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Ludwig Otto Hölder (December 22, 1859 – August 29, 1937) was a German mathematician born in Stuttgart. [2] Early life and education.
Hölder's inequality is used to prove the Minkowski inequality, which is the triangle inequality in the space L p (μ), and also to establish that L q (μ) is the dual space of L p (μ) for p ∈ [1, ∞). Hölder's inequality (in a slightly different form) was first found by Leonard James Rogers .
In fractal geometry, the generalized Hurst exponent has been denoted by H or H q in honor of both Harold Edwin Hurst and Ludwig Otto Hölder (1859–1937) by Benoît Mandelbrot (1924–2010). [3] H is directly related to fractal dimension, D, and is a measure of a data series' "mild" or "wild" randomness. [4]
In mathematics, Hölder's theorem states that the gamma function does not satisfy any algebraic differential equation whose coefficients are rational functions. This result was first proved by Otto Hölder in 1887; several alternative proofs have subsequently been found. [1] The theorem also generalizes to the -gamma function.
In mathematics, generalized means (or power mean or Hölder mean from Otto Hölder) [1] are a family of functions for aggregating sets of numbers. These include as special cases the Pythagorean means ( arithmetic , geometric , and harmonic means ).
The Knight's Cross of the Iron Cross and its higher grades were based on four separate enactments.The first enactment, Reichsgesetzblatt I S. 1573 of 1 September 1939 instituted the Iron Cross (Eisernes Kreuz), the Knight's Cross of the Iron Cross and the Grand Cross of the Iron Cross (Großkreuz des Eisernen Kreuzes).
K. Carl Kellner (optician) Friedrich Wilhelm August Ludwig Kiepert; Karl Johann Kiessling; Wilhelm Killing; Felix Klein; Georg Simon Klügel; Adolf Kneser
Title page of the document. Bekenntnis der Professoren an den Universitäten und Hochschulen zu Adolf Hitler und dem nationalsozialistischen Staat officially translated into English as the Vow of allegiance of the Professors of the German Universities and High-Schools to Adolf Hitler and the National Socialistic State was a document presented on 11 November 1933 at the Albert Hall in Leipzig.