Spectral properties of continuous representations of topological groups

Let \({\mathcal{L}(X)}\) be the algebra of all bounded operators on a Banach space X. \({\theta:G\rightarrow \mathcal{L}(X)}\) denotes a strongly continuous representation of a topological abelian group G on X. Set \({\sigma^1(\theta(g)):=\{\lambda/|\lambda|,\lambda\in\sigma(\theta(g))\}}\), where σ(θ(g)) is the spectrum of θ(g) and \({\Sigma:=\{g\in G/\enskip\text{there is no} \enskip P\in \mathcal{P}/P\subseteq \sigma^1(\theta(g))\}}\), where \({\mathcal{P}}\) is the set of regular polygons of \({\mathbb{T}}\) (we call polygon in \({\mathbb{T}}\) the image by a rotation of a closed subgroup of \({\mathbb{T}}\), the unit circle of \({\mathbb{C}}\)). We prove here that if G is a locally compact and second countable abelian group, then θ is uniformly continuous if and only if Σ is non-meager.     

Highly Charged Ruthenium(II) Polypyridyl Complexes as Effective Photosensitizer in Photodynamic Therapy

A comparative study between two novel, highly water soluble, ruthenium(II) polypyridyl complexes, [Ru(phen)₂ L ′] and [Ru(phen)₂Cu(II) L ′] ( L and L -Cu^II), containing the polyaazamacrocyclic unit 4,4′-(2,5,8,11,14-pentaaza[15])-2,2′-bipyridilophane ( L ′), is herein reported. L and L -Cu^II interact with calf-thymus DNA and efficiently cleave DNA plasmid when light-activated. They also possess great penetration abilities and photo-induced biological activities, evaluated on an A375 human melanoma cell line, with L -Cu^II being the most effective. Our study highlights the key role of the Fenton active Cu^II center within the macrocycle framework, that would play a synergistic role with light activation in the formation of cytotoxic ROS species. Based on these results, an optimal design of Ru^II polypyridyl systems featuring specific Cu^II-chelating polyamine units could represent a suitable strategy for the development of novel and effective photosensitizers in photodynamic therapy.     

Time-Stepping Approximation of Rigid-Body Dynamics with Perfect Unilateral Constraints. I: The Inelastic Impact Case

We consider a discrete mechanical system with a non-trivial mass matrix, subjected to perfect unilateral constraints described by the geometrical inequalities ${f_{\alpha} (q) \geqq 0, \alpha \in \{1, \dots, \nu\} (\nu \geqq 1)}$ . We assume that the transmission of the velocities at impact is governed by Newton’s Law with a coefficient of restitution e = 0 (so that the impact is inelastic). We propose a time-discretization of the second order differential inclusion describing the dynamics, which generalizes the scheme proposed in Paoli (J Differ Equ 211:247–281, 2005) and, for any admissible data, we prove the convergence of approximate motions to a solution of the initial-value problem.     

Global existence result for rate-independent processes in viscous solids with heat transfer

This note deals with three-dimensional models for rate-independent processes describing materials undergoing phase transformations with heat transfer. The problem is formulated within the framework of generalized standard solids by the coupling of the momentum equilibrium equation and the flow rule with the heat transfer equation. The existence of a global solution for this thermodynamically consistent problem is obtained by using a fixed-point argument combined with global energy estimates. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Chemical composition of the essential oils from the aerial parts of two Malagasy endemic species (Apiaceae): Billburttia capensoides Sales & Hedge and Billburttia vaginoides Sales & Hedge

The chemical composition of twenty-five essential oil samples from the aerial parts of two Malagasy endemic species Billburttia capensoides Sales & Hedge and B. vaginoides Sales & Hedge, were investigated for the first time. Based on chromatographic profiles, three selected samples were investigated using GC(RI), GC-MS and ¹³C NMR. The content of the main components varied drastically from sample to sample: p-mentha-1,3,8-triene (0.2–52.7%), terpinolene (2.8–40.7%) and dill apiole (0.0–22.2%). Statistical analysis of the 25 oil compositions allowed the distinction of two well-differentiated groups. Samples of group I contained mainly p-mentha-1,3,8-triene while the Group II was dominated by terpinolene and dill apiole.     

