11,109 research outputs found
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
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
On bouncing solutions in non-local gravity
A non-local modified gravity model with an analytic function of the
d'Alembert operator is considered. This model has been recently proposed as a
possible way of resolving the singularities problem in cosmology. We present an
exact bouncing solution, which is simpler compared to the already known one in
this model in the sense it does not require an additional matter to satisfy all
the gravitational equations.Comment: 5 pages; v2: matching the jounral versio
On Modified Gravity
We consider some aspects of nonlocal modified gravity, where nonlocality is
of the type . In particular, using ansatz of the form
we find a few solutions for the spatially flat
FLRW metric. There are singular and nonsingular bounce solutions. For late
cosmic time, scalar curvature R(t) is in low regime and scale factor a(t) is
decelerated. R (t) = 0 satisfies all equations when k = -1.Comment: added references; made some clarifications; 8 page
Rationality and Brauer group of a moduli space of framed bundles
We prove that the moduli spaces of framed bundles over a smooth projective
curve are rational. We compute the Brauer group of these moduli spaces to be
zero under some assumption on the stability parameter.Comment: 7 pages, to appear in Tbilisi Math. J; v2. reference adde
Nonlocal Gravitational Models and Exact Solutions
A nonlocal gravity model with a function , where is
the d'Alembert operator, is considered. The algorithm, allowing to reconstruct
, corresponding to the given Hubble parameter and the state
parameter of the matter, is proposed. Using this algorithm, we find the
functions , corresponding to de Sitter solutions.Comment: 5 pages, v2: refs. added, to appear in the proceedings of the
International Workshop "Supersymmetries and Quantum Symmetries" (SQS'2011),
Dubna, Russia, July 18-23, 2011, http://theor.jinr.ru/sqs/2011
Quantum Gravity Equation In Schroedinger Form In Minisuperspace Description
We start from classical Hamiltonian constraint of general relativity to
obtain the Einstein-Hamiltonian-Jacobi equation. We obtain a time parameter
prescription demanding that geometry itself determines the time, not the matter
field, such that the time so defined being equivalent to the time that enters
into the Schroedinger equation. Without any reference to the Wheeler-DeWitt
equation and without invoking the expansion of exponent in WKB wavefunction in
powers of Planck mass, we obtain an equation for quantum gravity in
Schroedinger form containing time. We restrict ourselves to a minisuperspace
description. Unlike matter field equation our equation is equivalent to the
Wheeler-DeWitt equation in the sense that our solutions reproduce also the
wavefunction of the Wheeler-DeWitt equation provided one evaluates the
normalization constant according to the wormhole dominance proposal recently
proposed by us.Comment: 11 Pages, ReVTeX, no figur
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