Quantitative analysis of fast and slow diffusion from abdominal Diffusion-weighted MRI has the potential to provide important new insights into physiological and microstructural properties of the body. However, the commonly used, independent voxel-wise fitting of the signal decay model leads to imprecise parameter estimates, which has hampered their practical usage. In this work we evaluated th...

Lp–Lq decay estimates of solutions to Cauchy problems of linear thermoelastic systems with second sound in three spatial variables are studied. By carefully analysis of the different effects of higher, middle and lower frequencies in phase space, the asymptotic behaviour of characteristic roots of coefficient matrices is obtained. Then, with the help of the information on characteristic roots a...

In [7], [1], [2], local decay estimates were proven for the (decoupled) Schrödinger, wave, and Regge-Wheeler equations on the Schwarzschild manifold, using commutator methods. Here, we correct a step in the commutator argument. The corrected argument works either for radial semilinear equations or general linear equations. This recovers the results in [7] and [2], but does not recover the non r...

We consider a prototypical nonlinear reaction-diffusion system arising in reversible chemistry. Based on recent existence results of global weak and classical solutions derived from entropy-decay related apriori estimates and duality methods, we prove exponential convergence of these solutions towards equilibrium with explicit rates in all space dimensions. The key step of the proof establishes...

Abstract. In this paper, we prove almost global existence of solutions to certain quasilinear wave equations with quadratic nonlinearities in infinite homogeneous waveguides with Neumann boundary conditions. We use a Galerkin method to expand the Laplacian of the compact base in terms of its eigenfunctions. For those terms corresponding to zero modes, we obtain decay using analogs of estimates ...

The maximum likelihood approach to jointly model the survival time and its longitudinal covariates has been successful to model both processes in longitudinal studies. Random effects in the longitudinal process are often used to model the survival times through a proportional hazards model, and this invokes an EM algorithm to search for the maximum likelihood estimates (MLEs). Several intriguin...

Remotely sensed estimates of crop residue cover (fR) are required to assess the extent of conservation tillage over large areas; the impact of decay processes on estimates of residue cover is unknown. Changes in wheat straw composition and spectral reflectance were measured during the decay process and their impact on estimates of fR were assessed. Proportions of cellulose and hemicellulose dec...