Appendix/Ramblings/ForPJinApril2021: Difference between revisions
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==Potentially Relevant Initial Links== | ==Potentially Relevant Initial Links== | ||
* [[ | * [[H_BookTiledMenu#Tiled_Menu|Tiled Menu]] | ||
* [[ | * [[ThreeDimensionalConfigurations/BinaryFission#Fission_Hypothesis_of_Binary_Star_Formation|Fission Hypothesis of Binary Star Formation]] | ||
* [[ | * [[ThreeDimensionalConfigurations/ChallengesPt2#COLLADA-Based_Representation|COLLADA-based Representation of Riemann Type 1 Ellipsoid]] | ||
==Challenges to Young, Applied Mathematicians== | ==Challenges to Young, Applied Mathematicians== | ||
<font color="red">'''Note from J. E. Tohline to Students with Good Mathematical Skills'''</font>: 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. | <font color="red">'''Note from J. E. Tohline to Students with Good Mathematical Skills'''</font>: 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. | ||
* [[ | * [[MathProjects/EigenvalueProblemN1|Find Analytic Solutions to an Eigenvalue Problem]] | ||
=See Also= | =See Also= | ||
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Latest revision as of 16:56, 13 April 2022
Potentially Relevant Initial Links
- Tiled Menu
- Fission Hypothesis of Binary Star Formation
- COLLADA-based Representation of Riemann Type 1 Ellipsoid
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.
See Also
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Appendices: | VisTrailsEquations | VisTrailsVariables | References | Ramblings | VisTrailsImages | myphys.lsu | ADS | |