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Peter Michael Blau (February 7, 1918 – March 12, 2002) was an Austrian and American sociologist and theorist. Born in Vienna, Austria , he immigrated to the United States in 1939. He completed his PhD doctoral thesis with Robert K. Merton at Columbia University in 1952, laying an early theory for the dynamics of bureaucracy.
There are three inequalities between means to prove. There are various methods to prove the inequalities, including mathematical induction, the Cauchy–Schwarz inequality, Lagrange multipliers, and Jensen's inequality. For several proofs that GM ≤ AM, see Inequality of arithmetic and geometric means.
Judith was awarded a BA from the University of Chicago in 1964 and a MA, also from Chicago, in 1967, and a PhD in 1972, from Northwestern University. [1] Blau taught at Baruch College as an assistant professor from 1973 to 1976, held a post-doctoral fellowship at Albert Einstein College of Medicine (1976–1978), taught at the State University of New York at Albany (1978–1982), and the ...
Inequality grew because the ones moving to the private sector would become wealthier in the city with a private-sector job, while the agricultural sector stayed stagnant. Once the transition was over, inequality was at its lowest because the final stages of growth were complete and everyone was sharing in the wealth generated.
A function : is said to be operator convex if for all and all , with eigenvalues in , and < <, the following holds (+ ()) + (). Note that the operator + has eigenvalues in , since and have eigenvalues in .
When Ω is a ball, the above inequality is called a (p,p)-Poincaré inequality; for more general domains Ω, the above is more familiarly known as a Sobolev inequality. The necessity to subtract the average value can be seen by considering constant functions for which the derivative is zero while, without subtracting the average, we can have ...
In mathematics, the following inequality is known as Titu's lemma, Bergström's inequality, Engel's form or Sedrakyan's inequality, respectively, referring to the article About the applications of one useful inequality of Nairi Sedrakyan published in 1997, [1] to the book Problem-solving strategies of Arthur Engel published in 1998 and to the book Mathematical Olympiad Treasures of Titu ...
where x n+1 = x 1 and x n+2 = x 2. The special case with n = 3 is Nesbitt's inequality. For greater values of n the inequality does not hold, and the strict lower bound is γ n / 2 with γ ≈ 0.9891… (sequence A245330 in the OEIS). The initial proofs of the inequality in the pivotal cases n = 12 [2] and n = 23 [3] rely on numerical