The honors class: hilbert’s problems and their solvers

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Laguerre approximation of stable manifolds with application to connecting orbits

We present an algorithm, based on approximation by Laguerre polynomials, for computing a point on the stable manifold of a stationary solution of an autonomous system. A superconvergence phenomenon means that the accuracy of our results is much higher than the usual spectral accuracy. Both the theory and the implementation of the method are considered. Finally, as an application of the algorithm, we describe a fully spectral approximation of homo- and heteroclinic orbits.

     

Outflow refreshment angiography: A bright blood, bright static tissue technique

A new “bright blood” strategy, outflow refreshment imaging, is introduced in which a number of overlapping slices are excited in rapid succession. Flowing spins that refresh each overlapped slice portion contribute a bright signal. Additionally, static tissue in each non-overlapped slice portion also yields a bright signal. However, the flow/static contrast is comparable to that produced in inflow refreshment images, and angiograms can be generated by conventional maximum intensity projection processing. The dual ability to visualize angiograms and static tissue images is a major benefit of the strategy. Computer simulations of flow sensitivities and in vivo results are presented which compare the outflow and inflow refreshment imaging strategies.     

Some Experiences with the Teaching of Decision Support Systems to Management Students

There are essentially two schools of thought regarding the function of decision support systems. One is that the main purpose is to support the decision-maker in whatever style of decision-making he or she wishes. The other is that the support, while suiting the decision-maker's individual style, must also be based on an appropriate theoretical paradigm. The work with students of decision support systems reported here suggests that the latter, normative, view is not one which comes naturally to many of the students, even when working on an example where it seemed relatively easy to incorporate. Other conclusions are also presented, relating to the choice of software for decision support system development, the process of teaching about decision support systems, and group formation.