Packet 7: Bonus 4
Young’s inequality is used to prove this other inequality, which reduces to the Cauchy-Schwarz inequality when “p equals q equals two.” For 10 points each:
[10h] Name this ubiquitous inequality in analysis, which states that the L1 (“L-one”) norm of “f times g” is less than or equal to “the Lp (“L-p”) norm of f” times “the Lq (“L-q”) norm of g,” where “one over p” plus “one over q” is one.
ANSWER: Hölder's inequality
[10m] The Riesz-Thorin theorem, which concerns this task for operators, is proved by using Hölder’s inequality with suitably chosen conjugate exponents. Runge’s phenomenon can arise when using polynomials for this task.
ANSWER: interpolation [or word forms like interpolating; prompt on estimation or imputation or word forms]
[10e] Hölder’s inequality is used to prove Minkowski’s inequality, which is this statement for Lp (“L-p”) spaces. For vectors x and y, this inequality states that the length of “x plus y” cannot exceed the sum of their individual lengths.
ANSWER: triangle inequality
<TM, Other Science (Math)> | NAFTA-Packet-7
| Heard | PPB | E % | M % | H % |
|---|---|---|---|---|
| 36 | 18.33 | 100% | 56% | 28% |
Conversion
| Team | Opponent | Part 1 | Part 2 | Part 3 | Total | Parts |
|---|---|---|---|---|---|---|
| David Foster Gromit | Copán Seethe | 0 | 0 | 10 | 10 | E |
| It's something unpredictable/that in the end is right/please refrain from e-mailing my wife | Polish Orthographers Posting Their Łs | 0 | 0 | 10 | 10 | E |
Summary
| Tournament | Edition | Match | Heard | PPB | E % | M % | H % |
|---|---|---|---|---|---|---|---|
| 2026 NAFTA at Stanford | 01/17/2026 | ✓ | 4 | 20.00 | 100% | 75% | 25% |
| 2026 NAFTA at UBC | 01/17/2026 | ✓ | 2 | 10.00 | 100% | 0% | 0% |
| 2025 NAFTA Online | 02/14/2026 | ✕ | 4 | 15.00 | 100% | 50% | 0% |
| 2026 NAFTA at Vanderbilt | 02/14/2026 | ✕ | 3 | 23.33 | 100% | 67% | 67% |
| 2025 NAFTA at Toronto | 09/13/2025 | ✓ | 5 | 18.00 | 100% | 60% | 20% |
| 2025 NAFTA at Maryland | 09/27/2025 | ✓ | 5 | 24.00 | 100% | 100% | 40% |
| 2025 NAFTA at Harvard | 10/04/2025 | ✓ | 3 | 26.67 | 100% | 67% | 100% |
| 2025 NAFTA at Oxford | 10/11/2025 | ✓ | 4 | 15.00 | 100% | 25% | 25% |
| 2025 NAFTA at Chicago | 11/08/2025 | ✓ | 6 | 15.00 | 100% | 50% | 0% |
| 2025 NAFTA at Columbia | 11/08/2025 | ✓ | 5 | 20.00 | 100% | 60% | 40% |
| 2025 NAFTA at Richmond | 12/20/2025 | ✓ | 2 | 10.00 | 100% | 0% | 0% |