A new crystal form of the NSAID dexketoprofen

Dexketoprofen [(2S)‐2‐(3‐benzoylphenyl)propanoic acid], C₁₆H₁₄O₃, is the S‐enantiomer of ketoprofen, a nonsteroidal anti‐inflammatory drug (NSAID) that has analgesic, antipyretic and anti‐inflammatory properties, and finds applications for the short‐term treatment of mild to moderate pain. A new crystalline phase of dexketoprofen is reported. Its solid‐state structure was determined by single‐crystal X‐ray diffraction (SCXRD). The molecular structure of the two independent molecules found in the asymmetric unit of this new phase ( DXKP‐β ) were compared to those of the already known crystal form of dexketoprofen ( DXKP‐α ) and with the S‐enantiomer of the racemic compound. The three different conformers of dexketoprofen found in DXKP‐α and DXKP‐β were then investigated by computational methods. The optimized structures are very close to the corresponding starting geometries and do not differ significantly in energy. The crystal packing of DXKP‐β was studied by means of Hirshfeld surface (HS) analysis; interaction energies were also calculated. A comparison with DXKP‐α shows close similarities between the two crystal forms, i.e. in both cases, molecules assemble through the catemer O—H…O synthon of the carboxylic acid stabilized by additional C—H…O contacts and, accordingly, the interaction energies, as well as the contributions to the HS area, are very similar. Finally, the thermal behaviour of the two polymorphs of dexketoprofen was assessed by means of XRD (both from single crystal and microcrystalline powder) and differential scanning calorimetry (DSC); both crystal forms are stable under the experimental conditions adopted (air, 300–350 K for DXKP‐α and 300–340 K DXKP‐β ) and no solid–solid phase transition occurs between the two crystal forms in the investigated temperature range (from 100 K up to ca 350 K).     

The solid‐state structure of the β‐blocker metoprolol: a combined experimental and in silico investigation

Metoprolol {systematic name: (RS)‐1‐isopropylamino‐3‐[4‐(2‐methoxyethyl)phenoxy]propan‐2‐ol}, C₁₅H₂₅NO₃, is a cardioselective β₁‐adrenergic blocking agent that shares part of its molecular skeleton with a large number of other β‐blockers. Results from its solid‐state characterization by single‐crystal and variable‐temperature powder X‐ray diffraction and differential scanning calorimetry are presented. Its molecular and crystal arrangements have been further investigated by molecular modelling, by a Cambridge Structural Database (CSD) survey and by Hirshfeld surface analysis. In the crystal, the side arm bearing the isopropyl group, which is common to other β‐blockers, adopts an all‐trans conformation, which is the most stable arrangement from modelling data. The crystal packing of metoprolol is dominated by an O—H…N/N…H—O pair of hydrogen bonds (as also confirmed by a Hirshfeld surface analysis), which gives rise to chains containing alternating R and S metoprolol molecules extending along the b axis, supplemented by a weaker O…H—N/N—H…O pair of interactions. In addition, within the same stack of molecules, a C—H…O contact, partially oriented along the b and c axes, links homochiral molecules. Amongst the solid‐state structures of molecules structurally related to metoprolol deposited in the CSD, the β‐blocker drug betaxolol shows the closest analogy in terms of three‐dimensional arrangement and interactions. Notwithstanding their close similarity, the crystal lattices of the two drugs respond differently on increasing temperature: metoprolol expands anisotropically, while for betaxolol, an isotropic thermal expansion is observed.     

New ferromagnetic La3Co2TaO9 double perovskite: Structural and magnetic properties

The new double perovskite La₃Co₂TaO₉ has been prepared by a solid-state procedure. The crystal and magnetic structures have been studied from X-ray powder diffraction (XRPD) and neutron powder diffraction (NPD) data. Rietveld refinements were performed in the monoclinic space group P2₁/n. The structure consists of an ordered array of alternating B′O₆ and B″O₆ octahedra sharing corners, tilted along the three pseudocubic axes according to the Glazer notation a⁻b⁻c⁺. Rietveld refinements show that at RT the cell parameters are a=5.6005(7) Å, b=5.6931(7) Å, c=7.9429(9) Å and β=89.9539(7)°, and the refined crystallographic formula of this “double perovskite” can be written as La₂(Co)_2d(Co_1/3Ta_2/3)_2cO₆. Magnetization measurements and low-temperature NPD data show that the perovskite is a ferromagnet with T_C=72 K. At high T it follows the Curie–Weiss law with an effective magnetic moment of 3.82μ_B per Co ion which is very close to spin only Co²⁺ (HS).     

Natural α-Glucosidase and Protein Tyrosine Phosphatase 1B Inhibitors: A Source of Scaffold Molecules for Synthesis of New Multitarget Antidiabetic Drugs

Diabetes mellitus (DM) represents a group of metabolic disorders that leads to acute and long-term serious complications and is considered a worldwide sanitary emergence. Type 2 diabetes (T2D) represents about 90% of all cases of diabetes, and even if several drugs are actually available for its treatment, in the long term, they show limited effectiveness. Most traditional drugs are designed to act on a specific biological target, but the complexity of the current pathologies has demonstrated that molecules hitting more than one target may be safer and more effective. The purpose of this review is to shed light on the natural compounds known as α-glucosidase and Protein Tyrosine Phosphatase 1B (PTP1B) dual-inhibitors that could be used as lead compounds to generate new multitarget antidiabetic drugs for treatment of T2D.