Significato proiettivo di alcuni tipi di equazioni differenziali del secondo ordine

Sunto. Ogni elemento di 2^o ordine di curva di una superficie (ad asintotiche distinte e non rettilinee) determina duequadriche asintotiche osculatrici. Gli elementi di 2^o ordine tali che queste quadriche abbiano, in ogni punto della superficie, un contatto assegnato con una retta, conica o cubica sghemba associata al punto appartengono alle curve integrali di equazioni differenziali del tipov″P _i (v′)=P _i+3(v′) (i=1, 2) oveP _k (v′) è un polinomio di gradok inv′=dv/du a coefficienti funzioni diu ev. Determinazione della configurazione geometrica a partire dall'equazione.     

On the Cauchy problem for non-effectively hyperbolic operators,the Gevrey 5 well-posedness

In this paper, we prove that for non-effectively hyperbolic operators with smooth double characteristics exhibiting a Jordan block of size 4 on the double manifold, the Cauchy problem is well-posed in the Gevrey 5 class, beyond the generic Gevrey class 2 (see, e.g., [5]). Moreover, we show that this value is optimal, due to certain geometric constraints on the Hamiltonian flow of the principal symbol. These results, together with results already proved, give a complete picture of the well-posedness of the Cauchy problem around hyperbolic double characteristics.     

The proteolytic activity of insulin‐degrading enzyme: a mass spectrometry study

The prominent role that insulin‐degrading enzyme (IDE) has on amyloidogenic peptides degradation has recently boosted a lot of attention toward this enzyme. Although many substrates are known to be degraded by IDE, little is known about the changes in the proteolytic activity of the enzyme upon modification of environmental factors. In a previous work we have already shown the great potentiality of atmospheric pressure/laser desorption ionization‐mass spectrometry (AP/MALDI‐MS) for studying the interaction between IDE and insulin. Here, the activity of IDE was investigated regarding cleavage sites' preferentiality upon modification of environmental factors by AP/MALDI‐MS. The roles that IDE/insulin concentration ratio, reaction time, adenosine 5′‐triphosphate (ATP) and metal ions (Zn and Cu) have on the insulin cleavage pattern produced by IDE are investigated and a plausible interpretation involving the proteolytic action of the different IDE oligomeric forms is proposed. Copyright © 2009 John Wiley & Sons, Ltd.