Dynamic contrast enhancement appears to provide a new, time-dependent dimension in the assessment of lymph node pathology and supplements the morphological information provided by grey scale and Doppler sonographic interrogation.
Real-time sonography during contrast administration (dynamic contrast enhancement) adds a new, time-dependent dimension to the evaluation of lymph node vascularity, and has been shown to provide information on lymph node parenchymal perfusion [68].
One motivation for systems with time-dependent dimensions is efficient control law synthesis for discrete-time systems with asynchronous inputs, for which a novel modeling framework resulting in low dimensional models is proposed.
CAMM is a time dependent meta-model, with four dimensions related to post-deployment adoption: availability, use, clinical behaviour, and clinical outcomes.
In [7], Cheng and Shu presented a new DG method for solving some kinds of time dependent partial differential equations in one dimension.
Exact nonreflecting boundary conditions are derived for the time dependent Maxwell equations in three space dimensions.
An exact nonreflecting boundary condition was derived previously for use with the time dependent wave equation in three space dimensions.
We find explicit formulae for the fundamental solution for the heat and time dependent Schrödinger equations with point interaction in dimension n ≤ 3. We discuss in detail the small time asymptotics of these fundamental solutions.
Further, a numerical investigation is performed based on test examples originating from spatial discretization of time dependent partial differential equations in two and three space dimensions.
Numerical examples of time dependent HJ equations in 2, 3 and 4 dimensions illustrate the accuracy of the new methods.
A detailed description of a time dependent, 2-D ULF wave model with e imϕ variation in the third dimension, using distorted dipole coordinates was given by Lysak (2004) and Waters and Sciffer (2008).
