Graphs with prescribed Levi form trace

Abstract We prove existence and uniqueness of a viscosity solution of the Dirichlet problem related to the prescribed Levi mean curvature equation, under suitable assumptions on the boundary data and on the Levi curvature of the domain. We also show that such a solution is Lipschitz continuous by proving that it is the uniform limit of a sequence of classical solutions of elliptic problems and by building Lipschitz continuous barriers. Keywords: Levi mean curvature, Quasilinear degenerate elliptic PDE’s, Viscosity solutions, Comparison principle, Global Lipschitz estimates     

Hydroxymethyl 18-crown-6 and hydroxymethyl [2.2.2]cryptand: versatile derivatives for binding the two polyethers to lipophilic chains and to polymer matrices

The presence of the hydroxymethyl group allows facile functionalisation of 18-crown-6 and of [2.2.2]cryptand. A variety of lipophilic and polymer-supported macrocyclic polyethers is thus available. They are efficient and easily recyclable phase-transfer catalysts.     

Localization from Incomplete Noisy Distance Measurements

We consider the problem of positioning a cloud of points in the Euclidean space ? ^d , using noisy measurements of a subset of pairwise distances. This task has applications in various areas, such as sensor network localization and reconstruction of protein conformations from NMR measurements. It is also closely related to dimensionality reduction problems and manifold learning, where the goal is to learn the underlying global geometry of a data set using local (or partial) metric information. Here we propose a reconstruction algorithm based on semidefinite programming. For a random geometric graph model and uniformly bounded noise, we provide a precise characterization of the algorithm’s performance: in the noiseless case, we find a radius r ₀ beyond which the algorithm reconstructs the exact positions (up to rigid transformations). In the presence of noise, we obtain upper and lower bounds on the reconstruction error that match up to a factor that depends only on the dimension d, and the average degree of the nodes in the graph.     

Seasonal Changes in Essential Oil Constituents of Cystoseira compressa: First Report

Marine macroalgae are well known to release a wide spectrum of volatile organic components, the release of which is affected by environmental factors. This paper aimed to identify the essential oil (EO) compounds of the brown algae Cystoseira compressa collected in the Adriatic Sea monthly, from May until August. EOs were isolated by hydrodistillation using a Clavenger-type apparatus and analyzed by gas chromatography coupled with mass spectrometry (GC–MS). One hundred four compounds were identified in the volatile fraction of C. compressa, accounting for 84.37–89.43% of the total oil. Samples from May, June, and July were characterized by a high share of fatty acids (56, 69, and 34% respectively) with palmitic acid being the dominant one, while in the August sample, a high content of alcohols (mainly phytol and oleyl alcohol) was found. Changes in the other minor components, which could be important for the overall aroma and biological activities of the algal samples, have also been noted during the vegetation periods. The results of this paper contribute to studies of algal EOs and present the first report on C. compressa EOs.     

Fatty acids by high-performance liquid chromatography and evaporative light-scattering detector

A high-performance liquid chromatographic (HPLC) separation method with an evaporative light-scattering detector (ELSD) has been developed for the separation and quantitative analysis of fatty acid methyl esters (FAME) in three different oils. Reverse-phased C18 HPLC separation of 13 FAME is achieved using a methanol/water eluent mixture. The retention times (RT) reflect the elution behavior of these compounds on C18 reversed-phase HPLC. The proposed method is tested on: soybean oil (Glycine max L.) as reference sample, rice bran oil (Oryza sativa L.), pumpkin seed oil (Cucurbita pepo L.) and algal oil (Arthrospira platensis Nordst.).     

On 6-(thenoyl)-7,8-dichloro-4-oxo-4H-1-benzopyran-2-carboxylic acid

The annulation of the oxyacetic chain of thienylic acid into a γ-pyrone ring is described. The resulting 6-(2-thenoyl)-7,8-dichloro-4-oxo-4H-1-benzopyran-2-carboxylic acid retains almost 80% of the diuretic activity of the parent compound.     

Modelling hydrological data with and without long memory

The paper focuses on the problem of long-range dependence when analysing time series of hydrological data. Three time series are analysed: the monthly rainfall in the town of Florence, Italy; the daily minimum temperatures in the same town; and, finally, the daily water inflow to Lake Maggiore, Italy. Heuristic methods and maximum likelihood estimation of a parametric model are used to investigate the Hurst phenomena and to detect whether long-range dependence is present in any of the time series. We found that long-range dependence is not present in the first series but it is present in the last two. The daily water inflow to Lake Maggiore was modelled by a fractionally differenced arima model (farima) which contains a long-range dependence component. It is shown that the fit is much better than the one provided by more traditional arima models that do not have such a component.

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Sommario Lo studio considera il problema dell'identificazione dei fenomeni di dipendenza a lungo termine (long range dependence) nelle serie temporali di dati idrologici. Allo scopo sono state analizzate tre serie temporali, rispettivamente quella dei totali mensili di precipitazione rilevati alla stazione dell'Osservatorio Ximeniano de Firenze, quella delle temperature minime giornaliere per la stessa stazione e quella degli afflussi giornalieri al Lago Maggiore. Per identificare la presenza di fenomeni di dipendenza long range, attraverso la valutazione della consistenza del fenomeno di Hurst, sono stati utilizzati sia metodi euristici, sia la stima a massima verosimiglianza di un modello parametrico. Due delle tre serie analizzate sono risultate caratterizzate da tale dipendenza. Per la serie degli afflussi al Lago Maggiore, si è inoltre proceduto alla simulazione attraverso un modello arima a differenziazione frazionaria (farima), la cui struttura contiene una componente long-range. I risultati ottenuti, mostrano che tale modello fornisce risultati significativamente migliori dei tradizionali modelli arima, privi di tale componente.