Un teorema di unicità per una equazione iperbolica,non lineare

We prove the uniqueness of weak solutions of initial boundary value problems Each functiona _i is required to be sufficiently smooth and must satisfy the following conditions: \(e) \sum\limits_1^n {ij} \partial _{\eta _j \eta _h }^2 a_i (x, \ldots , \eta 1, \ldots , \eta _n )\xi _i \xi _j \leqslant 0, h = 1, \ldots , n,\) for some positive constantsK ₀, α, some non negative constantsK _i , some positive functionsH(t)∈L ¹(0,T) and for all ξ≡(ξ _i ), η≡(η _i )∈R ⁿ      

Positive\partial \bar \partial - closed currents and non-Kähler geometrycurrents and non-Kähler geometry

In this paper some new results on positive \(\partial \bar \partial - closed\) currents are applied to modifications \(f:\bar M \to M\) . The main result in this topic is that every smooth proper modification of a compact Kähler manifoldM is balanced. Moreover, under suitable hypotheses on the map, the Kähler degrees of \(\bar M\) corresponds to homological properties of the exceptional set of the modification. More examples ofp-Kähler manifolds are discussed in the last section of the paper.     

The Chemistry of Coumarin Derivatives. Part 5. Unusual course of the reaction of 4-hydroxycoumarin and aliphatic aldehydes

The reaction of 4-hydroxycoumarin and certain aliphatic aldehydes affords 1:1 or complex 2:2 adducts besides (or in place) of the expected 2:1 bis(coumarin) adducts. Reaction with heptanal, cyclohexanecarbaldehyde, and pivalaldehyde are reported as representative. The structure of the reaction products was established by spectroscopical techniques, including X-ray analysis, and their formation was mechanistically rationalized. Some of the 1:1 adducts are synthetically useful for the preparation of 3-alkyl-4-hydroxycoumarins.     

Alignment of molecules in pulsed resonant laser fields

We investigate by numerical simulations the dynamics of alignment of linear molecules in resonant pulsed laser fields and its dependence on pulse length, field strength, and molecular parameters. We propose an analytical short-time approximation for the time-dependent wave packets. We provide a theoretical basis for the occurrence of saturation in the rotational pumping. We present a formula to predict the time at which the maximum alignment occurs. We discuss the magnitude of the laser-induced alignment and we relate it to a theoretical upper limit.     

On elliptic equations with an axial symmetry

Sunto Si considera l'equazione (*) au_xx+2bu_xy+cu_yy+(d/y)u_y=f dove a, b, c, d L, d > 0, f L². Supponendo che (*) sia uniformemente eliittica e che l'oscillazione del quoziente d/a verifichi una resirizione vicino all'asse della x, si provano stime a priori e un teorema di esistenza per soluzioni W^2,2 di un problema di Dirichlet relativo all'equazione (*).

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Work supported by the Istituto di Analisi Globale e Applicazioni.     

GO-SWCNT Buckypapers as an Enhanced Technology for Water Decontamination from Lead

Water decontamination is an important challenge resulting from the incorrect disposal of heavy metal waste into the environment. Among the different available techniques (e.g., filtration, coagulation, precipitation, and ion-exchange), adsorption is considered the cheapest and most effective procedure for the removal of water pollutants. In the last years, several materials have been tested for the removal of heavy metals from water, including metal-organic frameworks (MOFs), single-walled carbon nanotubes (SWCNTs), and graphene oxide (GO). Nevertheless, their powder consistency, which makes the recovery and reuse after adsorption difficult, is the main drawback for these materials. More recently, SWCNT buckypapers (SWCNT BPs) have been proposed as self-standing porous membranes for filtration and adsorption processes. In this paper, the adsorption capacity and selectivity of Pb²⁺ (both from neat solutions and in the presence of other interferents) by SWCNT BPs were evaluated as a function of the increasing amount of GO used in their preparation (GO-SWCNT buckypapers). The highest adsorption capacity, 479 ± 25 mg g⁻¹, achieved for GO-SWCNT buckypapers with 75 wt.% of graphene oxide confirmed the effective application of such materials for cheap and fast water decontamination from lead.     

Exploring the Parallel G-Quadruplex Nucleic Acid World: A Spectroscopic and Computational Investigation on the Binding of the c-myc Oncogene NHE III1 Region by the Phytochemical Polydatin

Trans-polydatin (tPD), the 3-β-D-glucoside of the well-known nutraceutical trans-resveratrol, is a natural polyphenol with documented anti-cancer, anti-inflammatory, cardioprotective, and immunoregulatory effects. Considering the anticancer activity of tPD, in this work, we aimed to explore the binding properties of this natural compound with the G-quadruplex (G4) structure formed by the Pu22 [d(TGAGGGTGGGTAGGGTGGGTAA)] DNA sequence by exploiting CD spectroscopy and molecular docking simulations. Pu22 is a mutated and shorter analog of the G4-forming sequence known as Pu27 located in the promoter of the c-myc oncogene, whose overexpression triggers the metabolic changes responsible for cancer cells transformation. The binding of tPD with the parallel Pu22 G4 was confirmed by CD spectroscopy, which showed significant changes in the CD spectrum of the DNA and a slight thermal stabilization of the G4 structure. To gain a deeper insight into the structural features of the tPD-Pu22 complex, we performed an in silico molecular docking study, which indicated that the interaction of tPD with Pu22 G4 may involve partial end-stacking to the terminal G-quartet and H-bonding interactions between the sugar moiety of the ligand and deoxynucleotides not included in the G-tetrads. Finally, we compared the experimental CD profiles of Pu22 G4 with the corresponding theoretical output obtained using DichroCalc, a web-based server normally used for the prediction of proteins’ CD spectra starting from their “.pdb” file. The results indicated a good agreement between the predicted and the experimental CD spectra in terms of the spectral bands’ profile even if with a slight bathochromic shift in the positive band, suggesting the utility of this predictive tool for G4 DNA CD investigations.     

Surface anchoring,polarization fields and memory states in polymer dispersed liquid crystals

We have investigated the formation and development of memory states in polymer dispersed liquid crystals induced by the application of a strong electric field. Both the optical transmittance and polarization field have been followed as functions of time. We have been able to distinguish between the contributions to the memory states arising from the surface anchoring of the liquid crystal at the droplet interface and from the electrical reorientation of the mesogenic molecules. The dependence of both residual transmittance and polarization field on temperature is reported and a simple model is proposed.     

Highly reduced iron-doped lithium niobate for optoelectronic tweezers

We investigate the applicability of highly reduced lithium niobate samples doped with iron for the use as optoelectronic tweezers. Increasing the reduction degree of Fe-doped lithium niobate is well known to increase the photoconductivity and reduce the writing time of internal space-charge fields. Based on our measurements of the photorefractive properties, we determine the optimal conditions for dielectrophoretic trapping and present the application of Fe-doped lithium niobate as optoelectronic tweezers. For higher reduction degrees, an unexpected decrease in the photovoltaic current density and the saturation space-charge field is reported.