Sulle equazioni differenziali astratte lineari del primo e del secondo ordine negli spazi di Hilbert

Sunto Si studia il problema di Cauchy per equazioni differenziali lineari astratte in spazi di Hilbert, in una impostazione che permette di trattare contemporaneamente sia le equazioni differenziali astratte usuali, sia quelle con argomenti ritardati, sia le equazioni integro-differenziali. Lavoro eseguito nell'ambito delle attività dei gruppi di ricerca del Comitato per la Matematica del C.N.R.     

Linear series onk-gonal curves

Here we prove the following result. Theorem 1.1.Let X be an integral projective curve of arithmetic genus g and k≧ ≧4 an integer. Assume the existence of L ∈ Pic^k (X) with h ⁰ (X, L)=2 and L spanned. Fix a rank 1 torsion free sheaf M on X with h ⁰(X,M)=r+1≧2, h¹ (X, M)≧2 and M spanned by its global sections. Set d≔deg(M) and s≔max {n≧0:h ⁰ (X, M ⊗(L^*)^⊗n)>0}. Then one of the following cases occur:

Quantitative NIR-Raman analysis of methyl-parathion pesticide microdroplets on aluminum substrates

The potential of Raman spectroscopy in the quantitative analysis of dilute organic contaminants on aluminum substrates is evidenced in this work. Methyl-parathion microdroplets, an organophosphorus pesticide, has been used as a probe for this purpose. The samples were analyzed on an aluminum foil, which is very easy to acquire and to adapt. Moreover, aluminum foil does not need a previous treatment. Linear and no-linear curves as a function of the concentration of methyl-parathion versus the Raman intensity of the 1345 and 1110 cm(-1) peaks were established by means of a simple mathematical expression. A comparison with calibration curves fits very well, allowing quantification at concentration levels as low as parts per million.     

Characterisation by high-performance liquid chromatography-multiple mass spectrometry of intermediate compounds formed from mepanipyrim photoinduced degradation

Mepanipyrim, a widely used pyrimidinic fungicide, has been photocatalytically degraded in aqueous solution on TiO2. The purpose of this study is to artificially produce degradation compounds similar to those formed in the environment. Numerous intermediates have been identified and characterised through a MSn spectra analysis, allowing us to give insight into the early steps of the degradation process. Several concomitant pathways occur concerning both reductive and/or oxidative attacks; the main steps involve the cleavage of triple bond, mono and bihydroxylation of the parent molecule, loss of benzene moiety and/or propynylic chain. All these structures are easily degraded themselves, so that the only species recognised to endure in the investigated times is guanidine. A mechanism of transformation accounting for the identified intermediates is proposed.     

On the Singularities of the Magnetic Spectral Shift Function at the Landau Levels

We consider the three-dimensional Schrödinger operators and where , A is a magnetic potential generating a constant magnetic field of strength , and where decays fast enough at infinity. Then, A. Pushnitskis representation of the spectral shift function (SSF) for the pair of operators is well defined for energies We study the behaviour of the associated representative of the equivalence class determined by the SSF, in a neighbourhood of the Landau levels Reducing our analysis to the study of the eigenvalue asymptotics for a family of compact operators of Toeplitz type, we establish a relation between the type of the singularities of the SSF at the Landau levels and the decay rate of V at infinity. Communicated by Bernard HelfferSubmitted 23/09/03, accepted 15/01/04     

Quintessence or Phoenix?

We show that it is impossible to determine the state equation of quintessence models on the basis of pure observational SNIa data. An independent estimate of _M0 is necessary. Also in this most favourable case the situation can be problematic.     

Ammonium detoxifying activity is maintained after 72 hours of cold preservation of rat hepatocytes in University of Wisconsin (UW) solution

The ammonium removal efficiency (ARE) and cell viability was investigated in freshly isolated rat hepatocytes exposed to increasing ammonium loads (0.1-2.0 mM). No difference was observed in both ARE and cell viability at the different ammonium concentrations tested. Storage of hepatocytes at 0 degrees C for 72 hours inhibited ammonium removal and urea synthesis. Rewarming of cells at 37 degrees C for 120 min was followed by an ARE fully comparable to freshly isolated hepatocytes. These data indicated that cold preservation of rat hepatocytes for 3 days in UW followed by a rewarming is associated with normal ammonium detoxification efficiency.