On the Equivalence Between Type I Liouville Dynamical Systems in the Plane and the Sphere

Producción CientíficaSeparable Hamiltonian systems either in sphero-conical coordinates on an S2 sphere or in elliptic coordinates on a R2 plane are described in a unified way. A back and forth route connecting these Liouville Type I separable systems is unveiled. It is shown how the gnomonic projection and its inverse map allow us to pass from a Liouville Type I separable system with a spherical configuration space to its Liouville Type I partners where the configuration space is a plane and back. Several selected spherical separable systems and their planar cousins are discussed in a classical context

Nonintegrability of the two-body problem in constant curvature spaces

We consider the reduced two-body problem with the Newton and the oscillator potentials on the sphere ${\bf S}^{2}$ and the hyperbolic plane ${\bf H}^{2}$. For both types of interaction we prove the nonexistence of an additional meromorphic integral for the complexified dynamic systems.Comment: 20 pages, typos correcte

Characteristic Energy of the Coulomb Interactions and the Pileup of States

Tunneling data on $\mathrm{La_{1.28}Sr_{1.72}Mn_2O_7}$ crystals confirm Coulomb interaction effects through the $\sqrt{\mathrm{E}}$ dependence of the density of states. Importantly, the data and analysis at high energy, E, show a pileup of states: most of the states removed from near the Fermi level are found between ~40 and 130 meV, from which we infer the possibility of universal behavior. The agreement of our tunneling data with recent photoemission results further confirms our analysis.Comment: 4 pages, 4 figures, submitted to PR

Two-body quantum mechanical problem on spheres

The quantum mechanical two-body problem with a central interaction on the sphere ${\bf S}^{n}$ is considered. Using recent results in representation theory an ordinary differential equation for some energy levels is found. For several interactive potentials these energy levels are calculated in explicit form.Comment: 41 pages, no figures, typos corrected; appendix D was adde

Developmental malformation of the corpus callosum: a review of typical callosal development and examples of developmental disorders with callosal involvement

This review provides an overview of the involvement of the corpus callosum (CC) in a variety of developmental disorders that are currently defined exclusively by genetics, developmental insult, and/or behavior. I begin with a general review of CC development, connectivity, and function, followed by discussion of the research methods typically utilized to study the callosum. The bulk of the review concentrates on specific developmental disorders, beginning with agenesis of the corpus callosum (AgCC)—the only condition diagnosed exclusively by callosal anatomy. This is followed by a review of several genetic disorders that commonly result in social impairments and/or psychopathology similar to AgCC (neurofibromatosis-1, Turner syndrome, 22q11.2 deletion syndrome, Williams yndrome, and fragile X) and two forms of prenatal injury (premature birth, fetal alcohol syndrome) known to impact callosal development. Finally, I examine callosal involvement in several common developmental disorders defined exclusively by behavioral patterns (developmental language delay, dyslexia, attention-deficit hyperactive disorder, autism spectrum disorders, and Tourette syndrome)

Entry Mode Degree of Control, Firm Performance and Host Country Institutional Development: A Meta-Analysis

Among studies on performance outcomes of entry mode choices disagreement fueled by ambiguous research findings is apparent as regards whether the best per- formers are those firms that enter foreign countries with high or low entry mode degree of control. To solve this dilemma and test new hypotheses, the relationship between entry mode degree of control and firm performance is examined by meta- analyzing 133 studies (740,114 observations) covering entry mode choices from 1980 to 2010. We find that (a) overall high-control entry modes lead to higher per- formance, and (b) adopting high-control entry modes is particularly important for firms entering developing countries