For Pranav Jadhav in April 2021
Potentially Relevant Initial Links
Challenges to Young, Applied Mathematicians
Note from J. E. Tohline to Students with Good Mathematical Skills: The astronomy community's understanding of the Structure, Stability, and Dynamics of stars and galaxies would be strengthened if we had, in hand, closed-form analytic solutions to the following well-defined mathematical problems. (Solutions can be obtained numerically with relative ease, but here the challenge is to find a closed-form analytic solution.) As is true with most meaningful scientific research projects, it is not at all clear whether each of these problems has a solution. In my judgment, however, it seems plausible that a closed-form solution can be discovered in each case and such a solution would be of sufficient interest to the astronomical community that it would likely be publishable in a professional astronomy or physics journal. At the very least, each of these projects represents an opportunity for a graduate student, an undergraduate, or even a talented high-school student (perhaps in connection with a mathematics science fair project?) to hone her/his research skills in applied mathematics. Also, I would be thrilled to include a solution to any one of these problems — along with full credit to the solution's author — as a chapter in this online H_Book. Having retired from LSU, I am not in a position to financially support or formally advise students who are in pursuit of a higher-education degree. I would nevertheless be interested in sharing my expertise — and, perhaps, developing a collaborative relationship — with individuals who are interested in pursuing answers to the questions posed by this identified set of problems.
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