Memories Made & Remembered

2010 essay contest winner Jordan Jacobo\u27s Memories Made & Remembere

Welcome to Nottingham!

Postcard from Jordan Jacobo, during the Linfield College Semester Abroad Program in Nottingham, Englan

Bifurcation of Fredholm maps II; The dimension of the set of bifurcation points

We obtain an estimate for the covering dimension of the set of bifurcation points for solutions of nonlinear elliptic boundary value problems from the principal symbol of the linearization of the problem along the trivial branch of solutions.Comment: 15 pages, corrected typos, minor changes; La Matematica e le sue Applicazioni N5(2010). To appear on TMN

Bifurcation of Fredholm Maps I; The Index Bundle and Bifurcation

We associate to a parametrized family $f$ of nonlinear Fredholm maps possessing a trivial branch of zeroes an {\it index of bifurcation} $\beta(f)$ which provides an algebraic measure for the number of bifurcation points from the trivial branch. The index $\beta(f)$ is derived from the index bundle of the linearization of the family along the trivial branch by means of the generalized $J$-homomorphism. Using the Agranovich reduction and a cohomological form of the Atiyah-Singer family index theorem, due to Fedosov, we compute the bifurcation index of a multiparameter family of nonlinear elliptic boundary value problems from the principal symbol of the linearization along the trivial branch. In this way we obtain criteria for bifurcation of solutions of nonlinear elliptic equations which cannot be achieved using the classical Lyapunov-Schmidt method.Comment: 42 pages. Changes: added Lemma 2.31 and a reference + minor corrections. To appear on TMN

Parity and generalized multiplicity

Assuming that X and Y are Banach spaces and that T is a path of linear Fredholm operators with invertible endpoints, in [F-Pl] we defined a homotopy invariant "the parity of T . The parity plays a fundamental role in bifurcation problems, and in degree theory for nonlinear Fredholm-type mappings. Here we prove that, generically, the parity is a mod 2 count of the number of transversal intersections of T with the set of singular operators, that at an isolated singular point of x of T the local parity remains invariant under Lyapunov-Schmidt reduction, and that it coincides with the mod 2 reduction of any one of the various concepts of generalized multiplicity which have been defined in the context of linearized bifurcation data

Building Reliable Models of M Dwarf Chromospheres: The Spectral Diagnostics

As part of an ongoing project to study how reliable are the chromospheric models constructed semiempirically to fit the chromospheric spectrum of cold stars, in this paper we study how changes in the assumed chromospheric structure of dM and dMe stars affect the emitted spectrum. In this way, we study if a given set of features can wholly determine the atmospheric structure, how large are the indeterminations in the atmospheric parameters deduced, and to what extent the atmospheric model computed can be considered unique. We find that the profiles of the Ca II K line or the Na D lines can be used to determine the structure of the Tmin region and that the Hα profile can provide good information on the structure of the chromosphere. The Lyα flux, in turn, can be used to constrain the position of the transition region.Fil: Mauas, Pablo Jacobo David. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; Argentin

The Bank of Canada's Management of Foreign Currency Reserves

This article describes the Bank's management of the liquid foreign currency portion of the government's official reserves. It broadly outlines the operations of the Exchange Fund Account (EFA), the main account in which Canada's reserves are held. It then briefly reviews the evolution of the objectives and management of the EFA over the past 25 years, particularly in light of the changing level of reserves and developments in financial markets. The EFA is funded by Canada's foreign currency borrowings in capital markets. The article focuses on the comprehensive portfolio framework used to manage the Account, which matches assets and liabilities. Under this framework, funds are invested in assets that match, as closely as possible, the characteristics of foreign currency liabilities issued, helping to immunize the portfolio against currency and interest rate risks.