2,167 research outputs found
PHP64 A 10-Year Review of the Canadian Common Drug Review: Pharmaceutical Manufacturers’ Success Rate
Higher-order splitting algorithms for solving the nonlinear Schr\"odinger equation and their instabilities
Since the kinetic and the potential energy term of the real time nonlinear
Schr\"odinger equation can each be solved exactly, the entire equation can be
solved to any order via splitting algorithms. We verified the fourth-order
convergence of some well known algorithms by solving the Gross-Pitaevskii
equation numerically. All such splitting algorithms suffer from a latent
numerical instability even when the total energy is very well conserved. A
detail error analysis reveals that the noise, or elementary excitations of the
nonlinear Schr\"odinger, obeys the Bogoliubov spectrum and the instability is
due to the exponential growth of high wave number noises caused by the
splitting process. For a continuum wave function, this instability is
unavoidable no matter how small the time step. For a discrete wave function,
the instability can be avoided only for \dt k_{max}^2{<\atop\sim}2 \pi, where
.Comment: 10 pages, 8 figures, submitted to Phys. Rev.
Finite Generation of Canonical Ring by Analytic Method
In the 80th birthday conference for Professor LU Qikeng in June 2006 I gave a
talk on the analytic approach to the finite generation of the canonical ring
for a compact complex algebraic manifold of general type. This article is my
contribution to the proceedings of that conference from my talk. In this
article I give an overview of the analytic proof and focus on explaining how
the analytic method handles the problem of infinite number of interminable
blow-ups in the intuitive approach to prove the finite generation of the
canonical ring. The proceedings of the LU Qikeng conference will appear as
Issue No. 4 of Volume 51 of Science in China Series A: Mathematics
(www.springer.com/math/applications/journal/11425)
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
Cohomology of bundles on homological Hopf manifold
We discuss the properties of complex manifolds having rational homology of
including those constructed by Hopf, Kodaira and
Brieskorn-van de Ven. We extend certain previously known vanishing properties
of cohomology of bundles on such manifolds.As an application we consider
degeneration of Hodge-deRham spectral sequence in this non Kahler setting.Comment: To appear in Proceedings of 2007 conference on Several complex
variables and Complex Geometry. Xiamen. Chin
Fermionic Modular Categories and the 16-fold Way
We study spin and super-modular categories systematically as inspired by
fermionic topological phases of matter, which are always fermion parity
enriched and modelled by spin TQFTs at low energy. We formulate a -fold way
conjecture for the minimal modular extensions of super-modular categories to
spin modular categories, which is a categorical formulation of gauging the
fermion parity. We investigate general properties of super-modular categories
such as fermions in twisted Drinfeld doubles, Verlinde formulas for naive
quotients, and explicit extensions of with an eye towards a
classification of the low-rank cases.Comment: Latest post-referee version. Many typos fixed, many explanations
expanded, several inconsistencies corrected. 8 figure
An assessment of the readiness for introduction of the HPV vaccine in Uganda
Formative research assessing human papillomavirus (HPV) vaccine readiness in Uganda was conducted in 2007. The objective was to generate evidence for government decision-making and operationalplanning for HPV vaccine introduction. Qualitative research methods with children, parents, teachers, community leaders, health workers, technical experts and political leaders were used to captureunderstanding of socio-cultural, health system and policy environments. We found low levels of knowledge about cervical cancer and HPV. Vaccination and its benefits were well-understood;respondents were positive about HPV vaccination. Health systems were deemed adequate for HPV vaccine delivery. Schools were identifie as a vaccination venue, given high attendance by girls aged10-12 years. Communication and advocacy strategies to foster acceptance should provide information on cervical cancer, HPV vaccine safety, and side effects. Policymakers requested further detail on costs.Introduction of HPV vaccine could be integrated into existing reproductive health and immunization policies (Afr J Reprod Health 2008; 12[3]:159-172)
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