Question
Liouville’s theorem states that every entire function that is bounded also has this property. For 10 points each:
[10m] Identify this property of functions whose Fourier transform is a delta function at the origin.
ANSWER: constant [accept equivalents mentioning that the function’s value does not change]
[10e] A constant function will have only one term when represented as one of these series named for a British mathematician. When these series are centered on zero, they’re called Maclaurin series.
ANSWER: Taylor series
[10h] If a function is non-constant and entire, its range spans at least the whole complex plane minus one point according to this mathematician’s “little theorem.” It’s not Cauchy, but this mathematician also names a theorem with Ernst Lindelöf that characterizes the unique solution of initial value problems.
ANSWER: Émile Picard [or Charles Émile Picard; accept Picard’s little theorem or Picard-Lindelöf theorem]
<Science - Other Science>
Summary
| 2024 Booster Shot (Columbia) | 02/23/2024 | Y | 6 | 8.33 | 67% | 17% | 0% |
| 2024 Booster Shot (Great Lakes) | 03/09/2024 | Y | 6 | 18.33 | 100% | 50% | 33% |
| 2024 Booster Shot (Vanderbilt) | 03/02/2024 | Y | 5 | 30.00 | 220% | 80% | 0% |
| 2024 Booster Shot (WUSTL) | 03/09/2024 | Y | 3 | 10.00 | 100% | 0% | 0% |
| 2024 Booster Shot (Waterloo) | 02/23/2024 | Y | 4 | 17.50 | 100% | 50% | 25% |
Data
| Penn State A | Iowa State | 10 | 10 | 10 | 30 |
| Michigan B | Penn State B | 0 | 10 | 0 | 10 |
| North Carolina | Iowa | 10 | 10 | 10 | 30 |
| Ohio | Michigan C | 0 | 10 | 0 | 10 |
| Stanford | Michigan A | 0 | 10 | 0 | 10 |
| Ohio State | WUSTL | 10 | 10 | 0 | 20 |