This paper studies the rst passage times to at boundaries for a double exponential jump di usion process, which consists of a continuous part driven by a Brownian motion and a jump part with jump sizes having a double exponential distribution. Explicit solutions of the Laplace transforms, of both the distribution of the rst passage times and the joint distribution of the process and its running...

The redistribution of Be during growth of GaInP layers by gas source molecular beam epitaxy has been studied using secondary ion mass spectrometry for the "rst time. Apparent Be di!usion occurs at doping level over 4]1019 cm~3 at growth temperature of 5003C. At lower temperature the Be di!usion pro"le exhibits a signi"cant increase of Be concentration and reduced di!usion. In contrast to Zn beh...

The rst part of this thesis concerns the formulation of numerical methods that are local in time for the solution of equations with memory. The main idea is that the solution will be updated in the Fourier domain in order to avoid evaluating time convolution integrals that have memory. This work was made possible by the development of a good quadrature[31] of the Fourier integral where a small ...

We present a semi discrete method for constructing approximate solutions to the initial value problem for the m dimensional convection di usion equation ut r f u u The method is based on the use of operator splitting to isolate the convection part and the di usion part of the equation In the casem dimensional splitting is used to reduce the m dimensional convection problem to a series of one di...

Di usion Tensor Imaging (DTI) is a relatively new modality for human brain imaging. During the last years, this modality has become widely used in medical studies. Tractography is currently the favorite technique to characterize and analyse the structure of the brain white matter. Only a few studies have been proposed to group data of particular interest. Rather than working on extracted bers o...

The rst part of this thesis concerns the formulation of numerical methods that are local in time for the solution of equations with memory. The main idea is that the solution will be updated in the Fourier domain in order to avoid evaluating time convolution integrals that have memory. This work was made possible by the development of a good quadrature[31] of the Fourier integral where a small ...

We propose a single-index di usion model in this paper. This model can avoid the `curse of dimensionality' in estimating a multivariate nonparametric conditional variance. We adopt an absolute deviation estimation method to estimate the model. Comparing with the commonly used estimators, the absolute deviation estimator is more stable and efcient. Some simulations and applications to real data ...

This paper addresses the issue of reconstructing the unknown eld of absorption and scattering coe cients from time-resolved measurements of di used light in a computationally e cient manner. The intended application is optical tomography, which has generated considerable interest in recent times. The inverse problem is posed in the Bayesian framework. The maximum a posteriori (MAP) estimate is ...

The prior estimate and decay property of positive solutions are derived for a system of quasilinear elliptic 9 di$erential equations 3rst. Then, the nonexistence result for radially nonincreasing positive solutions of the system is implied. By using this nonexistence result, blow-up estimates for a class of quasilinear reaction–di$usion 11 systems (non-Newtonian 3ltration systems) are establish...