On the Structure of the Small Quantum Cohomology Rings of Projective Hypersurfaces

We give an explicit procedure which computes for degree $d \leq 3$ the correlation functions of topological sigma model (A-model) on a projective Fano hypersurface $X$ as homogeneous polynomials of degree $d$ in the correlation functions of degree 1 (number of lines). We extend this formalism to the case of Calabi-Yau hypersurfaces and explain how the polynomial property is preserved. Our key tool is the construction of universal recursive formulas which express the structural constants of the quantum cohomology ring of $X$ as weighted homogeneous polynomial functions in the constants of the Fano hypersurface with the same degree and dimension one more. We propose some conjectures about the existence and the form of the recursive formulas for the structural constants of rational curves of arbitrary degree. Our recursive formulas should yield the coefficients of the hypergeometric series used in the mirror calculation. Assuming the validity of the conjectures we find the recursive laws for rational curves of degree 4 and 5.Comment: 32 pages, changed fonts, exact results on quintic rational curves are added. To appear in Commun. Math. Phy

A two-strain ecoepidemic competition model

In this paper we consider a competition system in which two diseases spread by contact. We characterize the system behavior, establishing that only some configurations are possible. In particular we discover that coexistence of the two strains is not possible, under the assumptions of the model. A number of transcritical bifurcations relate the more relevant system's equilibria. Bistability is shown between a situation in which only the disease-unaffected population thrives and another one containing only the second population with endemic disease. An accurate computation of the separating surface of the basins of attraction of these two mutually exclusive equilibria is obtained via novel results in approximation theory

Monotone and Consistent discretization of the Monge-Ampere operator

We introduce a novel discretization of the Monge-Ampere operator, simultaneously consistent and degenerate elliptic, hence accurate and robust in applications. These properties are achieved by exploiting the arithmetic structure of the discrete domain, assumed to be a two dimensional cartesian grid. The construction of our scheme is simple, but its analysis relies on original tools seldom encountered in numerical analysis, such as the geometry of two dimensional lattices, and an arithmetic structure called the Stern-Brocot tree. Numerical experiments illustrate the method's efficiency

La manifestación de la huella a través de los espacios narrativos : una lectura de Nanina de Germán García

La novela Nanina genera interrogantes desde su creación hasta el momento posterior a su lectura. La irregularidad de la estructura nos lleva a reflexionar acerca de lo que significó el impacto de este novedoso recurso entre los lectores de la época (1968), en el marco de un contexto social y político controvertido

Domain Decomposition Method for Maxwell's Equations: Scattering off Periodic Structures

We present a domain decomposition approach for the computation of the electromagnetic field within periodic structures. We use a Schwarz method with transparent boundary conditions at the interfaces of the domains. Transparent boundary conditions are approximated by the perfectly matched layer method (PML). To cope with Wood anomalies appearing in periodic structures an adaptive strategy to determine optimal PML parameters is developed. We focus on the application to typical EUV lithography line masks. Light propagation within the multi-layer stack of the EUV mask is treated analytically. This results in a drastic reduction of the computational costs and allows for the simulation of next generation lithography masks on a standard personal computer.Comment: 24 page