21,728 research outputs found
On the generic finiteness of outcome distributions for bimatrix game forms
We provide an example of an outcome game form with two players for which there is in an open set of
utilities for both players such that, in each of the associated games, the set of Nash equilibria induce a
continuum of outcome distributions. The case for three or more players has been settled by Govindan and
McLennan [3]
On the generic finiteness of equilibrium outcome distributions in bimatrix game forms
We provide an example of an outcome game form with two players for which there is an open set of utilities for both players such that, in each of the associated games, the set of Nash equilibria induces a continuum of outcome distributions.Publicad
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
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
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