| 31. | Extremal graph theory started in 1941 when Tur�n proved his result a vital tool in attacking extremal problems.
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| 32. | The Rindler spacetime has a horizon, and locally any non-extremal black hole horizon is Rindler.
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| 33. | In the area of econophysics, he discovered extremal properties of fixed point profits of elementary merchant tactics.
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| 34. | That is to re-iterate the concern about extremal cases not being equivalent in the list immediately above.
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| 35. | One difference was that Strominger and Vafa considered only extremal black holes in order to make the calculation tractable.
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| 36. | The calculation makes use of the notion of dynamical horizon and is done for non-extremal black holes.
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| 37. | Extremal combinatorics owes to him a whole approach, derived in part from the tradition of analytic number theory.
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| 38. | It has been suggested by Sean Carroll that the entropy of an extremal black hole is equal to zero.
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| 39. | Much of extremal combinatorics concerns Sperner's theorem, which gave rise to much of extremal set theory.
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| 40. | Much of extremal combinatorics concerns Sperner's theorem, which gave rise to much of extremal set theory.
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