On the integrability of Degasperis–Procesi equation: Control of the Sobolev norms and Birkhoff resonances

We consider the dispersive Degasperis–Procesi equation $u_t?u_{xxt}?\mathtt{c}{u}_{xxx}+4\mathtt{c}{u}_x?u{u}_{xxx}?3u_x{u}_{xx}+4u{u}_x=0$ with $\mathtt{c}\in \mathbb{R}?\{0\}$. In [15] the authors proved that this equation possesses infinitely many conserved quantities. We prove that there are infinitely many of such constants of motion which control the Sobolev norms and which are analytic in a neighborhood of the origin of the Sobolev space $H^s$ with $s\ge 2$, both on $\mathbb{R}$ and $\mathbb{T}$. By the analysis of these conserved quantities we deduce a result of global well-posedness for solutions with small initial data and we show that, on the circle, the formal Birkhoff normal form of the Degasperis–Procesi at any order is action-preserving.     

Development of a Novel Microwave Distillation Technique for the Isolation of Cannabis sativa L. Essential Oil and Gas Chromatography Analyses for the Comprehensive Characterization of Terpenes and Terpenoids,Including Their Enantio-Distribution

A microwave distillation method was optimized for the extraction and isolation of cannabis essential oil from fresh and dried hemp inflorescences. The developed method enabled us to obtain a distilled product rich in terpenes and terpenoid compounds, responsible of the typical and unique smell of the cannabis plant. The distillate from different hemp cultivars, including Kompolti, Futura 75, Carmagnola, Felina 32 and Finola were characterized by using a gas chromatograph equipped with both mass spectrometer and flame ionization detectors. In a single chromatographic run, the identity and absolute amounts of distilled compounds were determined. Peak assignment was established using a reliable approach based on the usage of two identification parameters, named reverse match, and linear retention index filter. Absolute quantification (mg g⁻¹) of the analytes was performed using an internal standard method applying the flame ionization detector (FID) response factors according to each chemical family. An enantio-GC-MS method was also developed in order to evaluate the enantiomeric distribution of chiral compounds, an analytical approach commonly utilized for establishing the authenticity of suspicious samples.     

Boosting Conjugate Addition to Nitroolefins Using Lithium Tetraorganozincates: Synthetic Strategies and Structural Insights

We report the first transition metal catalyst- and ligand-free conjugate addition of lithium tetraorganozincates (R₄ZnLi₂) to nitroolefins. Displaying enhanced nucleophilicity combined with unique chemoselectivity and functional group tolerance, homoleptic aliphatic and aromatic R₄ZnLi₂ provide access to valuable nitroalkanes in up to 98 % yield under mild conditions (0 °C) and short reaction time (30 min). This is particularly remarkable when employing β-nitroacrylates and β-nitroenones, where despite the presence of other electrophilic groups, selective 1,4 addition to the C=C is preferred. Structural and spectroscopic studies confirmed the formation of tetraorganozincate species in solution, the nature of which has been a long debated issue, and allowed to unveil the key role played by donor additives on the aggregation and structure of these reagents. Thus, while chelating N,N,N’,N’-tetramethylethylenediamine (TMEDA) and (R,R)-N,N,N’,N’-tetramethyl-1,2-diaminocyclohexane (TMCDA) favour the formation of contacted-ion pair zincates, macrocyclic Lewis donor 12-crown-4 triggers an immediate disproportionation process of Et₄ZnLi₂ into equimolar amounts of solvent-separated Et₃ZnLi and EtLi.     

IR Tools: a MATLAB package of iterative regularization methods and large-scale test problems

Numerical Algorithms - This paper describes a new MATLAB software package of iterative regularization methods and test problems for large-scale linear inverse problems. The software package, called...     

Evaluation of methoxy polyethylene glycol‐polylactide diblock copolymers as additive in hypromellose film coating

This paper deals with a new application of diblock methoxy polyethylene glycol‐polylactide block copolymers, a class of synthetic biomaterials largely studied in the pharmaceutical and biomedical fields owing to their favorable properties such as biocompatibility, biodegradability, low immunogenicity, and good mechanical properties. In this work, these materials were evaluated as additives for gastro‐soluble pharmaceutical coating aimed to reduce film stiffness and water permeability. Two copolymers with different polylactide chain lengths were synthesized and characterized in term of molecular weight and solid‐state properties. A series of free films with different hypromellose/copolymers ratio were prepared and characterized in terms of appearance, components miscibility, plasticity, and water vapor permeability. The obtained results demonstrate that copolymers effectively influence hypromellose film properties according to their concentration and molecular weight. Specifically, the addition of the copolymer with a molecular weight of 6.5 kDa in a ratio hypromellose:polymer 5:1, allowed to obtain films with good appearance, improved plasticization, and water permeability properties. For higher molecular weight, copolymer or different ratios was not possible to observe the improvement of all the properties at the same time. The results also make possible to define the critical features to improve in order to use block copolymers as additive in hypromellose film coating. The availability of new water‐soluble additives able to work as plasticizer and moisture sealer in polymeric films represents an important progress not only in the field of pharmaceutical coating but also in that of food coatings, as for example in the formulation of edible films. Copyright © 2013 John Wiley & Sons, Ltd.     

Nonnegative Matrix Factorization based on the Geometry of Positive Numbers

We consider the problem of nonnegative matrix factorization where the typical objective function is altered based on geometrical arguments. A noneuclidean geometry on positive real numbers is used to describe the nonnegative entries of a nonnegative matrix, influencing the factorization model. We design an optimization procedure from a differential geometric point of view for the newly proposed model. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)