A Talenti Comparison Result for Solutions to Elliptic Problems with Robin Boundary Conditions

Comparison results of Talenti type for elliptic problems with Dirichlet boundary conditions have been widely investigated in recent decades. In this paper, we deal with Robin boundary conditions. Surprisingly, contrary to the Dirichlet case, Robin boundary conditions make the comparison sensitive to the dimension, and while the planar case seems to be completely settled, in higher dimensions some open problems are yet unsolved. © 2023 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC.     

A variational method for the calculation of spin-rovibronic energy levels of triatomic molecules with three interacting electronic states

A general method is presented for the evaluation of the spin rovibronic energy levels of triatomic molecules with up to three interacting potential energy surfaces. The full theory is outlined in detail, both for singlet and for doublet electronic states and the method is then applied to the benchmark example of C₂H. High quality multireference configuration interaction calculations have been carried out to generate the 3-dimensional near-equilibrium adiabatic potential energy surfaces of the three lowest 1²A'(X²Σ⁺), 2²A'(A²Π), 1²A''(A²Π) electronic states of C₂H, and the pair of interacting states of A 0 symmetry have then been diabatized. Results are presented for J up to 7/2 and compared with gas-phase high resolution experimental results for energies up to 5600 cm¹.     

Isoparametric submanifolds in two-dimensional complex space forms

We show that an isoparametric submanifold of a complex hyperbolic plane, according to the definition of Heintze, Liu and Olmos’, is an open part of a principal orbit of a polar action. We also show that there exists a non-isoparametric submanifold of the complex hyperbolic plane that is isoparametric according to the definition of Terng’s. Finally, we classify Terng-isoparametric submanifolds of two-dimensional complex space forms.     

Weakly <Emphasis Type="Italic">φ</Emphasis>-pairs and common fixed points in cone metric spaces

In this paper we introduce a weak contractive condition, called weakly φ-pair, for two mappings in the framework of cone metric spaces and we prove a theorem which ensures existence and uniqueness of common fixed points for such mappings. Also we obtain a result on points of coincidence. These results extend and generalize well-known comparable results in the literature. The authors are supported by Università degli Studi di Palermo, R. S. ex 60%.     

Chemical Characterization and Bioactivity of Commercial Essential Oils and Hydrolates Obtained from Portuguese Forest Logging and Thinning

Essential oils (EOs) and hydrolates (Hds) are natural sources of biologically active ingredients with broad applications in the cosmetic industry. In this study, nationally produced (mainland Portugal and Azores archipelago) EOs (11) and Hds (7) obtained from forest logging and thinning of Eucalyptus globulus, Pinus pinaster, Pinus pinea and Cryptomeria japonica, were chemically evaluated, and their bioactivity and sensorial properties were assessed. EOs and Hd volatiles (HdVs) were analyzed by GC-FID and GC-MS. 1,8-Cineole was dominant in E. globulus EOs and HdVs, and α- and β-pinene in P. pinaster EOs. Limonene and α-pinene led in P. pinea and C. japonica EOs, respectively. P. pinaster and C. japonica HVs were dominated by α-terpineol and terpinen-4-ol, respectively. The antioxidant activity was determined by DPPH, ORAC and ROS. C. japonica EO showed the highest antioxidant activity, whereas one of the E. globulus EOs showed the lowest. Antimicrobial activity results revealed different levels of efficacy for Eucalyptus and Pinus EOs while C. japonica EO showed no antimicrobial activity against the selected strains. The perception and applicability of emulsions with 0.5% of EOs were evaluated through an in vivo sensory study. C. japonica emulsion, which has a fresh and earthy odour, was chosen as the most pleasant fragrance (60%), followed by P. pinea emulsion (53%). In summary, some of the studied EOs and Hds showed antioxidant and antimicrobial activities and they are possible candidates to address the consumers demand for more sustainable and responsibly sourced ingredients.     

