153 research outputs found
Irreducible Hamiltonian BRST-anti-BRST symmetry for reducible systems
An irreducible Hamiltonian BRST-anti-BRST treatment of reducible first-class
systems based on homological arguments is proposed. The general formalism is
exemplified on the Freedman-Townsend model.Comment: LaTeX 2.09, 35 page
Concerning the Wave equation on Asymptotically Euclidean Manifolds
We obtain KSS, Strichartz and certain weighted Strichartz estimate for the
wave equation on , , when metric
is non-trapping and approaches the Euclidean metric like with
. Using the KSS estimate, we prove almost global existence for
quadratically semilinear wave equations with small initial data for
and . Also, we establish the Strauss conjecture when the metric is radial
with for .Comment: Final version. To appear in Journal d'Analyse Mathematiqu
Strichartz estimates on Schwarzschild black hole backgrounds
We study dispersive properties for the wave equation in the Schwarzschild
space-time. The first result we obtain is a local energy estimate. This is then
used, following the spirit of earlier work of Metcalfe-Tataru, in order to
establish global-in-time Strichartz estimates. A considerable part of the paper
is devoted to a precise analysis of solutions near the trapping region, namely
the photon sphere.Comment: 44 pages; typos fixed, minor modifications in several place
The Strauss conjecture on asymptotically flat space-times
By assuming a certain localized energy estimate, we prove the existence
portion of the Strauss conjecture on asymptotically flat manifolds, possibly
exterior to a compact domain, when the spatial dimension is 3 or 4. In
particular, this result applies to the 3 and 4-dimensional Schwarzschild and
Kerr (with small angular momentum) black hole backgrounds, long range
asymptotically Euclidean spaces, and small time-dependent asymptotically flat
perturbations of Minkowski space-time. We also permit lower order perturbations
of the wave operator. The key estimates are a class of weighted Strichartz
estimates, which are used near infinity where the metrics can be viewed as
small perturbations of the Minkowski metric, and the assumed localized energy
estimate, which is used in the remaining compact set.Comment: Final version, to appear in SIAM Journal on Mathematical Analysis. 17
page
Global well-posedness of the KP-I initial-value problem in the energy space
We prove that the KP-I initial value problem is globally well-posed in the
natural energy space of the equation
Strichartz Estimates for the Vibrating Plate Equation
We study the dispersive properties of the linear vibrating plate (LVP)
equation. Splitting it into two Schr\"odinger-type equations we show its close
relation with the Schr\"odinger equation. Then, the homogeneous Sobolev spaces
appear to be the natural setting to show Strichartz-type estimates for the LVP
equation. By showing a Kato-Ponce inequality for homogeneous Sobolev spaces we
prove the well-posedness of the Cauchy problem for the LVP equation with
time-dependent potentials. Finally, we exhibit the sharpness of our results.
This is achieved by finding a suitable solution for the stationary homogeneous
vibrating plate equation.Comment: 18 pages, 4 figures, some misprints correcte
Pharmacological Benefits of Herbal Formulations in the Management of <i>Psoriasis vulgaris<i>
Psoriasis is a chronic inflammatory skin disease, with an important impact on the patient's quality of life. Its incidence and prevalence are continuously increasing. The complex ethiopathology of this disorder is only partially known; there is a clear genetic predisposition, which associates a number of environmental triggering factors such as an unbalanced diet and lifestyle. The conventional therapeutic options are not always satisfactory in terms of efficiency and safety, therefore, complementary and alternative medicine approaches are frequently chosen by patients, mostly as self-medication. This review, based on recent literature flow data, outlines the pharmacological benefits of herbal formulations with antipsoriatic activity. It also reveals the molecules esponsible for their effects, as well as their interference with the metabolic and immunopathogenic mechanisms of this disease. An important number of plants have been proved to act as antipsoriatic agents, many botanical-based preparations containing key-phytochemical molecules (belonging mainly to phenolics, triterpenoids and phytosterols or unsaturated fatty acids, as mentioned in specific phyto-pharmaceutical databases). Specific mechanisms of action, which can explain their activity (such as lipoxygenase inhibition, antioxidant, anti-inflammatory, anti prostaglandin), were recently described. Only some of these formulations have been actively tested in vitro or in vivo . Most publications in the field agree on the need for more in vitro and in vivo studies, especially clinical assessment on patients with Psoriasis vulgaris . These would provide more accurate data on the efficacy and safety of such herbal formulations for this disease
Spectral Analysis for Matrix Hamiltonian Operators
In this work, we study the spectral properties of matrix Hamiltonians
generated by linearizing the nonlinear Schr\"odinger equation about soliton
solutions. By a numerically assisted proof, we show that there are no embedded
eigenvalues for the three dimensional cubic equation. Though we focus on a
proof of the 3d cubic problem, this work presents a new algorithm for verifying
certain spectral properties needed to study soliton stability. Source code for
verification of our comptuations, and for further experimentation, are
available at http://www.math.toronto.edu/simpson/files/spec_prop_code.tgz.Comment: 57 pages, 22 figures, typos fixe
On the uniqueness and global dynamics of AdS spacetimes
We study global aspects of complete, non-singular asymptotically locally AdS
spacetimes solving the vacuum Einstein equations whose conformal infinity is an
arbitrary globally stationary spacetime. It is proved that any such solution
which is asymptotically stationary to the past and future is itself globally
stationary.
This gives certain rigidity or uniqueness results for exact AdS and related
spacetimes.Comment: 18pp, significant revision of v
Resolvent estimates for normally hyperbolic trapped sets
We give pole free strips and estimates for resolvents of semiclassical
operators which, on the level of the classical flow, have normally hyperbolic
smooth trapped sets of codimension two in phase space. Such trapped sets are
structurally stable and our motivation comes partly from considering the wave
equation for Kerr black holes and their perturbations, whose trapped sets have
precisely this structure. We give applications including local smoothing
effects with epsilon derivative loss for the Schr\"odinger propagator as well
as local energy decay results for the wave equation.Comment: Further changes to erratum correcting small problems with Section 3.5
and Lemma 4.1; this now also corrects hypotheses, explicitly requiring
trapped set to be symplectic. Erratum follows references in this versio
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