Integral Representations for the Class of Generalized Metaplectic Operators

This article gives explicit integral formulas for the so-called generalized metaplectic operators, i.e. Fourier integral operators (FIOs) of Schr\"odinger type, having a symplectic matrix as canonical transformation. These integrals are over specific linear subspaces of R^d, related to the d x d upper left-hand side submatrix of the underlying 2d x 2d symplectic matrix. The arguments use the integral representations for the classical metaplectic operators obtained by Morsche and Oonincx in a previous paper, algebraic properties of symplectic matrices and time-frequency tools. As an application, we give a specific integral representation for solutions to the Cauchy problem of Schr\"odinger equations with bounded perturbations for every instant time t in R, even in the so-called caustic points.Comment: 19 pages in Journal of Fourier Analysis and Applications, 201

An equation of state for purely kinetic k-essence inspired by cosmic topological defects

We investigate the physical properties of a purely kinetic k-essence model with an equation of state motivated in superconducting membranes. We compute the equation of state parameter $w$ and discuss its physical evolution via a nonlinear equation of state. Using the adiabatic speed of sound and energy density, we restrict the range of parameters of the model in order to have an acceptable physical behavior. Furthermore, we analyze the evolution of the luminosity distance $d_{L}$ with redshift $z$ by comparing (normalizing) it with the $\Lambda$CDM model. Since the equation of state parameter is $z$-dependent the evolution of the luminosity distance is also analyzed using the Alcock-Paczy\'{n}ski test.Comment: 19 pages, 13 figures, typos corrected and references adde

Cosmological constraints for a two brane-world system with single equation of state

We present the study of two 3-brane system embedded in a 5-dimensional space-time in which the fifth dimension is compactified on a $S^{1}/Z_{2}$ orbifold. Assuming isotropic, homogeneous, and static branes, it can be shown that the dynamics of one brane is dominated by the other one when the metric coefficients have a particular form. We study the resulting cosmologies when one brane is dominated by a given single-fluid component.Comment: This work was presented at the VIII Taller of the DGFM, Tuxtla Gutierrez, Chiapas, Mexico noviembre 22-26, 201

Two-brane system in a vacuum bulk with a single equation of state

We study the cosmology of a two-brane model in a five-dimensional spacetime, where the extra spatial coordinate is compactifed on an orbifold. Additionally, we consider the existence on each brane of matter fields that evolve in time. Solving the Einstein equations in a vacuum bulk, we can show how the matter fields in both branes are connected and they do not evolve independentlyComment: This work was presented at the IX Taller de la Division de Gravitacion y Fisica Matematica, Colima 201

Algebraic treatment of the confluent Natanzon potentials

Using the so(2,1) Lie algebra and the Baker, Campbell and Hausdorff formulas, the Green's function for the class of the confluent Natanzon potentials is constructed straightforwardly. The bound-state energy spectrum is then determined. Eventually, the three-dimensional harmonic potential, the three-dimensional Coulomb potential and the Morse potential may all be considered as particular cases.Comment: 9 page

One Size Does Not Fit All: Meeting the Health Care Needs of Diverse Populations

Proposes a framework for meeting patients' cultural and linguistic needs: policies and procedures that support cultural competence, data collection, population-tailored services, and internal and external collaborations. Includes a self-assessment tool

Analysis of biopharma raw materials by electrophoresis microchips with contactless conductivity detection

Detailed information concerning the composition of the raw materials employed in the production of biologics is important for the efficient control and optimization of bioprocesses. We demonstrate the application of electrophoresis microchips with capacitively-coupled contactless conductivity detection (C4D) to the analysis of wa-ter-soluble vitamins and metal cations in raw material solutions that are subse-quently fed into bioreactors for the production of biologics