Singularity of eigenfunctions at the junction of shrinking tubes,Part II

In continuation with [17], we investigate the asymptotic behavior of weighted eigenfunctions in two half-spaces connected by a thin tube. We provide several improvements about some convergences stated in [17]; most of all, we provide the exact asymptotic behavior of the implicit normalization for solutions given in [17] and thus describe the (N−1)$(N-1)$-order singularity developed at a junction of the tube (where N is the space dimension).     

On the sharp effect of attaching a thin handle on the spectral rate of convergence

Consider two domains connected by a thin tube: it can be shown that the resolvent of the Dirichlet Laplacian is continuous with respect to the channel section parameter. This in particular implies the continuity of isolated simple eigenvalues and the corresponding eigenfunctions with respect to domain perturbation. Under an explicit nondegeneracy condition, we improve this information providing a sharp control of the rate of convergence of the eigenvalues and eigenfunctions in the perturbed domain to the relative eigenvalue and eigenfunction in the limit domain. As an application, we prove that, again under an explicit nondegeneracy condition, the case of resonant domains features polynomial splitting of the two eigenvalues and a clear bifurcation of eigenfunctions.     

Impact of Peels Extracts from an Italian Ancient Tomato Variety Grown under Drought Stress Conditions on Vascular Related Dysfunction

Background: Tomato by-products contain a great variety of biologically active substances and represent a significant source of natural antioxidant supplements of the human diet. The aim of the work was to compare the antioxidant properties of a by-product from an ancient Tuscan tomato variety, Rosso di Pitigliano (RED), obtained by growing plants in normal conditions (-Ctr) or in drought stress conditions (-Ds) for their beneficial effects on vascular related dysfunction. Methods: The antioxidant activity and total polyphenol content (TPC) were measured. The identification of bioactive compounds of tomato peel was performed by HPLC. HUVEC were pre-treated with different TPC of RED-Ctr or RED-Ds, then stressed with H₂O₂. Cell viability, ROS production and CAT, SOD and GPx activities were evaluated. Permeation of antioxidant molecules contained in RED across excised rat intestine was also studied. Results: RED-Ds tomato peel extract possessed higher TPC than compared to RED-Ctr (361.32 ± 7.204 mg vs. 152.46 ± 1.568 mg GAE/100 g fresh weight). All extracts were non-cytotoxic. Two hour pre-treatment with 5 µg GAE/mL from RED-Ctr or RED-Ds showed protection from H₂O₂-induced oxidative stress and significantly reduced ROS production raising SOD and CAT activity (* p < 0.05 and ** p < 0.005 vs. H₂O₂, respectively). The permeation of antioxidant molecules contained in RED-Ctr or RED-Ds across excised rat intestine was high with non-significant difference between the two RED types (41.9 ± 9.6% vs. 26.6 ± 7.8%). Conclusions: RED-Ds tomato peel extract represents a good source of bioactive molecules, which protects HUVECs from oxidative stress at low concentration.     

A C and N experimental NMR and theoretical study of the structure of linear primary aliphatic amines and ammonium salts: from C1 to C18

Eighteen aliphatic linear amines, from methylamine to stearylamine, have been experimentally studied by NMR and theoretically calculated at the GIAO/B3LYP/6-311++G(d,p) level. A partial exploration of their conformation has been carried out, mainly to determine the effect on the chemical shifts. In solution and for neutral amines, ¹⁵N chemical shifts indicate a mixture of two conformations. In the solid state (CPMAS NMR) only the subset of solid amines has been studied (from C14 to C18). The ¹⁵N signals of the corresponding ammonium salts in the solid state depend on the counteranions, Cl⁻ and CF₃CO₂⁻, a result that is theoretically proven.     

Associated production evidence against Higgs impostors and anomalous couplings

We analyze bicovariant differential calculus on κ-Minkowski spacetime. It is shown that corresponding Lorentz generators and noncommutative coordinates compatible with bicovariant calculus cannot be realized in terms of commutative coordinates and momenta. Furthermore, κ-Minkowski space and NC forms are constructed by twist related to a bicrossproduct basis. It is pointed out that the consistency condition is not satisfied. We present the construction of κ-deformed coordinates and forms (super-Heisenberg algebra) using extended twist. It is compatible with bicovariant differential calculus with κ-deformed $\mathfrak{igl}(4)$ -Hopf algebra. The extended twist leading to κ-Poincaré-Hopf algebra is also discussed.     

