10,304 research outputs found
Knowledge disclosure as intellectual property rights
We study a model in which an inventor discloses knowledge about its innovation and
then a rival chooses the probability of attaining a competing invention. Disclosures, by
creating prior art, diminish the probability that the rival has of receiving a patent for its
invention (legal externality), but, by revealing knowledge, they decrease the marginal
cost of R&D (knowledge externality). We stress the following result. If the knowledge
externality is large compared to the legal externality, decreasing the patentability
standards leads to fewer disclosures and may hinder R&D. We also determine the
impact of changes in market payoffs on the equilibrium level of disclosures and R&D
Cosmological model with variable equations of state for matter and dark energy
We construct a cosmological model which is physically reasonable,
mathematically tractable, and extends the study of CDM models to the case where
the equations of state (EoS) for matter and dark energy (DE) vary with time. It
is based on the assumptions of (i) flatness, (ii) validity of general
relativity, (iii) the presence of a DE component that varies between two
asymptotic values, (iv) the matter of the universe smoothly evolves from an
initial radiation stage - or a barotropic perfect fluid - to a phase where it
behaves as cosmological dust at late times. The model approximates the CDM ones
for small but significantly differ from them for large . We focus our
attention on how the evolving EoS for matter and DE can modify the CDM
paradigm. We discuss a number of physical scenarios. One of them includes, as a
particular case, the so-called generalized Chaplygin gas models where DE
evolves from non-relativistic dust. Another kind of models shows that the
current accelerated expansion is compatible with a DE that behaves like
pressureless dust at late times. We also find that a universe with variable DE
can go from decelerated to accelerated expansion, and vice versa, several
times
Brane-world models emerging from collisions of plane waves in 5D
We consider brane-world models embedded in a five-dimensional bulk spacetime
with a large extra dimension and a cosmological constant. The cosmology in
possesses "wave-like" character in the sense that the metric coefficients in
the bulk are assumed to have the form of plane waves propagating in the fifth
dimension. We model the brane as the "plane" of collision of waves propagating
in opposite directions along the extra dimension. This plane is a jump
discontinuity which presents the usual symmetry of brane models.
The model reproduces the {\em generalized} Friedmann equation for the evolution
on the brane, regardless of the specific details in . Model solutions with
spacelike extra coordinate show the usual {\em big-bang} behavior, while those
with timelike extra dimension present a {\em big bounce}. This bounce is an
genuine effect of a timelike extra dimension. We argue that, based on our
current knowledge, models having a large timelike extra dimension cannot be
dismissed as mathematical curiosities in non-physical solutions. The size of
the extra dimension is small today, but it is {\em increasing} if the universe
is expanding with acceleration. Also, the expansion rate of the fifth dimension
can be expressed in a simple way through the four-dimensional "deceleration"
and Hubble parameters as . These predictions could have important
observational implications, notably for the time variation of rest mass,
electric charge and the gravitational "constant". They hold for the three models with arbitrary cosmological constant, and are independent
of the signature of the extra dimension.Comment: In V2 the signature of the extra dimension is discussed and new
references are added. In V3 typos are correcte
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