55,694 research outputs found
A normal form algorithm for the Brieskorn lattice
This article describes a normal form algorithm for the Brieskorn lattice of
an isolated hypersurface singularity. It is the basis of efficient algorithms
to compute the Bernstein-Sato polynomial, the complex monodromy, and
Hodge-theoretic invariants of the singularity such as the spectral pairs and
good bases of the Brieskorn lattice. The algorithm is a variant of Buchberger's
normal form algorithm for power series rings using the idea of partial standard
bases and adic convergence replacing termination.Comment: 23 pages, 1 figure, 4 table
Ellipticity in Pseudodifferential Algebras of Toeplitz Type
Let L^\star be a filtered algebra of abstract pseudodifferential operators
equipped with a notion of ellipticity, and T^\star be a subalgebra of operators
of the form P_1AP_0, where P_0 and P_1 are two projections. The elements of
L^\star act as linear continuous operators in certain scales of abstract
Sobolev spaces, the elements of the subalgebra in the corresponding subspaces
determined by the projections. We study how the ellipticity in L^\star descends
to T^\star, focusing on parametrix construction, Fredholm property, and
homogeneous principal symbols. Applications concern SG-pseudodifferential
operators, pseudodifferential operators on manifolds with conical
singularities, and Boutet de Monvel's algebra for boundary value problems. In
particular, we derive invertibilty of the Stokes operator with Dirichlet
boundary conditions in a subalgebra of Boutet de Monvel's algebra. We indicate
how the concept generalizes to parameter-dependent operators.Comment: 29 page
Randomized crossover comparison of proportional assist ventilation and patient-triggered ventilation in extremely low birth weight infants with evolving chronic lung disease
Background: Refinement of ventilatory techniques remains a challenge given the persistence of chronic lung disease of preterm infants. Objective: To test the hypothesis that proportional assist ventilation ( PAV) will allow to lower the ventilator pressure at equivalent fractions of inspiratory oxygen (FiO(2)) and arterial hemoglobin oxygen saturation in ventilator-dependent extremely low birth weight infants in comparison with standard patient-triggered ventilation ( PTV). Methods: Design: Randomized crossover design. Setting: Two level-3 university perinatal centers. Patients: 22 infants ( mean (SD): birth weight, 705 g ( 215); gestational age, 25.6 weeks ( 2.0); age at study, 22.9 days ( 15.6)). Interventions: One 4- hour period of PAV was applied on each of 2 consecutive days and compared with epochs of standard PTV. Results: Mean airway pressure was 5.64 ( SD, 0.81) cm H2O during PAV and 6.59 ( SD, 1.26) cm H2O during PTV ( p < 0.0001), the mean peak inspiratory pressure was 10.3 ( SD, 2.48) cm H2O and 15.1 ( SD, 3.64) cm H2O ( p < 0.001), respectively. The FiO(2) ( 0.34 (0.13) vs. 0.34 ( 0.14)) and pulse oximetry readings were not significantly different. The incidence of arterial oxygen desaturations was not different ( 3.48 ( 3.2) vs. 3.34 ( 3.0) episodes/ h) but desaturations lasted longer during PAV ( 2.60 ( 2.8) vs. 1.85 ( 2.2) min of desaturation/ h, p = 0.049). PaCO2 measured transcutaneously in a subgroup of 12 infants was similar. One infant met prespecified PAV failure criteria. No adverse events occurred during the 164 cumulative hours of PAV application. Conclusions: PAV safely maintains gas exchange at lower mean airway pressures compared with PTV without adverse effects in this population. Backup conventional ventilation breaths must be provided to prevent apnea-related desaturations. Copyright (c) 2007 S. Karger AG, Base
Long-range interactions in Sznajd consensus model
The traditional Sznajd model, as well as its Ochrombel simplification, for
opinion spreading are modified to have a convincing strength proportional to a
negative power of the spatial distance. We find the usual phase transition in
the full Sznajd model, but not in the Ochrombel simplification. We also mix the
two rules, which favours a phase transition.Comment: Not ye4t submittted, waiting for your comments; 6 page
Diversity Spectra of Spatial Multipath Fading Processes
We analyse the spatial diversity of a multipath fading process for a finite
region or curve in the plane. By means of the Karhunen-Lo\`eve (KL) expansion,
this diversity can be characterised by the eigenvalue spectrum of the spatial
autocorrelation kernel. This justifies to use the term diversity spectrum for
it. We show how the diversity spectrum can be calculated for any such
geometrical object and any fading statistics represented by the power azimuth
spectrum (PAS). We give rigorous estimates for the accuracy of the numerically
calculated eigenvalues. The numerically calculated diversity spectra provide
useful hints for the optimisation of the geometry of an antenna array.
Furthermore, for a channel coded system, they allow to evaluate the time
interleaving depth that is necessary to exploit the diversity gain of the code.Comment: 32 pages, 10 figure
Competition of languages in the presence of a barrier
Using the Schulze model for Monte Carlo simulations of language competition,
we include a barrier between the top half and the bottom half of the lattice.
We check under which conditions two different languages evolve as dominating in
the two halves.Comment: 6 pages including 3 figure
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