Search results for "Partial"
showing 10 items of 1477 documents
Regularity of solutions to differential equations with non-Lipschitz coefficients
2008
AbstractWe study the ordinary and stochastic differential equations whose coefficients satisfy certain non-Lipschitz conditions, namely, we study the behaviors of small subsets under the flows generated by these equations.
Adapted Metrics for Dominated splittings.
2007
International audience; A Riemannian metric is adapted to an hyperbolic set of a diffeomorphism if, for this metric, the expansion/contraction of the unstable/stable directions can be seen after only one iteration. A dominated splitting is a notion of weak hyperbolicity where the tangent bundle of the manifold splits in invariant subbundles such that the vector expansion on one bundle is uniformly smaller than on the next bundle. The existence of an adapted metric for a dominated splitting has been asked by Hirsch Pugh and Shub who answer positively to the question in the special case of a dominated splitting in two bundles, one being of dimension 1. This paper gives a complete answer to th…
Partially hyperbolic diffeomorphisms with a compact center foliation with finite holonomy
2011
The thesis classifies partially hyperbolic diffeomorphisms with a compact center foliation with finite holonomy. Under the further assumption of a one-dimensional unstable bundle we show the following: If the unstable bundle is oriented then the system fibers over a hyperbolic toral automorphism. We further establish that the system has a dense orbit of center leaves. During the proof we show a Shadowing Lemma and the dynamical coherence without restrictions of the dimensions.
Spatial Besov regularity for stochastic partial differential equations on Lipschitz domains
2010
We use the scale of Besov spaces B^\alpha_{\tau,\tau}(O), \alpha>0, 1/\tau=\alpha/d+1/p, p fixed, to study the spatial regularity of the solutions of linear parabolic stochastic partial differential equations on bounded Lipschitz domains O\subset R^d. The Besov smoothness determines the order of convergence that can be achieved by nonlinear approximation schemes. The proofs are based on a combination of weighted Sobolev estimates and characterizations of Besov spaces by wavelet expansions.
AC is Equivalent to the Coherence Principle. Corrigendum to my Paper "Induction Principles for Sets"
2009
Theorem 3.7 of [1] is corrected. Two coherence principles and the ultrafilter property for partial functions contained in a relation are formulated. The equivalence of the coherent principles with AC and the equivalence of the ultrafilter property with BPI is shown.
Convergence of a high-order compact finite difference scheme for a nonlinear Black–Scholes equation
2004
A high-order compact finite difference scheme for a fully nonlinear parabolic differential equation is analyzed. The equation arises in the modeling of option prices in financial markets with transaction costs. It is shown that the finite difference solution converges locally uniformly to the unique viscosity solution of the continuous equation. The proof is based on a careful study of the discretization matrices and on an abstract convergence result due to Barles and Souganides.
Control of essential supremum of solutions of quasilinear degenerate parabolic equations
2001
Sufficient conditions are obtained so that a weak subsolution of a class of quasilinear degenerate parabolic equations, bounded from above on theparabolic boundary of the cylinder Q, turns out to be bounded from above in Q.
Some Algebraic Properties of Machine Poset of Infinite Words
2008
The complexity of infinite words is considered from the point of view of a transformation with a Mealy machine that is the simplest model of a finite automaton transducer. We are mostly interested in algebraic properties of the underlying partially ordered set. Results considered with the existence of supremum, infimum, antichains, chains and density aspects are investigated.
Initiation of high-frequency oscillatory ventilation and its effects upon cerebral circulation in pigs: an experimental study
2006
BACKGROUND: Current practice at high-frequency oscillatory ventilation (HFOV) initiation is a stepwise increase of the constant applied airway pressure to achieve lung recruitment. We hypothesized that HFOV would lead to more adverse cerebral haemodynamics than does pressure controlled ventilation (PCV) in the presence of experimental intracranial hypertension (IH) and acute lung injury (ALI) in pigs with similar mean airway pressure settings. METHODS: In 12 anesthetized pigs (24-27 kg) with IH and ALI, mean airway pressure (P(mean)) was increased (to 20, 25, 30 cm H(2)O every 30 min), either with HFOV or with PCV. The order of the two ventilatory modes (cross-over) was randomized. Mean art…
Comparison of near and mid infrared spectroscopy as green analytical tools for the determination of total polar materials in fried oils
2017
Abstract Total polar materials (TPM) are used as an indicator of the quality in the frying oil because of high values may be harmful for human health. Spanish legislation establishes the maximum level of total polar materials for frying fats and oils for human consumption around 25% (w/w). Official methods to monitor oil quality are time consuming and use a lot of chemicals; therefore it is necessary a simple and quick analytical technique to evaluate fried oils. Transmittance near-infrared (NIR) and attenuated total reflection mid-infrared (ATR-MIR) spectroscopy measurements, combined with partial least squares (PLS) regression, offer alternatives to determine TPM in fried oils with relati…