Baryogenesis via leptogenesis in multi-field inflation

In multi-field reheating after modular j-inflation we investigate the conditions under which baryogenesis via non-thermal leptogenesis can be successfully realized. We introduce three heavy right-handed neutrinos to the non-supersymmetric Standard Model of particle physics, assuming hierarchical neutrino masses. Considering a typical mass for the first right-handed neutrino of the order of \(10^{11}\) GeV, suggested from the seesaw mechanism and also from concrete SO(10) grand unification models, we obtain the allowed parameter space for viable baryogenesis. An upper bound for the inflaton mass as well as a lower bound for its branching ratio to the pair of lightest right-handed neutrinos are found and reported.     

Left Kan extensions preserving finite products

We give conditions that ensure the preservation of finite products by left Kan extensions into cocomplete subcanonical sites. The conditions involve a suitable notion of flatness (interpreted in the internal logic of the site) of the functor that is extended and a good behavior of colimits used in the calculation of the left Kan extension. When the recipient category is a Grothendieck topos the good behavior of the colimits is granted and the flatness conditions turn out to be necessary as well as sufficient. We also show that the category of compactly generated Hausdorff spaces and that of small categories are equipped with suitable topologies that account for the well-known phenomenon of preservation of finite products by the geometric and categorical realization, respectively, of simplicial sets.     

Synthesis and solution behavior of carbon nanotubes decorated with amphiphilic block polyelectrolytes

The aqueous solubilization of carbon nanotubes (CNTs) with the aid of a block copolymer possessing one polyelectrolyte block (namely polystyrene-b-sodium (sulfamate/carboxylate polyisoprene)) is reported. The solubilization protocol, based on the co-dissolution of the copolymer and the CNTs, leads to the formation of supramolecular assemblies on the side walls of the tubes. Electron microscopy as well as infrared spectroscopy and thermogravimetric analysis were employed as meaningful probes to identify the adsorption of the polymer onto the surface of CNTs and the composition of the final hybrid material. Viscosity measurements on solutions of the copolymer decorated CNTs indicate that the polyelectrolyte effect, which is observed in the case of net polymers, is preserved in a lesser extent in the case of the copolymer/CNTs dispersions.     

Amphiphilic block copolymers by a combination of anionic polymerization and selective post-polymerization functionalization

Anionic polymerization is the oldest known living/controlled polymerization methodology that leads to well defined macromolecules. It has been also used, with considerable success, for the synthesis of amphiphilic block copolymers (AmBC), a class of functional copolymers having interesting self-assembling properties and high potential for applications in various technological fields. The use of mild and effective post-polymerization functionalization/chemical modification reactions on block copolymers has substantially increased the synthetic capabilities of anionic polymerization methodologies, toward the creation of a variety of AmBC. In this feature article we review work done on these directions in the last ten years. Some perspectives and future work on this particular field of polymer science are also discussed.     

Concentration of mass on isotropic convex bodies

We establish sharp concentration of mass for isotropic convex bodies: there exists an absolute constant $c>0$ such that if K is an isotropic convex body in ${\mathbb{R}}^n$, then

$\mathrm{Prob}\left(\right\{x\in K:6x{6}_2?c\sqrt{n}{L}_{K}t\left\}\right)?\exp (?\sqrt{n}t)$

for every $t?1$, where $L_K$ denotes the isotropic constant. To cite this article: G. Paouris, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Concentration of mass on the Schatten classes

Let 1?p?∞ and be the unit ball of the Schatten trace class of matrices on Cn or on Rn, normalized to have Lebesgue measure equal to one. We prove that

     

Non-compact quadratics-manifolds

The aim of the present paper is the classification of the non — compact quadratics-manifolds.     

Probabilistic Condition Number Estimates for Real Polynomial Systems I: A Broader Family of Distributions

Foundations of Computational Mathematics - We consider the sensitivity of real roots of polynomial systems with respect to perturbations of the coefficients. In particular—for a version of...     

Grafting living polymers onto carbon nanohorns

In the present paper we describe a new way for the covalent functionalization of carbon nanohorns by means of anionic polymerization with the "grafting to" approach. Polyisoprene homopolymers, as well as polyisoprene-b-polystyrene block copolymers have been attached on the surface of carbon nanohorns. The functionalized carbon nanostructures have been fully characterized by means of complementary spectroscopic techniques, electron microscopy, thermogravimetric analysis, and light scattering.