In probability theory, the Azuma–Hoeffding inequality (named after Kazuoki Azuma and Wassily Hoeffding) gives a concentration result for the values of martingales that have bounded differences.
Mayumi Azuma | Inequality of bargaining power | gender inequality | Wirtinger's inequality | Steffensen's inequality | Samuelson's inequality | Minkowski inequality | Masao Azuma | Kazuoki Azuma | Inequality for All | Hölder's inequality | Hitchin–Thorpe inequality | Hiroki Azuma | Fisher's inequality | Economic inequality | Chebyshev's sum inequality | Cauchy's inequality | Cauchy–Schwarz inequality |
A fundamental theorem, Fisher's inequality, named after the statistician Ronald Fisher, is that b ≥ v in any 2-design.
According to his biography, he has played onstage with renowned guitarists Sergio and Odair Assad, Badi Assad, Romero Lubambo, Yamandu Costa, Cristina Azuma, Peter Finger, and Solorazaf and has been an opening act for legendary Brazilian jazz musicians including Gilberto Gil and Bebel Gilberto.
For 0 < p ≤ q ≤ ∞, the class Hq is a subset of Hp, and the Hp-norm is increasing with p (it is a consequence of Hölder's inequality that the Lp-norm is increasing for probability measures, i.e. measures with total mass 1).
Azuma launched his career as a literary critic in 1993 with a postmodern style influenced by leading Japanese critics Kojin Karatani and Akira Asada.
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Azuma handed the work directly to Karatani during his lecture series at Hosei University which Azuma was auditing.
Tristan Needham (1993) "A Visual Explanation of Jensen's Inequality", American Mathematical Monthly 100(8):768–71.
Steffensen's inequality and Steffensen's method (an iterative numerical method) are named after him.
Since the right-hand side of the identity is clearly non-negative, it implies Cauchy's inequality in the finite-dimensional real coordinate space ℝn and its complex counterpart ℂn.
The remaining six rounds saw erratic and relatively poor results from Azuma, while his title rivals Marco Melandri and Emilio Alzamora gained on him in the Championship.
"A Two-Triangle Inequality", Daniel Pedoe, The American Mathematical Monthly, volume 70, number 9, page 1012, November, 1963.
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In geometry, Pedoe's inequality, named after Daniel Pedoe, states that if a, b, and c are the lengths of the sides of a triangle with area ƒ, and A, B, and C are the lengths of the sides of a triangle with area F, then
The inequality in the above form was proved independently by Kullback, Csiszár, and Kemperman.
It is possible to determine the bounds of the roots of a polynomial using Samuelson's inequality.
Kitano plays sociopathic detective Azuma, a Dirty Harry-type whose single-mindedness leads to self-destruction.
: For other inequalities named after Wirtinger, see Wirtinger's inequality.