Non-triviality conditions for integer-valued polynomial rings on algebras

Let D be a commutative domain with field of fractions K and let A be a torsion-free D-algebra such that \(A \cap K = D\). The ring of integer-valued polynomials on A with coefficients in K is \( Int _K(A) = \{f \in K[X] \mid f(A) \subseteq A\}\), which generalizes the classic ring \( Int (D) = \{f \in K[X] \mid f(D) \subseteq D\}\) of integer-valued polynomials on D. The condition on \(A \cap K\) implies that \(D[X] \subseteq Int _K(A) \subseteq Int (D)\), and we say that \( Int _K(A)\) is nontrivial if \( Int _K(A) \ne D[X]\). For any integral domain D, we prove that if A is finitely generated as a D-module, then \( Int _K(A)\) is nontrivial if and only if \( Int (D)\) is nontrivial. When A is not necessarily finitely generated but D is Dedekind, we provide necessary and sufficient conditions for \( Int _K(A)\) to be nontrivial. These conditions also allow us to prove that, for D Dedekind, the domain \( Int _K(A)\) has Krull dimension 2.     

Antioxidant activity and cytotoxicity on tumour cells of the essential oil from Cedronella canariensis var. canariensis (L.) Webb & Berthel. (Lamiaceae)

Cedronella canariensis is a lemon-scented species of the family Lamiaceae endemic to the Canary Islands where it is used in the traditional medicine to prepare infusions or inhalations for anti-catarrhal, tonic, diuretic, hypoglycaemiant, hypotensive, anti-inflammatory and decongestant of the respiratory tract. In this work we investigated for the first time the antioxidant activity of the essential oil and its inhibitory effects on tumour cells (A375, MDA-MB-231, HCT 116) proliferation by DPPH, ABTS, FRAP and MTT assays, respectively. The oil, analysed by GC-ionisation flame detector and GC–MS, was characterised by pinocarvone (58.0%) and β-pinene (10.8%) as the major constituents, being typical of the chemotype ‘canariensis’. Noteworthy was the cytotoxic activity of the oil against the tumour cells examined, with IC₅₀ values of 4.3, 7.3 and 11.4 μg/mL on A375, MDA-MB-231 and HCT 116 tumour cells, respectively, as well as the scavenging activity against the ABTS radical (IC₅₀ of 10.5 μg/mL).     

Halogen and Hydrogen Bonding Benzothiophene Diol Derivatives: A Study Using ab initio Calculations and X-Ray Crystal Structure Measurements

The aim of this study is to describe and compare the supramolecular interactions, in the solid state, of chloro-, bromo-, and iodobenzothiophene diols. The compounds were obtained through organo-catalyzed reactions starting from 3-substituted halobenzothiophene carbaldehydes. Energies of the noncovalent interactions were obtained by density functional theory calculations. Bond distances and angles were found to be in accordance with those determined by X-ray structure analysis. anti-Bromobenzothiophene derivatives showed strong halogen⋅⋅⋅π interactions between bromine and the heterocyclic phenyl ring, corresponding to an energy of 7.5 kcal mol⁻¹. syn-Bromo and syn-iodo derivatives appeared to be isostructural, showing X⋅⋅⋅O (carbonyl) interactions, π stacking, and formation of extended hydrogen bonding networks. In contrast, the chloro derivatives displayed no halogen bonding interactions.     

Stochastic equilibrium assignment with variable demand: Theoretical and implementation issues

Recently, it has been pointed out that transport models should reflect all significant traveler choice behavior. In particular, trip generation, trip distribution, modal split as well as route choice should be modeled in a consistent process based on the equilibrium between transport supply and travel demand. In this paper a general fixed-point approach that allows dealing with multi-user stochastic equilibrium assignment with variable demand is presented. The main focus was on investigating the effectiveness of internal and external approaches and of different algorithmic specifications based on the method of successive averages within the internal approach. The vector demand function was assumed non-separable, non-symmetric cost functions were adopted and implementation issues, such updating step and convergence criterion, were investigated. In particular the aim was threefold: (i) compare the internal and the external approaches; (ii) investigate the effectiveness of different algorithmic specifications to solve the variable demand equilibrium assignment problem through the internal approach; (iii) investigate the incidence of the number of the links with non-separable and/or asymmetrical cost functions. The proposed analyses were carried out with respect to two real-scale urban networks regarding medium-size urban contexts in Italy.     

Compact fibre-based coherent anti-Stokes Raman scattering spectroscopy and interferometric coherent anti-Stokes Raman scattering from a single femtosecond fibre-laser oscillator

We demonstrate a new approach to CARS spectroscopy by efficiently synthesizing synchronized narrow-bandwidth (less than 10 cm⁻¹) pump and Stokes pulses (frequency difference continuously tunable upto ≈3000 cm⁻¹) based on spectral compression together with second harmonic generation (in periodically-poled nonlinear crystals) of femtosecond pulses emitted by a single compact Er-fibre oscillator. For a far better signal to non-resonant background contrast, interferometric CARS (I-CARS) is demonstrated and CARS signal enhancement upto three orders of magnitude is achieved by constructive interference with an auxiliary local oscillator at anti-Stokes field, also synthesized by spectral compression of pulses emitted from the same fibre oscillator.     

Spectral Theory of a Neumann–Poincaré-Type Operator and Analysis of Cloaking Due to Anomalous Localized Resonance

The aim of this paper is to give a mathematical justification of cloaking due to anomalous localized resonance (CALR). We consider the dielectric problem with a source term in a structure with a layer of plasmonic material. Using layer potentials and symmetrization techniques, we give a necessary and sufficient condition on the fixed source term for electromagnetic power dissipation to blow up as the loss parameter of the plasmonic material goes to zero. This condition is written in terms of the Newtonian potential of the source term. In the case of concentric disks, we make the condition even more explicit. Using the condition, we are able to show that for any source supported outside a critical radius, CALR does not take place, and for sources located inside the critical radius satisfying certain conditions, CALR does take place as the loss parameter goes to zero.     

Determination,aerobic biodegradation and environmental occurrence of aliphatic alcohol polyethoxylate sulfates (AES)

A new analytical method was developed for the routine specific determination of the anionic surfactant Alcohol polyEthoxylate Sulfate (AES) in environmental aqueous samples. An enrichment/fractionation of the target analytes in water samples was performed by solid-phase extraction (SPE) on graphitized carbon black (GCB) (recoveries: 90–103%), followed by hydrolysis/derivatization with fluorescent reagents and separation/detection by reversed-phase high performance liquid chromatography coupled with fluorescence (HPLC-FLD). The developed procedure was applied to the study of the aerobic biodegradation of AES under laboratory conditions and to a ten-month monitoring of AES, as well as of linear alkylbenzene sulfonates (LAS), nonylphenol polyethoxylates (NPE) and alcohol polyethoxylates (AE) surfactants, in the Po river (Northern Italy). The residual concentrations found in the river waters were compared and used for a preliminary estimation of the annual average loads of monitored surfactants in the Adriatic Sea.