On Cr−C^r-closing for flows on 2-manifolds

For some full measure subset B of the set of iet's (i.e. interval exchange transformations) the following is satisfied: Let X be a $C^r$, $1\le r\le \infty$, vector field, with finitely many singularities, on a compact orientable surface M. Given a nontrivial recurrent point $p\in M$ of X, the holonomy map around p is semi-conjugate to an iet $E :[0,1) \to [0,1).$ If $E\in B$ then there exists a $C^r$ vector field Y, arbitrarily close to X, in the $C^r-$topology, such that Y has a closed trajectory passing through p.Comment: 7 pages, 1 figur

Custom in Our Courts: Reconciling Theory with Reality in the Debate about Erie Railroad and Customary International Law

One of the most heated debates of the last two decades in U.S. legal academia focuses on customary international law’s domestic status after Erie Railroad v. Tompkins. At one end, champions of the “modern position” support customary international law’s (“CIL”) wholesale incorporation into post-Erie federal common law. At the other end, “revisionists” argue that federal courts cannot apply CIL as federal law absent federal legislative authorization. Scholars on both sides of the Erie debate also make claims about the sources judges reference when discerning CIL. They then use these claims to support their arguments regarding CIL’s domestic status. Interestingly, neither side of the debate has conducted an empirical analysis of what U.S. federal courts have actually done. This Article undertakes such an analysis and suggests that U.S. federal courts have, for the most part, behaved in a manner unanticipated by revisionists and modernists alike—the courts have followed themselves. After tracking the sources considered as evidence of CIL and cited in both pre-Erie and post-Erie case law, it turns out that, at all times before and after Erie in 1938, U.S. federal judges have relied primarily on domestic case law when making CIL determinations. Put starkly, the great Erie debate about CIL determinations in U.S. federal courts—and the authority the judiciary ought to attach to certain international sources—may have been occurring somewhat orthogonally to the fact that U.S. courts do not seem to pay much attention to these sources in practice

Asymptotic stability at infinity for differentiable vector fields of the plane

Let X:R2\Dr->R2 be a differentiable (but not necessarily C1) vector field, where r>0 and Dr={z\in R2:|z|\le r}. If for some e>0 and for all p\in R2\Dr, no eigenvalue of D_p X belongs to (-e,0]\cup {z\in\C:\mathcal{R}(z)\ge 0}, then (a)For all p\in R2\Dr, there is a unique positive semi--trajectory of X starting at p; (b)\mathcal{I}(X), the index of X at infinity, is a well defined number of the extended real line [-\infty,\infty); (c) There exists a constant vector v\in R2 such that if \mathcal{I}(X) is less than zero (resp. greater or equal to zero), then the point at infinity \infty of the Riemann sphere R2\cup\set{\infty} is a repellor (resp. an attractor) of the vector field X+v.Comment: 16 pages, 7 figure

Inheritance of disc flower color in Helianthus petiolaris

Disc flowers of Helianthus petiolaris (Asteraceae) are usually purple reddue to anthocyanin pigments in corolla lobes, style and stigma. However, yellow-flowered plants are occasionally found. The inheritance of this trait wasstudied through crosses between different phenotypes and the results indicatedthat flower color is controlled by two genes with complementary action,both loci being dominant and independently inherited. This agrees with resultsobtained in cultivated sunflower, H. annuus, where one to three dominantgenes have been proposed for anthocyanin expression in different organs.Fil: Gutierrez, Agustina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Centro de Recursos Naturales Renovables de la Zona Semiárida. Universidad Nacional del Sur. Centro de Recursos Naturales Renovables de la Zona Semiárida; ArgentinaFil: Delucchi, C.. Instituto Nacional de Tecnología Agropecuaria. Centro Regional Buenos Aires Norte. Estación Experimental Agropecuaria Pergamino; ArgentinaFil: Poverene, María Mónica. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Centro de Recursos Naturales Renovables de la Zona Semiárida. Universidad Nacional del Sur. Centro de Recursos Naturales Renovables de la Zona Semiárida; Argentin

Authoring courses with rich adaptive sequencing for IMS learning design

This paper describes the process of translating an adaptive sequencing strategy designed using Sequencing Graphs to the semantics of IMS Learning Design. The relevance of this contribution is twofold. First, it combines the expressive power and flexibility of Sequencing Graphs, and the interoperability capabilities of IMS. Second, it shows some important limitations of IMS specifications (focusing on Learning Design) for the sequencing of learning activities