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

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

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

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

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

Analysis of water-soluble vitamins in biopharma raw materials by electrophoresis micro-chips 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. The analytical methods used in these applications must be simple and fast as well as be easily transferable from one site to another. In that context, microchip‐based electrophoresis represents a promising tool for application in the analysis of raw materials in biologics. Using electrophoresis micro‐chips, analysis times can be reduced to seconds and high separation efficiencies can be achieved using extremely low volume samples, minimal reagent consumption and waste generation, low cost/disposability, portability and ease of mass‐production [1]. Additionally the use of Capacitively Coupled Contactless Conductivity Detection (C4D) offers a rather simple and yet sensitive method for detection of ionic species. Recently, C4D has gained much popularity as on‐chip detection in electrophoresis micro‐chips [2]. The main reason for this is that there is no physical contact of the detection electrodes with the electrolyte solution. Therefore, the integration of this detection mode within the analytical system is rather simple. Furthermore, the background noise is significantly reduced leading to lower detection limits than the conventional contact conductivity detection. Vitamins are present at very low concentrations in biopharma raw materials and are usually determined using HPLC and CE methods [3]. Electrophoresis micro‐chips are a very good alternative to these techniques due to the shorter analysis time and yet very good resolution, among others. In this paper, we present the application of electrophoresis micro‐chips with C4D detection to the analysis of water‐soluble vitamins in raw materials used for the production of biologics in bioreactors. For that purpose, hybrid PDMS/glass chips were fabricated by using standard photolithographic techniques (Figure 1). The chip structure contains an extremely long channel of 101 mm (50 x 50 μm width x depth). Figure 2 shows the setup used for vitamins detection

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