Chemical Approach to the Optimization of Conditions Using HS-SPME/GC–MS for Characterization of Volatile Compounds in Eugenia brasiliensis Fruit

Grumixama (Eugenia brasiliensis Lam.) is a native fruit of the Brazilian Atlantic Forest, belonging to the Myrtaceae family, which designatesthe most significant number of species with food potential. It stands out due to its phytochemical characteristics because of the presence of polyphenols and volatile organic compounds. Volatile compounds are substances released by foods that give off an aroma and influence flavor. Solid-phase microextraction is a technique that allows for low-cost, fast, and solvent-free extraction, has an affinity for numerous analytes, and is easily coupled to gas chromatography. The objectives of this work were to evaluate the efficiency of different fibers of SPME (solid-phase microextraction) in the extraction of volatile organic compounds from grumixama pulp; optimize a method for extraction time, temperature, and sample weight; and to determine the characteristic volatile profile of this fruit. For the extraction of volatile compounds, three fibers of different polarities were used: polar polyacrylate (PA) fibers, divinylbenzene/carboxyne/polydimethylsiloxane (DVB/CAR/PDMS) semipolar fibers, and polydimethylsiloxane/divinylbenzene (PDMS/DVB). Fourteen volatile organic compounds (VOCs) were identified by DVB/CAR/PDMS, six by PA, and seven by PDMS/DVB through solid-phase microextraction in the headspace mode (SPME-HS). Considering the total number of compounds identified, regardless of the fiber used, and the optimization of the method, Eugenia brasiliensis presented sesquiterpene fractions (85.7%, 83.3%, and 85.7% of total VOCs) higher than the monoterpene fractions (14.3%, 16.7%, and 14.3%) for DVB/CAR/PDMS, PA, and PDMS/DVB, respectively in its composition. In addition, it was possible to verify that the fiber DVB/CAR/PDMS presented a better efficiency due to the larger chromatographic area observed when the grumixama pulp was subjected to conditions of 75 °C, 2.0 g, and an adsorption time of 20 min.     

Copper acetylacetonate anchored onto amine-functionalised clays

Copper (II) acetylacetonate was immobilised directly onto two clays, laponite (Lap) and K10-montmorillonite (K10), and after their amine functionalisation with (3-aminopropyl)triethoxysilane (APTES). All the materials were characterised by nitrogen adsorption isotherms at -196 degrees C, elemental analysis, TG-DSC, XRD, and IR spectroscopy. The K10-based materials were also characterised by XPS. The APTES-functionalised K10 showed higher copper loading than K10, indicating that the clay functionalisation enhanced the complex immobilisation; on the contrary, in Lap-based materials higher metal content was obtained by direct complex anchoring, probably due to the delaminated nature of Lap which induced the particles aggregation on functionalisation with APTES. All the results pointed out that the Cu complex was anchored onto the amine-functionalised clays by Schiff condensation between the amine groups of anchored APTES and the carbonyl groups of the acetylacetonate ligand, whereas direct immobilisation proceeded mostly through interaction between the metal centre and the clay surface hydroxyl groups.     

A computational study on the interaction of the nitric oxide ions NO+ and NO- with the side groups of the aromatic amino acids

The interaction of the nitric oxide ions NO+ and NO- with benzene (C6H6) and the aromatic R-groups of the amino acids phenylalanine (Phe), tyrosine (Tyr), histidine (His), and tryptophan (Trp) have been examined using the DFT method B3LYP and the conventional electron correlation method MP2. In particular, the structures and complexation energies of the resulting half-sandwich Ar...NO+/- and sandwich [Ar...NO...Ar]+/- complexes have been considered. For the Ar...NO+ complexes, the presence of an electron rich heteroatom within or attached to the ring is found to not preclude the cation...pi bound complex from being the most stable. Furthermore, unlike the anionic complexes, the pi...cation...pi ([Ar...NO...Ar]+) complexes do not correspond to a "doubling" of the parent half-sandwich.