17,472 research outputs found
The CWKB approach to non-reflecting potential and cosmological implications
We discuss the method of calculating the reflection coefficient using complex
trajectory WKB (CWKB) approximation. This enables us to give an interpretation
of non-reflecting nature of the potential under certain conditions and clarify
some points, reported incorrectly elsewhere [vs:ejp] for the potential
. We show that the repeated reflectios between the
turning points are essential, which most authors overlooked, in obtaining the
non-reflecting c ondition. We find that the considered repeated reflection
paths are in conformity with Bogolubov transformation technique. We discuss the
implications of the results when applied to the particle production scenario,
considering as a time variable and also stress the cosmological
implications of the result with reference to radiation domonated and de Sitter
spacetime.Comment: 9 pages, late
Secrecy versus patents: process innovations and the role of uncertainty
Whilst firms often prefer secrecy to patents and process innovations particu- larly lend themselves to secrecy, we establish a rationale for process innovators who patent. Using a simple two-period model, we show that under myopic op- timisation, the incentive to patent rather than pursue secrecy increases as the probability that the rival firm attaches to it being low-cost falls and as the pro- portion of the cost reduction due to the innovation, secured by the rival firm in the period after the patent has expired, falls. However, the gain to the innovating firm from patenting rather than secrecy strictly increases if the cost reduction due to the innovation is sufficiently small that the high-cost firm could profitably bluff that it is low-cost. Finally, allowing the low-cost firm the option of using an output signal in such cases, may make the patent strategy more or less attractive relative to the case of myopic optimisation
Measuring the Balance of Intra-Regional Trade
We introduce an original method of measuring the extent of the overall balance of migration among countries within a region which allows comparisons of the balance over time as well as between regions and various possible sub-regions
Effect of realistic interatomic interactions and two-body correlation on the heat capacity of a trapped BEC
An approximate many-body theory has been used to calculate the heat capacity
and the condensate fraction of a BEC with effective repulsive interaction. The
effect of interactions has been analyzed and compared with the non-interacting
case. It has been found that the repulsive interaction lowers the critical
temperature from the value found in the non-interacting case. The difference
between the critical temperatures increases with the increase in the total
number of atoms in the trap.Comment: 15 pages, 5 figure
Monodromy group for a strongly semistable principal bundle over a curve, II
Let be a geometrically irreducible smooth projective curve defined over a
field . Assume that has a -rational point; fix a -rational point
. From these data we construct an affine group scheme
defined over the field as well as a principal -bundle
over the curve . The group scheme is
given by a --graded neutral Tannakian category built out of all
strongly semistable vector bundles over . The principal bundle is tautological. Let be a linear algebraic group, defined over ,
that does not admit any nontrivial character which is trivial on the connected
component, containing the identity element, of the reduced center of . Let
be a strongly semistable principal -bundle over . We associate to
a group scheme defined over , which we call the monodromy group
scheme of , and a principal -bundle over , which we call the
monodromy bundle of . The group scheme is canonically a quotient of
, and is the extension of structure group of
. The group scheme is also canonically embedded in the
fiber over of the adjoint bundle.Comment: This final version includes strengthening of the result by referee's
comments. K-Theory (to appear
The Holography Hypothesis in Pre-Big-Bang Cosmology with String Sources
The holographic ratio in Pre-big bang string cosmology is obtained in the
presence string sources. An iterative procedure is adopted to solve the
equations of motion and derive the ratio in four dimensional world. First the
zeroth order ratio is computed in the remote past, i.e. at , then
the holographic ratio is obtained taking into account the evolution of the
backgrounds following the iterative procedure. The corrections to the zeroth
order value of the ratio depends on the form of the initial number distribution
of the strings chosen. Moreover, we estimate the holographic ratio in the
recent past (i.e. when ) and in the remote past (i.e. when
), , in different dimensions in the
Einstein frame and in the string frame. We find that in the first case it has
similar time dependences in both the frames, especially in four dimensions the
ratio is explicitly computed to be the same in the two cases, whereas for
case the time dependence is different.Comment: 33 pages, latex, five figure
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