions for the exponential Radon transform is introduced. Partially supported by NSF EPSCOR Grant and Wesley Foundation Grant no. 9012019. Partially supported by NSF Grant 33-1807-231.     

Synthesis and Antiproliferative Effect of Halogenated Coumarin Derivatives

A series of 6- and 6,8-halocoumarin derivatives have been investigated as potential antiproliferative compounds against a panel of tumor and normal cell lines. Cytotoxic effects were determined by the MTT method. To investigate the potential molecular mechanism involved in the cytotoxic effect, apoptosis assay, cell cycle analysis, reactive oxygen species (ROS), and reduced glutathione analysis were performed. Among the screened compounds, coumarins 6,8-dibromo-2-oxo-2H-chromene-3-carbonitrile 2h and 6,8-diiodo-2-oxo-2H-chromene-3-carbonitrile 2k exhibited the most antiproliferative effect in thyroid cancer-derived cells TPC-1. The apoptosis assay showed that both 2h and 2k induced apoptosis in TPC-1 thyroid cancer cells. According to these experiments, both coumarins induced a slight increase in TPC-1 cells in the G2/M phase and a decrease in the S phase. A significant increase in ROS levels was observed in TPC-1 treated with diiodocoumarin 2k, while the dibromocoumarin 2h induced a decrease in ROS in a dose and time-dependent manner.     

Nonequilibrium charge recombination from the excited adiabatic state of donor-acceptor complexes

A model of nonequilibrium charge recombination from an excited adiabatic state of a donor-acceptor complex induced by the nonadiabatic interaction operator is considered. The decay of the excited state population prepared by a short laser pulse is shown to be highly nonexponential. The influence of the excitation pulse carrier frequency on the ultrafast charge recombination dynamics of excited donor-acceptor complexes is explored. The charge recombination rate constant is found to decrease with increasing excitation frequency. The variation of the excitation pulse carrier frequency within the charge transfer absorption band of the complex can alter the effective charge recombination rate by up to a factor 2. The magnitude of this spectral effect decreases strongly with increasing electronic coupling.     

Synthesis and characterization of some vanadyl complexes with flavonoid derivatives as potential insulin-mimetic agents

Two new complexes with formula VOL₂·nH₂O ((1) L: 4′,5,7-trihydroxyflavone-7-rhamnoglucoside (naringin), n = 8; (2) L: 3′,4′,7-tris[O-(2-hydroxyethyl)]rutin (troxerutin), n = 0) were synthesised and characterised. The IR and UV–Vis spectral data indicate that these flavones act as bidentate chelating ligands and generate VO(II) complexes with a square-pyramidal stereochemistry. The thermal analysis (TG, DTA) elucidated the composition and also the number and nature of the water molecules. The thermal behavior indicates also a strong interaction between oxovanadium (IV) and these oxygen donor ligands.     

Characterization of Collagen/Lipid Nanoparticle–Curcumin Cryostructurates for Wound Healing Applications

Curcumin‐loaded collagen cryostructurates have been devised for wound healing applications. Curcumin displays strong antioxidant, antiseptic, and anti‐inflammatory properties, while collagen is acknowledged for promoting cell adhesion, migration and differentiation. However, when curcumin is loaded directly into collagen hydrogels, it forms large molecular aggregates and clogs the matrix pores. A double‐encapsulation strategy is therefore developed by loading curcumin into lipid nanoparticles (LNP), and embedding these particles inside collagen scaffolds. The resulting collagen/LNP cryostructurates have an optimal fibrous structure with ≈100 µm average pore size for sustaining cell migration. Results show that collagen is structurally unaltered and that nanoparticles are homogeneously distributed amidst collagen fibers. Hydrogels soaked in saline buffer release about 20 to 30% of their nanoparticles content within 24 h, while achieved 100% release after 25 days. When exposed to NIH 3T3 fibroblasts, these hydrogels provide a satisfactory scaffold for cell interaction as early as 4 h after seeding, with no cytotoxic counter effect. These positive features make the collagen/lipid cryostructurates a promising material for further use in wound healing.     

Synthesis, physicochemical properties and antioxidant activity of deferiprone-cyclodextrin conjugates and their iron(III) complexes

3-Hydroxy-1,2-dimethylpyridin-4(1H)-one (deferiprone) is a successful iron chelator, which has been widely investigated for its activity in mitigating iron overload and in protecting against oxidative stress due to Reactive Oxygen Species (ROS). Herein, we present the synthesis, characterisation, physicochemical properties and antioxidant activity of two novel bioconjugates of β-cyclodextrin bearing the deferiprone moiety either on the upper rim (1) or on the lower rim (2) of the cyclodextrin and their iron(III) complexes. Protonation and iron stability constants were measured by spectrophotometric titration for the two systems and antioxidant activity studied for both the ligands and the iron(III) complexes.