70,625 research outputs found
Klein-Gordon Oscillator in Kaluza-Klein Theory
In this contribution we study the Klein-Gordon oscillator on the curved
background within the Kaluza-Klein theory. The problem of interaction between
particles coupled harmonically with a topological defects in Kaluza-Klein
theory is studied. We consider a series of topological defects, that treat the
Klein-Gordon oscillator coupled to this background and find the energy levels
and corresponding eigenfunctions in these cases. We show that the energy levels
depend on the global parameters characterizing these spacetimes. We also
investigate a quantum particle described by the Klein-Gordon oscillator
interacting with a cosmic dislocation in Som-Raychaudhuri spacetime in the
presence of homogeneous magnetic field in a Kaluza-Klein theory. In this case,
the spectrum of energy is determined, and we observe that these energy levels
are the sum of the term related with Aharonov-Bohm flux and of the parameter
associated to the rotation of the spacetime.Comment: 15 pages, no figur
Price Recall, Bertrand Paradox and Price Dispersion With Elastic Demand
This paper studies the consequence of an imprecise recall of the price by the consumers in the Bertrand price competition model for a homogeneous good. It is shown that firms can exploit this weakness and charge prices above the competitive price. This markup increases for rougher recall of the price. If firms have different production costs, those with higher costs are not driven out of the market. However they choose to have a higher price in equilibrium, therefore price dispersion arises. It is shown that firms behave on average as a monopolist with stricter demand and that price dispersion increases with the price recall errors. If bigger recall errors happen, then both consumers and firms on the aggregate level are worse off, for some parameter choices. Furthermore being given the irrational choice that some consumers make, there are situations where the protection of a monopolist against entrants is a welfare maximizing policy. The introduction of more firms in the market does not have a significant impact on the prices. Even though the presented model is static, it can be interpreted as a stage game of an infinitely repeated game where a Nash Equilibrium is played in every stage. The intuition is that consumers do not actually seek information before every purchase, but have a vague idea of the price they faced in previous purchases.Behavioral Industrial Organization;Bounded Rationality;Price Recall;Price Dispersion;Bertrand Paradox
A rigorous definition of axial lines: ridges on isovist fields
We suggest that 'axial lines' defined by (Hillier and Hanson, 1984) as lines
of uninterrupted movement within urban streetscapes or buildings, appear as
ridges in isovist fields (Benedikt, 1979). These are formed from the maximum
diametric lengths of the individual isovists, sometimes called viewsheds, that
make up these fields (Batty and Rana, 2004). We present an image processing
technique for the identification of lines from ridges, discuss current
strengths and weaknesses of the method, and show how it can be implemented
easily and effectively.Comment: 18 pages, 5 figure
A Tractable State-Space Model for Symmetric Positive-Definite Matrices
Bayesian analysis of state-space models includes computing the posterior
distribution of the system's parameters as well as filtering, smoothing, and
predicting the system's latent states. When the latent states wander around
there are several well-known modeling components and
computational tools that may be profitably combined to achieve these tasks.
However, there are scenarios, like tracking an object in a video or tracking a
covariance matrix of financial assets returns, when the latent states are
restricted to a curve within and these models and tools do not
immediately apply. Within this constrained setting, most work has focused on
filtering and less attention has been paid to the other aspects of Bayesian
state-space inference, which tend to be more challenging. To that end, we
present a state-space model whose latent states take values on the manifold of
symmetric positive-definite matrices and for which one may easily compute the
posterior distribution of the latent states and the system's parameters, in
addition to filtered distributions and one-step ahead predictions. Deploying
the model within the context of finance, we show how one can use realized
covariance matrices as data to predict latent time-varying covariance matrices.
This approach out-performs factor stochastic volatility.Comment: 22 pages: 16 pages main manuscript, 4 pages appendix, 2 pages
reference
Nonlinear Boundary Value Problems via Minimization on Orlicz-Sobolev Spaces
We develop arguments on convexity and minimization of energy functionals on
Orlicz-Sobolev spaces to investigate existence of solution to the equation
\displaystyle -\mbox{div} (\phi(|\nabla u|) \nabla u) = f(x,u) + h \mbox{in}
\Omega under Dirichlet boundary conditions, where
is a bounded smooth domain, is a
suitable continuous function and
satisfies the Carath\'eodory conditions, while is a measure.Comment: 14 page
Renormalization in the Henon family, I: universality but non-rigidity
In this paper geometric properties of infinitely renormalizable real
H\'enon-like maps in are studied. It is shown that the appropriately
defined renormalizations converge exponentially to the one-dimensional
renormalization fixed point. The convergence to one-dimensional systems is at a
super-exponential rate controlled by the average Jacobian and a universal
function . It is also shown that the attracting Cantor set of such a map
has Hausdorff dimension less than 1, but contrary to the one-dimensional
intuition, it is not rigid, does not lie on a smooth curve, and generically has
unbounded geometry.Comment: 42 pages, 5 picture
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