An NMR study of the interaction between Melanin Free Acid and Mn ions as a model to mimic the enhanced proton relaxation rates in melanotic melanoma

The interaction of a soluble Melanin Free Acid (MFA) from Sepia melanin with Mn²⁺ ions is investigated by measuring the proton water relaxation rates. The similarity between MFA and the parent melanin is assessed by means of their high resolution ¹³C cross polarization magic angle spinning NMR spectra. The observed marked increase in longitudinal proton relaxation rates and the characteristic 1/T₁ NMRD profile are associated to the formation of a macromolecular metal complex. The presence of similar paramagnetic species is expected to cause the high contrast shown by melanotic tissues in MRI.     

Time-fractional telegraph equations and telegraph processes with brownian time

We study the fundamental solutions to time-fractional telegraph equations of order 2. We are able to obtain the Fourier transform of the solutions for any and to give a representation of their inverse, in terms of stable densities. For the special case =1/2, we can show that the fundamental solution is the distribution of a telegraph process with Brownian time. In a special case, this becomes the density of the iterated Brownian motion, which is therefore the fundamental solution to a fractional diffusion equation of order 1/2 with respect to time.This research has been partially supported by the NATO grant No. SA (PST.CLG.976361) 5437.     

Generalizzazione dei teoremi di minimo volume di Wirtinger a tutte le varietà kähleriane o quasi-kähleriane

Sunto Si dimostra che le varietà k?hleriane o quasi-k?hleriane subordinate ad una varietà k?hleriana o quasi-k?hleriana, sono varietà di volume minimo. Ad Antonio Signorini nel suo 70^mo compleanno.     

On the definition of extensive property energy by the first postulate of thermodynamics

In the domain in which the definition of property energy is available, a rigorous and general proof of additivity is provided. Then, both the definition of energy and the proof of additivity are extended to broader domains.     

Positivity preserving property for a class of biharmonic elliptic problems

The lack of a general maximum principle for biharmonic equations suggests to study under which boundary conditions the positivity preserving property holds. We show that this property holds in general domains for suitable linear combinations of Dirichlet and Navier boundary conditions. The spectrum of this operator exhibits some unexpected features: radial data may generate nonradial solutions. These boundary conditions are also of some interest in semilinear equations, since they enable us to give explicit radial singular solutions to fourth order Gelfand-type problems.     

Complex zeroes of the d = 3 Ising model: Finite-size scaling and critical amplitudes

By means of an MC simulation of lattices of size 4³ to 8³, we study the distribution of the complex zeroes closest to the real β axis of the d = 3 Ising model. We observe they do scale and we measure in this way ν and A₊/A_-. We obtain the prediction A₊/A_- = 0.45±0.07.     

Perturbative Analysis of Disordered Ising Models Close to Criticality

We consider a two-dimensional Ising model with random i.i.d. nearest-neighbor ferromagnetic couplings and no external magnetic field. We show that, if the probability of supercritical couplings is small enough, the system admits a convergent cluster expansion with probability one. The associated polymers are defined on a sequence of increasing scales; in particular the convergence of the above expansion is compatible with the infinite differentiability of the free energy but does not imply its analyticity. The basic tools in the proof are a general theory of graded cluster expansions and a stochastic domination of the disorder. MSC2000. Primary 82B44, 60K35.