Sul problema preliminare di una classica questione di calcolo delle variazioni

Sunto L'Autore fa la trattazione rigorosa del problema preliminare relativo alla classica questione di minimizzare l'integrale , (n>0). Fissato un puntoP ₀ del piano, determina l'insiemeE nel quale bisognerà assegnare un secondo punto P, che possa essere congiunto aP ₀ mediante un estremale Γ relativa a ℑ. Dà l'equazione della frontiera Γ* diE e ne studia l'andamento e le relazioni con le estremali uscenti daP ₀. Dimostra che perP ₀ e per un puntoP diE passa una sola estremale (non estremante) seP è in Γ*, ne passano due seP è interno aE, e assegna il criterio per decidere quale delle due può realizzare il minimo per ℑ.     

A note on existence and uniqueness of limit cycles for Liénard systems

We consider the Liénard equation and we give a sufficient condition to ensure existence and uniqueness of limit cycles. We compare our result with some other existing ones and we give some applications.     

Electronic properties of nanoporous TiO2 films investigated in real space by means of scanning tunnelling spectroscopy

Nanoporous TiO₂ films with a thickness between 100 nm and 8 μm were studied by scanning tunnelling spectroscopy. The bias voltage of significantly increased differential conductivity, indicating the conduction and valence bands, was found to be strongly dependent on layer thickness and the underlying substrate material. This effect is traced back to the high resistivity of the oxide films and the formation of Schottky barriers at the TiO₂-substrate contact. All films showed a strong hysteresis as a function of sweep direction of the bias voltage pointing towards the existence of a high number of localized electronic trap states. This effect is getting even more pronounced upon sample ageing. Laterally resolved measurements show that the major part of the surface exhibits similar I(V) characteristics with minor deviations, while smaller areas with significantly different response are identified. These areas are comparable in size to the individual crystals the material is composed of.     

The Lamb-dip spectrum of the J = 1 ← 0 transition of DF: Crossing resonances and hyperfine components

The Lamb-dip technique has been applied to the observation of the J = 1 ← 0 transition of DF: for the first time, the hyperfine structure due to D and F have been resolved by using microwave spectroscopy. The high accuracy of this technique allows us to provide hyperfine parameters that are in very good agreement with those obtained from molecular beam experiment. In addition, our frequencies together with the unresolved ones up to J″ value of 47 allow us to provide the most accurate ground state rotational constants of DF known at the moment. Furthermore, due to the presence of a relevant number of strong crossing resonances, the J = 1 ← 0 transition of DF can be considered an illustrative case to show how they modify the shape of Lamb-dip spectra.     

Predicting Deliquescence Relative Humidities of Crystals and Crystal Mixtures

The presence of water in the form of relative humidity (RH) may lead to deliquescence of crystalline components above a certain RH, the deliquescence RH (DRH). Knowing the DRH values is essential, e.g., for the agrochemical industry, food industry, and pharmaceutical industry to identify stability windows for their crystalline products. This work applies the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) to purely predict the DRH of single components (organic acids, sugars, artificial sweeteners, and amides) and multicomponent crystal mixtures thereof only based on aqueous solubility data of the pure components. The predicted DRH values very well agree with the experimental ones. In addition, the temperature influence on the DRH value could be successfully predicted with PC-SAFT. The DRH prediction also differentiates between formation of hydrates and anhydrates. PC-SAFT-predicted phase diagrams of hydrate-forming components illustrate the influence of additional components on the hydrate formation as a function of RH. The DRH prediction via PC-SAFT allows for the determining of the stability of crystals and crystal mixtures without the need for time-consuming experiments.     

Partially disposable biosensors for the quick assessment of damage in foodstuff after thermal treatment

A novel approach towards a quick, easy and reliable solution to the quite complex problems connected with the Amadori's compounds and furosine formation in several foodstuff is here proposed and based on enzymatic reactions, either as far as L-lysine release after partial hydrolysis from proteic material of the food matrix (bioavailable L-lysine), or as far as the determination of total and free L-lysine is concerned.The contribution proposes the use of specific L-lysine sensitive bioelectrodes for the evaluation of the possible heat damage through the rapid measure of L-lysine consumption. The L-lysine biosensor has been realized by immobilizing the enzyme L-lysine-α-oxidase (LOx) on an amperometric H₂O₂ sensitive electrode.The bioelectrode-enzymatic reaction arrangement allows to perform determinations of L-lysine and bioavailable L-lysine in foodstuff from different sources and after different thermal treatments in a very rapid inexpensive and reliable way in the range 1.0–33 ppm, with a limit of detection LOD = 0.5 ppm, so that a considerable number of samples can be easily monitored quickly and with very low costs.     

Palladium catalyzed multicomponent reactions in ordered sequence: new syntheses of o,o′-dialkylsubstituted diarylacetylenes and diarylalkylidenehexahydromethanofluorenes

Catalytic one-pot reactions of aromatic iodides with alkyl halides, phenylacetylene or diphenylacetylene, potassium acetate or carbonate, norbornene and palladium acetate in DMF or DMA are reported. A high selectivity towards dialkylsubstituted diarylacetylenes and diarylalkylidenehexahydromethanofluorenes, respectively, has been reached.