A Chiellini type integrability condition for the generalized first kind Abel differential equation

The Chiellini integrability condition of the first order first kind Abel equation $dy/dx=f(x)y^2+g(x)y^3$ is extended to the case of the general Abel equation of the form $dy/dx=a(x)+b(x)y+f(x)y^{\alpha -1}+g(x)y^{\alpha}$, where $\alpha \in \Re$, and $\alpha > 1$. In the case $\alpha =2$ the generalized Abel equations reduces to a Riccati type equation, for which a Chiellini type integrability condition is obtained.Comment: 4 pages, no figure

Arbitrary scalar field and quintessence cosmological models

The mechanism of the initial inflationary scenario of the universe and of its late-time acceleration can be described by assuming the existence of some gravitationally coupled scalar fields $\phi$, with the inflaton field generating inflation and the quintessence field being responsible for the late accelerated expansion. Various inflationary and late-time accelerated scenarios are distinguished by the choice of an effective self-interaction potential $V(\phi )$, which simulates a temporarily non-vanishing cosmological term. In this work, we present a new formalism for the analysis of scalar fields in flat isotropic and homogeneous cosmological models. The basic evolution equation of the models can be reduced to a first order non-linear differential equation. Approximate solutions of this equation can be constructed in the limiting cases of the scalar field kinetic energy and potential energy dominance, respectively, as well as in the intermediate regime. Moreover, we present several new accelerating and decelerating exact cosmological solutions, based on the exact integration of the basic evolution equation for scalar field cosmologies. More specifically, exact solutions are obtained for exponential, generalized cosine hyperbolic, and power law potentials, respectively. Cosmological models with power law scalar field potentials are also analyzed in detail.Comment: 22 pages, 4 figures; references added; major revision; accepted for publication in EPJ

On thin-shell wormholes evolving in flat FRW spacetimes

We analize the stability of a class of thin-shell wormholes with spherical symmetry evolving in flat FRW spacetimes. The wormholes considered here are supported at the throat by a perfect fluid with equation of state $\mathcal{P}=w\sigma$ and have a physical radius equal to $aR$, where $a$ is a time-dependent function describing the dynamics of the throat and $R$ is the background scale factor. The study of wormhole stability is done by means of the stability analysis of dynamic systems.Comment: 8 pages; to appear in MPL

Bianchi type I cosmological models in Eddington-inspired Born-Infeld gravity

We consider the dynamics of a barotropic cosmological fluid in an anisotropic, Bianchi type I space-time in Eddington-inspired Born-Infeld (EiBI) gravity. By assuming an isotropic pressure distribution, we obtain the general solution of the field equations in an exact parametric form. The behavior of the geometric and thermodynamic parameters of the Bianchi type I Universe is studied, by using both analytical and numerical methods, for some classes of high density matter, described by the stiff causal, radiation, and pressureless fluid equations of state. In all cases the study of the models with different equations of state can be reduced to the integration of a highly nonlinear second order ordinary differential equation for the energy density. The time evolution of the anisotropic Bianchi type I Universe strongly depends on the initial values of the energy density and of the Hubble function. An important observational parameter, the mean anisotropy parameter is also studied in detail, and we show that for the dust filled Universe the cosmological evolution always ends into an isotropic phase, while for high density matter filled universes the isotropization of Bianchi type I universes is essentially determined by the initial conditions of the energy density.Comment: 23 pages, 12 figures; to appear in a Special Issue of Galaxies: "Beyond Standard Gravity and Cosmology". V2: references added, 24 pages; matches published versio

The Effects of Explicitly Teaching a Component of Self-regulated Strategy Development on Bilingual Kindergartners

The purpose of this study was to examine the effects of a modified version of a self-regulated strategy development model on the writing of bilingual kindergarten students. This was an important study because kindergarten bilingual children are falling behind in writing as they try to master two languages. The procedures for this study involved choosing eight students to take part in the study. The eight students were separated into an intervention group and a non-intervention group. The intervention group received small group instruction using a modified version of the self-regulated strategy development model. Data was collected by giving the eight students a picture prompt one time per week and rating their writing based on a rubric. Findings demonstrated that the intervention group made more progress using more story components and number of words in their writing than the non-intervention group. This study showed that the writing of bilingual kindergartners can be improved by explicit instruction, teacher modeling, and clear expectations. Recommendations for teachers of bilingual kindergarten children include explicit teaching of story elements, teacher modeling of language and writing, peer cooperation in writing, and providing clear expectations for students’ writing (such as a rubric). As a result of this study, the researcher hopes that bilingual kindergarten students are able to write more advanced stories and therefore be able to express themselves better. Self-regulation is important because it gives the students a foundation to start their writing. Students are taught strategies to make sure they are following the steps of a good writer. Being a stronger writer will help students in their future academic careers