sends the point z ∈ C to its inversion image about the circle of radius r ∈ R centered at the point a ∈ C. Dynamically, this map is not interesting since iterating twice yields the identity mapping. Using three circles we invert a point z about each circle and form a new map by sending z to the arithmetic mean of the three inversion images. We refer to this as inverting z about the three circle...

Arterial spin labeling (ASL) provides a noninvasive method to measure brain perfusion and is becoming an increasingly viable alternative to more invasive MR methods due to improvements in acquisition, such as the use of a three-dimensional GRASE readout. A potential source of error in ASL measurements is signal arising from intravascular blood that is destined for more distal tissue. This is ty...

A patient undergoing chemotherapy for multiple myeloma had a sudden onset of heart failure. Cardiac magnetic resonance was performed after echocardiography to rule out myocardial late enhancement, which was not detected. In- terestingly, the inversion time of the T1-weighted inversion recovery late enhancement sequence needed to be significantly increased (from the usual 250-300 to 490 ms) to ...

We present a new inversion formula for the classical, finite, and asymptotic Laplace transform f̂ of continuous or generalized functions f . The inversion is given as a limit of a sequence of finite linear combinations of exponential functions whose construction requires only the values of f̂ evaluated on a Müntz set of real numbers. The inversion sequence converges in the strongest possible sens...

In characterizing reservoirs, we are often interested in retrieving detailed elastic parameters for only a very limited part of the subsurface. One way of doing so involves studying the seismic reflection response within the region of interest. To that end, we introduce a local solver that uses an acoustic solver to propagate the wavefield to a subdomain on which we use a local elastic solver. ...

Inversion recovery sequences that vary the inversion time (t(i)) have been employed to determine T(1) and, more recently, quantitative magnetization transfer parameters. Specifically, in previous work, the inversion recovery pulse sequences varied t(i) only while maintaining a constant delay (t(d)) between repetitions. T(1) values were determined by fitting to a single exponential function, and...