A Variational Approach to Discontinuous Problems with Critical Sobolev Exponents

We employ variational techniques to study the existence and multiplicity of positive solutions of semilinear equations of the form − Δu = λh(x)H(u − a)u^q + u^2* − 1 in R^N, where λ, a > 0 are parameters, h(x) is both nonnegative and integrable on R^N, H is the Heaviside function, 2* is the critical Sobolev exponent, and 0 ≤ q < 2* − 1. We obtain existence, multiplicity and regularity of solutions by distinguishing the cases 0 ≤ q ≤ 1 and 1 < q < 2* − 1.     

Gamma rays from the Galactic bulge and large extra dimensions

An intriguing feature of extra dimensions is the possible production of Kaluza-Klein gravitons by nucleon-nucleon bremsstrahlung, in the course of core collapse of massive stars, with gravitons then being trapped around the newly born neutron stars and decaying into two gamma rays, making neutron stars gamma-ray sources. We strengthen the limits on the radius of compactification of extra dimensions for a small number n of them, or alternatively the fundamental scale of quantum gravity, considering the gamma-ray emission of the whole population of neutron stars sitting in the Galactic bulge, instead of the closest member of this category. For n=1 the constraint on the compactification radius is R<400 microm.     

Identification of weakly interacting massive particles through a combined measurement of axial and scalar couplings

We study the prospects for detecting weakly interacting massive particles (WIMPs) in a number of phenomenological scenarios, with a detector composed of a target simultaneously sensitive to both spin-dependent and spin-independent couplings, as is the case of COUPP (Chicagoland Observatory for Underground Particle Physics). First, we show that sensitivity to both couplings optimizes chances of initial WIMP detection. Second, we demonstrate that, in case of detection, a comparison of the signal on two complementary targets, such as in COUPP CF3I and C4F10 bubble chambers, allows a significantly more precise determination of the dark matter axial and scalar couplings. This strategy would provide crucial information on the nature of the WIMPs and possibly allow discrimination between neutralino and Kaluza-Klein dark matter.     

Recent progress with functional biosupramolecular systems

The objective of this account is to summarize our recent progress with functional biosupramolecular systems concisely. The functions covered are artificial photosynthesis, anion transport, and sensing in lipid bilayer membranes. With artificial photosynthesis, the current emphasis is on the construction of ordered and oriented architectures on solid surfaces. Recent examples include the zipper assembly of photosystems with supramolecular n/p-heterojunctions and oriented antiparallel redox gradients. Current transport systems in lipid bilayers reveal new interactions at work. Examples include anion-macrodipole or anion-π interactions. Current attention with membrane-based sensing systems shifts from biosensor approaches with enzymatic signal generation to aptamers (i.e., the DNA version of immunosensing) and differential sensing with dynamic polyion-counterion transporters. The functional diversity accessible with biosupramolecular systems is highlighted, as is the critical importance of cross-fertilization at intertopical convergence zones.     

Positivity of Chern classes for reflexive sheaves on <Emphasis Type="Bold">P</Emphasis><Superscript><Emphasis Type="Italic">N</Emphasis></Superscript>

In this paper we study the Brill–Noether theory of invertible subsheaves of a general, stable rank-two vector bundle on a curve C with general moduli. We relate this theory to the geometry of unisecant curves on smooth, non-special scrolls with hyperplane sections isomorphic to C. Most of our results are based on degeneration techniques. The first three authors are members of G.N.S.A.G.A. at I.N.d.A.M. “Francesco Severi”.