Dissipative Bohmian mechanics within the Caldirola–Kanai framework: A trajectory analysis of wave-packet dynamics in viscid media

Classical viscid media are quite common in our everyday life. However, we are not used to find such media in quantum mechanics, and much less to analyze their effects on the dynamics of quantum systems. In this regard, the Caldirola–Kanai time-dependent Hamiltonian constitutes an appealing model, accounting for friction without including environmental fluctuations (as it happens, for example, with quantum Brownian motion). Here, a Bohmian analysis of the associated friction dynamics is provided in order to understand how a hypothetical, purely quantum viscid medium would act on a wave packet from a (quantum) hydrodynamic viewpoint. To this purpose, a series of paradigmatic contexts have been chosen, such as the free particle, the motion under the action of a linear potential, the harmonic oscillator, or the superposition of two coherent wave packets. Apart from their analyticity, these examples illustrate interesting emerging behaviors, such as localization by “quantum freezing” or a particular type of quantum–classical correspondence. The reliability of the results analytically determined has been checked by means of numerical simulations, which has served to investigate other problems lacking of such analyticity (e.g., the coherent superpositions).     

On Gevrey solutions of threefold singular nonlinear partial differential equations

We study Gevrey asymptotics of the solutions to a family of threefold singular nonlinear partial differential equations in the complex domain. We deal with both Fuchsian and irregular singularities, and allow the presence of a singular perturbation parameter. By means of the Borel–Laplace summation method, we construct sectorial actual holomorphic solutions which turn out to share a same formal power series as their Gevrey asymptotic expansion in the perturbation parameter. This result rests on the Malgrange–Sibuya theorem, and it requires to prove that the difference between two neighboring solutions is exponentially small, what in this case involves an asymptotic estimate for a particular Dirichlet-like series.     

Gas-phase reactions of halogenated radical carbene anions with sulfur and oxygen containing species

The reactivities of mono- and dihalocarbene anions (CHCl⁻, CHBr⁻, CF₂⁻, CCl₂⁻, and CBrCl⁻) were studied using a tandem flowing afterglow-selected ion flow tube instrument. Reaction rate constants and product branching ratios are reported for the reactions of these carbene anions with six neutral reagents (CS₂, COS, CO₂, O₂, CO, and N₂O). These anions were found to demonstrate diverse chemistry as illustrated by formation of multiple product ions and by the observed reaction trends. The reactions of CHCl⁻ and CHBr⁻ occur with similar efficiencies and reactivity patterns. Substitution of a Cl atom for an H atom to form CCl₂⁻ and CBrCl⁻ decreases the rate constants; these two anions react with similar efficiencies and reactivity trends. The CF₂⁻ anion displays remarkably different reactivity; these differences are discussed in terms of its lower electron binding energy and the effect of the electronegative fluorine substituents. The results presented here are compared to the reactivity of the CH₂⁻ anion, which has previously been reported.     

Thermal behaviour of new Ni(II) and Cu(II) complexes with macrocyclic ligands functionalised with 1,2,4-triazole

The investigations concerning the thermal behaviour of a series of Ni(II) and Cu(II) complexes of type [NiLCl₂]·mH₂O ((1) L:L₁, m=6; (3) L:L₂, m=4) or [CuLCl]_nCl _n ·mnH₂O ((2) L:L₁, m=6; (4) L:L₂, m=4) are presented. The ligands L(1) and L(2) have been synthesised by template condensation of 3,6-diazaoctane-1,8-diamine or 1,2-diaminoethane with formaldehyde and 2-amino-4H-1,2,4-triazole. The bonding and stereochemistry of the complexes have been characterised by IR, electronic and magnetic studies at room temperature. The in vitro qualitative and quantitative antimicrobial activity assays showed that the complexes exhibited variable antimicrobial activity against planktonic as well as biofilm embedded Gram-negative, Gram-positive and fungal strains. The thermal behaviour provided confirmation of the complexes composition as well as the number and nature of water molecules and the intervals of thermal stability.     

New complexes of Ni(II) and Cu(II) with Schiff bases functionalised with 1,3,4-thiadiazole: spectral,magnetic, biological and thermal characterisation

Schiff bases obtained by the condensation of 2-amino-5-mercapto-1,3,4-thiadiazole with 2,4-pentandione or 1-phenyl-1,3-butandione were synthesized and characterized in order to obtain polydentate ligands HL¹ and HL², respectively. The complexes with these ligands of the type M(L)Cl·nH₂O [(1) M:Ni, L:L¹, n = 0.5; (3) M:Ni, L:L², n = 0.5]; [(2) M:Cu, L:L¹, n = 1; (4) M:Cu, L:L², n = 0] were also synthesized and characterized. The modifications evidenced in IR spectra of complexes were correlated with the presence of monodeprotonate Schiff bases. The electronic spectra display the characteristic pattern of square-planar stereochemistry. The in vitro qualitative and quantitative antimicrobial activity assays showed that the new complexes exhibited variable antimicrobial activity. The thermal analyses have evidenced the thermal intervals of stability and also the thermodynamic effects that accompany them. Schiff bases and complexes have a similar thermal behaviour. Processes as water elimination, melting, chloride anion removal as well as oxidative degradation of the organic ligands were observed.