90 research outputs found
Perturbations of Spatially Closed Bianchi III Spacetimes
Motivated by the recent interest in dynamical properties of topologically
nontrivial spacetimes, we study linear perturbations of spatially closed
Bianchi III vacuum spacetimes, whose spatial topology is the direct product of
a higher genus surface and the circle. We first develop necessary mode
functions, vectors, and tensors, and then perform separations of (perturbation)
variables. The perturbation equations decouple in a way that is similar to but
a generalization of those of the Regge--Wheeler spherically symmetric case. We
further achieve a decoupling of each set of perturbation equations into
gauge-dependent and independent parts, by which we obtain wave equations for
the gauge-invariant variables. We then discuss choices of gauge and stability
properties. Details of the compactification of Bianchi III manifolds and
spacetimes are presented in an appendix. In the other appendices we study
scalar field and electromagnetic equations on the same background to compare
asymptotic properties.Comment: 61 pages, 1 figure, final version with minor corrections, to appear
in Class. Quant. Gravi
Geometric Aspects of the Moduli Space of Riemann Surfaces
This is a survey of our recent results on the geometry of moduli spaces and
Teichmuller spaces of Riemann surfaces appeared in math.DG/0403068 and
math.DG/0409220. We introduce new metrics on the moduli and the Teichmuller
spaces of Riemann surfaces with very good properties, study their curvatures
and boundary behaviors in great detail. Based on the careful analysis of these
new metrics, we have a good understanding of the Kahler-Einstein metric from
which we prove that the logarithmic cotangent bundle of the moduli space is
stable. Another corolary is a proof of the equivalences of all of the known
classical complete metrics to the new metrics, in particular Yau's conjectures
in the early 80s on the equivalences of the Kahler-Einstein metric to the
Teichmuller and the Bergman metric.Comment: Survey article of our recent results on the subject. Typoes
corrrecte
Positivity of relative canonical bundles and applications
Given a family of canonically polarized manifolds, the
unique K\"ahler-Einstein metrics on the fibers induce a hermitian metric on the
relative canonical bundle . We use a global elliptic
equation to show that this metric is strictly positive on , unless
the family is infinitesimally trivial.
For degenerating families we show that the curvature form on the total space
can be extended as a (semi-)positive closed current. By fiber integration it
follows that the generalized Weil-Petersson form on the base possesses an
extension as a positive current. We prove an extension theorem for hermitian
line bundles, whose curvature forms have this property. This theorem can be
applied to a determinant line bundle associated to the relative canonical
bundle on the total space. As an application the quasi-projectivity of the
moduli space of canonically polarized varieties
follows.
The direct images , , carry natural hermitian metrics. We prove an
explicit formula for the curvature tensor of these direct images. We apply it
to the morphisms that are induced by the Kodaira-Spencer map and obtain a differential
geometric proof for hyperbolicity properties of .Comment: Supercedes arXiv:0808.3259v4 and arXiv:1002.4858v2. To appear in
Invent. mat
Remarks on symplectic twistor spaces
We consider some classical fibre bundles furnished with almost complex
structures of twistor type, deduce their integrability in some cases and study
\textit{self-holomorphic} sections of a \textit{symplectic} twistor space. With
these we define a moduli space of -compatible complex structures. We
recall the theory of flag manifolds in order to study the Siegel domain and
other domains alike, which is the fibre of the referred twistor space. Finally
the structure equations for the twistor of a Riemann surface with the canonical
symplectic-metric connection are deduced, based on a given conformal coordinate
on the surface. We then relate with the moduli space defined previously.Comment: 20 pages, title changed since v2, accepted in AMPA toda
Phase Contrast X-Ray Synchrotron Microtomography for Virtual Dissection of the Head of <i>Rhodnius prolixus</i>
n/
Virtual histological assessment of the prenatal life history and age at death of the Upper Paleolithic fetus from Ostuni (Italy)
