Search results for "Differential"
showing 10 items of 6566 documents
Shape optimization utilizing consistent sensitivities
2010
Systematic implementation of higher order Whitney forms in methods based on discrete exterior calculus
2022
AbstractWe present a systematic way to implement higher order Whitney forms in numerical methods based on discrete exterior calculus. Given a simplicial mesh, we first refine the mesh into smaller simplices which can be used to define higher order Whitney forms. Cochains on this refined mesh can then be interpolated using higher order Whitney forms. Hence, when the refined mesh is used with methods based on discrete exterior calculus, the solution can be expressed as a higher order Whitney form. We present algorithms for the three required steps: refining the mesh, solving the coefficients of the interpolant, and evaluating the interpolant at a given point. With our algorithms, the order of…
Approximation of heat equation and backward SDEs using random walk : convergence rates
2018
This thesis addresses questions related to approximation arising from the fields of stochastic analysis and partial differential equations. Theoretical results regarding convergence rates are obtained by using discretization schemes where the limiting process, the Brownian motion, is approximated by a simple discrete-time random walk. The rate of convergence is derived for a finite-difference approximation of the solution of a terminal value problem for the backward heat equation. This weak approximation result is proved for a terminal function which has bounded variation on compact sets. The sharpness of the according rate is achieved by applying some new results related to the first exit time …
Spectral multipliers and wave equation for sub-Laplacians: lower regularity bounds of Euclidean type
2018
Let $\mathscr{L}$ be a smooth second-order real differential operator in divergence form on a manifold of dimension $n$. Under a bracket-generating condition, we show that the ranges of validity of spectral multiplier estimates of Mihlin--H\"ormander type and wave propagator estimates of Miyachi--Peral type for $\mathscr{L}$ cannot be wider than the corresponding ranges for the Laplace operator on $\mathbb{R}^n$. The result applies to all sub-Laplacians on Carnot groups and more general sub-Riemannian manifolds, without restrictions on the step. The proof hinges on a Fourier integral representation for the wave propagator associated with $\mathscr{L}$ and nondegeneracy properties of the sub…
A graph-based multigrid with applications
2010
Variational parabolic capacity
2015
We establish a variational parabolic capacity in a context of degenerate parabolic equations of $p$-Laplace type, and show that this capacity is equivalent to the nonlinear parabolic capacity. As an application, we estimate the capacities of several explicit sets.
"Table 6" of "$\rm{K}^{*}(\rm{892})^{0}$ and $\phi(1020)$ production at midrapidity in pp collisions at $\sqrt{s}$ = 8 TeV"
2020
No table description available.
"Table 8" of "$\rm{K}^{*}(\rm{892})^{0}$ and $\phi(1020)$ production at midrapidity in pp collisions at $\sqrt{s}$ = 8 TeV"
2020
No table description available.
"Table 5" of "$\rm{K}^{*}(\rm{892})^{0}$ and $\phi(1020)$ production at midrapidity in pp collisions at $\sqrt{s}$ = 8 TeV"
2020
No table description available.
Methylprednisolone-induced hepatotoxicity in a 16-year-old girl with multiple sclerosis.
2018
Multiple sclerosis (MS) is a chronic inflammatory disease with demyelination of the central nervous system. High-dosage corticosteroids are the first-line therapy in the acute relapsing of MS. We report a case of severe high-dose methylprednisolone-induced acute hepatitis in a patient with a new diagnosis of MS. A 16-year-old girl was admitted for urticaria, angioedema, nausea and vomiting a month later she had been diagnosed with MS and treated with high-dosage methylprednisolone. Laboratory investigations showed hepatic insufficiency with grossly elevated liver enzymes. A liver biopsy showed focal centrilobular hepatocyte necrosis with interface hepatitis. Methylprednisolone-induced hepat…