Growth properties of Sobolev space functions over unbounded domains

Summary We study Sobolev space functions with prescribed growth properties on large spheres. In particular, we prove a weighted Poincaré type inequality for such functions. An extension to weighted Sobolev spaces is sketched.

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Sunto Si studiano funzioni che appartengono a certi spazi di Sobolev e che hanno crescita assegnata su sfere di grande raggio. Per tali funzioni si dimostra una disuguaglianza di tipo Poincaré con peso. Si indica inoltre anche una estensione di tale risultato a funzioni in spazi di Sobolev con peso.

     

Lipschitz and darbo conditions for the superposition operator in ideal spaces

Summary In this paper we give necessary and sufficient conditions for the superposition operator Fx(s)=f(s, x(s)) to satisfy a Lipschitz condition Fx₁ - Fx₂kx₁ - x₂ or a Darbo condition (FN)k(N) in ideal spaces of measurable functions, where is the Hausdorff measure of noncompactness. Moreover, we characterize a large class of spaces in which the above mentioned two conditions are equivalent.

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Sunto In questo lavoro diamo delle condizioni necessarie e sufficienti perchè l'operatore di sovrapposizione Fx(s)=f (s, x(s)) soddisfi alla condizione di Lipschitz Fx₁–Fx₂ kx₁–x₂ o quella di Darbo (FN)k(N) in spazi ideali di funzioni misurabili, ove è la misura di non compattezza di Hausdorff. Inoltre, caratterizziamo un'ampia classe di spazi in cui le suddette due condizioni sono equivalenti.

     

Chemiluminescent ion-molecule reactions in the system C+ + H2

The optical emission resulting from collisions between C⁺ ions and H₂ gas was measured in the energy range 2 to 20 eV_c.m.. The observed spectrum consists mainly of the CH⁺ A ¹Π → X ¹Σ⁺ band system; CH⁺ (A ^fΠ) is shown to be formed in the chemiluminescent reactio: C⁺(²P⁰) + H₂ → CH⁺(A ¹Π) + H(²S). The energy dependence of the emission cross section was measured. The occurrence of this reaction is discussed in terms of a electronic state correlation diagram for the system.     

Extreme swelling of a lyotropic lamellar liquid crystal

The evolution of the OBS/water/decane/pentanol lyotropic lamellar crystal is followed from 0% to more than 90% decane content. The lamellar spacing (d) varies then from 35 Å to 11000 Å. The swelling is followed with small angle x-ray scattering and the Bragg divergence in the intensity is found to disappear in moderately swollen lamellar crystal (d from 200 Å up to 800 Å) while the central scattering increases. More striking is the reappearance of the Bragg divergences observed by SAXS (d from 800 Å to 1100 Å) and for extremely swollen lamellar crystals in the angular distribution of scattered light (d from 2 000 Å to 10 000 Å). We discuss these observations along the lines of the recent models of swollen lamellar liquid crystals and in particular the apparent evolution of the dilute lamellae.     

Spectroscopic and time-dependent density functional investigation of the role of structure on the acid-base effects of citrinin detection

A time-dependent density functional theory (TD-DFT) study was carried out on tautomers of the mycotoxin citrinin in the neutral, anionic, and cationic forms to gain insight into the role of chemical structure on detection. Steady-state fluorescence studies of citrinin in micellar aqueous solutions produced unusual results for ionic surfactants and the neutral Triton X-100 enhanced fluorescence emission. Ground-state and time-dependent density functional studies were carried out on five tautomers of citrinin using the B3LYP density functional and the 6-311+G(2df,2p) basis set. The investigation revealed that deprotonation is a major factor governing the shifts in fluorescence excitation and emission maxima. Moreover, the position of the lowest unoccupied molecular orbitals is removed from the fluorophore moiety of citrinin in the dianionic state which is consistent with the diminished fluorescence of the toxin in basic solutions. The ionic characteristics of certain chemosensors can influence the structure and intrinsic spectroscopic properties of citrinin.     

Interactions between cyclodextrins and fluorescent T-2 and HT-2 toxin derivatives: a physico-chemical study

T-2 and HT-2 toxins are mycotoxins produced by several Fusarium species that are commonly found in various cereal grains, including oats, barley, wheat and maize. Intake estimates indicate that the presence of these mycotoxins in the diet can be of concern for public health. In this work, the inclusion processes occurring between fluorescent anthracene-derivatives of T-2 and HT-2 toxins and different cyclodextrin (CD) molecules were investigated in aqueous solutions by means of UV–Vis absorption, fluorescence emission and dynamic light scattering. Binding constant values and chemico-physical parameters were calculated. It was found that β-CDs give stronger inclusion reactions with both T-2 and HT-2 derivatives, as stated by important emission intensity increments. Such interactions were found to be fundamentally enthalpy-driven. Among β-CDs, the effect of the methylation at hydroxyl groups was tested: as a result, the di-methyl form of β-CD was found to induce the best fluorescence intensity enhancements.