First steps towards total reality of meromorphic functions

It was earlier conjectured by the second and the third authors that any rational curve $g:{\mathbb C}P^1\to {\mathbb C}P^n$ such that the inverse images of all its flattening points lie on the real line ${\mathbb R}P^1\subset {\mathbb C}P^1$ is real algebraic up to a linear fractional transformation of the image ${\mathbb C}P^n$. (By a flattening point $p$ on $g$ we mean a point at which the Frenet $n$-frame $(g',g'',...,g^{(n)})$ is degenerate.) Below we extend this conjecture to the case of meromorphic functions on real algebraic curves of higher genera and settle it for meromorphic functions of degrees $2,3$ and several other cases.Comment: 10 pages, 1 figur

On total reality of meromorphic functions

We show that if a meromorphic function of degree at most four on a real algebraic curve of an arbitrary genus has only real critical points then it is conjugate to a real meromorphic function after a suitable projective automorphism of the image.Comment: 13 page

Caustic formation in expanding condensates of cold atoms

We study the evolution of density in an expanding Bose-Einstein condensate that initially has a spatially varying phase, concentrating on behaviour when these phase variations are large. In this regime large density fluctuations develop during expansion. Maxima have a characteristic density that diverges with the amplitude of phase variations and their formation is analogous to that of caustics in geometrical optics. We analyse in detail caustic formation in a quasi-one dimensional condensate, which before expansion is subject to a periodic or random optical potential, and we discuss the equivalent problem for a quasi-two dimensional system. We also examine the influence of many-body correlations in the initial state on caustic formation for a Bose gas expanding from a strictly one-dimensional trap. In addition, we study a similar arrangement for non-interacting fermions, showing that Fermi surface discontinuities in the momentum distribution give rise in that case to sharp peaks in the spatial derivative of the density. We discuss recent experiments and argue that fringes reported in time of flight images by Chen and co-workers [Phys. Rev. A 77, 033632 (2008)] are an example of caustic formation.Comment: 10 pages, 5 figures. Published versio

Impact of Rotation on Quark-Hadron Hybrid Stars

Many recent observations give restrictions to the equation of state (EOS) for high-density matter. Theoretical studies are needed to try to elucidate these EOSs at high density and/or temperature. With the many known rapidly rotating neutron stars, e.g., pulsars, several theoretical studies have tried to take into account the effects of rotation. In our study of these systems, we find that one of our EOSs is consistent with recent observation, whereas the other is inconsistent.Comment: Quarks and Compact Stars 201

The Impact Of Cold Dark Matter Variants On The Halos Of The First Stars And Galaxies: Angular Momentum And Vortex Creation In BEC Dark Matter

If cold dark matter elementary particles form a Bose-Einstein condensate, their superfluidity may distinguish them from other forms of cold dark matter, including the creation of quantum vortices. We have shown that such vortices are favored in strongly-coupled condensates. Vortex creation causes central densities to drop, thus affecting the dynamics of the gaseous baryonic component and subsequently star formation.Astronom

Introduction to the physics of weightlessness

Equations of motion for describing weightlessness phenomena during space fligh

An Intuitive Graphical Query Interface for Protégé Knowledge Bases

Emily is a graphical query engine for Protégé knowledge bases that was developed by the Structural Informatics Group (SIG) at the University of Washington. Currently this application is adapted for a specific knowledge model, the Foundational Model of Anatomy (FMA) [1], but it could readily be generalized for use with other Protégé knowledge bases. In developing the Emily query interface, our intent was to provide a tool that was simple and intuitive to use, like the Queries tab provided with Protégé, but with improved information retrieval capabilities. Although some more advanced query mechanisms exist, currently they are too complicated for non-expert end users. The Algernon tab [2], for example, provides extensive Protégé query capabilities but requires users to learn a query scripting language. We sought to develop a query interface that was intuitive enough for end users to operate, with only minor instruction, yet was powerful enough to gather interesting information from a knowledge base that was not easily attained by browsing alone

Hurwitz numbers and intersections on moduli spaces of curves

This article is an extended version of preprint math.AG/9902104. We find an explicit formula for the number of topologically different ramified coverings of a sphere by a genus g surface with only one complicated branching point in terms of Hodge integrals over the moduli space of genus g curves with marked points.Comment: 30 pages (AMSTeX). Minor typos are correcte