Synthesis of lupeol derivatives and their antileishmanial and antitrypanosomal activities

The natural product lupeol 1 was isolated from aerial parts of Vernonia scorpioides with satisfactory yield, which made it viable to be used as starting material in semisynthetic approach. Ten lupeol derivatives 2–11 were prepared by classical procedures. Including, five new esters derivatives 7–11, which were obtained by structural modifications in the isopropylidene fragment. All semisynthetic compounds and lupeol 1–11 were confirmed by ¹H NMR, ¹³C NMR and HRMS. Their antiprotozoal activity was evaluated in vitro against L. amazonensis and T. cruzi. Derivative 6 showed the best antitrypanosomal activity (IC₅₀ = 12.48 μg/mL) and the lowest cytotoxic derivative (CC₅₀ = 161.50 μg/mL). The mechanism of action of the most active derivatives (4, 6 and 11) is not dependent from the enzyme trypanothione reductase.     

Fluorine containing phosphazene polymers

In this paper we highlighted the synthesis, characterization, and practical exploitation of different types of polyphosphazenes substituted with fluorinated groups. There are several ways in which fluorine atoms can be inserted into polyphosphazenes, all of which leading to different polymers showing a wide range of characteristics. In general it is true that the insertion of fluorine atoms into phosphazene macromolecules leads to an enhancement of the thermal stability, flame resistance, low-temperature elastomericity, and chemical inertness of the phosphazenes obtained. The contribution of Italian research groups to the preparation and exploitation of organic commercial macromolecules grafted onto fluorinated polyphosphazenes is also reviewed.     

A landscape of time asymmetry

This is a conceptual overview on a polemical subject: the problem of time asymmetry. It is proved that time asymmetry can be considered as a global generalized symmetry breaking, produced by a choice of a physically admissible state space, in a global Gel'fand triplet. The well-known physics of irreversible process can be studied using this mathematical structure and all the arrows of time can be explained and coordinated. But the deeper problems of time definition and time arrow in quantum gravity remain outside of this landscape.     

Involutions for upper triangular matrix algebras

In this paper we describe completely the involutions of the first kind of the algebra UT_n(F) of n×n upper triangular matrices. Every such involution can be extended uniquely to an involution on the full matrix algebra. We describe the equivalence classes of involutions on the upper triangular matrices. There are two distinct classes for UT_n(F) when n is even and a single class in the odd case.Furthermore we consider the algebra UT₂(F) of the 2×2 upper triangular matrices over an infinite field F of characteristic different from 2. For every involution *, we describe the *-polynomial identities for this algebra. We exhibit bases of the corresponding ideals of identities with involution, and compute the Hilbert (or Poincaré) series and the codimension sequences of the respective relatively free algebras.Then we consider the *-polynomial identities for the algebra UT₃(F) over a field of characteristic zero. We describe a finite generating set of the ideal of *-identities for this algebra. These generators are quite a few, and their degrees are relatively large. It seems to us that the problem of describing the *-identities for the algebra UT_n(F) of the n×n upper triangular matrices may be much more complicated than in the case of ordinary polynomial identities.     

Quotient probabilistic normed spaces and completeness results

We introduce the concept of quotient in PN spaces and give some examples. We prove some theorems with regard to the completeness of a quotient.     

Higher order bad loci

Zero-schemes on smooth complex projective varieties, forcing all elements of ample and free linear systems to be reducible, are studied. Relationships among the minimal length of such zero-schemes, the positivity of the line bundle associated with the linear system, and the dimension of the variety are established. Bad linear spaces are also investigated.