47,323 research outputs found
Base manifolds for fibrations of projective irreducible symplectic manifolds
Given a projective irreducible symplectic manifold of dimension , a
projective manifold and a surjective holomorphic map with
connected fibers of positive dimension, we prove that is biholomorphic to
the projective space of dimension . The proof is obtained by exploiting two
geometric structures at general points of : the affine structure arising
from the action variables of the Lagrangian fibration and the structure
defined by the variety of minimal rational tangents on the Fano manifold
Quantum fluctuations of Cosmological Perturbations in Generalized Gravity
Recently, we presented a unified way of analysing classical cosmological
perturbation in generalized gravity theories. In this paper, we derive the
perturbation spectrums generated from quantum fluctuations again in unified
forms. We consider a situation where an accelerated expansion phase of the
early universe is realized in a particular generic phase of the generalized
gravity. We take the perturbative semiclassical approximation which treats the
perturbed parts of the metric and matter fields as quantum mechanical
operators. Our generic results include the conventional power-law and
exponential inflations in Einstein's gravity as special cases.Comment: 5 pages, revtex, no figure
Unified Analysis of Cosmological Perturbations in Generalized Gravity
In a class of generalized Einstein's gravity theories we derive the equations
and general asymptotic solutions describing the evolution of the perturbed
universe in unified forms. Our gravity theory considers general couplings
between the scalar field and the scalar curvature in the Lagrangian, thus
includes broad classes of generalized gravity theories resulting from recent
attempts for the unification. We analyze both the scalar-type mode and the
gravitational wave in analogous ways. For both modes the large scale evolutions
are characterized by the same conserved quantities which are valid in the
Einstein's gravity. This unified and simple treatment is possible due to our
proper choice of the gauges, or equivalently gauge invariant combinations.Comment: 4 pages, revtex, no figure
A conserved variable in the perturbed hydrodynamic world model
We introduce a scalar-type perturbation variable which is conserved in
the large-scale limit considering general sign of three-space curvature (),
the cosmological constant (), and time varying equation of state. In a
pressureless medium is {\it exactly conserved} in all scales.Comment: 4 pages, no figure, To appear in Phys. Rev.
Relativistic Hydrodynamic Cosmological Perturbations
Relativistic cosmological perturbation analyses can be made based on several
different fundamental gauge conditions. In the pressureless limit the variables
in certain gauge conditions show the correct Newtonian behaviors. Considering
the general curvature () and the cosmological constant () in the
background medium, the perturbed density in the comoving gauge, and the
perturbed velocity and the perturbed potential in the zero-shear gauge show the
same behavior as the Newtonian ones in general scales. In the first part, we
elaborate these Newtonian correspondences. In the second part, using the
identified gauge-invariant variables with correct Newtonian correspondences, we
present the relativistic results with general pressures in the background and
perturbation. We present the general super-sound-horizon scale solutions of the
above mentioned variables valid for general , , and generally
evolving equation of state. We show that, for vanishing , the
super-sound-horizon scale evolution is characterised by a conserved variable
which is the perturbed three-space curvature in the comoving gauge. We also
present equations for the multi-component hydrodynamic situation and for the
rotation and gravitational wave.Comment: 16 pages, no figure, To appear in Gen. Rel. Gra
Conserved cosmological structures in the one-loop superstring effective action
A generic form of low-energy effective action of superstring theories with
one-loop quantum correction is well known. Based on this action we derive the
complete perturbation equations and general analytic solutions in the
cosmological spacetime. Using the solutions we identify conserved quantities
characterizing the perturbations: the amplitude of gravitational wave and the
perturbed three-space curvature in the uniform-field gauge both in the
large-scale limit, and the angular-momentum of rotational perturbation are
conserved independently of changing gravity sector. Implications for
calculating perturbation spectra generated in the inflation era based on the
string action are presented.Comment: 5 pages, no figure, To appear in Phys. Rev.
Cosmological Vorticity in a Gravity with Quadratic Order Curvature Couplings
We analyse the evolution of the rotational type cosmological perturbation in
a gravity with general quadratic order gravitational coupling terms. The result
is expressed independently of the generalized nature of the gravity theory, and
is simply interpreted as a conservation of the angular momentum.Comment: 5 pages, revtex, no figure
Analyses of decay constants and light-cone distribution amplitudes for s-wave heavy meson
In this paper, a study of light-cone distribution amplitudes (LCDAs) for
-wave heavy meson are presented in both general and heavy quark frameworks.
Within the light-front approach, the leading twist light-cone distribution
amplitudes, , and their relevant decay constants of heavy
pseudoscalar and vector mesons, , have simple relations. These relations
can be further simplified when the heavy quark limit is taken into
consideration. After fixing the parameters that appear in both Gaussian and
power-law wave functions, the corresponding decay constants are calculated and
compared with those of other theoretical approaches. The curves and the first
six -moments of are plotted and estimated. A conclusion is
drawn from these results: Even though the values of the decay constants of the
distinct mesons are almost equal, the curves of their LCDAs may have quite
large differences, and vice versa. Additionally, in the heavy quark limit, the
leading twist LCDAs, and , are compared
with the -meson LCDAs, , suggested by the other theoretical
groups.Comment: 25 pages, 3 figures, 4 tables, some typos are corrected, version to
be published in Phys. Rev.
Price Discovery in Time and Space: The Course of Condominium Prices in Singapore
Despite evidence that aggregate housing price are predictable, a random walk in time and independence in space are two maintained hypotheses in the empirical models for housing price measurement used by government and commercial companies. This paper examines the price discovery process in individual dwellings over time and space by relaxing both assumptions, using data from the Singapore private condominium market. We develop a model that tests directly the hypotheses that the prices of individual dwellings follow a random walk over time and that the price of an individual dwelling is independent of the price of a neighboring dwelling. The model is general enough to include other widely used models of housing price determination, such as Bailey, Muth, and Nourse (1963), Case and Shiller (1987) and Redfearn and Quigley (2000), as special cases. The empirical results clearly support mean reversion in housing prices and also diffusion of innovations over space. Our estimates of the level of housing prices, derived from a generalized repeat sales model, suggest that serial and spatial correlation matters in the computation of price indices and the estimation of price levels. investment returns is completely absent.
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