Hölder's inequality - 2025 NAFTA

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 L^p (“L-p”) norm of f” times “the L^q (“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 L^p (“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%

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Conversion

Team	Opponent	Part 1	Part 2	Part 3	Total	Parts
BHSU	Northwestern	0	10	10	20	ME
C R A B S	Dour Straits	0	0	10	10	E
Capital One in the Twenty-First Century	Middlesex County Fetty Wap Fan Club	10	0	10	20	HE
Chicago !A	1000000 Delinquents	0	10	10	20	ME
Constans Constantius and Constantine Jr.	Berkeley B	10	10	10	30	HME
Contessa Dora	UNC Charity	10	10	10	30	HME
David Foster Gromit	Copán Seethe	0	0	10	10	E
Execute Order 6 7	Quebecois Olga Tokarczuk be like 'freins de jacob interdits'	0	0	10	10	E
Guelph Cloze	The lion does not concern itself with negging teammates out of their own categories	0	10	10	20	ME
H Charlson's Washed Up Scrubs	Vacuous Tortoise	0	0	10	10	E
Habitat 67	Negged Five Times in a Yellow Cab Against the Gottis and Gambinos	10	10	10	30	HME
In the Mood for Transportation Equipment	(give me an) ANSWER: die for baseball	0	0	10	10	E
Invective Against Swans	Indiana	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
Licence to Bill	William of Baskerville attempts to investigate John P. Robarts, gets turned away for not having a student card	0	0	10	10	E
Licence to C. Wright Mill	I fear not the man who has reviewed 10000 cards once, but I fear the man who has reviewed one card 10000 times	0	10	10	20	ME
Maryland F♯ A♯ ∞	Rosslyn Academic Team	0	10	10	20	ME
Munir Siddiqui Fan Club	JHU	10	10	10	30	HME
Muscle Mass Extinction Event	The tram is not in service; please use the moving walkway.	0	10	10	20	ME
NYU A	NYU B or not NYU B (that is the question)	0	0	10	10	E
No Country for Old Quizzers	A Neg of Beauty is a Joy Forever	0	10	10	20	ME
Noah Sheidlower	The "C" Team	0	0	10	10	E
Penn State	Mike and Psmith	0	10	10	20	ME
Shipping Down from Ballston	Untitled Keyal Team	0	10	10	20	ME
Stanford A	Not Old! (Old)	0	10	10	20	ME
Stanford B	Team 7	0	10	10	20	ME
Strange Case of Dr. Joker and Mr. Pennywise	I'm just here (being trivia club president) so I won't get fined	0	10	10	20	ME
Surrealist Subcommandante Marcos be like Esto no es una pipa	The Fire Neg Time	10	10	10	30	HME
Team 8	Berkeley A	0	0	10	10	E
The Third Time when she was Given to Answer the Hard and the Easy, and Answered Only the Easy	Dielectrical Materialism	10	0	10	20	HE
The Unbearable Heaviness of History Players	UBC B	0	0	10	10	E
UBC A	Abbas I founded the Abbasids	0	0	10	10	E
Untitled by Alexander McQueen by Premeditated Chaos by Alexander McQueen by Percival Everett	Six Quizbowlers in Search of Owen Minmo	10	10	10	30	HME
You Don't Have the Cards	Where's the nearest library, I need to have a public crashout.	10	0	10	20	HE
consumption smoothing by borrowing future big law income	The Saint-Straw that Broke the Camille's Back	10	10	10	30	HME
https://i.imgur.com/C6nN2FE.png	Catholic University A	0	10	10	20	ME

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%