The fetal remains from the Ostuni 1 burial (Italy, ca 27 ka) represent a unique opportunity to explore the prenatal biological parameters, and to reconstruct the possible patho-biography, of a fetus (and its mother) in an Upper Paleolithic context. Phase-contrast synchrotron X-ray microtomography imaging of two deciduous tooth crowns and microfocus CT measurements of the right hemimandible of the Ostuni 1b fetus were performed at the SYRMEP beamline and at the TomoLab station of the Elettra - Sincrotrone laboratory (Trieste, Italy) in order to refne age at death and to report the enamel developmental history and dental tissue volumes for this fetal individual. The virtual histology allowed to estimate the age at death of the fetus at 31â33 gestational weeks. Three severe physiological stress episodes were also identifed in the prenatal enamel. These stress episodes occurred during the last two months and half of pregnancy and may relate to the death of both individuals. Compared with modern prenatal standards, Os1bâs skeletal development was advanced. This cautions against the use of modern skeletal and dental references for archaeological fnds and emphasizes the need for more studies on prenatal archaeological skeletal samples
Prenatal exposures and exposomics of asthma
This review examines the causal investigation of preclinical development of childhood asthma using exposomic tools. We examine the current state of knowledge regarding early-life exposure to non-biogenic indoor air pollution and the developmental modulation of the immune system. We examine how metabolomics technologies could aid not only in the biomarker identification of a particular asthma phenotype, but also the mechanisms underlying the immunopathologic process. Within such a framework, we propose alternate components of exposomic investigation of asthma in which, the exposome represents a reiterative investigative process of targeted biomarker identification, validation through computational systems biology and physical sampling of environmental medi
Stochastic Differential Systems with Memory: Theory, Examples and Applications
The purpose of this article is to introduce the reader to certain aspects of stochastic differential systems, whose evolution depends on the past history of the state.
Chapter I begins with simple motivating examples. These include the noisy feedback loop, the logistic time-lag model with Gaussian noise , and the classical ``heat-bath model of R. Kubo , modeling the motion of a ``large molecule in a viscous fluid. These examples are embedded in a general class of stochastic functional differential equations (sfde\u27s). We then establish pathwise existence and uniqueness of solutions to these classes of sfde\u27s under local Lipschitz and linear growth hypotheses on the coefficients. It is interesting to note that the above class of sfde\u27s is not covered by classical results of Protter, Metivier and Pellaumail and Doleans-Dade.
In Chapter II, we prove that the Markov (Feller) property holds for the trajectory random field of a sfde. The trajectory Markov semigroup is not strongly continuous for positive delays, and its domain of strong continuity does not contain tame (or cylinder) functions with evaluations away from zero. To overcome this difficulty, we introduce a class of quasitame functions. These belong to the domain of the weak infinitesimal generator, are weakly dense in the underlying space of continuous functions and generate the Borel -algebra of the state space. This chapter also contains a derivation of a formula for the weak infinitesimal generator of the semigroup for sufficiently regular functions, and for a large class of quasitame functions.
In Chapter III, we study pathwise regularity of the trajectory random field in the time variable and in the initial path. Of note here is the non-existence of the stochastic flow for the singular sdde and a breakdown of linearity and local boundedness. This phenomenon is peculiar to stochastic delay equations. It leads naturally to a classification of sfde\u27s into regular and singular types. Necessary and sufficient conditions for regularity are not known. The rest of Chapter III is devoted to results on sufficient conditions for regularity of linear systems driven by white noise or semimartingales, and Sussman-Doss type nonlinear sfde\u27s.
Building on the existence of a compacting stochastic flow, we develop a multiplicative ergodic theory for regular linear sfde\u27s driven by white noise, or general helix semimartingales (Chapter IV). In particular, we prove a Stable Manifold Theorem for such systems.
In Chapter V, we seek asymptotic stability for various examples of one-dimensional linear sfde\u27s. Our approach is to obtain upper and lower estimates for the top Lyapunov exponent.
Several topics are discussed in Chapter VI. These include the existence of smooth densities for solutions of sfde\u27s using the Malliavin calculus, an approximation technique for multidimensional diffusions using sdde\u27s with small delays, and affine sfde\u27s
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