6,328 research outputs found
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 is extended to the case of the general Abel
equation of the form , where
, and . In the case 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 , 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
, 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
and have a physical radius equal to , where is a
time-dependent function describing the dynamics of the throat and 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
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